**Electromagnetic and Acoustic Transformation of Surface Acoustic Waves and Its Application in Various Tasks**

Sergey E. Babkin

380 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

& E International. 42: 669-677

[70] Gloria N B S, Areiza M C L, Miranda I V J, Rebello J M A (2009) Development Of A Magnetic Sensor for Detection And Sizing of Internal Pipeline Corrosion Defects, NDT

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/56307

## **1. Introduction**

## **1.1. Electromagnetic and acoustic transformation**

Electromagnetic and acoustic transformation (EMAT) is transformation of high-pitched electromagnetic oscillations in the inductive sensor over a specimen into acoustic oscillations in the specimen. For the transformation to be performed the padding constant magnetic field is required. This process is referred to as a direct EMAT. Further oscillations are extended in the specimen in the shape of acoustic waves. Acoustic waves can be deduced outside by means of revertive EMAT when acoustic oscillations in the surface layer of a specimen will be transformed to electromagnetic oscillations in the receiving sensor. The overall process is as follows: a direct EMAT, a distribution of acoustic waves and a revertive EMAT, which is in practice referred to as a double EMAT or just EMAT [1, 2].

Materials in which EMAT is possible to occur:


## *EMAT mechanisms*

EMAT may proceed by three basic mechanisms.

1. A vortical current mechanism (Lorentz force mechanism). Electrons in a surface layer will fluctuate under the influence of Lorentz force:

$$F\_L = f \text{ (} \text{ ${}\_{L}H$ } \text{)} \text{ }$$

Electromagnetic and Acoustic Transformation of Surface Acoustic Waves and Its Application in Various Tasks 383

EMAT sensor can be to used as a revertive EMAT sensor, if the sensor receives a

Each technique developed for a PET method are suitable for pulse EMAT (an echo method,

Key informational parameters of the pulse technique: amplitude of the received signal,

Classically the term «the surface acoustic waves» (SAW) is considered to involve the extending of the waves along the surface of the solid and vacuum; waves poorly fade extending along the surface boundary, the waves quickly fade when moving away from surface boundary into a solid. It concerns only Rayleigh waves and the Guljaev-Blyushteyna

There is an expanded treatment of the term «the surface acoustic waves» [3]. Firstly, surface waves at the boundary of the solid body and the gases are considered. It allows Stonly waves and the waves of leak being referred to SAW. They have vertical polarization and a quasyrayleigh structure. Secondly, the expanded treatment considers waves in a layer on the solid body surfaces, or waves with the inhomogeneous elastic properties which are observed in a closely to a surface layer. Loves waves and generalized Lamb waves are considered as well. Thirdly, if the wave extending along the surface is thought to be the main factor, the waves in plates, i.e. Lamb waves and horizontal polarization waves (SH-

**3. Electromagnetic and acoustic transformation of surface acoustic waves** 

The surface waves in a solid body can be generated in the different ways. The most widespread way is the way using PET. The main advantages of the EMA method of SAW generation in comparison with PET consist of a) not – contact generation and SAW receiving and b)availability to use different SAW which are hardly generated by PET. To reach this purpose it is enough to change a configuration of the wire EMA coil as well as its orientation

From the practical point of view Rayleigh and Lamb waves being waves vertical polarization as well as SH–waves and Love waves being waves of horizontal polarization

The Rayleigh wave can be generated and received by means of meandr EMAT at the normal and tangential magnetic field, Hz and Hx (fig. 1). The double EMAT effectiveness is characterized by the amplitude of the received signal in the receiving coil (Е). He is

speed of a wave, size of a magnetic field, wave attenuation.

reflected signal.

a shadow method etc.).

**2. The surface acoustic waves** 

wave) can be referred to surface waves.

regarding the magnetic field.

1. Waves of vertical polarization.

are of great interest.

measured in volt usually.

waves but in piezocrystals.

where J is a current density, H is a magnetic field.

In conductors this thin layer is called as a skin layer.

2. A magnetic mechanism. This mechanism defines power interaction of an alternative electromagnetic field of the sensor, h, and a constant magnetic field of a specimen, H.

$$F\_m = f\left(h, \stackrel{\cdot}{H}, \stackrel{\cdot}{\mu}\_{\stackrel{\cdot}{\dot{\eta}}}\right),$$

where *ij* is a tensor of magnetic conductivity of a material.

3. A magnetostriction mechanism. For the materials possessing magnetostriction, this mechanism is responsible for changing linear dimensions of microvolumes in the surface layer of a specimen under the sensor depending on the alternative field of the sensor.

$$F\_{\mathbb{A}} = f\left(\mathbb{Q}\_{\mathbb{H}'} \,\, M\right).$$

where Qij is a tensor of magnetoelastic communication, M is magnetization of a specimen.

The first and the second mechanisms are often considered as one which is referred to as an electromagnetic or electrodynamic mechanism of transformation.

#### *Technical realization of EMAT*

In technical realization terms EMAT is defined a non-contact method of generation and reception of acoustic waves (ultrasonic waves). The method of generation and reception of ultrasonic waves by means of piezoelectric transducers (PET) appears to be the nearest and best analog in this field. Therefore, the technical methods developed for PET methods generally are appropriate for EMAT methods as well.

There are two main techniques, i.e. a resonance technique and a pulse technique.

1. A resonance technique. A small specimen (a cylinder or a rectangular parallelepiped) is placed into solenoid in order to create a magnetic field. By means of a round wire EMA coil which is put on the specimen the loose oscillations are generated in it. A standing waves resonance is reached by changing the frequency of generation. Thus receiving EMA coil shows a signal maximum. A resonance technique is hard to realizing for a PET method, because the contact is required. These problems are easily solved by the non-contact EMAT method.

An amplitude of the received signal, a resonance frequency, a size of a magnetic field are the key information parameters. The attenuation and Q-factor of the system is possible to define.

2. A pulse technique. Short electric pulses of the generator are transformed to acoustic waves by means of EMAT. These pulses are of high-pitched filling. The generation Electromagnetic and Acoustic Transformation of Surface Acoustic Waves and Its Application in Various Tasks 383

EMAT sensor can be to used as a revertive EMAT sensor, if the sensor receives a reflected signal.

Each technique developed for a PET method are suitable for pulse EMAT (an echo method, a shadow method etc.).

Key informational parameters of the pulse technique: amplitude of the received signal, speed of a wave, size of a magnetic field, wave attenuation.

## **2. The surface acoustic waves**

382 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

is a tensor of magnetic conductivity of a material.

electromagnetic or electrodynamic mechanism of transformation.

generally are appropriate for EMAT methods as well.

where J is a current density, H is a magnetic field.

where *ij* 

*Technical realization of EMAT* 

non-contact EMAT method.

define.

In conductors this thin layer is called as a skin layer.

, , *<sup>L</sup> F f JH*

2. A magnetic mechanism. This mechanism defines power interaction of an alternative electromagnetic field of the sensor, h, and a constant magnetic field of a specimen, H.

*F f hH m i* , , ,

3. A magnetostriction mechanism. For the materials possessing magnetostriction, this mechanism is responsible for changing linear dimensions of microvolumes in the surface layer of a specimen under the sensor depending on the alternative field of the sensor.

*F fQ M*

where Qij is a tensor of magnetoelastic communication, M is magnetization of a specimen.

The first and the second mechanisms are often considered as one which is referred to as an

In technical realization terms EMAT is defined a non-contact method of generation and reception of acoustic waves (ultrasonic waves). The method of generation and reception of ultrasonic waves by means of piezoelectric transducers (PET) appears to be the nearest and best analog in this field. Therefore, the technical methods developed for PET methods

1. A resonance technique. A small specimen (a cylinder or a rectangular parallelepiped) is placed into solenoid in order to create a magnetic field. By means of a round wire EMA coil which is put on the specimen the loose oscillations are generated in it. A standing waves resonance is reached by changing the frequency of generation. Thus receiving EMA coil shows a signal maximum. A resonance technique is hard to realizing for a PET method, because the contact is required. These problems are easily solved by the

An amplitude of the received signal, a resonance frequency, a size of a magnetic field are the key information parameters. The attenuation and Q-factor of the system is possible to

2. A pulse technique. Short electric pulses of the generator are transformed to acoustic waves by means of EMAT. These pulses are of high-pitched filling. The generation

, , *ij*

There are two main techniques, i.e. a resonance technique and a pulse technique.

*<sup>j</sup>*

> Classically the term «the surface acoustic waves» (SAW) is considered to involve the extending of the waves along the surface of the solid and vacuum; waves poorly fade extending along the surface boundary, the waves quickly fade when moving away from surface boundary into a solid. It concerns only Rayleigh waves and the Guljaev-Blyushteyna waves but in piezocrystals.

> There is an expanded treatment of the term «the surface acoustic waves» [3]. Firstly, surface waves at the boundary of the solid body and the gases are considered. It allows Stonly waves and the waves of leak being referred to SAW. They have vertical polarization and a quasyrayleigh structure. Secondly, the expanded treatment considers waves in a layer on the solid body surfaces, or waves with the inhomogeneous elastic properties which are observed in a closely to a surface layer. Loves waves and generalized Lamb waves are considered as well. Thirdly, if the wave extending along the surface is thought to be the main factor, the waves in plates, i.e. Lamb waves and horizontal polarization waves (SHwave) can be referred to surface waves.

## **3. Electromagnetic and acoustic transformation of surface acoustic waves**

The surface waves in a solid body can be generated in the different ways. The most widespread way is the way using PET. The main advantages of the EMA method of SAW generation in comparison with PET consist of a) not – contact generation and SAW receiving and b)availability to use different SAW which are hardly generated by PET. To reach this purpose it is enough to change a configuration of the wire EMA coil as well as its orientation regarding the magnetic field.

From the practical point of view Rayleigh and Lamb waves being waves vertical polarization as well as SH–waves and Love waves being waves of horizontal polarization are of great interest.

1. Waves of vertical polarization.

The Rayleigh wave can be generated and received by means of meandr EMAT at the normal and tangential magnetic field, Hz and Hx (fig. 1). The double EMAT effectiveness is characterized by the amplitude of the received signal in the receiving coil (Е). He is measured in volt usually.

On tangential magnetizing (Hx) the amplitude of the received signal according to the mechanisms of transformation is described by the following approximate formulas[1, 4].

**Figure 1.** Position of the meandrovy coil on an specimen.

For the magnetostriction mechanism:

$$E^{ms} \approx \frac{1}{\mu\_d} \left(\frac{d\mathcal{X}}{dH}\right)^2 P\_{1'} \tag{1}$$

Electromagnetic and Acoustic Transformation of Surface Acoustic Waves and Its Application in Various Tasks 385

<sup>4</sup> () , *<sup>i</sup> E BP* (4)

= f(H) [12].

2

The dependence of the amplitude of the received signal (Е) on the magnetic field size, the so-called «field curve EMAT» is the total characteristic EMAT SAW [5]. Two sensor (such as in fig. 1) place on a surface of the sample. One sensor generates the surface wave, the second sensor accepts a wave. The accepted signal strengthen and measure in volt. Often Е normalized in relation to any value E (for example, to the maximum value) and receive abs. units. This size postpone on axis Y. The magnetic field size in the sample is shown on an

Fig. 2 shows a typical field curve for Rayleigh waves EMAT taking ARMCO iron as an example (curve 1). The curves for the transformation mechanisms calculated on the basis of equation (1) and (2) are presented in fig.2 as well (curve 2 and 3, accordingly). At calculation

**Figure 2.** The experimental EMAT field curve of Rayleigh waves in a tangential field for iron (curve 1).

An EMAT field curve of Rayleigh waves registered in a normal magnetic field(curve 1) and the curves 2, 3 calculated using (3) and (4) are shown in fig.3. As seen from fig.2 and fig.3 the

where *B* is a magnetic induction, 4*P* is constant factor the similar <sup>1</sup>*P* .

of the equations use known functions for a material: B=0H,

The theoretical curve 2, 3 are presented equations (1) and (2).

experimental process is well described by the formulas.

The amplitude of the signal (E) is normalized concerning a maximum.

axis X (B (T) or H (A/cm), as B=0H).

where *<sup>d</sup>* is differential magnetic permeability, is the linear magnetostriction ( =l/l is specific elongation of the specimen), 1*P* is constant factor which depends from parametres of the generating sensor, the reception sensor; physical constants of a material (for example, density, electroconductivity); strengthenings of a reception path, H is a magnetic intensity.

For the sum of vortical current and magnetic mechanisms (the electrodynamic mechanism):

$$E^i + E^m \approx (\mu\_0 H^i)^2 P\_{2'} \tag{2}$$

where 0 is a permeability of vacuum, 2*P* is constant factor the similar <sup>1</sup>*P* .

At normal magnetization (Hz).

For the magnetic mechanism:

$$E^{\prime \prime} \approx (\mu \mathcal{M})^2 P\_{\odot \prime} \tag{3}$$

where, *M* are magnetic conductivity and magnetization of the material in this orientation, 3*P* is constant factor the similar <sup>1</sup>*P* .

For the vortical current mechanism:

Electromagnetic and Acoustic Transformation of Surface Acoustic Waves and Its Application in Various Tasks 385

$$E^i \approx \text{(B)}^2 P\_{4\prime} \tag{4}$$

where *B* is a magnetic induction, 4*P* is constant factor the similar <sup>1</sup>*P* .

384 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

**Figure 1.** Position of the meandrovy coil on an specimen.

is differential magnetic permeability,

For the magnetostriction mechanism:

where *<sup>d</sup>* 

where 0 

where,

At normal magnetization (Hz).

For the magnetic mechanism:

orientation, 3*P* is constant factor the similar <sup>1</sup>*P* .

For the vortical current mechanism:

On tangential magnetizing (Hx) the amplitude of the received signal according to the mechanisms of transformation is described by the following approximate formulas[1, 4].

2

<sup>1</sup> , *ms d <sup>d</sup> E P dH* 

 

specific elongation of the specimen), 1*P* is constant factor which depends from parametres of the generating sensor, the reception sensor; physical constants of a material (for example, density, electroconductivity); strengthenings of a reception path, H is a magnetic intensity.

For the sum of vortical current and magnetic mechanisms (the electrodynamic mechanism):

is a permeability of vacuum, 2*P* is constant factor the similar <sup>1</sup>*P* .

0 2 ( ), *i m EE HP* 

2 <sup>3</sup> ( ), *mE MP* 

*M* are magnetic conductivity and magnetization of the material in this

1

2

(1)

(2)

(3)

=l/l is

is the linear magnetostriction (

The dependence of the amplitude of the received signal (Е) on the magnetic field size, the so-called «field curve EMAT» is the total characteristic EMAT SAW [5]. Two sensor (such as in fig. 1) place on a surface of the sample. One sensor generates the surface wave, the second sensor accepts a wave. The accepted signal strengthen and measure in volt. Often Е normalized in relation to any value E (for example, to the maximum value) and receive abs. units. This size postpone on axis Y. The magnetic field size in the sample is shown on an axis X (B (T) or H (A/cm), as B=0H).

Fig. 2 shows a typical field curve for Rayleigh waves EMAT taking ARMCO iron as an example (curve 1). The curves for the transformation mechanisms calculated on the basis of equation (1) and (2) are presented in fig.2 as well (curve 2 and 3, accordingly). At calculation of the equations use known functions for a material: B=0H, = f(H) [12].

The amplitude of the signal (E) is normalized concerning a maximum.

**Figure 2.** The experimental EMAT field curve of Rayleigh waves in a tangential field for iron (curve 1). The theoretical curve 2, 3 are presented equations (1) and (2).

An EMAT field curve of Rayleigh waves registered in a normal magnetic field(curve 1) and the curves 2, 3 calculated using (3) and (4) are shown in fig.3. As seen from fig.2 and fig.3 the experimental process is well described by the formulas.

**Figure 3.** 1 – is the experimental EMAT field curve of Rayleigh waves in a normal field for iron. The theoretical curve 2, 3 are presented equations (3) and (4).

2. Waves of horizontal polarization.

Waves of horizontal polarization are generated in a case when current elements of the meander coil are parallel to a magnetic field. In this case the elementary volumes of the specimen under the EMA coil are in the cross fields, i.e. under the big constant magnetize field and the small variable magnetic field of the coil. Such an arrangement results in shear modes of horizontal polarization which are synchronized under EMA current elements of the coil (fig. 1 field Ну).

The following simplified formula [6] is derived based on the theoretical calculation for SH waves in a **d-** thick specimen [6]:

$$E\_{SH} \approx \frac{1}{d} \left(\frac{\lambda}{H}\right)^2 P\_{\mathfrak{F}'} \tag{5}$$

Electromagnetic and Acoustic Transformation of Surface Acoustic Waves and Its Application in Various Tasks 387

**Figure 4.** The experimental field curve of EMAT of SH waves in iron (1), in comparison with Rayleigh

Love waves have been studied using 20-80 microns thick nickel films applied on the surface

**Figure 5.** The experimental field curve of EMAT of Love waves in a nickel film on an aluminum

substrate (1), in comparison with Rayleigh waves (2).

of an aluminum substrate. The field curve is presented on fig. 5.

waves (2).

where 5*P* is constant factor the similar <sup>1</sup>*P* .

A structurally similar formula is deduced for the waves of horizontal polarization in the layer (Love waves), but a layer thickness and some known restrictions concerning speeds ratio should be taken into consideration.

The experimental field curve of EMAT of SH waves in ARMCO iron is presented in fig. 4.

If I construct the chart of the equation (5) on this coordinates, I also will see good coincidence to experiment.

Electromagnetic and Acoustic Transformation of Surface Acoustic Waves and Its Application in Various Tasks 387

386 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

**Figure 3.** 1 – is the experimental EMAT field curve of Rayleigh waves in a normal field for iron. The

Waves of horizontal polarization are generated in a case when current elements of the meander coil are parallel to a magnetic field. In this case the elementary volumes of the specimen under the EMA coil are in the cross fields, i.e. under the big constant magnetize field and the small variable magnetic field of the coil. Such an arrangement results in shear modes of horizontal polarization which are synchronized under EMA current elements of

The following simplified formula [6] is derived based on the theoretical calculation for SH

<sup>1</sup> , *SH E P d H* 

A structurally similar formula is deduced for the waves of horizontal polarization in the layer (Love waves), but a layer thickness and some known restrictions concerning speeds

The experimental field curve of EMAT of SH waves in ARMCO iron is presented in fig. 4.

If I construct the chart of the equation (5) on this coordinates, I also will see good

2 5

(5)

theoretical curve 2, 3 are presented equations (3) and (4).

2. Waves of horizontal polarization.

the coil (fig. 1 field Ну).

waves in a **d-** thick specimen [6]:

where 5*P* is constant factor the similar <sup>1</sup>*P* .

ratio should be taken into consideration.

coincidence to experiment.

**Figure 4.** The experimental field curve of EMAT of SH waves in iron (1), in comparison with Rayleigh waves (2).

Love waves have been studied using 20-80 microns thick nickel films applied on the surface of an aluminum substrate. The field curve is presented on fig. 5.

**Figure 5.** The experimental field curve of EMAT of Love waves in a nickel film on an aluminum substrate (1), in comparison with Rayleigh waves (2).

## *SAW identification*

SAW identification is essential in studying EMAT of the surface wave experimentally.

SAW signals should be distinguished from the signals of other waves. E.g. from the volume waves signals starting from the surface of the specimen to its depth at different angles with interfering reflections in the receiving EMA sensor. It is also necessary for SAW to be recognized in between.

Electromagnetic and Acoustic Transformation of Surface Acoustic Waves and Its Application in Various Tasks 389

generates the surface wave in a specimen 1, another accepts the surface waves. It is a separate testing regime. It is possible to use the combined testing regime when one half-cell

**Figure 6.** Design of the EMAT sensor of waves of Reley. 1-an specimen, 2 - a housing, 3 -

A magnetic field can be created the strong permanent magnets, but in this case it will be uncontrollable. Electromagnets permits operating a magnetic field, choosing the working

EMAT loses to a way PET in sensitivity, but in this case a contact is not required. It is meant it that using the EMAT method an immediate contact between EMA of the sensor and a specimen is not needed, and the sensor can operates through air or other gaps. For example, the layer of scale or paint isn't an absolute obstacle for EMAT. The amplitude of the received signal has been recognized to be strongly dependent on the gap size. It is due to two factors: 1) an electromagnetic field of EMA of the sensor in a gap called "the sensor – an specimen surface" decreases according to the exponential curve law, 2) a magnetic field of the specimen decreases as a gap occurs. For ferromagnetic materials the field curve of Rayleigh waves EMAT effectiveness has a characteristic maximum defined by the magnetostriction mechanism (fig. 2). The amplitude of the received signal depends on a working point choice

Usually the working point at non-destructive monitoring is chosen at top of the main maximum of the field curve (point H1 in fiq.2). The maximal receiving signal is obtained in this way. For most ferromagnetic materials this maximum lies within 100 – 300A/cm magnetic fields. The same effectiveness using the vortical current mechanism is reached in

If the working point of monitoring is chosen at the maximum top (Н1 in fig. 2), the emergence of the gap in a magnetic circuit will result in decreasing the magneticfield in size

electromagnets, 4 - filler, 5, 6 - generating and receiving EMA coils.

point on field curve EMAT.

in a field curve.

magnetic fields about 5000A/cm in size.

generates a wave and accepts the signal reflected from defect.

## *Basic identification methods*


Thus, we can tell the following.


## **4. Using EMAT surface acoustic waves**

## **4.1. Non-destructive testing**

## *4.1.1. Defectoscopy of the surface defects*

Using an ultrasonic method for testing materials and products EMAT incorporates all the advantages of ultrasonic testing methods. A piezoelectric transducers (PET) method is similar to EMAT. The main ultrasonic techniques developed for PET, are applied to EMAT.

In fig. 6 the design of EMA of the Rayleigh wave converter on the basis of П-shaped electromagnets [7] is shown.

The sensor consists of two identical half-cells: П-shaped electromagnet 3 and meandrovy coil 5, 6. Both converters are located in the case 2 and are filled in with a filler 4. One half-cell generates the surface wave in a specimen 1, another accepts the surface waves. It is a separate testing regime. It is possible to use the combined testing regime when one half-cell generates a wave and accepts the signal reflected from defect.

388 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

amplitude and a 7 % decrease of SH waves are observed.

SAW identification is essential in studying EMAT of the surface wave experimentally.

SAW signals should be distinguished from the signals of other waves. E.g. from the volume waves signals starting from the surface of the specimen to its depth at different angles with interfering reflections in the receiving EMA sensor. It is also necessary for SAW to be

1. Pulp method. It involves simple damping by a finger of the surface of the specimen which strongly affects the SAW wave amplitudes but doesn't affect other waves. As long as it is a subjective method to make it being more objective a method of buttered drops is used. Using a pipette to drop the oil from the same height an identical damping is obtained. It allows distinguishing even the Rayleigh surface waves from SH waves. In the same conditions using a 6-drop method a 28 % decrease of Rayleigh wave

2. A Rayleigh wave CR strongly differs from longitudinal waves Cl in speed, its speed being slightly differs from the speed of transverse waves Ct (CR= 0, 87 -0, 96 Ct). A zero mode of a SH wave speed is equal to Ct. To be more sure in distinguishing from a

3. A sensor driving method is based on the following: if a generating sensor moves regarding to the receiving one, the signals on the a receiving oscilloscope screen move



Using an ultrasonic method for testing materials and products EMAT incorporates all the advantages of ultrasonic testing methods. A piezoelectric transducers (PET) method is similar to EMAT. The main ultrasonic techniques developed for PET, are applied to EMAT.

In fig. 6 the design of EMA of the Rayleigh wave converter on the basis of П-shaped

The sensor consists of two identical half-cells: П-shaped electromagnet 3 and meandrovy coil 5, 6. Both converters are located in the case 2 and are filled in with a filler 4. One half-cell

Rayleigh wave the accuracy of speed determination is be within 0, 5 %.

*SAW identification* 

recognized in between.

*Basic identification methods* 

synchronously.

Thus, we can tell the following.

**4.1. Non-destructive testing** 

electromagnets [7] is shown.

*4.1.1. Defectoscopy of the surface defects* 

waves in the theory and in practice.

**4. Using EMAT surface acoustic waves** 

**Figure 6.** Design of the EMAT sensor of waves of Reley. 1-an specimen, 2 - a housing, 3 electromagnets, 4 - filler, 5, 6 - generating and receiving EMA coils.

A magnetic field can be created the strong permanent magnets, but in this case it will be uncontrollable. Electromagnets permits operating a magnetic field, choosing the working point on field curve EMAT.

EMAT loses to a way PET in sensitivity, but in this case a contact is not required. It is meant it that using the EMAT method an immediate contact between EMA of the sensor and a specimen is not needed, and the sensor can operates through air or other gaps. For example, the layer of scale or paint isn't an absolute obstacle for EMAT. The amplitude of the received signal has been recognized to be strongly dependent on the gap size. It is due to two factors: 1) an electromagnetic field of EMA of the sensor in a gap called "the sensor – an specimen surface" decreases according to the exponential curve law, 2) a magnetic field of the specimen decreases as a gap occurs. For ferromagnetic materials the field curve of Rayleigh waves EMAT effectiveness has a characteristic maximum defined by the magnetostriction mechanism (fig. 2). The amplitude of the received signal depends on a working point choice in a field curve.

Usually the working point at non-destructive monitoring is chosen at top of the main maximum of the field curve (point H1 in fiq.2). The maximal receiving signal is obtained in this way. For most ferromagnetic materials this maximum lies within 100 – 300A/cm magnetic fields. The same effectiveness using the vortical current mechanism is reached in magnetic fields about 5000A/cm in size.

If the working point of monitoring is chosen at the maximum top (Н1 in fig. 2), the emergence of the gap in a magnetic circuit will result in decreasing the magneticfield in size

and falling transformation effectiveness, i.e., the amplitude of the received signal. However, if the working point is chosen on the slope of the field curve (Н2), a magnetic field decreases with the gap increasing which leads to the transformation effectiveness. Thus, both factors, i.e., the removal of EMA of the coil from a surface of the specimen and a magnetic field decrease in an specimen compensate each other. [8].

Electromagnetic and Acoustic Transformation of Surface Acoustic Waves and Its Application in Various Tasks 391

So the dependence between the amplitude of the received signal of Rayleigh waves sensor (fig. 6) and the hardness of the steel 38ХГС specimens being treated at different temperatures is practically linear. To increase the specimen hardness it was treated at high temperatures. The coefficient of correlation was equal to 0, 92. It allows EMAT controlling.

Another structural component is anisotropy of the material properties which can be also measured by the sensor described above. The sensor is rotated on the specimen surface showing the information parameters change. However, the data can be distorted due to

To overcome this trouble a meander -curve sensor was suggested to be curved into a ring

In this case each element of the dl coil generates SAW in K1 and К2 directions. In general two circular waves are observed: a coverging to the center wave and a diverging from the center one. A converging to the O point wave then turns into a diverging wave. It is

Two case of magnetizing are likely to observed for the circular EMA sensor. In case of normal magnetizing a rod electromagnet is used (fig. 9a), and in case of a tangential magnetizing it is realized by means of a cylindrical m-shaped electromagnet (fig. 9b). Cracks

But the most interesting area for the sensor to be applied is in controlling anisotropy of sheet ferromagnetic materials. It allows revealing three types of anisotropy: elastic, magnetoelastic

At generation and reception of a circular surface wave in a completely isotropic metal we have the individual fine-bored received pulse which is a superposition of the signals from all directions (fig. 10a). In case of elastic anisotropy (anisotropy of sound speed) signals in

received by the same circular EMA coil when the wave moves under it.

different factors.

**Figure 8.** Circular EMAT sensor.

are revealed by such a sensor.

and magnetic.

(fig. 8) [9].

If the gap between the coil and the surface is introduced before the measurements are carried out the measurement results are more reliable. In this case the uncontrollable gap less influences on the received signal. If the working point is chosen in the slope of the field curve the signal received does not depend on the gap (fig. 7).

**Figure 7.** Dependence of the received signal from dimension of the gap between sensor and specimen at the working point H1(1), at the working point H2 and preliminary gap (2).

The experiments on detection of model defects showed that by means of EMA of the converter of Rayleigh waves presented in fig. 6, it is possible to reveal the surface defects such as cracks 5мм in length, 0, 5мм in depth. Such defects come to light both at reflection from the defect, and when weakening a signal passing the defect (weakening of 20 %).

## *4.1.2. Structurescopy of metals*

Structural changes are well recognized by EMAT in ferromagnetic materials taking place in technological processes. This results from the fact that at EMAT four subsystems are involved in a material: magnetic, electric, magnetoelastic and elastic. All these factors influence informational parameters of the EMAT method.

Thus, if a dependence between the parameters of the technological process and the information parameters of the method of one subsystem is not a one- direction dependence the EMAT method can be used.

So the dependence between the amplitude of the received signal of Rayleigh waves sensor (fig. 6) and the hardness of the steel 38ХГС specimens being treated at different temperatures is practically linear. To increase the specimen hardness it was treated at high temperatures. The coefficient of correlation was equal to 0, 92. It allows EMAT controlling.

Another structural component is anisotropy of the material properties which can be also measured by the sensor described above. The sensor is rotated on the specimen surface showing the information parameters change. However, the data can be distorted due to different factors.

To overcome this trouble a meander -curve sensor was suggested to be curved into a ring (fig. 8) [9].

In this case each element of the dl coil generates SAW in K1 and К2 directions. In general two circular waves are observed: a coverging to the center wave and a diverging from the center one. A converging to the O point wave then turns into a diverging wave. It is received by the same circular EMA coil when the wave moves under it.

**Figure 8.** Circular EMAT sensor.

390 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

decrease in an specimen compensate each other. [8].

curve the signal received does not depend on the gap (fig. 7).

and falling transformation effectiveness, i.e., the amplitude of the received signal. However, if the working point is chosen on the slope of the field curve (Н2), a magnetic field decreases with the gap increasing which leads to the transformation effectiveness. Thus, both factors, i.e., the removal of EMA of the coil from a surface of the specimen and a magnetic field

If the gap between the coil and the surface is introduced before the measurements are carried out the measurement results are more reliable. In this case the uncontrollable gap less influences on the received signal. If the working point is chosen in the slope of the field

**Figure 7.** Dependence of the received signal from dimension of the gap between sensor and specimen

The experiments on detection of model defects showed that by means of EMA of the converter of Rayleigh waves presented in fig. 6, it is possible to reveal the surface defects such as cracks 5мм in length, 0, 5мм in depth. Such defects come to light both at reflection from the defect, and when weakening a signal passing the defect (weakening of 20 %).

Structural changes are well recognized by EMAT in ferromagnetic materials taking place in technological processes. This results from the fact that at EMAT four subsystems are involved in a material: magnetic, electric, magnetoelastic and elastic. All these factors

Thus, if a dependence between the parameters of the technological process and the information parameters of the method of one subsystem is not a one- direction dependence

at the working point H1(1), at the working point H2 and preliminary gap (2).

influence informational parameters of the EMAT method.

*4.1.2. Structurescopy of metals* 

the EMAT method can be used.

Two case of magnetizing are likely to observed for the circular EMA sensor. In case of normal magnetizing a rod electromagnet is used (fig. 9a), and in case of a tangential magnetizing it is realized by means of a cylindrical m-shaped electromagnet (fig. 9b). Cracks are revealed by such a sensor.

But the most interesting area for the sensor to be applied is in controlling anisotropy of sheet ferromagnetic materials. It allows revealing three types of anisotropy: elastic, magnetoelastic and magnetic.

At generation and reception of a circular surface wave in a completely isotropic metal we have the individual fine-bored received pulse which is a superposition of the signals from all directions (fig. 10a). In case of elastic anisotropy (anisotropy of sound speed) signals in

the different directions take different time. And the received pulse extends, or splits into a number of pulses. An elastic anisotropy of the material is characterized by the pulse duration or the distance between extreme pulses (fig. 10b).

Electromagnetic and Acoustic Transformation of Surface Acoustic Waves and Its Application in Various Tasks 393

The developed technique was tested on various materials and showed high effectiveness.

EMAT SAW enables tension and operational loadings controlling. For this purpose the sensor (fig.6) was used. The sensor platform area is to be 30 x 60мм. Adjusting to obtain a magnetostriction maximum the amplitude of the received signal is an information

At stretching the specimen made of steel 25 in the elastic area it has been shown that the amplitude behaves depending on the positions of the sensor i.e. lengthwise and crosswise of

On measuring the sound speed, it has been found out that in the elastic area it changes less than 0, 5 %. Hence, at controlling tension concerning the sound speed more precise

The studying of the field curve of Rayleigh waves EMAT under «the sensor is along loading» shows that at specimen stretching in the elastic area and at the beginning of the area plastic deformation both the amplitude of the received signal and an optimal field of magnetizing (a field of the maximal signal in the EMAT curve) for a magnetostriction maximum have changed. It depends on whether magnetostriction is positive or negative

For materials with the negative magnetostriction of saturation, s, (nickel, constructional

Fig. 11 shows the dependence of the maximum point of the field curve of EMAT on loading, the maximum point being normalized in relation with its initial value. At the initial stage of a loading the amplitude of the maximum grows, and this maximum is displaced to the area of the bigger fields. Then, in the area of the inflection point a decrease of a maximum value is observed. The inflection point lies in the area of the elasticity limit (the conditional point

It can be explained from the physical point of view. In [4] it is noted that at <sup>s</sup> 0 pulling stresses of are considered to be positive, two factors being competitive: on the one hand the energy of a magnetic field, , on the other hand the crystallographic anisotropy and magnetoelastic energies. Tension in a metal makes a magnetization vector turn perpendicular to the magnetic field. As a result, it is more difficult to obtain an amplitude

The amplitude of the EMA signal is described by formula (1). As the loading in the elastic

in the received signal growth. At larger loadings there is tension which leads to the signal

0

grows. It results

*d dH* 

*4.1.3. Tension controlling* 

the loading. Thus dependence is almost linear.

steel) the dependence is as follows.

maximum of EMAT.

equipment and computer processing of signals should be applied.

where the size of permanent deformations makes 0, 05 %).

area increases magnetic conductivity, , decreases, and the parameter

decrease. So a maximum occurs in the elasticity limit.

parameter.

[10].

The amplitude of the obtained pulses (А1, А2) demonstrates the effectiveness of EMAT in different directions which is defined by magnetoelastic properties of a material. Magnetoelastic anisotropy of materials is defined by the amplitude distinction of pulses.

**Figure 9.** Tangential (a) and normal (в) magnetization of EMAT sensor.

**Figure 10.** Oscillograms of signals, isotropic material (а), non-isotropic material (b), which are received by means circular EMAT sensor.

The magnetic anisotropy of a sheet is shown as follows. Effectiveness of EMAT from a magnetize field has a maximum. In case of a magnetic anisotropy the maximum of EMAT signal is reached in different directions at different currents of magnetization. Thus, on changing a magnetization current for an isotropic material the range of optimal currents is narrow, and for a magnetic anisotropic material the range is wider the one mentioned above.

Electromagnetic and Acoustic Transformation of Surface Acoustic Waves and Its Application in Various Tasks 393

The developed technique was tested on various materials and showed high effectiveness.

## *4.1.3. Tension controlling*

392 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

duration or the distance between extreme pulses (fig. 10b).

**Figure 9.** Tangential (a) and normal (в) magnetization of EMAT sensor.

by means circular EMAT sensor.

above.

the different directions take different time. And the received pulse extends, or splits into a number of pulses. An elastic anisotropy of the material is characterized by the pulse

The amplitude of the obtained pulses (А1, А2) demonstrates the effectiveness of EMAT in different directions which is defined by magnetoelastic properties of a material. Magnetoelastic anisotropy of materials is defined by the amplitude distinction of pulses.

**Figure 10.** Oscillograms of signals, isotropic material (а), non-isotropic material (b), which are received

The magnetic anisotropy of a sheet is shown as follows. Effectiveness of EMAT from a magnetize field has a maximum. In case of a magnetic anisotropy the maximum of EMAT signal is reached in different directions at different currents of magnetization. Thus, on changing a magnetization current for an isotropic material the range of optimal currents is narrow, and for a magnetic anisotropic material the range is wider the one mentioned EMAT SAW enables tension and operational loadings controlling. For this purpose the sensor (fig.6) was used. The sensor platform area is to be 30 x 60мм. Adjusting to obtain a magnetostriction maximum the amplitude of the received signal is an information parameter.

At stretching the specimen made of steel 25 in the elastic area it has been shown that the amplitude behaves depending on the positions of the sensor i.e. lengthwise and crosswise of the loading. Thus dependence is almost linear.

On measuring the sound speed, it has been found out that in the elastic area it changes less than 0, 5 %. Hence, at controlling tension concerning the sound speed more precise equipment and computer processing of signals should be applied.

The studying of the field curve of Rayleigh waves EMAT under «the sensor is along loading» shows that at specimen stretching in the elastic area and at the beginning of the area plastic deformation both the amplitude of the received signal and an optimal field of magnetizing (a field of the maximal signal in the EMAT curve) for a magnetostriction maximum have changed. It depends on whether magnetostriction is positive or negative [10].

For materials with the negative magnetostriction of saturation, s, (nickel, constructional steel) the dependence is as follows.

Fig. 11 shows the dependence of the maximum point of the field curve of EMAT on loading, the maximum point being normalized in relation with its initial value. At the initial stage of a loading the amplitude of the maximum grows, and this maximum is displaced to the area of the bigger fields. Then, in the area of the inflection point a decrease of a maximum value is observed. The inflection point lies in the area of the elasticity limit (the conditional point where the size of permanent deformations makes 0, 05 %).

It can be explained from the physical point of view. In [4] it is noted that at <sup>s</sup> 0 pulling stresses of are considered to be positive, two factors being competitive: on the one hand the energy of a magnetic field, , on the other hand the crystallographic anisotropy and magnetoelastic energies. Tension in a metal makes a magnetization vector turn perpendicular to the magnetic field. As a result, it is more difficult to obtain an amplitude maximum of EMAT.

The amplitude of the EMA signal is described by formula (1). As the loading in the elastic area increases magnetic conductivity, , decreases, and the parameter 0 *d dH* grows. It results

in the received signal growth. At larger loadings there is tension which leads to the signal decrease. So a maximum occurs in the elasticity limit.

Electromagnetic and Acoustic Transformation of Surface Acoustic Waves and Its Application in Various Tasks 395

**Figure 12.** The shift of the maximum point of a field curve of Rayleigh waves EMAT in H18 alloy from the loading (the loading is given in MPa, and the length change after loading is given in percent).

It has been shown that the EMAT SAW method are defined by different subsystems of the material. Information on the parameters of the material related to these subsystems is

Magnetostriction is one of the important characteristics of a material. Due to the wide use of these materials in science and industry the assessment of magnetostriction properties of a

The main characteristic of magnetostriction properties of a material is the field curve of magnetostriction, i.e., dependence of the linear magnetostriction, , on a magnetic field. Though

At magnetostriction measurement the method based on tension resistivity of sensors stuck by glue on an specimen is the most extensively used. There are some shortcomings in this method. Alternatively a quick test based on non-contact EMAT SAW [11] may be suggested.

So for Rayleigh waves EMAT formula (1) is used. The task is as following: based on the known curve of EMAT we are to obtain a curve of magnetostriction, =f(H). It is clear that from curve (1) a field curve of magnetostriction can be obtained by the integration method

from the practical point of view it is enough to know magnetostriction of saturation, s.

**4.2. Physical study of materials** 

material is of great importance.

revealed by the information parameters of the EMA method.

*4.2.1. Magnetostriction assessment of a material* 

only. This process is difficult and inaccurate.

**Figure 11.** The shift of the maximum point of a field curve of Rayleigh waves EMAT in nickel from the loading (the loading is given in MPa, and the length change after loading is given in percent).

If materials have a positive magnetostriction of saturation, the behaviour of the maximum of the field curve for Rayleigh waves EMAT is essentially different. Using alloy Н18 (18% Ni, 82 % Fe) s› 0 as an example it is shown that a received EMA signal unequivocally falls (fig. 12). As to a magnetic field first an optimal magnetic field decreases and then it becomes larger, the change takes place at the point close to a limit of material elasticity. It can be also explained from the physical point of view.

Thus, it has been shown that using Rayleigh waves EMAT at least two information parameters are obtained which are used for the applied loadings to be characterized.

It can be carried out either by calibration curves at monitoring or without calibration curves if the tendency of change of parameters EMA is used.

**Figure 12.** The shift of the maximum point of a field curve of Rayleigh waves EMAT in H18 alloy from the loading (the loading is given in MPa, and the length change after loading is given in percent).

## **4.2. Physical study of materials**

394 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

**Figure 11.** The shift of the maximum point of a field curve of Rayleigh waves EMAT in nickel from the

If materials have a positive magnetostriction of saturation, the behaviour of the maximum of the field curve for Rayleigh waves EMAT is essentially different. Using alloy Н18 (18% Ni, 82 % Fe) s› 0 as an example it is shown that a received EMA signal unequivocally falls (fig. 12). As to a magnetic field first an optimal magnetic field decreases and then it becomes larger, the change takes place at the point close to a limit of material elasticity. It can be also

Thus, it has been shown that using Rayleigh waves EMAT at least two information

It can be carried out either by calibration curves at monitoring or without calibration curves

parameters are obtained which are used for the applied loadings to be characterized.

loading (the loading is given in MPa, and the length change after loading is given in percent).

explained from the physical point of view.

if the tendency of change of parameters EMA is used.

It has been shown that the EMAT SAW method are defined by different subsystems of the material. Information on the parameters of the material related to these subsystems is revealed by the information parameters of the EMA method.

## *4.2.1. Magnetostriction assessment of a material*

Magnetostriction is one of the important characteristics of a material. Due to the wide use of these materials in science and industry the assessment of magnetostriction properties of a material is of great importance.

The main characteristic of magnetostriction properties of a material is the field curve of magnetostriction, i.e., dependence of the linear magnetostriction, , on a magnetic field. Though from the practical point of view it is enough to know magnetostriction of saturation, s.

At magnetostriction measurement the method based on tension resistivity of sensors stuck by glue on an specimen is the most extensively used. There are some shortcomings in this method. Alternatively a quick test based on non-contact EMAT SAW [11] may be suggested.

So for Rayleigh waves EMAT formula (1) is used. The task is as following: based on the known curve of EMAT we are to obtain a curve of magnetostriction, =f(H). It is clear that from curve (1) a field curve of magnetostriction can be obtained by the integration method only. This process is difficult and inaccurate.

Horizontal polarization waves EMAT (SH wave) is more preferable to be used to obtain =f(H). A field curve of SH waves EMAT is described by the simplified formula:

$$E\_{SH} \approx \frac{1}{\mu d} \left(\frac{\mathcal{A}}{H}\right)^2 P \tag{7}$$

Electromagnetic and Acoustic Transformation of Surface Acoustic Waves and Its Application in Various Tasks 397

In 800A/cm fields magnetostriction of materials approaches saturation. To obtain the quantitative value of saturation magnetostriction the required data were obtained by a method of tension resistors. The comparative table on the magnetostriction of saturation received by an EMAT method and a method of resistance strain gages is given in table 1.

As shown in the table, the relative ratios for the EMA method are obtained with an accuracy

It should be noted that EMA method allows defining the magnetostriction module λ only. A sign of magnetostriction is complicated to be defined, but it is quite possible. To carry it out it is necessary to observe a phase of the received signal and then to compare it with a signal

**Figure 14.** Field curves of the magnetostriction module calculated based on the experimental data (a) the data are given according to literature data [12] (b) (1-iron, 2 - cobalt, 3 - alloy 49КФ2

of 5-7 %.

phase of the known material.

(Permendur), 4 – nickel).

where - / *<sup>t</sup> P C* is a material parameter, is a static magnetic conductivity, *d* is a sheet thickness, is material density, *Ct* is a speed of shift waves, is an electrical conductivity. Thus we obtain :

$$
\mathcal{A} = \sqrt{\frac{E\_{SH}d}{P}} H \sqrt{\mu} \tag{8}
$$

Knowing В=f (H) it is easy to calculate =f (H), and then knowing the material parameters it quite easy to calculate a curve =f (H).

The calculations above have been used to obtain =f (H) for four materials: iron, cobalt, nickel, permendur (brand 49КФ2). Fig. 1 presents the orientation scheme of the magnetic Hy field for EMAT of SH waves. Fig. 13 shows field characteristics of EMAT of the materials mentioned above. In fig. 14á field characteristics of the magnetostriction module calculated on the basis of formula (8) are presented. Fig. 14б shows the same curves based on data [12]. High curves coincidence is observed.

**Figure 13.** The experimental EMAT field curve of SH- waves (1-iron, 2 - cobalt, 3 – alloy 49КФ2, 4 – nickel).

In 800A/cm fields magnetostriction of materials approaches saturation. To obtain the quantitative value of saturation magnetostriction the required data were obtained by a method of tension resistors. The comparative table on the magnetostriction of saturation received by an EMAT method and a method of resistance strain gages is given in table 1.

396 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

is a material parameter,

is material density, *Ct* is a speed of shift waves,

where - / *<sup>t</sup> P C* 

Thus we obtain :

thickness,

nickel).

quite easy to calculate a curve =f (H).

High curves coincidence is observed.

=f(H). A field curve of SH waves EMAT is described by the simplified formula:

Horizontal polarization waves EMAT (SH wave) is more preferable to be used to obtain

*SH E dH P*

Knowing В=f (H) it is easy to calculate =f (H), and then knowing the material parameters it

The calculations above have been used to obtain =f (H) for four materials: iron, cobalt, nickel, permendur (brand 49КФ2). Fig. 1 presents the orientation scheme of the magnetic Hy field for EMAT of SH waves. Fig. 13 shows field characteristics of EMAT of the materials mentioned above. In fig. 14á field characteristics of the magnetostriction module calculated on the basis of formula (8) are presented. Fig. 14б shows the same curves based on data [12].

**Figure 13.** The experimental EMAT field curve of SH- waves (1-iron, 2 - cobalt, 3 – alloy 49КФ2, 4 –

<sup>2</sup> <sup>1</sup> *SH E P d H* 

(7)

is a static magnetic conductivity, *d* is a sheet

is an electrical conductivity.

(8)

As shown in the table, the relative ratios for the EMA method are obtained with an accuracy of 5-7 %.

It should be noted that EMA method allows defining the magnetostriction module λ only. A sign of magnetostriction is complicated to be defined, but it is quite possible. To carry it out it is necessary to observe a phase of the received signal and then to compare it with a signal phase of the known material.

**Figure 14.** Field curves of the magnetostriction module calculated based on the experimental data (a) the data are given according to literature data [12] (b) (1-iron, 2 - cobalt, 3 - alloy 49КФ2 (Permendur), 4 – nickel).


Electromagnetic and Acoustic Transformation of Surface Acoustic Waves and Its Application in Various Tasks 399

When studying various acoustic waves the EMAT method is more perspective due to easy

There are combined methods of generating and receiving acoustic waves where EMAT is used together with other methods, for example, with laser methods and with methods of an

All we said above allows us to draw a conclusion that the EMAT methods are very

[1] Комаров В.А. Квазистационарное электромагнитно-акустическое преобразование

[2] Васильев А.В., Бучельников В.Д., Гуревич С.Ю., Каганов М.И., Гайдуков Ю.П. Электромагнитное возбуждение звука в металлах. – Челябинск. – М.: Издательство

[3] Викторов И.А. Звуковые поверхностные волны в твердых телах. М.: Наука, 1981. [4] Ильясов Р.С., Бабкин С.Э., Комаров В.А. О механизмах ЭМА преобразования волн

[5] Thompson R.B. A Model for the Electromagnetic Generation and Detection of Rayleigh and Lamb Waves. – IEEE Trans. Sonics and Ultras., 1973, v.20, N 4, p.340-346. [6] Комаров В.А., Бабкин С.Э., Ильясов Р.С. ЭМА преобразование волн горизонта льной поляризации в магнитоупругих материалах. - Дефектоскопия, 1993, №2,

[7] Бабкин С.Э., Ильясов Р.С., Комаров В.А., Рубцов В.И. Устройство для бесконтактного возбуждения и приема волн Рэлея в ферромагнетиках. –

[8] Бабкин С.Э., Ильясов Р.С., Зверев Н.Н. Отстройка от зазора при электромагнитно-

[9] Бабкин С.Э., Ильясов Р.С. Кольцевой электромагнитно-акустический преобразователь поверхностных волн. - Дефектоскопия, 2002, №1, с.78-82. [10] Бабкин С.Э., Ильясов Р.С. О возможности использования параметров ЭМАП для оценки предела упругости и остаточных деформаций ферромагнитных

[11] Бабкин С.Э., Ильясов Р.С., Комаров В.А. Бесконтактный метод оценки

акустическом способе контроля. - Дефектоскопия, 1998, №4, с.19-22.

магнитострикции материалов. - Дефектоскопия, 1996, №1, с.41-45.

Рэлея при различных частотах. - Дефектоскопия, 1988, №10, с.77 – 82.

*Physical-Technical Institute, Ural Branch of Russian Academy of Sciences,* 

в металлах. – Свердловск: УНЦ АН СССР, 1986, 235с.

generation of acoustic waves.

optical interferometry.

promising in the future.

**Author details** 

Sergey E. Babkin

*Izhevsk, Russia* 

**5. References** 

с.11 – 17.

ЮурГУ. – 2001. –339 с.

Дефектоскопия, 1989, №6, с.93-94.

материалов. - Дефектоскопия, 2010, №1, с.83-89.

**Table 1.** The comparative table on the magnetostriction of saturation received by an EMAT method and a method of resistance strain gages.

## *4.2.2. Assessment of other characteristics of a material*

Electric properties of ferromagnetic materials can be estimated using the amplitude of the received signal in large magnetic fields (more than 800A/cm). EMAT effectiveness depends on the electrical conductivity of a material under the same conditions.

Magnetic properties of a material can be estimated by the location of the magnetostriction maximum.

Two parameters are used to estimate elastic properties of a material:

Firstly, a sound speed in a material. To measure the speed of the Rayleigh surface wave, CR, and the speed of horizontal polarization waves, CSH, the techniques described are employed. Here, it is should be considered that CSH for a zero mode is equal to the speed of shift waves of the material, Сt,. These measurements enables estimating the elastic constants of a material such as shift modulus and a Poisson's ratio. The constants defined allows us to determine the remained elastic modules of a material.

Secondly, sound attenuation in a material is estimated by EMAT SAW methods. In this case two receiving EMA coils are used.

Having defined the attenuation parameter it is easy to find such important production characteristics as good quality of the system and an internal friction parameter of a material.

## **4.3. Prospects of use of EMAT SAW**

The main examples of using the surface waves EMAT are presented in the paper only. The use of EMAT SAW in non-destructive monitoring as well as in studying new materials and the phenomena is possible in the nearest future.

Love waves EMAT may be used for non-destructive monitoring of coatings and thin films and for their thickness measurements as well. SH waves EMAT of can be applied in cylindrical specimens where such waves are known to be generated and received very efficiently.

One can find papers on the use of surface waves EMAT to study magnetic phenomena in rare-earth metals. At the increased or decreased temperatures of the specimens it is easier to apply the EMAT method than the method of piezoelements.

Electromagnetic and Acoustic Transformation of Surface Acoustic Waves and Its Application in Various Tasks 399

When studying various acoustic waves the EMAT method is more perspective due to easy generation of acoustic waves.

There are combined methods of generating and receiving acoustic waves where EMAT is used together with other methods, for example, with laser methods and with methods of an optical interferometry.

All we said above allows us to draw a conclusion that the EMAT methods are very promising in the future.

## **Author details**

398 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

Fe 1 1 Co 2, 62, 8 Ni 5, 25, 0 49КФ2 6, 26, 5

**Table 1.** The comparative table on the magnetostriction of saturation received by an EMAT method and

Electric properties of ferromagnetic materials can be estimated using the amplitude of the received signal in large magnetic fields (more than 800A/cm). EMAT effectiveness depends

Magnetic properties of a material can be estimated by the location of the magnetostriction

Firstly, a sound speed in a material. To measure the speed of the Rayleigh surface wave, CR, and the speed of horizontal polarization waves, CSH, the techniques described are employed. Here, it is should be considered that CSH for a zero mode is equal to the speed of shift waves of the material, Сt,. These measurements enables estimating the elastic constants of a material such as shift modulus and a Poisson's ratio. The constants defined allows us to

Secondly, sound attenuation in a material is estimated by EMAT SAW methods. In this case

Having defined the attenuation parameter it is easy to find such important production characteristics as good quality of the system and an internal friction parameter of a material.

The main examples of using the surface waves EMAT are presented in the paper only. The use of EMAT SAW in non-destructive monitoring as well as in studying new materials and

Love waves EMAT may be used for non-destructive monitoring of coatings and thin films and for their thickness measurements as well. SH waves EMAT of can be applied in cylindrical specimens where such waves are known to be generated and received very

One can find papers on the use of surface waves EMAT to study magnetic phenomena in rare-earth metals. At the increased or decreased temperatures of the specimens it is easier to

λmax/λmax Fe Tenzometod

EMA method

*4.2.2. Assessment of other characteristics of a material* 

determine the remained elastic modules of a material.

two receiving EMA coils are used.

**4.3. Prospects of use of EMAT SAW** 

the phenomena is possible in the nearest future.

apply the EMAT method than the method of piezoelements.

on the electrical conductivity of a material under the same conditions.

Two parameters are used to estimate elastic properties of a material:

Material λmax/λmax Fe

a method of resistance strain gages.

maximum.

efficiently.

Sergey E. Babkin *Physical-Technical Institute, Ural Branch of Russian Academy of Sciences, Izhevsk, Russia* 

## **5. References**


[12] Bozort R.M., Ferromagnetism, D.Van Nostrand Co., Princeton, 1951.

**Chapter 17** 

© 2013 Mandloi and Mishra, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2013 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2013 Mandloi and Mishra, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

**Acoustics in Optical Fiber** 

Abhilash Mandloi and Vivekanand Mishra

Additional information is available at the end of the chapter

Optical filters are the heart of optical networks; without the wavelength selective device wavelength division multiplexing and dense wavelength division multiplexing network will not exist. As the networks are progressing towards closer wavelength spacing, performance requirement for filters are becoming more demanding. Currently, the popular filters include gratings, thin-film filters, and Fabry-Perot filters and acoustoi optic tunable

Acousto-optic (AO) effect in fibers has been studied to produce tunable filters, gain flatteners, modulators, frequency shifters, and optical switches reported. Most AO devices work on coupling from the fundamental mode (LP11) of light to a higher order asymmetrical (LPll, LP12 .... LP1n) modes. Acousto-optics is defined as the discipline devoted to the interactions between the acoustic waves and the light waves in a material medium. Acoustic (vibrational) waves can be made to modulate, deflect and focus light waves by causing a variation in the refractive index. Acousto optic tunable filters are a promising technology for dynamic gain equalization of optical fiber amplifiers [1]. By launching an acoustic wave directly on the fiber, the device combines the merits of fiber and AOTF devices namely the low insertion loss, low polarization dependence loss, wide tunability, fast tuning speed and ease of packaging. When a flexural acoustic wave is applied to a tapered single mode fiber, coupling takes place between the core mode and the cladding mode. The coupled energy in the cladding mode is essentially absorbed by the fiber jacket as reported so that the device is a notch filter. It means the centre frequency and the rejection efficiency can be tuned by adjustment of the frequency and voltage being applied. Varying the amplitudes and

frequency of a RF generator can change the spectral profile of these filters.

between the cladding and core can be changed.

To improve the rejection efficiency of the filters, the thickness of the fiber can be reduced. This is achieved through the heating and the acid-etching method. In the heating method, the ratio of cladding to core size is maintained while in the acid etching-method, the ratio

http://dx.doi.org/10.5772/54477

**1. Introduction** 

filters (AOTFs).

## **Acoustics in Optical Fiber**

Abhilash Mandloi and Vivekanand Mishra

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/54477

## **1. Introduction**

400 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

[12] Bozort R.M., Ferromagnetism, D.Van Nostrand Co., Princeton, 1951.

Optical filters are the heart of optical networks; without the wavelength selective device wavelength division multiplexing and dense wavelength division multiplexing network will not exist. As the networks are progressing towards closer wavelength spacing, performance requirement for filters are becoming more demanding. Currently, the popular filters include gratings, thin-film filters, and Fabry-Perot filters and acoustoi optic tunable filters (AOTFs).

Acousto-optic (AO) effect in fibers has been studied to produce tunable filters, gain flatteners, modulators, frequency shifters, and optical switches reported. Most AO devices work on coupling from the fundamental mode (LP11) of light to a higher order asymmetrical (LPll, LP12 .... LP1n) modes. Acousto-optics is defined as the discipline devoted to the interactions between the acoustic waves and the light waves in a material medium. Acoustic (vibrational) waves can be made to modulate, deflect and focus light waves by causing a variation in the refractive index. Acousto optic tunable filters are a promising technology for dynamic gain equalization of optical fiber amplifiers [1]. By launching an acoustic wave directly on the fiber, the device combines the merits of fiber and AOTF devices namely the low insertion loss, low polarization dependence loss, wide tunability, fast tuning speed and ease of packaging. When a flexural acoustic wave is applied to a tapered single mode fiber, coupling takes place between the core mode and the cladding mode. The coupled energy in the cladding mode is essentially absorbed by the fiber jacket as reported so that the device is a notch filter. It means the centre frequency and the rejection efficiency can be tuned by adjustment of the frequency and voltage being applied. Varying the amplitudes and frequency of a RF generator can change the spectral profile of these filters.

To improve the rejection efficiency of the filters, the thickness of the fiber can be reduced. This is achieved through the heating and the acid-etching method. In the heating method, the ratio of cladding to core size is maintained while in the acid etching-method, the ratio between the cladding and core can be changed.

## **2. Acousto-optic tunable filter**

#### **2.1. Device design**

The fiber used in our experiment is a Corning SMF-28, standard telecommunication single mode fiber. A region of SMF is etched by dipping the fiber in a hydrofluoric acid solution, which has a concentration of 40%. Etching rate controls the thickness of the SMF and the diameter reduction is observed using a CCD camera.

Acoustics in Optical Fiber 403

where *cs* is the longitudinal velocity inside silica, *vs* is the density silica and *As* is the cross section of fiber. Acoustic impedance inside the fiber is counted twice because of bidirectional acoustic movement along the fiber. Optimum transduction occurs when Zr = Zs and since acoustic impedance of silica is almost matching that of aluminium, according to engan et. al maximum acoustic wave transfer occurs when horn tip diameter is almost

By driving a piezoelectric (PZT) device at an ultrasonic frequency the periodic perturbations can be created inside the fiber. In a phase-matched condition, where the momentum and energy conservation requirement *(LB* =˄) are met, the resonant frequency of an acoustic wave

> 2 2 *ext ext*

 

(3)

*B bC bC <sup>f</sup> <sup>L</sup>* 

where *b* is the radius of the fiber, Cext is the speed of fundamental acoustic mode, which for

Assuming a phase-matched condition, the frequency needed to transfer the modes from core to cladding mode for various thickness of the fiber is given in Fig 2 and Fig 3. As the fiber diameter is reduced, the values of *df/dλ get* smaller. For unetched fibres, the frequencies used to create the micro bends and thus, convert the modes are from l.75 MHz to 2.25 MHz. For thin

**Figure 2.** Calculated RF frequency to convert the LP01 mode to LP11 mode plotted against wavelength

1 A microbend is the physical deformation of fiber achieved mechanically or chemically done to perturbing the optical

diameter fibers (20 *µ* m, 30 *µ* m, *40 µ* m), the frequencies are from 800 kHz to 1.1 MHz.

matching that of the fiber.

**2.3. Tuning of peak wavelength** 

(for various thickness of fibre diameter).

modes to study mode coupling between core and cladding mode.

according to Birks, Russel and Culverhouse (1992) is given by

silica is 5760 ms-1, ˄ is the period of the microbend1.

When the optical signal enters the fiber and interacts with the acoustic energy in a jacket stripped segment of the fiber, the core mode of the light is converted to a higher order cladding mode producing a notch filter like characteristics in the transmission spectrum. Core mode converting to various cladding modes will produce a few notch filters, with each having its peak notch at a separate wavelength [2-4]. A vibrating PZT transducer driven by a RF generator produces the acoustic energy as stated by Yun, Hwang and Kim, (1996). The acoustic energy is further amplified and concentrated to the fiber by a machined aluminium horn.

**Figure 1.** The setup to study AO interaction inside a fiber.

#### **2.2. Horn design**

An acoustic horn functions to transfer and amplify the surface acoustic wave to the fiber. All horns made were conical in shape, where the tip is narrow and the base is broad as described by Lee, Kim Hwang and Yun, (2003). All the horns fabricated for the AOTF experiment have a ratio of length to outer diameter ratio of 2. Length is defined as the length from the tip of the horn to the base of the horn. Horns taken are 1cm in length. Outer diameter of the horn is defined at the diameter at the base. The inside of the horns are made hollow. When the horn is made considerably small, the frequency dependence on the acoustic generator is low. In the experiments done, no transduction is observed when the fiber is not etched. Potential problems can be attributed to the size of the transducer and the adhesive used to bond the tip of the horn to the fiber. Solder acts as a strong, metallic, thermally stable, and acoustically transmitting joint. In these experiments however glue was chosen as the bonding agent. Of particular interest will be the horn tip size. Acoustic impedance at the horn tip is given by:

$$Z\_r = \ c\_a v\_a A\_r \tag{1}$$

where *ca* is the longitudinal velocity inside aluminium, va is the density aluminium and *Ar* is the cross section of the horn tip. Acoustic impedance at the bond junction along the fiber is given by:

$$Z\_s = \ 2c\_s v\_s A\_s \tag{2}$$

where *cs* is the longitudinal velocity inside silica, *vs* is the density silica and *As* is the cross section of fiber. Acoustic impedance inside the fiber is counted twice because of bidirectional acoustic movement along the fiber. Optimum transduction occurs when Zr = Zs and since acoustic impedance of silica is almost matching that of aluminium, according to engan et. al maximum acoustic wave transfer occurs when horn tip diameter is almost matching that of the fiber.

#### **2.3. Tuning of peak wavelength**

402 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

The fiber used in our experiment is a Corning SMF-28, standard telecommunication single mode fiber. A region of SMF is etched by dipping the fiber in a hydrofluoric acid solution, which has a concentration of 40%. Etching rate controls the thickness of the SMF and the

When the optical signal enters the fiber and interacts with the acoustic energy in a jacket stripped segment of the fiber, the core mode of the light is converted to a higher order cladding mode producing a notch filter like characteristics in the transmission spectrum. Core mode converting to various cladding modes will produce a few notch filters, with each having its peak notch at a separate wavelength [2-4]. A vibrating PZT transducer driven by a RF generator produces the acoustic energy as stated by Yun, Hwang and Kim, (1996). The acoustic energy is

An acoustic horn functions to transfer and amplify the surface acoustic wave to the fiber. All horns made were conical in shape, where the tip is narrow and the base is broad as described by Lee, Kim Hwang and Yun, (2003). All the horns fabricated for the AOTF experiment have a ratio of length to outer diameter ratio of 2. Length is defined as the length from the tip of the horn to the base of the horn. Horns taken are 1cm in length. Outer diameter of the horn is defined at the diameter at the base. The inside of the horns are made hollow. When the horn is made considerably small, the frequency dependence on the acoustic generator is low. In the experiments done, no transduction is observed when the fiber is not etched. Potential problems can be attributed to the size of the transducer and the adhesive used to bond the tip of the horn to the fiber. Solder acts as a strong, metallic, thermally stable, and acoustically transmitting joint. In these experiments however glue was chosen as the bonding agent. Of particular interest will be the horn tip size. Acoustic

where *ca* is the longitudinal velocity inside aluminium, va is the density aluminium and *Ar* is the cross section of the horn tip. Acoustic impedance at the bond junction along the fiber is

*Z cvA r aa r* (1)

2 *Z cvA s ss s* (2)

further amplified and concentrated to the fiber by a machined aluminium horn.

**2. Acousto-optic tunable filter** 

diameter reduction is observed using a CCD camera.

**Figure 1.** The setup to study AO interaction inside a fiber.

impedance at the horn tip is given by:

**2.1. Device design** 

**2.2. Horn design** 

given by:

By driving a piezoelectric (PZT) device at an ultrasonic frequency the periodic perturbations can be created inside the fiber. In a phase-matched condition, where the momentum and energy conservation requirement *(LB* =˄) are met, the resonant frequency of an acoustic wave according to Birks, Russel and Culverhouse (1992) is given by

$$f = \frac{\pi bC\_{ext}}{L\_B^2} = \frac{\pi bC\_{ext}}{\Lambda^2} \tag{3}$$

where *b* is the radius of the fiber, Cext is the speed of fundamental acoustic mode, which for silica is 5760 ms-1, ˄ is the period of the microbend1.

Assuming a phase-matched condition, the frequency needed to transfer the modes from core to cladding mode for various thickness of the fiber is given in Fig 2 and Fig 3. As the fiber diameter is reduced, the values of *df/dλ get* smaller. For unetched fibres, the frequencies used to create the micro bends and thus, convert the modes are from l.75 MHz to 2.25 MHz. For thin diameter fibers (20 *µ* m, 30 *µ* m, *40 µ* m), the frequencies are from 800 kHz to 1.1 MHz.

**Figure 2.** Calculated RF frequency to convert the LP01 mode to LP11 mode plotted against wavelength (for various thickness of fibre diameter).

<sup>1</sup> A microbend is the physical deformation of fiber achieved mechanically or chemically done to perturbing the optical modes to study mode coupling between core and cladding mode.

Acoustics in Optical Fiber 405

**3. Tuning of attenuation depth** 

supplied to PZT is 1.6 W to allow mode conversion.

conversion, is given by

amplitude which is given by:

The RF generator's Vp-p level will be used to control the attenuation depth of the filter. Vp-p level is actually referring to the acoustic power transferred to the fiber. Increasing the Vp-p level will generally increase the bottom level of the filter as seen from Fig. 5. However in some cases increasing the V p-p level will only distort the shape of the filter without increasing the notch's depth. For this strong over-coupled phenomenon, side lobes of the filter is actually increasing. One way to eliminate the problem is by limiting the interaction length of light inside the etched region. Here the power means RF generator's Vp-p level which will be used to control the attenuation depth of the filter [8-10]. Vp-p level is actually referring to the acoustic power transferred to the fiber. Increasing the Vp-p level will generally increase the bottom level of the filter as seen from Fig. 5. Here acoustic power

**Figure 5.** Measured attenuation variation of filter when the power of RF generator (Vp-p) is increased.

An effort to reduce the acoustic power fed into the fiber is by reducing the thickness of the fiber. The minimum acoustic power required by the device to operate or to allow mode

> 3 22 2 ( )( ) *<sup>g</sup> <sup>t</sup> P fR u*

where *ρ* is the mass density of the fiber *(ρ* =2200kg/m3 for fused silica), *Vg* is the group velocity of the wave and R is is curvature of fiber, and *ut* is the transverse acoustic

> 2 0.908 *t B <sup>a</sup> u L*

where *L* is referring to the interaction length of acoustic and light inside the fiber and *LB* is the optical beat length. Fig. 6 shows the calculated power required for mode conversion is

*L*

1

(4)

(5)

**Figure 3.** Calculated RF frequency to convert the LP0l mode to LP12 mode plotted against wavelength (for various thickness of fibre diameter).

Frequency from the RF generator can be used to control the peak wavelength tuning of the notch filters (Fig.4). The fiber used in the experiment has a diameter of 30 µm, and length of 17 cm. Higher frequencies of the RF generator will blue shift the peak wavelength of the filter [3-7]. The tuning range of the filter is slightly less than 300 nrn. From Eq.1.3, we deduce that, micro bend's period is inversely proportional to the frequency of the RF generator. For a larger value of period, the filter's peak is red shifted. Thin fibers have lower period values, thus etching the fibres will blue shift the peak wavelength of the notch filters. Frequency used to tune the peak wavelength as in for thin fibres is from 800 kHz to 1.1 MHz, which is in excellent agreement with the theory as in Fig.3 and Fig.4.

**Figure 4.** Measured peak wavelength tuning of the filter by changing the RF frequency. Frequency used is from 970 kHz to 1045 kHz. The fiber used has a thickness of 30 µm and length of 17 cm.

## **3. Tuning of attenuation depth**

404 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

**Figure 3.** Calculated RF frequency to convert the LP0l mode to LP12 mode plotted against wavelength

Frequency from the RF generator can be used to control the peak wavelength tuning of the notch filters (Fig.4). The fiber used in the experiment has a diameter of 30 µm, and length of 17 cm. Higher frequencies of the RF generator will blue shift the peak wavelength of the filter [3-7]. The tuning range of the filter is slightly less than 300 nrn. From Eq.1.3, we deduce that, micro bend's period is inversely proportional to the frequency of the RF generator. For a larger value of period, the filter's peak is red shifted. Thin fibers have lower period values, thus etching the fibres will blue shift the peak wavelength of the notch filters. Frequency used to tune the peak wavelength as in for thin fibres is from 800 kHz to 1.1 MHz, which is

**Figure 4.** Measured peak wavelength tuning of the filter by changing the RF frequency. Frequency used

is from 970 kHz to 1045 kHz. The fiber used has a thickness of 30 µm and length of 17 cm.

(for various thickness of fibre diameter).

in excellent agreement with the theory as in Fig.3 and Fig.4.

The RF generator's Vp-p level will be used to control the attenuation depth of the filter. Vp-p level is actually referring to the acoustic power transferred to the fiber. Increasing the Vp-p level will generally increase the bottom level of the filter as seen from Fig. 5. However in some cases increasing the V p-p level will only distort the shape of the filter without increasing the notch's depth. For this strong over-coupled phenomenon, side lobes of the filter is actually increasing. One way to eliminate the problem is by limiting the interaction length of light inside the etched region. Here the power means RF generator's Vp-p level which will be used to control the attenuation depth of the filter [8-10]. Vp-p level is actually referring to the acoustic power transferred to the fiber. Increasing the Vp-p level will generally increase the bottom level of the filter as seen from Fig. 5. Here acoustic power supplied to PZT is 1.6 W to allow mode conversion.

**Figure 5.** Measured attenuation variation of filter when the power of RF generator (Vp-p) is increased.

An effort to reduce the acoustic power fed into the fiber is by reducing the thickness of the fiber. The minimum acoustic power required by the device to operate or to allow mode conversion, is given by

$$P = 2\pi^3 \rho \nu\_{\llcorner \llcorner} (f\mathbb{R})^2 (\mu\_{\llcorner})^2 \tag{4}$$

where *ρ* is the mass density of the fiber *(ρ* =2200kg/m3 for fused silica), *Vg* is the group velocity of the wave and R is is curvature of fiber, and *ut* is the transverse acoustic amplitude which is given by:

$$
\mu\_{\rm t} = \frac{\pi}{2} L\_B \frac{a}{L} \frac{1}{0.908} \tag{5}
$$

where *L* is referring to the interaction length of acoustic and light inside the fiber and *LB* is the optical beat length. Fig. 6 shows the calculated power required for mode conversion is lower for etched fibers. When the fiber is unetched the power required will be 287 mW. For a 20 µ m fiber, the power required for conversion is only 1.17 mW.

Acoustics in Optical Fiber 407

(6)

**4. Tuning of 3-dB bandwidth** 

Ostling, H.E. Engan (1995):

The 3-dB bandwidth of the notch filter is given by the equation below as reported by D.

1 0.8 ( ) <sup>2</sup> ( ) *<sup>B</sup>*

*<sup>L</sup> <sup>L</sup>*

Where λ is the wavelength of the light, L is the length of the coupling interaction, and *LB* is the optical beat length [11-14]. For a broadband filter, a short coupling length, a long beat length and small beat length dispersion is required. Without making the device short, only by etching the fiber to that thickness a broad filter can be obtained as reported. However this bandwidth is not tuneable and so is not suitable for spectral shaping. In this section, a similar achievement by only using a SMF to tune the 3-dB bandwidth of the filter is demonstrated. In this device, the notch filter's attenuation, peak wavelength tuning and 3-

To achieve this, a tunable acoustic absorber is added to the original AO setup as shown in Fig. 8. By moving the acoustic absorber along the etched region of the fiber, the interaction of light inside the acoustic region can be controlled. From Eq.6, we know that by controlling the coupling interaction length the 3-dB bandwidth of the filter can be controlled [15]. A strong acoustic absorbing material such as cotton or polystyrene can be used as the acoustic absorber [16]. The absorbing material functions to ensure no surface acoustic wave beyond the absorber's position are present. Since the interaction length of light inside the acoustic region can be controlled, over-coupling phenomenon can be monitored, to reduce the effects of undesirable side lobes. Broad filters require higher power to operate when the

*L*

dB bandwidth can be simultaneously controlled in a single device.

attenuation level is maintained the same as a narrow filter.

to cover a wavelength span of 100 nm (1520 om-1620 nm).

**Figure 8.** Setup to study the bandwidth variation using the AO interaction inside fiber.

From Fig. 9, the narrowest filter with a 3-dB bandwidth of 13 nm is obtained when maintaining the interaction length at 14 cm while the broadest filter with a 3-dB bandwidth of 28 nm is obtained when the interaction length is reduced to 7 cm. For an interaction length of 11.5 cm the spectral width is 16 nm and for 9 cm the spectral width will be 21 nm. The frequency used for wavelength tuning was from 960 kHz to 995 kHz and was sufficient

For the broadest filter, the RF generator's Vp-p needed to generate coupling between the modes, seem to be the highest at 14 V. Meanwhile, for the narrowest filter, the Vp-p needed is only 6 V. Thus, we need a higher Vp-p to generate filters for shorter interaction length of light

*B*

 

Experimentally, as seen from Fig. 7 for a 37 µm thick fiber, the acoustic power supplied to PZT is 1.6 W to allow mode conversion. Mode conversion was confirmed using far-field radiation pattern as reported by Doma, and Blake (1992). However, in a *26* µ m fiber, power requirement for mode conversion is reduced to a mere value of 42 mW. The difference in the power reduction with the calculated value, suggests that the loss at the point of contact is high[10]. It is believed that the horn design is still not optimized; nevertheless, this transduction is sufficient to demonstrate conversion between two modes. Typically, only the lowest order flexural acoustic mode should be made to travel inside the fiber, and this can be achieved by ensuring the horn tip's thickness is matching that of the fiber.

**Figure 6.** Calculated acoustic power required to allow mode conversion. Interaction length was set to 13 cm. Inset: Far field radiation pattern of modes involved in conversion. Left- LP01, Right- LP11.

**Figure 7.** Measured transmission spectrum when fiber is etched. Significant reduction in acoustic power is observed.

## **4. Tuning of 3-dB bandwidth**

406 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

a 20 µ m fiber, the power required for conversion is only 1.17 mW.

be achieved by ensuring the horn tip's thickness is matching that of the fiber.

lower for etched fibers. When the fiber is unetched the power required will be 287 mW. For

Experimentally, as seen from Fig. 7 for a 37 µm thick fiber, the acoustic power supplied to PZT is 1.6 W to allow mode conversion. Mode conversion was confirmed using far-field radiation pattern as reported by Doma, and Blake (1992). However, in a *26* µ m fiber, power requirement for mode conversion is reduced to a mere value of 42 mW. The difference in the power reduction with the calculated value, suggests that the loss at the point of contact is high[10]. It is believed that the horn design is still not optimized; nevertheless, this transduction is sufficient to demonstrate conversion between two modes. Typically, only the lowest order flexural acoustic mode should be made to travel inside the fiber, and this can

**Figure 6.** Calculated acoustic power required to allow mode conversion. Interaction length was set to 13 cm. Inset: Far field radiation pattern of modes involved in conversion. Left- LP01, Right- LP11.

**Figure 7.** Measured transmission spectrum when fiber is etched. Significant reduction in acoustic

power is observed.

The 3-dB bandwidth of the notch filter is given by the equation below as reported by D. Ostling, H.E. Engan (1995):

$$
\Delta \mathcal{X} = \frac{0.8}{L} \left[ \frac{\partial L\_B(\mathcal{X})}{\partial \mathcal{X}} \right]^{-1} \left[ L\_B(\mathcal{X}) \right]^2 \tag{6}
$$

Where λ is the wavelength of the light, L is the length of the coupling interaction, and *LB* is the optical beat length [11-14]. For a broadband filter, a short coupling length, a long beat length and small beat length dispersion is required. Without making the device short, only by etching the fiber to that thickness a broad filter can be obtained as reported. However this bandwidth is not tuneable and so is not suitable for spectral shaping. In this section, a similar achievement by only using a SMF to tune the 3-dB bandwidth of the filter is demonstrated. In this device, the notch filter's attenuation, peak wavelength tuning and 3 dB bandwidth can be simultaneously controlled in a single device.

To achieve this, a tunable acoustic absorber is added to the original AO setup as shown in Fig. 8. By moving the acoustic absorber along the etched region of the fiber, the interaction of light inside the acoustic region can be controlled. From Eq.6, we know that by controlling the coupling interaction length the 3-dB bandwidth of the filter can be controlled [15]. A strong acoustic absorbing material such as cotton or polystyrene can be used as the acoustic absorber [16]. The absorbing material functions to ensure no surface acoustic wave beyond the absorber's position are present. Since the interaction length of light inside the acoustic region can be controlled, over-coupling phenomenon can be monitored, to reduce the effects of undesirable side lobes. Broad filters require higher power to operate when the attenuation level is maintained the same as a narrow filter.

**Figure 8.** Setup to study the bandwidth variation using the AO interaction inside fiber.

From Fig. 9, the narrowest filter with a 3-dB bandwidth of 13 nm is obtained when maintaining the interaction length at 14 cm while the broadest filter with a 3-dB bandwidth of 28 nm is obtained when the interaction length is reduced to 7 cm. For an interaction length of 11.5 cm the spectral width is 16 nm and for 9 cm the spectral width will be 21 nm. The frequency used for wavelength tuning was from 960 kHz to 995 kHz and was sufficient to cover a wavelength span of 100 nm (1520 om-1620 nm).

For the broadest filter, the RF generator's Vp-p needed to generate coupling between the modes, seem to be the highest at 14 V. Meanwhile, for the narrowest filter, the Vp-p needed is only 6 V. Thus, we need a higher Vp-p to generate filters for shorter interaction length of light

inside the grating region [17]. The introduction of tuneable acoustic absorber will change the strain dependency on the device. To limit the strain change introduced in the device only the tip of the absorber is allowed to touch the fiber, in our case, the resonant frequency change corresponding to the strain change was maintained at +/- 0.7kHz. Throughout the experiment the total IL was maintained less than 0.1 dB and the PDL was less than 0.4 dB.

Acoustics in Optical Fiber 409

**5. Double-pass configuration** 

wavelength of the incident and returning light.

level of the main lobe of the notch filter.

filters. The filters however will be more expensive to fabricate.

One of the key problems in fiber-based AOTF is the low attenuation level of the notch filter. Superposing two or more filters according to Yun, Lee, Kim and Kim (1999) produced by multiple transducers can increase the attenuation level. But this method introduces a very high crosstalk in the device especially when the filter's peak: wavelengths are very near to each another and prove [18] highly impractical. Alternatively to improve the attenuation level of the filter, a double pass AO setup reported by Satorious, Dimmick, Burdge (2002) and Culverhouse, Yun, Richardson, Birks, Farwell, Russell (1997) can be used. In the new setup as in Fig 1.10, a 3-port circulator is added before and after the AO device. Light comes in from port 1 of circulator 1 and goes through the acoustic region and experiences mode conversion. The LP 11 coupled mode is converted back to the fundamental mode at the jacket of the fiber. The light rounds circulator 2 and goes through the AO device and experiences mode conversion again. The produced notch filter is observed using the OSA connected to the port 3 of circulator 1. Since the period of the acoustic inside the fiber is not changed, the light going through this region experiences mode conversion at the same

The insertion loss (IL) of a double-pass is increased to less than 3 dB and the Polarization Dependent Loss (PDL) was less than 0.6 dB. IL was not intentionally increased to a high value here, because 2 FC/FC connectors were introduced in the setup to connect port 2 of both circulators to the AO device. Splicing the ports to the device will reduce the IL loss to values less than 1 dB. Using higher quality circulators can further reduce PDL of the notch

**Figure 10.** Double pass configuration to increase the maximum attenuation of the notch filter.

The AO band pass filter by Satorius *et*. *al.*, mentions side lobe suppression and maximum attenuation suppression using the double-pass configuration. Unlike the band pass filter, the notch filter will increase the side lobe level and maximum attenuation level using the double-pass configuration. The side lobe increment is not significant to exceed the bottom

From Fig. 11 the maximum attenuation of the notch filter was -28 dB for the double pass configuration and -12 dB for the single pass configuration. The maximum attenuation of the filter was increased to more than two times. The 3-dB bandwidth of the single pass AO device is 6.14 nm and the 3-dB bandwidth of the double pass AO device is 2.383 nm. This technique will be useful in producing narrow filters with high attenuation suitable in

b)

**Figure 9.** Measured bandwidth variation of filters at different peak wavelengths

## **5. Double-pass configuration**

408 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

inside the grating region [17]. The introduction of tuneable acoustic absorber will change the strain dependency on the device. To limit the strain change introduced in the device only the tip of the absorber is allowed to touch the fiber, in our case, the resonant frequency change corresponding to the strain change was maintained at +/- 0.7kHz. Throughout the experiment the total IL was maintained less than 0.1 dB and the PDL was less than 0.4 dB.

a)

b)

**Figure 9.** Measured bandwidth variation of filters at different peak wavelengths

a) 1596 nm b) 1566 nm

One of the key problems in fiber-based AOTF is the low attenuation level of the notch filter. Superposing two or more filters according to Yun, Lee, Kim and Kim (1999) produced by multiple transducers can increase the attenuation level. But this method introduces a very high crosstalk in the device especially when the filter's peak: wavelengths are very near to each another and prove [18] highly impractical. Alternatively to improve the attenuation level of the filter, a double pass AO setup reported by Satorious, Dimmick, Burdge (2002) and Culverhouse, Yun, Richardson, Birks, Farwell, Russell (1997) can be used. In the new setup as in Fig 1.10, a 3-port circulator is added before and after the AO device. Light comes in from port 1 of circulator 1 and goes through the acoustic region and experiences mode conversion. The LP 11 coupled mode is converted back to the fundamental mode at the jacket of the fiber. The light rounds circulator 2 and goes through the AO device and experiences mode conversion again. The produced notch filter is observed using the OSA connected to the port 3 of circulator 1. Since the period of the acoustic inside the fiber is not changed, the light going through this region experiences mode conversion at the same wavelength of the incident and returning light.

The insertion loss (IL) of a double-pass is increased to less than 3 dB and the Polarization Dependent Loss (PDL) was less than 0.6 dB. IL was not intentionally increased to a high value here, because 2 FC/FC connectors were introduced in the setup to connect port 2 of both circulators to the AO device. Splicing the ports to the device will reduce the IL loss to values less than 1 dB. Using higher quality circulators can further reduce PDL of the notch filters. The filters however will be more expensive to fabricate.

**Figure 10.** Double pass configuration to increase the maximum attenuation of the notch filter.

The AO band pass filter by Satorius *et*. *al.*, mentions side lobe suppression and maximum attenuation suppression using the double-pass configuration. Unlike the band pass filter, the notch filter will increase the side lobe level and maximum attenuation level using the double-pass configuration. The side lobe increment is not significant to exceed the bottom level of the main lobe of the notch filter.

From Fig. 11 the maximum attenuation of the notch filter was -28 dB for the double pass configuration and -12 dB for the single pass configuration. The maximum attenuation of the filter was increased to more than two times. The 3-dB bandwidth of the single pass AO device is 6.14 nm and the 3-dB bandwidth of the double pass AO device is 2.383 nm. This technique will be useful in producing narrow filters with high attenuation suitable in

switching applications. However, there will be a frequency shift of 7 nm introduced using this setup.

Acoustics in Optical Fiber 411

(1999) uses two transducers with six synthesizers to obtain the desired spectral filters. In this technique, to shape the gain, the AOTF setup is using only one transducer and a singletaper. This is possible because the 3-dB [21-24] bandwidth of the filter we demonstrated can be varied on the same device. In our setup to flatten the gain profile of the Amplified Stimulated Emission (ASE) spectrum, an AOTF device with two frequency generators and a double-branched power combiner is used as in Fig 12. The power combiner typically introduces a 3-dB loss to the system, thus higher Vp-p from the RF generator is needed to produce the filters for spectral shaping. Total insertion loss of the setup is less than 0.2 dB. For the measurement, the EDF A was used as the ASE source and the output spectrum

measured [20] using an Optical Spectrum Analyser (OSA).

**Figure 12.** AOTF setup to flatten the gain of ASE spectrum.

successfully flattened using the same device.

The gain was flattened by changing the Vp-p level of the RF generator, and moving the tuneable acoustic absorber along the etched region of the SMF. The degree of freedom to shape the filter is very high, thus the necessity of cascading another AOTF to the setup is not needed. Fig. 13 shows the effect of shaping the filter on the Amplified Stimulated Emission spectrum of EDFA. Typically has it Amplified Stimulated Emission s peaks at 1532 run and 1550 run. For low gain, however there is a single broad peak at 1560 run. By using this method we show that, the [26-28] ASE spectrum can be flattened regardless of the peak's position and bandwidth using the same device. Since the tuning range is about 300 run, any Amplified Stimulated Emission spectrum that is lying from 1350 run to 1630 run can be

The optical signal coupled from the slow mode (LP01) to the fast mode (LP11) will be downshifted in frequency when the acoustic wave is in the same direction as the optical signal. Frequency is shifted up when the fast mode is coupled to the slow mode for the same acoustic wave [19]. The frequency shift direction is reversed when the acoustic wave is in opposite direction with the optical signal as reported by Kim, Blake, Engan, and Shaw, (1986). In a double-pass setup, the optical signal is both the same and opposite direction to the acoustic wave, while in a single-pass setup, optical signal is maintained in the same direction as the acoustic wave. Thus, a frequency shift is observed in a double-pass setup.

**Figure 11.** Measured normalized transmission spectrum using the double pass configuration. The result is compared with single pass configuration (refer to Fig4.1). There is a frequency shift of7 nm to the left using the double-pass setup.

## **6. Gain flattening filter**

The technique to vary the 3-dB bandwidth of filter inside SMF is then extended as a dynamic gain equalizer for the gain profile of an Erbidium Doped Fiber Amplifier (EDFA). This is just one of the possible applications of AO interaction as efficient spectral shaping devices. Various efforts to dynamically control the gain flatness of the ASE spectrum using acousto-optic tuneable filters (AOTF) were well demonstrated. Passive gain equalization as reported by Vengsarkar, Pedrazzani, Judkins, Lemaire, Bergano, and Davidson (1996) is unable to encounter gain variations due to different input optical power of Wavelength Division Multiplexing (WDM) channels. Meanwhile, integrated AOTF as gain flattening filters have a serious limitation of high insertion loss and crosstalk problems. Fiber-based AOTF by H.S. Kim, Park, and B.Y. Kim (1998) and the setup by Feced, Alegria, and Zervas (1999) uses two transducers with six synthesizers to obtain the desired spectral filters. In this technique, to shape the gain, the AOTF setup is using only one transducer and a singletaper. This is possible because the 3-dB [21-24] bandwidth of the filter we demonstrated can be varied on the same device. In our setup to flatten the gain profile of the Amplified Stimulated Emission (ASE) spectrum, an AOTF device with two frequency generators and a double-branched power combiner is used as in Fig 12. The power combiner typically introduces a 3-dB loss to the system, thus higher Vp-p from the RF generator is needed to produce the filters for spectral shaping. Total insertion loss of the setup is less than 0.2 dB. For the measurement, the EDF A was used as the ASE source and the output spectrum measured [20] using an Optical Spectrum Analyser (OSA).

**Figure 12.** AOTF setup to flatten the gain of ASE spectrum.

410 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

this setup.

the left using the double-pass setup.

**6. Gain flattening filter** 

switching applications. However, there will be a frequency shift of 7 nm introduced using

The optical signal coupled from the slow mode (LP01) to the fast mode (LP11) will be downshifted in frequency when the acoustic wave is in the same direction as the optical signal. Frequency is shifted up when the fast mode is coupled to the slow mode for the same acoustic wave [19]. The frequency shift direction is reversed when the acoustic wave is in opposite direction with the optical signal as reported by Kim, Blake, Engan, and Shaw, (1986). In a double-pass setup, the optical signal is both the same and opposite direction to the acoustic wave, while in a single-pass setup, optical signal is maintained in the same direction as the acoustic wave. Thus, a frequency shift is observed in a double-pass setup.

**Figure 11.** Measured normalized transmission spectrum using the double pass configuration. The result is compared with single pass configuration (refer to Fig4.1). There is a frequency shift of7 nm to

The technique to vary the 3-dB bandwidth of filter inside SMF is then extended as a dynamic gain equalizer for the gain profile of an Erbidium Doped Fiber Amplifier (EDFA). This is just one of the possible applications of AO interaction as efficient spectral shaping devices. Various efforts to dynamically control the gain flatness of the ASE spectrum using acousto-optic tuneable filters (AOTF) were well demonstrated. Passive gain equalization as reported by Vengsarkar, Pedrazzani, Judkins, Lemaire, Bergano, and Davidson (1996) is unable to encounter gain variations due to different input optical power of Wavelength Division Multiplexing (WDM) channels. Meanwhile, integrated AOTF as gain flattening filters have a serious limitation of high insertion loss and crosstalk problems. Fiber-based AOTF by H.S. Kim, Park, and B.Y. Kim (1998) and the setup by Feced, Alegria, and Zervas

The gain was flattened by changing the Vp-p level of the RF generator, and moving the tuneable acoustic absorber along the etched region of the SMF. The degree of freedom to shape the filter is very high, thus the necessity of cascading another AOTF to the setup is not needed. Fig. 13 shows the effect of shaping the filter on the Amplified Stimulated Emission spectrum of EDFA. Typically has it Amplified Stimulated Emission s peaks at 1532 run and 1550 run. For low gain, however there is a single broad peak at 1560 run. By using this method we show that, the [26-28] ASE spectrum can be flattened regardless of the peak's position and bandwidth using the same device. Since the tuning range is about 300 run, any Amplified Stimulated Emission spectrum that is lying from 1350 run to 1630 run can be successfully flattened using the same device.

412 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

Acoustics in Optical Fiber 413

Fig. 14 shows the flattened gain of ASE spectrum at various gain levels using this technique. For the lowest gain, at -30 dBm, which is achieved with a pump power of 96 mA, a broad filter is needed at 1545 nm; to obtain this; the tuneable acoustic absorber is positioned 14 cm after the AOTF device. The required resonant frequency to produce the coupling will be 990 kHz. A deeper notch is needed at 1532 nm; which is produced through the second frequency generator that is set at 993 kHz. The flattened gain is less than 0.8 dB. For gain at -25 dBm, which is achieved with a pump power of 150 mA, a filter is needed at 1556 nm; and a narrow deep notch is needed at 1532 nm; the required resonant frequency to produce the coupling respectively will be 986 kHz and 993 kHz. To obtain this, the tuneable acoustic absorber is positioned 16 cm after the AOTF device. The flattened gain is less than 0.9 dB.

Similarly for gain at -22 dBm, which is achieved with a pump power of 220 mA, a very deep filter is needed at 1532 nm and a small filter at 1545 nm. The resonant frequencies corresponding to these wavelengths are 990 kHz and 993 kHz respectively. To obtain the narrow filter, the tuneable acoustic absorber was set 17 cm after the AOTF device. And the measured flattened gain is less than 0.9 dB. Fig. 5 represents the notch filters obtained to

a)

flatten the gain of the Amplified Stimulated Emission (ASE) spectrum.

c)

**Figure 13.** The effect of moving the tuneable acoustic absorber on the Amplified Stimulated Emission spectrum at various gain levels: a) low gain single peak at 1560 nm b) and c) high gain two peaks at 1532 nm and 1550 nm.

Fig. 14 shows the flattened gain of ASE spectrum at various gain levels using this technique. For the lowest gain, at -30 dBm, which is achieved with a pump power of 96 mA, a broad filter is needed at 1545 nm; to obtain this; the tuneable acoustic absorber is positioned 14 cm after the AOTF device. The required resonant frequency to produce the coupling will be 990 kHz. A deeper notch is needed at 1532 nm; which is produced through the second frequency generator that is set at 993 kHz. The flattened gain is less than 0.8 dB. For gain at -25 dBm, which is achieved with a pump power of 150 mA, a filter is needed at 1556 nm; and a narrow deep notch is needed at 1532 nm; the required resonant frequency to produce the coupling respectively will be 986 kHz and 993 kHz. To obtain this, the tuneable acoustic absorber is positioned 16 cm after the AOTF device. The flattened gain is less than 0.9 dB.

412 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

a)

b)

c) **Figure 13.** The effect of moving the tuneable acoustic absorber on the Amplified Stimulated Emission spectrum at various gain levels: a) low gain single peak at 1560 nm b) and c) high gain two peaks at

1532 nm and 1550 nm.

Similarly for gain at -22 dBm, which is achieved with a pump power of 220 mA, a very deep filter is needed at 1532 nm and a small filter at 1545 nm. The resonant frequencies corresponding to these wavelengths are 990 kHz and 993 kHz respectively. To obtain the narrow filter, the tuneable acoustic absorber was set 17 cm after the AOTF device. And the measured flattened gain is less than 0.9 dB. Fig. 5 represents the notch filters obtained to flatten the gain of the Amplified Stimulated Emission (ASE) spectrum.

Acoustics in Optical Fiber 415

**Figure 15.** Corresponding filter spectrum to the flattened gain of various gain levels in Fig. 16.

energy and this produces a notch filter observed using an optical spectrum analyzer.

The presence of acoustics inside the fiber will create a sequence of bends periodic in nature along the direction of its propagation. Core mode's energy is transferred to a cladding mode's, when it passes through the sequence of bends. The fiber jacket absorbs the coupled

Acoustic horn functions to transfer the acoustic wave of the transducer to the fiber. Aluminium horn is preferred over silica horn because it can be easily reproduced. Furthermore, its acoustic impedance almost matches that of silica's. To allow optimum transmission of acoustics to the fiber, the tip of the horn is made small, with its diameter

No resonance peaks were observed when the fiber is unetched First peaks are observed when the thickness of fiber is approximately 40 µ m. Overlap integral between the modes is not high in thicker fiber, meaning the transfer of acoustic wave to the fiber is not optimized. Thickness reductions in fibers are observed using a CCD camera. The characteristics of the resonance peaks can be controlled electrically using a RF generator. Voltage of the generator can be used to tune the attenuation depth of the resonance peaks. Frequency of the generator can be used to tune the peak wavelength. Frequency is inversely related to period of bends, thus higher frequencies will shift the peak to lower wavelengths. The 3-dB bandwidth of the resonance peaks can be adjusted by limiting the acoustic bend produced inside the fiber. Introducing a tunable acoustic absorber along the fiber can do this. Frequency used in all experiments was from 800 kHz to 1.1 MHz. All the coupled energy to produce the resonance peaks were to LP11 modes, mode conversion observed using a beam

**7. Conclusion** 

matching that of silica's.

pro filer.

**Figure 14.** Gain profiles of the ASE spectrum and the flattened gain at various pump powers: a) 96 mA which has a gain of -30 dBm b) 150 mA which has a gain of -25 dBm and c) 220 mA which has a gain of - 22 dBm.

**Figure 15.** Corresponding filter spectrum to the flattened gain of various gain levels in Fig. 16.

## **7. Conclusion**

414 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

b)

c)

**Figure 14.** Gain profiles of the ASE spectrum and the flattened gain at various pump powers: a) 96 mA which has a gain of -30 dBm b) 150 mA which has a gain of -25 dBm and c) 220 mA which has a gain of -

22 dBm.

The presence of acoustics inside the fiber will create a sequence of bends periodic in nature along the direction of its propagation. Core mode's energy is transferred to a cladding mode's, when it passes through the sequence of bends. The fiber jacket absorbs the coupled energy and this produces a notch filter observed using an optical spectrum analyzer.

Acoustic horn functions to transfer the acoustic wave of the transducer to the fiber. Aluminium horn is preferred over silica horn because it can be easily reproduced. Furthermore, its acoustic impedance almost matches that of silica's. To allow optimum transmission of acoustics to the fiber, the tip of the horn is made small, with its diameter matching that of silica's.

No resonance peaks were observed when the fiber is unetched First peaks are observed when the thickness of fiber is approximately 40 µ m. Overlap integral between the modes is not high in thicker fiber, meaning the transfer of acoustic wave to the fiber is not optimized. Thickness reductions in fibers are observed using a CCD camera. The characteristics of the resonance peaks can be controlled electrically using a RF generator. Voltage of the generator can be used to tune the attenuation depth of the resonance peaks. Frequency of the generator can be used to tune the peak wavelength. Frequency is inversely related to period of bends, thus higher frequencies will shift the peak to lower wavelengths. The 3-dB bandwidth of the resonance peaks can be adjusted by limiting the acoustic bend produced inside the fiber. Introducing a tunable acoustic absorber along the fiber can do this. Frequency used in all experiments was from 800 kHz to 1.1 MHz. All the coupled energy to produce the resonance peaks were to LP11 modes, mode conversion observed using a beam pro filer.

The power fed to cause resonance peaks can be reduced by reducing the thickness of the fiber to a value close to 20 *µ* m. Allowing light to pass through the acoustic bend region twice, as proposed in the double pass configuration, can increase the attenuation peaks. However, a frequency shift of 13 nm is observed because the light is passing through the bend in opposite directions.

Acoustics in Optical Fiber 417

[11] Keiser G., (1991). Optical Fiber Communications. McGraw-Hill, Inc., (2nd Edition) Kim RY, Blake J.N., Engan H.E., Shaw H.J., (1986). All-fiber acousto-optic frequency shifter.

[12] Kim H.S., Yun S.H., Kim H.K., Park N., Kim B.Y., (1998). Actively Gain-Flattened Erbium-Doped Fiber Amplifier Over 35 nrn by Using All-Fiber Acoustooptic Tunable

[13] Kim H.S., Yun S.H., Kwang LK., Kim B.Y., (1997). All-fiber acousto-optic tunable notch filter with electronically controllable spectral profile. Optics Letters, 22 (19), 1476-1478 [14] Lee S.S., Kim H.S., Hwang LK., Yun S.H., (2003). Highly-efficient broadband acoustic

[15] Li Q., Au A.A., Lin C.H., Lyons E.R, Lee H.P., (2002). An Efficient All-Fiber Variable Optical Attenuator via Acoustooptic Mode Coupling. IEEE Photonics Technology

[16] Li Q., Liu X., Lee H.P., (2002), Demonstration of Narrow-Band Acoustooptic Tunable Filters on Dispersion-Enhanced Single Mode Fibers. IEEE Photonics Technology Letters,

[17] Li Q., Liu X., Peng J., Zhou B., Lyons E.R, Lee H.P., (2002). Highly Efficient Acoustooptic Tunable Filter Based on Cladding Etched Single-Mode Fiber. IEEE

[18] Liu Q., Chiang K.S., Rastogi V., (2003). Analysis of Corrugated Long-Period Gratings in Slab Waveguides and Their Polarization Dependence. Journal of Lightwave

[19] Love J.D., Henry W.M., Stewart W.J., Black RJ., Lacroix S., Gonthier F., (1991). Tapered Single-mode fibres and devices Part 1: Adiabaticity criteria. IEE Proceedings, 138, (5),

[20] Monerie M., (1982). Propagation in Doubly Clad Single-Mode Fibers. IEEE Transactions

[21] Mononobe S., Ohtsu M., (1996). Fabrication of a Pencil-Shaped Fiber Probe for Near-Field Optics by Selective Chemical Etching. Journal of Lightwave Technology, 14 (10),

[22] Ostling D., Engan H.E., (1995). Narrow-band acousto-optic tunable filtering in a

[23] Ostling D., Engan H.E., (1995). Spectral Flattening by an All-Fib er Acousto-Optic

[24] Pannell C.N., Wacogne B.F., Abdulhalim 1., (1995). In-Fib er and Fiber Compatible Acoustooptic Components. Journal of Lightwave Technology, 13 (7),1429-1434 [25] Satorius D.A., Dimmick T.E., Burdge G.L, (2002). Double-Pass Acoustooptic Tunable Bandpass Filter With Zero Frequency Shift and Reduced Polarization Sensitivity. IEEE

[26] Yun S.H, Lee B.W., Kim H.K., Kim B.Y., (1999). Dynamic Erbium-Doped Fiber Amplifier Based on Active Gain Flattening with Fiber Acoustooptic Tunable Filters.

transducer for all-fibre acousto-optic devices. Electronics Letters, 39 (18)

Filters. IEEE Photonics Technology Letters, 10 (6), 790-792

Optics Letters, 11 (6),389-391

Letters, 14 (11),1563-1565

Technology, 21 (12),3399-3405

Photonics Technology Letters, 14 (3), 337-339

on Microwave Theory and Techniques, MTT-30 (4), 381-388

twomode fiber. Optics Letters, 20 (11), 1247-1249

Photonics Technology Letters, 14 (9), 1324-1326

IEEE Photonics Technology Letters, 11 (10), 1229-1231

Tunable Filter. IEEE Ultrasonics Symposium, 837-840

14 (11), 1551-1553

343-354

2231-2235

As a spectral shaping tool, the attenuator is efficient as a gain flattening filter for an erbium doped amplifier. The peak of an amplified spontaneous emission at 1531 nm can be reduced to flat levels for various gains of the EDF A pump power. Insertion loss is less than 0.2 dB and polarization dependence loss is less than 0.4 dB.

## **Author details**

Abhilash Mandloi and Vivekanand Mishra *Department of Electronics Engineering, S.V. National Institute of Technology, Surat 395007, Gujarat, India* 

## **8. References**


[11] Keiser G., (1991). Optical Fiber Communications. McGraw-Hill, Inc., (2nd Edition) Kim RY, Blake J.N., Engan H.E., Shaw H.J., (1986). All-fiber acousto-optic frequency shifter. Optics Letters, 11 (6),389-391

416 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

and polarization dependence loss is less than 0.4 dB.

Abhilash Mandloi and Vivekanand Mishra *Department of Electronics Engineering, S.V. National Institute of Technology, Surat 395007, Gujarat, India* 

bend in opposite directions.

**Author details** 

**8. References** 

Symposium, 625-629

Conference, 568-571

1278-1288

Technology, 6 (3), 428-436

The power fed to cause resonance peaks can be reduced by reducing the thickness of the fiber to a value close to 20 *µ* m. Allowing light to pass through the acoustic bend region twice, as proposed in the double pass configuration, can increase the attenuation peaks. However, a frequency shift of 13 nm is observed because the light is passing through the

As a spectral shaping tool, the attenuator is efficient as a gain flattening filter for an erbium doped amplifier. The peak of an amplified spontaneous emission at 1531 nm can be reduced to flat levels for various gains of the EDF A pump power. Insertion loss is less than 0.2 dB

[1] Sutharsanan Veeriah, "Design and Characterisation of All Fiber Optical Filters", Master of Science Thesis, Faculty of Engineering, Multimedia University, Malaysia, Feb 2006. [2] Abdulhalim 1., Pannell C.N., (1993). Acoustooptic in-fiber modulator using acoustic

[3] Au A. A., Liu Q., Lin C.H., Lee H.P., (2004). Effects of Acoustic Reflection on the Performance of a Cladding-Etched All-Fiber Acoustooptic Variable Optical Attenuator.

[4] Birks T.A., Russell P.SJ., Culverhouse D.O., (1992). The Acousto-Optic Effect in Single-Mode Fiber Tapers and Couplers. Journal of Lightwave Technology, 14 (11), 2519-2529 [5] Culverhouse D.O., Yun S.H., Richardson D.J., Birks T.A, Farwell S.G., Russell P.StJ., (1997). Low-loss all- fiber acousto-optic tunable filter. Optics Letters, 22 (2), 96-98 [6] Engan H.E., (2000). Acousto-Optic Coupling In Optical Fibers. IEEE Ultrasonics

[7] Engan H.E., Kim B.Y., Blake J.N., Shaw H.J., (1988). Propagation and Optical Interaction of Guided Acoustic Waves in Two-Mode Optical Fibers. Journal of Lightwave

[8] Engan H.E., Ostling D., Kval Per 0., Askautrud Jan 0 .. Wideband Operation of Horns for excitation of Acoustic Modes in Optical Fibers. 10th Optical Fibre Sensors

[9] Feced R., Alegria c., Zervas M.N., (1999). Acoustooptic Attenuation Filters Based on Tapered Optical Fibers. IEEE Journal of Selected Topics in Quantum Electronics, 5 (5),

[10] Jung Y., Lee S.B., Lee J.W., Oh K., (2005). Bandwidth control in a hybrid fiber

focusing. IEEE Photonics Technology Letters, 9 (5), 999-1002

IEEE Photonics Technology Letters, 16 (1), 150-152

acoustooptic filter. Optics Letters, 30 (1), 84-86

	- [27] Yun S.H., Kim B.Y., Jeong HJ., Kim B.Y., (1996). Suppression of polarization dependence in a two-mode-fiber acousto-optic device. Optics Letters, 21 (12), 908-910

**Section 5** 

**Technological Systems** 

[28] Yun S.H., Kim H.S., (2004). Resonance in Fiber-Based Acoustooptic Devices Via Acoustic Radiation to Air. IEEE Photonics Technology Letters, 16 (1), 147-149

**Technological Systems** 

418 Modeling and Measurement Methods for Acoustic Waves and for Acoustic Microdevices

[27] Yun S.H., Kim B.Y., Jeong HJ., Kim B.Y., (1996). Suppression of polarization dependence in a two-mode-fiber acousto-optic device. Optics Letters, 21 (12), 908-910 [28] Yun S.H., Kim H.S., (2004). Resonance in Fiber-Based Acoustooptic Devices Via Acoustic Radiation to Air. IEEE Photonics Technology Letters, 16 (1), 147-149

**Chapter 18** 

© 2013 El Hassan et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2013 El Hassan et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2013 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

**Techniques for Tuning BAW-SMR Resonators for** 

In telecommunication systems, all filters and resonators that constitute the RF part have the

In order to achieve miniaturization, bulk acoustic wave (BAW) technology is presented. BAW filters are very sensitive to surface contamination, and can exhibit very small sizes. In addition, BAW resonators could be fabricated using compatible material CMOS and BiCMOS [1]. In this context and in order to compensate the variation due to the fabrication process, the work presented in this paper focuses on the tuning of BAW-SMR resonators

This work is divided in two parts. The first part consists of designing BAW-SMR (Solidly Mounted Resonator) filters. In the second part, we propose the use of two methods to tune this type of filters. Thus, we present the design methodology, the study, and the

The bulk acoustic wave resonator is basically constituted by a piezoelectric layer sandwiched between two electrodes (Fig.1). The application of an electric field between the two electrodes generates a mechanical stress that is further propagated through the bulk of the structure (acoustic wave). The resonance condition is established when the acoustical path (in thickness direction) corresponds to odd integer multiples of the half acoustic wavelength. The bulk acoustic wave resonator is basically constituted by a piezoelectric

and reproduction in any medium, provided the original work is properly cited.

tendency to be integrated on the same chip that contains the information treatment.

**the 4th Generation of Mobile Communications** 

M. El Hassan, E. Kerherve, Y. Deval, K. Baraka, J.B. David and D. Belot

Additional information is available at the end of the chapter

experimental realization of the BAW-SMR tunable filters.

layer sandwiched between two electrodes (Fig.1) [2, 3].

**2. BAW impedance behavior** 

**2.1. SMR impedance behavior** 

http://dx.doi.org/10.5772/55131

**1. Introduction** 

and filters.
