**3. Characterization of SMBS gain and FBG reflection spectra in telecom applications**

#### **3.1. Characterization of SMBS gain spectra**

( )

where *ΔT* is temperature change, *ε* is the enclosed pressure, the second item composed in a figure brace reflects photo elasticity factor. This parity gives typical values of *λ*BG shift depending on temperature ~0,01 nm/°К from relative lengthening of a fiber ~ 103 (*ΔL* / *L* ) (nm)

The introduced phase shift (PS) [2] leads to the appearance of a narrow transmission band of width of a few tens of megahertz within the reflection band of FBG. Figure 2, b shows the calculated transmission spectrum of such FBG-PS grating. The phase shift in the grating can be introduced during the writing of the whole structure or later in the preliminary written grating. As the phase shift is increased (which is usually realized by writing two spatially separated gratings with the same FBG), the number of transmission regions in the reflection band increases, and such a structure is called, similarly to bulk optics, a Fabry-Perot interfer‐ ometer (or filter). FBG-PS becomes the grate instrument in telecommunication and sensor nets

The FBG reflective spectrum line shape can be approximated with a Gaussian profile [28]

where λ is wavelength, λ<sup>B</sup> is the center wavelength or peak wavelength of FBG, Δλ<sup>B</sup> is the full

As is known, the spectral dependence of the transmission band of FBG-PS has almost Lorent‐ zian profile [2, 29]. If we assume that the spectral line width of the laser emission lines is negligibly small (~ several KHz), the spectral dependence of the transmission band of FBG-PS

Basics for the use of poly-harmonic probing methods of spectral characteristics for resonant circuits of arbitrary shape were described by us in a number of papers [4,9-10]. It is noted that their effective use (maximum slope of the measurement conversion) is possible at the location of equal amplitude symmetrical components of the probe radiation on the FWHM of contour with average frequency at the central (resonant) wavelength. Based on this requirement, the synthesis of the poly-harmonic (two-or four-frequency) probe radiation desired characteristics

*R*(*λ*)=*RB*exp -4*ln*2 (*λ* - *λB*) / Δ*λ<sup>B</sup>*

*<sup>T</sup>* (*λ*)= *<sup>T</sup> <sup>B</sup>*(Δ*λ<sup>B</sup>* / 2)2

width at half maximum, and *R*B is the maximum reflectivity.

can be represented as follows:

**2.3. Discussion of results**

where *TB* is maximum transmittance on λB.

was carried out. The example results are shown in Tab. 1.

n

æ ö ì ü ï ï æ ö é ù ¶L ¶ D = L- - + + + D ç ÷ í ý é ù ç ÷ë û ê ú ï ï è ø ë û L¶ ¶ è ø î þ

*n P PP T*

1 1 2 1 , <sup>2</sup>

 e *n*

<sup>2</sup> . (13)

(<sup>λ</sup> - *<sup>λ</sup>B*)2 <sup>+</sup> (Δ*λ<sup>B</sup>* / 2)2 . (14)

(12)

*T nT*

2 ÂÐÁ ýô ô 12 11 12

62 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

x

l

[2].

[25-27].

Characterization of SMBS gain spectrum in single-mode optical fiber is necessary in a number of applications. These are: an assessment of the distortions brought by SMBS in information, transferred on fiber-optical lines [34], processing and conversion of optical carriers and microwave sub-carriers in communication networks such as «radio-over-fiber» [35], failure or measuring conversion of temperature on ONU in phonon microwave spectroscopy of optical fiber in PONs [36,37]. For silica fibers shift of Mandelstam-Brillouin frequency is about 10-20 GHz, and Mandelstam-Brillouin gain is observed in a bandwidth of 20-100 MHz [7].

The main parameters are the central frequency of a gain spectrum, its Q-factor and gain coefficient.

The classical method for characterization of Mandelstam-Brillouin gain spectrum (MBGS) is based on use of two lasers: one – for SMBS pumping, and another – for probing of generated gain spectrum [5]. The disadvantage of this method is need in strong control of a frequencies difference of two sources. An advanced method gives the solution of this problem. The optical modulator generates the double-frequency signal. This signal is the sidebands of the pump laser, which are used then for probing [38]. But the disadvantage of this method is need in considering the input power in the gain spectrum and mechanisms of energy transfer between the pumping and probing components. The absence of these components can lead to saturation of contour and appearance of significant inaccuracies in characterization of MBGS. A certain progress in systems of characterization of MBGS was reached by generating the scanning double-band amplitude modulated probing radiation from pumping radiation [39]. However this method is characterized by the low sensitivity, caused by need of reception and processing of signals in a wide bandwidth (10-20 GHz), and also strong influence on measurement inaccuracy of the upper sideband existence. The solution of this problem also was in use of the double-frequency radiation generated unlike [38] for pumping radiation [40]. One frequency corresponded to pump frequency, and the second-to its Stokes component, thus frequency shifted absorption contour corresponded to Mandelstam-Brillouin gain spectrum. The absorption contour was used for suppression of the upper sideband. However, this system has a high complexity and need in strong control of positions of Stokes component and pump component, and also an absorption contour, especially when scanning of a probing signal within 20-100 MHz [7].

Not long ago the measurement system which is free from this drawback [6] was presented. It is based on MBGS conversion from optical to the electrical field by single-sideband amplitude modulated radiation, in which the upper sideband is suppressed. Despite advantages, realization of this method is not always effective; because relevant low sensitivity of meas‐ urements is remained, similar to measurements by double-band amplitude modulated probing radiation in a wide bandwidth. The new method for characterization of gain spectrum of SMBS in single-mode optical fiber is presented in this part. It is based on use of advantages of single-band modulation and double-frequency probing radiation, which gives possibility of transfer the data signal's spectrum in the low noise region of a photo-detector. Also this radiation is characterized by effective procedure of processing of received spectral information by envelope's characteristics of beats of two spectral components [7].

#### **3.2. Two-frequency probing of MBGS**

For conversion of the complex MBGS from optical to the electrical field the optical singlesideband modulation with scanning of frequency of a sideband component is used, including the information about the frequency shift and Q-factor of the SMBS gain spectrum. The measurement method offered by us is based on the double-frequency probing radiation of a MBGS, not on the single-frequency one. Experimental setup for measurements is shown on fig. 3 [7].

The optical signal from a 1550-nm laser diode with a bandwidth about 100 kHz is divided into two paths by a fiber-optic coupler. In the first path signal is modulated by an optical singlesideband modulator. Signal from the frequency combiner is applied to one of the modulator's inputs. The optical single-sideband modulator is based on a dual-drive Mach-Zehnder modulator design. The modulated signal is applied to the Fiber under test (FUT), where the Poly-harmonic Analysis of Raman and Mandelstam-Brillouin Scatterings and Bragg Reflection Spectra http://dx.doi.org/10.5772/59144 65

**Figure 3.** Experimental setup: LD – laser diode; PC – polarization controller; PD– photo-detector

difference of two sources. An advanced method gives the solution of this problem. The optical modulator generates the double-frequency signal. This signal is the sidebands of the pump laser, which are used then for probing [38]. But the disadvantage of this method is need in considering the input power in the gain spectrum and mechanisms of energy transfer between the pumping and probing components. The absence of these components can lead to saturation of contour and appearance of significant inaccuracies in characterization of MBGS. A certain progress in systems of characterization of MBGS was reached by generating the scanning double-band amplitude modulated probing radiation from pumping radiation [39]. However this method is characterized by the low sensitivity, caused by need of reception and processing of signals in a wide bandwidth (10-20 GHz), and also strong influence on measurement inaccuracy of the upper sideband existence. The solution of this problem also was in use of the double-frequency radiation generated unlike [38] for pumping radiation [40]. One frequency corresponded to pump frequency, and the second-to its Stokes component, thus frequency shifted absorption contour corresponded to Mandelstam-Brillouin gain spectrum. The absorption contour was used for suppression of the upper sideband. However, this system has a high complexity and need in strong control of positions of Stokes component and pump component, and also an absorption contour, especially when scanning of a probing signal

64 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

Not long ago the measurement system which is free from this drawback [6] was presented. It is based on MBGS conversion from optical to the electrical field by single-sideband amplitude modulated radiation, in which the upper sideband is suppressed. Despite advantages, realization of this method is not always effective; because relevant low sensitivity of meas‐ urements is remained, similar to measurements by double-band amplitude modulated probing radiation in a wide bandwidth. The new method for characterization of gain spectrum of SMBS in single-mode optical fiber is presented in this part. It is based on use of advantages of single-band modulation and double-frequency probing radiation, which gives possibility of transfer the data signal's spectrum in the low noise region of a photo-detector. Also this radiation is characterized by effective procedure of processing of received spectral information

For conversion of the complex MBGS from optical to the electrical field the optical singlesideband modulation with scanning of frequency of a sideband component is used, including the information about the frequency shift and Q-factor of the SMBS gain spectrum. The measurement method offered by us is based on the double-frequency probing radiation of a MBGS, not on the single-frequency one. Experimental setup for measurements is shown on

The optical signal from a 1550-nm laser diode with a bandwidth about 100 kHz is divided into two paths by a fiber-optic coupler. In the first path signal is modulated by an optical singlesideband modulator. Signal from the frequency combiner is applied to one of the modulator's inputs. The optical single-sideband modulator is based on a dual-drive Mach-Zehnder modulator design. The modulated signal is applied to the Fiber under test (FUT), where the

by envelope's characteristics of beats of two spectral components [7].

**3.2. Two-frequency probing of MBGS**

fig. 3 [7].

within 20-100 MHz [7].

optical radiation passed through the second path counter propagates. That non modulated radiation is the SMBS pump radiation in FUT [7].

**Figure 4.** Probing of the gain spectrum by double-frequency signal

Thus, single-band double-frequency radiation with components *f* <sup>1</sup> = *f rf* −*Δf* , *f* <sup>2</sup> = *f rf* + *Δf* probes the MBGS and the frequency *ν*<sup>0</sup> − *f rf* tuned to the center of the gain spectrum conforms to its central frequency *νMB*, detuning *Δf* half of its FWHM, *ΔνMB* and the carrier frequency *ν*<sup>0</sup> pump frequency *ν<sup>P</sup>* =*c* / *λP*. Double-frequency radiation, passed through the FUT, is received by photo-detector. Probing process is schematically shown in fig. 4 [57].

Radiation at the output of the optical single-sideband modulator is given by

$$\begin{aligned} E\_{\text{in}}(t) &= A\_0 \exp(j2\pi\nu\_o t) + \\ + A\_{-} \exp[j2\pi(\nu\_o - f\_{rf} - \Delta f)t] &+ A\_{-} \exp[j2\pi(\nu\_o - f\_{rf} + \Delta f)t], \end{aligned} \tag{15}$$

where *A*<sup>0</sup> = | *A*<sup>0</sup> |exp( *jφ*0), *A*−<sup>1</sup> = | *A*−<sup>1</sup> |exp( *jφ*−1), *A*−<sup>2</sup> = | *A*−<sup>2</sup> |exp( *jφ*−2) complex amplitudes of the optical carrier and the double-frequency signal. This optical signal propagates through the FUT, which has an optical transfer function *H* (*ν*) characterizing the gain spectrum; therefore, the optical field at the output of the fiber is given by [57].

$$E\_{out}\left(t\right) = A\_0 \left| H\left(\mathbf{v}\_0\right) \right| \exp\left[j \arg H\left(\mathbf{v}\_0\right)\right] \exp\left(j2\pi\mathbf{v}\_{0\prime}\right) +$$

$$+ A\_{-1} \left| H\left(\mathbf{v}\_0 - f\_{\rm{r\prime}} - \Delta f\right) \right| \exp\left[j \arg H\left(\mathbf{v}\_0 - f\_{\rm{r\prime}} - \Delta f\right)\right] \times \exp\left[j2\pi\left(\mathbf{v}\_0 - f\_{\rm{r\prime}} - \Delta f\right)t\right] + \tag{16}$$

$$+ A\_{-2} \left| H\left(\mathbf{v}\_0 - f\_{\rm{r\prime}} + \Delta f\right) \right| \exp\left[j \arg H\left(\mathbf{v}\_0 - f\_{\rm{r\prime}} + \Delta f\right)\right] \times \exp\left[j2\pi\left(\mathbf{v}\_0 - f\_{\rm{r\prime}} + \Delta f\right)t\right].$$

The output current on the beat frequency of the two probing components 2 *Δf* is proportional to

$$\begin{aligned} \left| i\_{\rm out}(t) \right| &\propto \left| A\_{-1} \right| \left| A\_{-2} \right| \left| H(\nu\_{0} - f\_{\rm rf} - \Delta f) \right| \left| H(\nu\_{0} - f\_{\rm rf} + \Delta f) \right| \times \\ &\times \cos[4\pi t \Delta \mathbf{f} + \boldsymbol{\varphi}\_{\rm \downarrow} - \boldsymbol{\varphi}\_{\rm \downarrow} + \text{arg } \mathbf{H}(\nu\_{0} - f\_{\rm rf} - \Delta f) - \text{arg } \mathbf{H}(\nu\_{0} - f\_{\rm rf} + \Delta f) \right|. \end{aligned} \tag{17}$$

Analysis of (17) shows that, we can get the image of the optical transfer function at the frequencies of the two probing signals from the electrical output signal of the photo-detector. The optical transfer function of the FUT is equivalent to concatenation of the fiber linear transfer function and the MBGS [57].

#### **3.3. Four-frequency characterization of the MBGS**

As we mentioned above, the main parameters of the MBGS are the central frequency of a gain spectrum, its Q-factor and gain coefficient. It is significant that at the moment when center frequency of a double-frequency signal *ν*<sup>0</sup> − *f rf* gets to the resonance frequency of a gain spectrum *νMB*, the envelope of the output signal is matched in phase with the envelope of the two-frequency signal at the FUT's input, and the modulation index of the output doublefrequency signal's envelope is maximum and equal to 1 [57].

The measurement fractional inaccuracy of the central frequency can be 0,1% and determined by bandwidth of the laser radiation (in our case 0,1 MHz), and also by accuracy of keeping the difference frequency 2 *Δf* . Some part of the inaccuracy can be added by the appearance of not completely suppressed upper sideband of the double-frequency radiation in the spectrum. Among methods of its decreasing we can offer the usage of a chirp fiber Bragg grating, tuned on the suppression in the bandwidth of possible position change at scanning. We think that such solution is more effective, than offered in [40], as by efficiency of suppression, and also by ability to control the distortions, caused by chromatic dispersion [57].

Defining *ν*<sup>0</sup> − *f rf* =*νMB*, we can find Q-factor of the MBGS. For this we offer the four-frequency method [58] or the method of the variation of difference frequency, which based on the dependence

where *A*<sup>0</sup> = | *A*<sup>0</sup> |exp( *jφ*0), *A*−<sup>1</sup> = | *A*−<sup>1</sup> |exp( *jφ*−1), *A*−<sup>2</sup> = | *A*−<sup>2</sup> |exp( *jφ*−2) complex amplitudes of the optical carrier and the double-frequency signal. This optical signal propagates through the FUT, which has an optical transfer function *H* (*ν*) characterizing the gain spectrum; therefore,

() ( ) () ( )

*out t*

*A Hv f f j Hv f f j v f ft*

+ - -D <sup>é</sup> - -D ´ù é - -D +ù <sup>ë</sup> û ë <sup>û</sup>

*A Hv f f j Hv f f j v f ft*

+ - +D <sup>é</sup> - +D ´ù é - +D <sup>ù</sup> <sup>ë</sup> û ë <sup>û</sup>

*E t AHv j Hv j v*

( ) ( ) ( )

*rf rf rf*

exp arg exp 2

1 0 0 0

2 0 0 0

out 12 0 0

n

0 0 0 0

= + é ù ë û

exp arg exp 2

exp arg exp 2 .

*rf rf*

 n

*rf rf*

n

p

p

(16)

p

( ) ( ) ( )

*rf rf rf*

The output current on the beat frequency of the two probing components 2 *Δf* is proportional


*t ff ff*

Analysis of (17) shows that, we can get the image of the optical transfer function at the frequencies of the two probing signals from the electrical output signal of the photo-detector. The optical transfer function of the FUT is equivalent to concatenation of the fiber linear

As we mentioned above, the main parameters of the MBGS are the central frequency of a gain spectrum, its Q-factor and gain coefficient. It is significant that at the moment when center frequency of a double-frequency signal *ν*<sup>0</sup> − *f rf* gets to the resonance frequency of a gain spectrum *νMB*, the envelope of the output signal is matched in phase with the envelope of the two-frequency signal at the FUT's input, and the modulation index of the output double-

The measurement fractional inaccuracy of the central frequency can be 0,1% and determined by bandwidth of the laser radiation (in our case 0,1 MHz), and also by accuracy of keeping the difference frequency 2 *Δf* . Some part of the inaccuracy can be added by the appearance of not completely suppressed upper sideband of the double-frequency radiation in the spectrum. Among methods of its decreasing we can offer the usage of a chirp fiber Bragg grating, tuned on the suppression in the bandwidth of possible position change at scanning. We think that such solution is more effective, than offered in [40], as by efficiency of suppression, and also

µ - -D - +D ´ - - ´ D + - + - -D - - +D (17)

( ) ( )( )

*it AAH f fH f f*

 n

cos[4 f arg H( ) arg H( )].

the optical field at the output of the fiber is given by [57].

66 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications



p

 jj

transfer function and the MBGS [57].

**3.3. Four-frequency characterization of the MBGS**

frequency signal's envelope is maximum and equal to 1 [57].

by ability to control the distortions, caused by chromatic dispersion [57].

to

$$\mathcal{Q}\_{1,2} = \frac{\nu\_0 - f\_{rf}}{f\_1 - f\_2} \sqrt{\frac{\dot{i}\_{\text{out}\left(\nu\_0 - f\_{rf}\right)} }{\dot{i}\_{\text{out}1,2}}} - 1,\tag{18}$$

where *i* out(*ν*0<sup>−</sup> *<sup>f</sup> rf* ) and *<sup>i</sup>* out1,2 amplitudes at center frequency and at components of the doublefrequency signal at the output of the photo-detector when center frequency of the probing components at frequencies *f* <sup>1</sup> = *f rf* −*Δf* and *f* <sup>2</sup> = *f rf* + *Δf* is tuned on the center of gain spectrum. The value of *i* out1,2 is determined by output signal of the photo-detector, and the value *i* out(*ν*0− *f rf* ) is unknown. If we change the *Δf* by a certain value *Δf* ', not changing the tuning on the center of gain spectrum, then we will get the new value of frequencies *f* <sup>3</sup> = *f rf* −*Δf* −*Δ f* ' and *f* <sup>4</sup> = *f rf* + *Δf* + *Δ f* ' . For frequencies *f* <sup>3</sup> and *f* 4 we can rewrite the (18) as

$$Q\_{3,4} = \frac{\nu\_0 - f\_{\rm rf}}{f\_3 - f\_4} \sqrt{\frac{\dot{i}\_{\nu\_0 - f\_{\rm rf}}}{\dot{i}\_{3,4}}} - 1. \tag{19}$$

Since *Q*1,2 = *Q*3,4, from the combined solution of the equations (18) and (19) we get *i* out(*ν*0<sup>−</sup> *<sup>f</sup> rf* ) and then, inserting this value in one of the equations we find the Q-factor of the MBGS and halfwidth *ΔνMB*.

The advantage of the offered method is that in the measuring process the information signal is influenced by noises only of a bandwidth of the gain spectrum (20-100 MHz), not noises of all bandwidth from MBGS to the carrier (10-20 GHz). Therefore, SNR of the measurements in this case is 10<sup>2</sup> -10<sup>3</sup> greater than similar ratio in previously offered methods. Inserting the known and determined by previously mentioned procedures frequency parameters *νP*, *νMB* and *ΔνMB* in (3), we get the Mandelstam-Brillouin maximum gain coefficient value [7].

The presented method was tested in the laboratory of R&D Institute of Applied Electrody‐ namics, Photonics and Living Systems on the basis of coil of optical fiber Corning SMF-28 6 km long. At the pump power LDI-DFB 1550 5 mW, power of probing sideband components 90 nW we found the SMBS frequency shift is 10,54 GHz, gain coefficient – 20 dB, half-width – 36 MHz. The optical single-sideband modulator is based on a Mach-Zehnder JDS Uniphase OC-192 design. The oscilloscope Agilent InfiniiVision 7000, stabilized power supply PSS-1, the spectrum analyzer FTB 5240-S and the photodiode LSIPD-A75 were used [7].

So, a new method for characterization of gain spectrum of SMBS in single-mode optical fiber is presented. It is based on the usage of advantages of the scanning single-sideband modulation method and double-frequency probing method. For conversion of the complex SBS spectrum from optical to the electrical field single-sideband modulation is used. Detection of doublefrequency components position in the gain spectrum occurs through the amplitude modula‐ tion index of the envelope and the phase difference between envelopes of probing and passing components. The method is characterized by high resolution, SNR of the measurements increased of a two order, simplicity of the offered algorithms for finding the central frequency, Q-factor and Mandelstam-Brillouin maximum gain coefficient. Measurement algorithm is realized on simple and stable experimental setup. Among the methods of measurement inaccuracy decreasing, caused by not completely suppressed upper sideband of the doublefrequency radiation, the usage of a chirp fiber Bragg grating, tuned on the suppression of it in the bandwidth of possible position change at scanning, can be considered [7].

#### **3.4. Two-frequency characterization of FBG reflection spectra**

FBG represents a longitudinal, periodic variation in the refractive index in the core of an optical fiber [2]. The main parameters of the grating are the distributions of the amplitude and period of the refractive index modulation, as well as the average value of the induced refractive index along the fiber axis. These parameters specify the spectral and dispersion parameters of gratings and, thus, determine their use in different applications of the fiber optics. FBG are widely used fiber lasers and amplifiers, in the fiber systems for measuring physical quantities, optical communication lines, and etc.

One of possible ways to decide specified problems of FBG reflection spectra characteriza‐ tion is based on FBG probing by the two-frequency radiation which average frequency at calibration point is adjusted on the central wavelength of FGB spectrum, and its detune and-or amplitudes difference between components are used as informative factors for definition of enclosed physical field parameter [4, 41]. The two-frequency measurement technique finds more and more appendices in various problems, for example: research of atmospheric gases absorption contours [42,43], measurement of dielectric coverings thickness [44], the analysis of FBG spectrum contour [45], an estimation of communica‐ tion lines selective devices temperature drift [46], etc. Distinctions consist in parameters of used two-frequency signal or radiation, the requirements shown to their stability and techniques of measuring transformation.

In the given part we will use the two-frequency radiation received by Il'in-Morozov technique in Mach-Zender modulator [4], differing as high spectral cleanliness and stability at admissible change of formation parameters, and possibility of differential frequency simple tuning for use with various FBG characteristics. The specified generalized characteristics meet require‐ ments to construction of probing radiations sources for fiber-optical nets [3]. As a technique of measuring transformation we will choose an integrated technique of the passed through or reflected from FBG two-frequency radiation envelope characteristics analysis.

At FBG contour shift caused by the application of physical fields, there is inequality *R*<sup>1</sup> ≠*R*2 and restoration phase opposition of two-frequency radiation components. The kind of an inequal‐ ity and a phase sign is defined by a direction of FBG contour shift, i.e. increase or reduction of the enclosed field parameter. The analysis of amplitudes and phases of the received compo‐ nents can be spent separately after their allocation by optical filters or time division in the disperse environment; however these methods return us to problems of difficult spectral verification [47]. Therefore it was offered to spend processing of two-frequency radiation envelope [41].

Envelope amplitude *UR* defined as:

$$U\_R \approx \sqrt{R\_1^2 + R\_2^2 + 2R\_1R\_2\cos\left(k\Delta\delta t\right)},\tag{20}$$

and an instant phase:

from optical to the electrical field single-sideband modulation is used. Detection of doublefrequency components position in the gain spectrum occurs through the amplitude modula‐ tion index of the envelope and the phase difference between envelopes of probing and passing components. The method is characterized by high resolution, SNR of the measurements increased of a two order, simplicity of the offered algorithms for finding the central frequency, Q-factor and Mandelstam-Brillouin maximum gain coefficient. Measurement algorithm is realized on simple and stable experimental setup. Among the methods of measurement inaccuracy decreasing, caused by not completely suppressed upper sideband of the doublefrequency radiation, the usage of a chirp fiber Bragg grating, tuned on the suppression of it in

FBG represents a longitudinal, periodic variation in the refractive index in the core of an optical fiber [2]. The main parameters of the grating are the distributions of the amplitude and period of the refractive index modulation, as well as the average value of the induced refractive index along the fiber axis. These parameters specify the spectral and dispersion parameters of gratings and, thus, determine their use in different applications of the fiber optics. FBG are widely used fiber lasers and amplifiers, in the fiber systems for measuring physical quantities,

One of possible ways to decide specified problems of FBG reflection spectra characteriza‐ tion is based on FBG probing by the two-frequency radiation which average frequency at calibration point is adjusted on the central wavelength of FGB spectrum, and its detune and-or amplitudes difference between components are used as informative factors for definition of enclosed physical field parameter [4, 41]. The two-frequency measurement technique finds more and more appendices in various problems, for example: research of atmospheric gases absorption contours [42,43], measurement of dielectric coverings thickness [44], the analysis of FBG spectrum contour [45], an estimation of communica‐ tion lines selective devices temperature drift [46], etc. Distinctions consist in parameters of used two-frequency signal or radiation, the requirements shown to their stability and

In the given part we will use the two-frequency radiation received by Il'in-Morozov technique in Mach-Zender modulator [4], differing as high spectral cleanliness and stability at admissible change of formation parameters, and possibility of differential frequency simple tuning for use with various FBG characteristics. The specified generalized characteristics meet require‐ ments to construction of probing radiations sources for fiber-optical nets [3]. As a technique of measuring transformation we will choose an integrated technique of the passed through or

At FBG contour shift caused by the application of physical fields, there is inequality *R*<sup>1</sup> ≠*R*2 and restoration phase opposition of two-frequency radiation components. The kind of an inequal‐ ity and a phase sign is defined by a direction of FBG contour shift, i.e. increase or reduction of the enclosed field parameter. The analysis of amplitudes and phases of the received compo‐ nents can be spent separately after their allocation by optical filters or time division in the

reflected from FBG two-frequency radiation envelope characteristics analysis.

the bandwidth of possible position change at scanning, can be considered [7].

**3.4. Two-frequency characterization of FBG reflection spectra**

68 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

optical communication lines, and etc.

techniques of measuring transformation.

$$\phi\_{\mathbb{R}} \approx \operatorname{arctg} \left\{ \frac{\sin \left[ \left( \phi\_{\mathbb{R}\_2} - \phi\_{\mathbb{R}\_l} \right) + k \Delta \delta t \right]}{R\_l \sqrt{R\_2 + \cos \left[ \left( \phi\_{\mathbb{R}\_2} - \phi\_{\mathbb{R}\_l} \right) + k \Delta \delta t \right]}} \right\}, \tag{21}$$

where *ϕR*<sup>1</sup> , *ϕR*<sup>2</sup> are accordingly the phases of output components *R*1 and *R*2.

For processing of the received values on amplitude we will enter modulation factor *m*:

$$m \approx \sqrt{1 + \left(\delta\_0 + \Delta\delta/2\right)^2} \Big/ \sqrt{1 + \left(\delta\_0 - \left(\Delta\delta/2\right)^2\right)},\tag{22}$$

and on phase – we will find a difference of phases between envelopes of input and output radiations Δ*ϕ* [41].

The example of the received measuring characteristics of the temperature FBG sensor on amplitude and a phase is presented accordingly on fig. 5,a and fig. 5,b. Analysis of the envelope 2 *Δf* parameters (22) and (21) made it possible to depict the measurement characteristics for determination of the central frequency of the gain spectrum by its amplitude (Fig. 5, *а*) and phase difference or sign of the phase difference (Fig. 5, *b*) between the envelopes at the FBG's input and output, similar to [48]. If the amplitude characteristic of measurements (fig. 5,*a*) has symmetric character, phase (fig. 5,*b*) allows resolving shift sign. Advantages of the amplitude characteristic are shown at operation in the field of "zero" detune parameter where there is an area of small signals for the phase characteristic [41].

For practical realization a setup shown in fig. 6 was assembled. Setup consists of the laser LDI-DFB 1550-20/50-T2-SM3-FA-CWP, calibration source Superlum SLD Pilot-4, the oscilloscope Agilent InfiniVision 7000, random waveform signal generator AFG3000, multimeter, MZM JDS Uniphase OC-192 Modulator, stabilized power supply PSS-1, the spectrum analyzer FTB 5240-S, an optical splitter, a circulator, FBG, the photodiodes LSIPD-A75 [59]. The spectra of two-frequency laser radiation is shown in Fig. 7, carried out in a for the phase characteristic.

The example of the received measuring characteristics of the temperature FBG sensor on amplitude and a phase is presented accordingly on fig. 5,a and fig. 5,b. Analysis of the envelope 2 *f* parameters (22) and (21) made it possible to depict the measurement characteristics for determination of the central frequency of the gain spectrum by its amplitude (Fig. 5, *а*) and phase

of the amplitude characteristic are shown at operation in the field of "zero" detune parameter where there is an area of small signals

a function of detuning and of the central frequency of the FBG For practical realization a setup shown in fig. 6 was assembled. Setup consists of the laser LDI-DFB 1550-20/50-T2-SM3-FA-CWP, calibration source Superlum SLD Pilot-4, the oscilloscope Agilent InfiniVision 7000, random waveform signal generator AFG3000, **Figure 5.** Amplitude (а), phase difference and sign of the phase difference (b) between the envelopes at the FBG's input and output as a function of detuning and of the central frequency of the FBG

Mach-Zehnder modulator by the Il'in-Morozov method for frequencies 2 GHz (fig. 7,*a*) and 8 GHz (fig. 7,*b*) at the output of FBG [60]. multimeter, MZM JDS Uniphase OC-192 Modulator, stabilized power supply PSS-1, the spectrum analyzer FTB 5240-S, an optical splitter, a circulator, FBG, the photodiodes LSIPD-A75. The spectra of two-frequency laser radiation is shown in Fig. 7, carried out in a Mach-Zehnder modulator by the Il'in-Morozov method for frequencies 2 GHz (fig. 7,*a*) and 8 GHz (fig. 7,*b*) at the output of FBG.

**Figure 6.** Setup for four-frequency FBG reflection spectra characterization beat frequency of the two components of the probing signal, which will be determined by the change of their amplitudes and phases. At the moment when center frequency of a probing signal gets to the resonance frequency of a sensor (FBG) amplitudes and modules

#### **3.5. Four-frequency characterization of FBG reflection spectra** envelope of the signal is matched in phase with the envelope of the probing signal at the input.

The analysis presented in [7], [59] shows that from the electrical output signal we can get the image of the optical transfer function at the beat frequency of the two components of the probing signal, which will be determined by the change of their amplitudes and phases. At the moment when center frequency of a probing signal gets to the resonance frequency of a

of the phases of both components are equal, the modulation index of the output signal's envelope is maximum and equal to 1, and the

sensor (FBG) amplitudes and modules of the phases of both components are equal, the modulation index of the output signal's envelope is maximum and equal to 1, and the envelope of the signal is matched in phase with the envelope of the probing signal at the input.

Figure 7. The spectra of the two-frequency laser radiation at frequencies 2 GHz (a) and 8 GHz (b) **Figure 7.** The spectra of the two-frequency laser radiation at frequencies 2 GHz (a) and 8 GHz (b)

Mach-Zehnder modulator by the Il'in-Morozov method for frequencies 2 GHz (fig. 7,*a*) and

Figure 5. Amplitude (а), phase difference and sign of the phase difference (b) between the envelopes at the FBG's input and output as

For practical realization a setup shown in fig. 6 was assembled. Setup consists of the laser LDI-DFB 1550-20/50-T2-SM3-FA-CWP, calibration source Superlum SLD Pilot-4, the oscilloscope Agilent InfiniVision 7000, random waveform signal generator AFG3000, multimeter, MZM JDS Uniphase OC-192 Modulator, stabilized power supply PSS-1, the spectrum analyzer FTB 5240-S, an optical splitter, a circulator, FBG, the photodiodes LSIPD-A75. The spectra of two-frequency laser radiation is shown in Fig. 7, carried out in a Mach-Zehnder modulator by the Il'in-Morozov method for frequencies 2 GHz (fig. 7,*a*) and 8 GHz (fig. 7,*b*) at the output of

**Figure 5.** Amplitude (а), phase difference and sign of the phase difference (b) between the envelopes at the FBG's input

(a) (b)

70 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

and output as a function of detuning and of the central frequency of the FBG

The example of the received measuring characteristics of the temperature FBG sensor on amplitude and a phase is presented accordingly on fig. 5,a and fig. 5,b. Analysis of the envelope 2 *f* parameters (22) and (21) made it possible to depict the measurement characteristics for determination of the central frequency of the gain spectrum by its amplitude (Fig. 5, *а*) and phase difference or sign of the phase difference (Fig. 5, *b*) between the envelopes at the FBG's input and output, similar to [48]. If the amplitude characteristic of measurements (fig. 5,*a*) has symmetric character, phase (fig. 5,*b*) allows resolving shift sign. Advantages of the amplitude characteristic are shown at operation in the field of "zero" detune parameter where there is an area of small signals

The analysis presented in [7], [59] shows that from the electrical output signal we can get the image of the optical transfer function at the beat frequency of the two components of the probing signal, which will be determined by the change of their amplitudes and phases. At the moment when center frequency of a probing signal gets to the resonance frequency of a

The analysis presented in [7] shows that from the electrical output signal we can get the image of the optical transfer function at the beat frequency of the two components of the probing signal, which will be determined by the change of their amplitudes and phases. At the moment when center frequency of a probing signal gets to the resonance frequency of a sensor (FBG) amplitudes and modules of the phases of both components are equal, the modulation index of the output signal's envelope is maximum and equal to 1, and the

8 GHz (fig. 7,*b*) at the output of FBG [60].

a function of detuning and of the central frequency of the FBG

for the phase characteristic.

FBG.

**Figure 6.** Setup for four-frequency FBG reflection spectra characterization

Figure 6. Setup for four-frequency FBG reflection spectra characterization

**2.5. Four-frequency characterization of FBG reflection spectra** 

**3.5. Four-frequency characterization of FBG reflection spectra**

envelope of the signal is matched in phase with the envelope of the probing signal at the input.

the resonance frequency of a sensor (FBG), and the value of the detuning between the two components should be close to its band pass width at the half-maximum. Inaccuracy of the measurements will depend on the correctness of maintaining the equality of the amplitudes and modules of the phases of probing signal's components, and on the signal/noise ratio of measurements. The phase measurements in the 30-100 GHz band are a complex task. Therefore, synthesis of poly-harmonic method that does not require processing of the phase information is When the two-frequency probing method is used the maximum measurement sensitivity is achieved by tuning its center frequency to the resonance frequency of a sensor (FBG), and the value of the detuning between the two components should be close to its band pass width at the half-maximum.

When the two-frequency probing method is used the maximum measurement sensitivity is achieved by tuning its center frequency to

an important problem. This method has been found and is a four-frequency method with two different average and difference

frequencies. For reference, we note that in Section 2.3 we considered the four-frequency method with the overall average and different difference frequencies [7]. On fig.8 block diagram of device for precise four-frequency control method of FBG's resonant frequency is presented. In searching mode from driving generator of controller *10*, which is coupled with TFBG *3*, is coming retuning single frequency signal to the input of amplitude-phase four-frequency converter based on double port electro optic MZM. 1 Inaccuracy of the measurements will depend on the correctness of maintaining the equality of the amplitudes and modules of the phases of probing signal's components, and on the signal/ noise ratio of measurements. The phase measurements in the 30-100 GHz band are a complex task. Therefore, synthesis of poly-harmonic method that does not require processing of the phase information is an important problem. This method has been found and is a fourfrequency method with two different average and difference frequencies. For reference, we note that in Section 2.3 we considered the four-frequency method with the overall average and different difference frequencies [7].

2 3 4 5 10 7 8 9 6 On fig.8 block diagram of device for precise four-frequency control method of FBG's resonant frequency is presented. In searching mode from driving generator of controller *10*, which is coupled with TFBG *3*, is coming retuning single frequency signal to the input of amplitudephase four-frequency converter based on double port electro optic MZM.

11 Figure 9. The dependence of Figure 8. Device for precise four-frequency control method of FBG Signal with frequency Ω, which corresponds the central peak half width of TFBG *3* or near it, is coming to the control input of amplitude-phase converter. Formed two two-frequency signals with two different average and difference frequencies is coming to the input of TFBG *3*. Output signal from TFBG *3* sends to the input of first and second photo-detectors *4, 7*. Output four-frequency signal from TFBG *3* comes to the first and second selective filters *5, 9*. Controller *10* receives information from first selective filter *5* on the frequency Ω1 and second selective

resonant frequency: 1 – four-frequency converter; 2 – DFB laser; 3 – FBG under test (TFBG); 4, 7 – first and second photo-detectors; 5, 9 – first and second selective filters; 6 – computer; 8 – amplifier;

10 – controller; 11 - interface

the difference between the amplitudes of the envelopes of the signals' beats of the first and the second pair U1U<sup>2</sup> on detuning of pass band

pass width at the half-maximum.

different difference frequencies [7].

of amplitude-phase four-frequency converter based on double port electro optic MZM.

(а) (b)

When the two-frequency probing method is used the maximum measurement sensitivity is achieved by tuning its center frequency to the resonance frequency of a sensor (FBG), and the value of the detuning between the two components should be close to its band

Inaccuracy of the measurements will depend on the correctness of maintaining the equality of the amplitudes and modules of the phases of probing signal's components, and on the signal/noise ratio of measurements. The phase measurements in the 30-100 GHz band are a complex task. Therefore, synthesis of poly-harmonic method that does not require processing of the phase information is an important problem. This method has been found and is a four-frequency method with two different average and difference frequencies. For reference, we note that in Section 2.3 we considered the four-frequency method with the overall average and

Figure 7. The spectra of the two-frequency laser radiation at frequencies 2 GHz (a) and 8 GHz (b)

Figure 9. The dependence of the difference between the amplitudes of the envelopes of the signals' beats of the first Figure 8. Device for precise four-frequency control method of FBG resonant frequency: 1 – four-frequency converter; 2 – DFB laser; 3 – FBG under test (TFBG); 4, 7 – first and second photo-detectors; 5, 9 – first and second selective filters; 6 – computer; 8 – amplifier; **Figure 8.** Device for precise four-frequency control method of FBG resonant frequency: 1 – four-frequency converter; 2 – DFB laser; 3 – FBG under test (TFBG); 4, 7 – first and second photo-detectors; 5, 9 – first and second selective filters; 6 – computer; 8 – amplifier; 10 – controller; 11-interface

filter *9* on the frequency Ω2. Searching mode continuous till moment, when modulation index processing in controller detects UΩ1UΩ2=0. At the moment of resonance frequency adjustment output signal from controller *10* comes to the interface *11*, and computer *6* performs frequency measuring and begins to monitoring FBG spectra characteristics. Second photo-detector 7 and amplifier 8 are used for calibration between two two-frequency channels. and the second pair U1U<sup>2</sup> on detuning of pass band 10 – controller; 11 - interface

Fig. 9 shows the dependence of the amplitudes of the envelopes of the signals' beats of the first UΩ1 and the second UΩ2 pair, passed through FBG (left vertical axis), and their difference UΩ1- UΩ2 (right vertical axis) on detuning of FBG pass band (horizontal axis) for the case of supplying a signals with equal amplitude and center frequency matched with central frequency of pass band. Difference frequencies of the pairs Ω1 and Ω2 are not identical and are in the range up to 300 MHz. This allows the use of a narrow-band photo-detector [60].

In the generated pairs of signals passing through the FBG, amplitudes of the several compo‐ nents change according to the direction and value of frequency shift of pass band. When there is a frequency shift of FBG pass band depending on temperature changes, position of generated pair of signals' components with respect to the pass band will change, amplitudes of the envelopes of the pairs' beats will change and the differences between amplitudes of the envelopes of the first and second pairs' beats will change (passed through FBG according to presented dependence UΩ1-UΩ2). In this case, the measurements are taken at frequencies of envelopes, which are in a region of minimal noise of the photo-detectors [60].

Tests of the skilled device have been spent on FBG, made in FORC of the Russian Academy of Sciences (Moscow), calibrated in laboratories PGUTI (Samara), and have shown, that use of two-frequency probing FGB has allowed to reach errors of measurement of temperature 0,01 °С in a range 50 °С [41]. Thus the measurement error was defined basically by error of analogue

Poly-harmonic Analysis of Raman and Mandelstam-Brillouin Scatterings and Bragg Reflection Spectra http://dx.doi.org/10.5772/59144 73

**Figure 9.** The dependence of the difference between the amplitudes of the envelopes of the signals' beats of the first and the second pair UΩ1UΩ2 on detuning of pass band

to digital coder of the controller *10* for the definition of temperature. The range of measured physical fields (temperature, pressure etc.) is defined by sensitivity of a grating to the measured parameter and value of differential frequencies of probing radiation, so in extreme points of frequency range displacement of a grating making radiations should not leave for level (0,05-0,1) *R*0, where *R*0 – factor of FGB reflection on the central frequency.

So, to reduce the measurement inaccuracy caused by phase fluctuations of system elements new poly-harmonic method was applied, based on a four-frequency narrow-band measure‐ ments without the use of phase analysis. The advantage of this approach is the ability of the measurement in a band up to 300 MHz with narrow-band low-noise photo-detector [59].

#### **3.6. Discussion of results**

filter *9* on the frequency Ω2. Searching mode continuous till moment, when modulation index processing in controller detects UΩ1UΩ2=0. At the moment of resonance frequency adjustment output signal from controller *10* comes to the interface *11*, and computer *6* performs frequency measuring and begins to monitoring FBG spectra characteristics. Second photo-detector 7 and

Figure 8. Device for precise four-frequency control method of FBG resonant frequency: 1 – four-frequency converter; 2 – DFB laser; 3 – FBG under test (TFBG); 4, 7 – first and second photo-detectors; 5, 9 – first and second selective filters; 6 – computer; 8 – amplifier;

**Figure 8.** Device for precise four-frequency control method of FBG resonant frequency: 1 – four-frequency converter; 2 – DFB laser; 3 – FBG under test (TFBG); 4, 7 – first and second photo-detectors; 5, 9 – first and second selective filters; 6

(а) (b)

When the two-frequency probing method is used the maximum measurement sensitivity is achieved by tuning its center frequency to the resonance frequency of a sensor (FBG), and the value of the detuning between the two components should be close to its band

Inaccuracy of the measurements will depend on the correctness of maintaining the equality of the amplitudes and modules of the phases of probing signal's components, and on the signal/noise ratio of measurements. The phase measurements in the 30-100 GHz band are a complex task. Therefore, synthesis of poly-harmonic method that does not require processing of the phase information is an important problem. This method has been found and is a four-frequency method with two different average and difference frequencies. For reference, we note that in Section 2.3 we considered the four-frequency method with the overall average and

On fig.8 block diagram of device for precise four-frequency control method of FBG's resonant frequency is presented. In searching mode from driving generator of controller *10*, which is coupled with TFBG *3*, is coming retuning single frequency signal to the input

> Figure 9. The dependence of the difference between the amplitudes of the envelopes of the signals' beats of the first and the second pair U1U<sup>2</sup> on detuning of pass band

Figure 7. The spectra of the two-frequency laser radiation at frequencies 2 GHz (a) and 8 GHz (b)

of amplitude-phase four-frequency converter based on double port electro optic MZM.

2 3 4 5 10

7 8 9

pass width at the half-maximum.

different difference frequencies [7].

1

72 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

11

– computer; 8 – amplifier; 10 – controller; 11-interface

6

Fig. 9 shows the dependence of the amplitudes of the envelopes of the signals' beats of the first UΩ1 and the second UΩ2 pair, passed through FBG (left vertical axis), and their difference UΩ1- UΩ2 (right vertical axis) on detuning of FBG pass band (horizontal axis) for the case of supplying a signals with equal amplitude and center frequency matched with central frequency of pass band. Difference frequencies of the pairs Ω1 and Ω2 are not identical and are in the range up

In the generated pairs of signals passing through the FBG, amplitudes of the several compo‐ nents change according to the direction and value of frequency shift of pass band. When there is a frequency shift of FBG pass band depending on temperature changes, position of generated pair of signals' components with respect to the pass band will change, amplitudes of the envelopes of the pairs' beats will change and the differences between amplitudes of the envelopes of the first and second pairs' beats will change (passed through FBG according to presented dependence UΩ1-UΩ2). In this case, the measurements are taken at frequencies of

Tests of the skilled device have been spent on FBG, made in FORC of the Russian Academy of Sciences (Moscow), calibrated in laboratories PGUTI (Samara), and have shown, that use of two-frequency probing FGB has allowed to reach errors of measurement of temperature 0,01 °С in a range 50 °С [41]. Thus the measurement error was defined basically by error of analogue

amplifier 8 are used for calibration between two two-frequency channels.

10 – controller; 11 - interface

to 300 MHz. This allows the use of a narrow-band photo-detector [60].

envelopes, which are in a region of minimal noise of the photo-detectors [60].

This part of the chapter is devoted to poly-harmonic characterization of Mandelstam-Brillouin gain contour and FBG reflection spectra for telecommunication applications. Consideration of stimulated Raman scattering (SRS) in this part will be carried out only in general terms because of its negligible impact on the performance of telecommunication none-WDM lines [1]. We discussed the basics of MBGS and FBG spectrums characterization and proposed for the first time two new poly-harmonic methods. First is the four-frequency method with the overall average and different difference frequencies, discussed in section 2.3. Second is a fourfrequency method with two different average and difference frequencies, discussed in section 2.5. The advantage of both methods is the absence of the need to measure the phase charac‐ teristics of the tested contours. The results of its practical realization proved the results of mathematical modelling.

We call the first as "the method of difference frequency variation" analogically to the methods of frequency and capacity variations for Q-factor measuring. This method can be widely used in different systems for Q-factor measuring as in optical, so in microwave range. For example, in [49] we applied this method to monitoring of cure processes in composite materials. In optical range it can be applied to the measuring of Q-factor of transmitting window of CFBG with phase shift, for example presented in [23,50], which isn't effected to shift of central wavelength. The second method with it simple realization can be widely used in precise sensor monitoring loops in laboratory conditions and special circuits for temperature control in the range of 5-10 °C with accuracy 0,01°C [11,51].
