**5. Elements of perspective reflectometeric systems with poly-harmonic probing**

On the basis of two-frequency signal information structure investigation [4], [61], [62] with the purpose to find out main principles of combined interaction of its instantaneous values of amplitude, phase and frequency with arbitrary contour has been defined:

**•** instantaneous phase of two-frequency signal has a saw-tooth dependence. Speed of instantaneous phase changes is defined by components amplitude ratio. If A1/A2 =1 the maximal speed of phase changing is observed. When two-frequency envelope has its minimum value, instantaneous phase has a shift, which depends on harmonic components amplitude ratio. If the amplitudes of two-frequency signal components are equal, phase shift is equal to *π* ;

is characterized by high resolution and the ability to check-in without a shift of the center

FOT systems and FTM for down-hole telemetry – a developing area of science and technology in Russia, which would create a competition international manufacturers of similar systems for the oil and gas industry and solve the problem of import substitution, significantly reduce the cost of the components used, displace traditional systems on electronic components. Based on the analysis of advanced domestic and foreign developments at the level of patents in the field of fiber optic systems of down-hole telemetry shows the relevance and scientific novelty of research areas, which determines the need to develop an integrated fiber optic down-hole telemetry system which is used to record the measured parameters for all kinds of scatterings assessments and distributed FBG – for point and the quasi ratings, including to resolve the multiplicative response to temperature and deformation (pressure) for FBG and Brillouin systems and error analysis in Raman systems. The studies will be established scientifically based methodological basis for building and technical and algorithmic solutions for the downhole fiber optic telemetry systems based on a comprehensive nonlinear reflectometry and universal poly-harmonic probing of generated responses. These results allow to significantly improve the metrological characteristics of systems, including the reproducibility of results, because it will be used the measurement results with high redundancy on the basis of three or four feedback mechanisms of different nature of the optical fiber at the same environmental exposure. Scientific and methodological foundations and principles of systems can be used to monitor not only the down-hole structures, but any extended engineering structures and

Proposed by us for the first time the concept, approaches and methods for its implementation allow reasonably formulate and solve the problem of creation of scientific and technical basis for designing software-defined down-hole fiber optic telemetry systems based on the combi‐ nation of nonlinear reflectometry with improved metrological characteristics of poly-harmonic probing of sensing structures, including the removal of multiplicative and measurement errors

**5. Elements of perspective reflectometeric systems with poly-harmonic**

On the basis of two-frequency signal information structure investigation [4], [61], [62] with the purpose to find out main principles of combined interaction of its instantaneous values of

**•** instantaneous phase of two-frequency signal has a saw-tooth dependence. Speed of instantaneous phase changes is defined by components amplitude ratio. If A1/A2 =1 the maximal speed of phase changing is observed. When two-frequency envelope has its minimum value, instantaneous phase has a shift, which depends on harmonic components

caused by instability of the forming radiations in wide frequency range.

amplitude, phase and frequency with arbitrary contour has been defined:

wavelength, as shown in several studies [11,25,48,50].

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

**4.4. Discussion of results**

natural systems.

**probing**


All obtained dependences can be used in symmetric poly-harmonic reflectometeric systems as informative and directive functions and in order to get information from selective optical fiber structures, like SRS, SMBS and FBG contours and so on [61], [62].

A joint analysis of given information allows us to determine the range of individual tasks that must be addressed when constructing symmetrical poly-harmonic reflectometeric systems. These tasks include following problems: integral self heterodyning (A0 =0,A1 =A2); integral super heterodyning (A0 > >A1 =A2); differential self heterodyning (A0 =0,A1 ≠A2); differential super heterodyning (A0 > >A1 ≠A2); receiving and processing frequency information (ω<sup>0</sup> ≠(ω<sup>1</sup> + ω2)/2) ; receiving and processing of phase information (*ϕ*<sup>0</sup> ≠*ϕ*<sup>1</sup> =*ϕ*2, *ϕ*<sup>1</sup> ≠*ϕ*2); receiving and processing the polarization (A0⊥A1 A2) and spatial information; information about instability (A0≠0). Given the diversity of the set measuring tasks, their decisions, are presented further in this part of chapter, describing the methods, tools and systems parameters of means to get poly-harmonic radiation on the base of dual-drive MZM, scanning and poly-harmonic (more than four harmonics) methods for SMBS characterization, designing of notch filters for blocking of elastic Rayleigh scattering in SRS and SMBS measurements [61], [62].

Additionally Raman and Mandelstam-Brillouin scattering in sensor nets so as a FBG reflection carry vast amount information about fiber conditions but sometime have low energy level. That's why it's one more cause to detect these types of scattering with high SNR and determine their properties. Applying of photo mixing allows significantly increase the reflectometeric system sensitivity under the condition of weak signals and receives information from fre‐ quency pushing of backscattered signal spectrum. We offered previously to use two-frequency heterodyne and the second nonlinear receiver in the structure of reflectometers and discuss these questions in [4] [56].

#### **5.1. Numerical simulation of poly-harmonic conversion in dual-drive Mach-Zehnder modulator**

The numerical simulation in dual-drive Mach-Zehnder modulator [31,52] was carried out for signals with following parameters: amplitude of RF modulating signals was equal V1=V2=Vπ; for different phase difference between RF signals of two arms are presented on fig. 10-14.

**4. Elements of perspective reflectometeric systems with poly-harmonic probing** 

components are equal, modulation coefficient is maximal and equals unit value.

blocking of elastic Rayleigh scattering in SRS and SMBS measurements.

frequency signal components are equal, phase shift is equal to ;

equal, value of frequency overriding is infinity;

DC bias voltage applied to arm one and two was Vbias 1=Uπ/2 and Vbias 2=3Uπ/2, respectively; phase difference between RF signals of two arms was changing. Resulted spectrums of output MZM signal for different phase difference between RF signals of two arms are presented on fig. 10-14, [62]. previously to use two-frequency heterodyne and the second nonlinear receiver in the structure of reflectometers and discuss these questions in [4]. **4.1. Numerical simulation of poly-harmonic conversion in dual-drive Mach-Zehnder modulator**  The numerical simulation in dual-drive Mach-Zehnder modulator [31,52] was carried out for signals with following parameters: amplitude of RF modulating signals was equal V1 = V2 = Vπ; DC bias voltage applied to arm one and two was Vbias 1 = Uπ/2 and Vbias 2 = 3Uπ/2, respectively; phase difference between RF signals of two arms was changing. Resulted spectrums of output MZM signal

Additionally Raman and Mandelstam-Brillouin scattering in sensor nets so as a FBG reflection carry vast amount information about

SNR and determine their properties. Applying of photo mixing allows significantly increase the reflectometeric system sensitivity under the condition of weak signals and receives information from frequency pushing of backscattered signal spectrum. We offered

On the basis of two-frequency signal information structure investigation [4] with the purpose to find out main principles of combined




All obtained dependences can be used in symmetric poly-harmonic reflectometeric systems as informative and directive functions

A joint analysis of given information allows us to determine the range of individual tasks that must be addressed when constructing symmetrical poly-harmonic reflectometeric systems. These tasks include following problems: integral self heterodyning ( <sup>0</sup> A1 A2 A 0, ); integral super heterodyning ( A0 A1 A2 ); differential self heterodyning ( <sup>0</sup> A1 A2 A 0, ); differential super heterodyning ( A0 A1 A2 ); receiving and processing frequency information ω ω ω /2 <sup>0</sup> <sup>1</sup> <sup>2</sup> ; receiving and processing of phase information ( <sup>0</sup> <sup>1</sup> <sup>2</sup> , <sup>1</sup> <sup>2</sup> ); receiving and processing the polarization A0 A1 A2 and spatial information; information about instability (A00). Given the diversity of the set measuring tasks, their decisions, are presented further in this part of chapter, describing the methods, tools and systems parameters of means to get poly-harmonic radiation on the base of dual-drive MZM, scanning and poly-harmonic (more than four harmonics) methods for SMBS characterization, designing of notch filters for

and in order to get information from selective optical fiber structures, like SRS, SMBS and FBG contours and so on.

interaction of its instantaneous values of amplitude, phase and frequency with arbitrary contour has been defined:

**Figure 10.** MZM output signal spectrum for the case of Δψ=0° (*a* – dBm, *b* – W)

Figure 10. MZM output signal spectrum for the case of Δψ = 0 (*a* – dBm, *b* – W)

(a) (b)

(a) (b)

**Figure 11.** MZM output signal spectrum for the case of Δψ=45° (*a* – dBm, *b* – W)

Figure 11. MZM output signal spectrum for the case of Δψ = 45 (*a* – dBm, *b* – W)

Figure 12. MZM output signal spectrum for the case of Δψ = 90 (*a* – dBm, *b* – W)

Figure 13. MZM output signal spectrum for the case of Δψ = 135 (*a* – dBm, *b* – W)

Poly-harmonic Analysis of Raman and Mandelstam-Brillouin Scatterings and Bragg Reflection Spectra http://dx.doi.org/10.5772/59144 81

(a) (b)

**Figure 12.** MZM output signal spectrum for the case of Δψ=90° (*a* – dBm, *b* – W) (a) (b)

Figure 12. MZM output signal spectrum for the case of Δψ = 90 (*a* – dBm, *b* – W)

Figure 12. MZM output signal spectrum for the case of Δψ = 90 (*a* – dBm, *b* – W)

Figure 11. MZM output signal spectrum for the case of Δψ = 45 (*a* – dBm, *b* – W)

DC bias voltage applied to arm one and two was Vbias 1=Uπ/2 and Vbias 2=3Uπ/2, respectively; phase difference between RF signals of two arms was changing. Resulted spectrums of output

Additionally Raman and Mandelstam-Brillouin scattering in sensor nets so as a FBG reflection carry vast amount information about fiber conditions but sometime have low energy level. That's why it's one more cause to detect these types of scattering with high SNR and determine their properties. Applying of photo mixing allows significantly increase the reflectometeric system sensitivity under the condition of weak signals and receives information from frequency pushing of backscattered signal spectrum. We offered previously to use two-frequency heterodyne and the second nonlinear receiver in the structure of reflectometers and discuss these

On the basis of two-frequency signal information structure investigation [4] with the purpose to find out main principles of combined




All obtained dependences can be used in symmetric poly-harmonic reflectometeric systems as informative and directive functions

A joint analysis of given information allows us to determine the range of individual tasks that must be addressed when constructing symmetrical poly-harmonic reflectometeric systems. These tasks include following problems: integral self heterodyning ( <sup>0</sup> A1 A2 A 0, ); integral super heterodyning ( A0 A1 A2 ); differential self heterodyning ( <sup>0</sup> A1 A2 A 0, ); differential super heterodyning ( A0 A1 A2 ); receiving and processing frequency information ω ω ω /2 <sup>0</sup> <sup>1</sup> <sup>2</sup> ; receiving and processing of phase information ( <sup>0</sup> <sup>1</sup> <sup>2</sup> , <sup>1</sup> <sup>2</sup> ); receiving and processing the polarization A0 A1 A2 and spatial information; information about instability (A00). Given the diversity of the set measuring tasks, their decisions, are presented further in this part of chapter, describing the methods, tools and systems parameters of means to get poly-harmonic radiation on the base of dual-drive MZM, scanning and poly-harmonic (more than four harmonics) methods for SMBS characterization, designing of notch filters for

and in order to get information from selective optical fiber structures, like SRS, SMBS and FBG contours and so on.

interaction of its instantaneous values of amplitude, phase and frequency with arbitrary contour has been defined:

**4. Elements of perspective reflectometeric systems with poly-harmonic probing** 

components are equal, modulation coefficient is maximal and equals unit value.

blocking of elastic Rayleigh scattering in SRS and SMBS measurements.

frequency signal components are equal, phase shift is equal to ;

equal, value of frequency overriding is infinity;

MZM signal for different phase difference between RF signals of two arms are presented on

(a) (b)

(a) (b)

(a) (b)

(a) (b)

The numerical simulation in dual-drive Mach-Zehnder modulator [31,52] was carried out for signals with following parameters: amplitude of RF modulating signals was equal V1 = V2 = Vπ; DC bias voltage applied to arm one and two was Vbias 1 = Uπ/2 and Vbias 2 = 3Uπ/2, respectively; phase difference between RF signals of two arms was changing. Resulted spectrums of output MZM signal

**4.1. Numerical simulation of poly-harmonic conversion in dual-drive Mach-Zehnder modulator** 

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

for different phase difference between RF signals of two arms are presented on fig. 10-14.

Figure 10. MZM output signal spectrum for the case of Δψ = 0 (*a* – dBm, *b* – W)

Figure 11. MZM output signal spectrum for the case of Δψ = 45 (*a* – dBm, *b* – W)

**Figure 11.** MZM output signal spectrum for the case of Δψ=45° (*a* – dBm, *b* – W)

Figure 12. MZM output signal spectrum for the case of Δψ = 90 (*a* – dBm, *b* – W)

Figure 13. MZM output signal spectrum for the case of Δψ = 135 (*a* – dBm, *b* – W)

**Figure 10.** MZM output signal spectrum for the case of Δψ=0° (*a* – dBm, *b* – W)

fig. 10-14, [62].

questions in [4].

**Figure 13.** MZM output signal spectrum for the case of Δψ=135° (*a* – dBm, *b* – W)

Figure 13. MZM output signal spectrum for the case of Δψ = 135 (*a* – dBm, *b* – W)

Figure 14. MZM output signal spectrum for the case of Δψ = 180 (*a* – dBm, *b* – W) **Figure 14.** MZM output signal spectrum for the case of Δψ=180° (*a* – dBm, *b* – W)

side components were suppressed more than 20 dB. Signals, containing four spectral components, were obtained for a cases of phase difference Δψ = 45 and Δψ = 90. In order to get four-frequency signal with equal components differential regime of dual-drive Mach-Zehnder modulator has to be used. But in this case problem of not full suppression of initial carrier (one-frequency) radiation may arise. Utilization of notch filter for purpose of carrier suppression will be discussed in 4.5. **4.2. Two-frequency scanning for SMBS gain spectra characterization**  The questions of interaction between scanning two-frequency probing radiation and SMBS gain spectra are considered. If the laser wavelength is modulated by the frequency: Signal, containing only two spectral components, was obtained for a case of phase difference Δψ=180°. The career and the other side components were suppressed more than 20 dB. Signals, containing four spectral components, were obtained for a cases of phase difference Δψ=45° and Δψ=90°. In order to get four-frequency signal with equal components differential regime of dual-drive Mach-Zehnder modulator has to be used. But in this case problem of not full suppression of initial carrier (one-frequency) radiation may arise. Utilization of notch filter for purpose of carrier suppression will be discussed in 4.5.

Signal, containing only two spectral components, was obtained for a case of phase difference Δψ = 180. The career and the other

#### *t* cos*t* <sup>0</sup> , (23) **5.2. Two-frequency scanning for SMBS gain spectra characterization**

<sup>1</sup> <sup>0</sup> <sup>0</sup>

width, initial frequency of amplitude modulation is 0, and its frequency deviation is 2.

equation: 

where <sup>0</sup>

(2) 0 (1)

where 0 is initial laser frequency, is modulation rate, than the intensity of SMBS gain spectra signal will could define from the The questions of interaction between scanning two-frequency probing radiation and SMBS gain spectra are considered. If the laser wavelength is modulated by the frequency:

cos 0,25 cos 2 ..., <sup>2</sup>

<sup>0</sup> *T* ,*T* ,*T* are SMBS gain spectra transmittance (the reverse value of reflection) and its derivative by ,

0 0

$$\nu\left(t\right) = \nu\_0 + \Delta\nu\cos\Omega t,\tag{23}$$

<sup>2</sup> <sup>0</sup> <sup>0</sup>

(2)

correspondingly, *I*0 is source intensity. Selective amplifier, which is tuned to the frequency or 2, allowed signal recovering from SMBS GAIN SPECTRA even with low gain and eliminate high level constant component <sup>0</sup>*T* <sup>0</sup> *I* of the signal. Frequency modulation allows sensitivity increasing of spectral photometric method at least in two orders with good SNR. Spectral where ν0 is initial laser frequency, Δν is modulation rate, than the intensity of SMBS gain spectra signal will could define from the equation:

$$I\left(t\right) = I\_0 T\left(\nu\_o\right) + I\_0 T^{(l)}\left(\nu\_o\right) \Delta \nu \cos \Omega t - 0,\\ 25I\_0 T^{(2)}\left(\nu\_o\right) \Delta \nu^2 \cos 2\Omega t + \dots,\tag{24}$$

 / 2 *<sup>T</sup>* modulation of sweeping frequencies is defined by: , <sup>2</sup> <sup>1</sup> cos <sup>2</sup> 2 *<sup>t</sup> <sup>t</sup> <sup>t</sup>* . <sup>2</sup> <sup>1</sup> cos <sup>2</sup> 2 *t t t* (25) where *<sup>T</sup>* (*ν*0), *<sup>T</sup>* (1) (*ν*0), *<sup>T</sup>* (2) (*ν*0) are SMBS gain spectra transmittance (the reverse value of reflection) and its derivative by , correspondingly, *I*0 is source intensity. Selective amplifier, which is tuned to the frequency Ω or 2Ω, allowed signal recovering from SMBS GAIN

Interaction between frequency modulated laser radiation and SMBS gain spectra causes power amplitude modulation (AM) of receiving signal. Modulation rate of such signal is straight to *Q*-factor, and AM envelope follows linear-frequency modulation (LFM). When central laser wavelength is tuned to central peak of SMBS gain spectra and frequency deviation equals spectrum half

In work has been held modeling of signals processing for such system for direct and coherent detection. Usually in frequency ranging for extraction low frequency signal of telemetric frequencies which carries information of SMBS gain spectra properties within analyzing distance *R* in reception path received signal mixes with reference signal. In all cases measurement of subcarrier frequency increment *R c <sup>R</sup>* 2 is performed by means of registration diversity between subcarrier frequencies of transmitted and received

During two-frequency probing SMBS gain spectra is exploring by two signals with central frequencies <sup>0</sup> *T* and <sup>0</sup> *<sup>T</sup>* . When

SPECTRA even with low gain and eliminate high level constant component *I*0*T* (*ν*0) of the signal [10].

Frequency modulation allows sensitivity increasing of spectral photometric method at least in two orders with good SNR. Spectral resolution for derivative method is defined by frequency modulation rate Δν. Time resolution defines by modulation frequency Ω. Spectrum recovering accurate within constant component is accomplished by sequenced signal integration [8].

During two-frequency probing SMBS gain spectra is exploring by two signals with central frequencies *ν*<sup>0</sup> −*νT* and *ν*<sup>0</sup> + *ν<sup>T</sup>* . When *ν<sup>T</sup>* =*Δν* / 2 modulation of sweeping frequencies is defined by:

$$\nu\_1 \nu\_1(t) = \nu\_0 - \frac{\Delta \nu}{2} \left( 1 + \cos \left( \Omega\_0 t + \frac{\beta t^2}{2} \right) \right), \\ \nu\_2 \left( t \right) = \nu\_0 + \frac{\Delta \nu}{2} \left( 1 + \cos \left( \Omega\_0 t + \frac{\beta t^2}{2} \right) \right). \tag{25}$$

(a) (b)

Signal, containing only two spectral components, was obtained for a case of phase difference Δψ = 180. The career and the other side components were suppressed more than 20 dB. Signals, containing four spectral components, were obtained for a cases of phase difference Δψ = 45 and Δψ = 90. In order to get four-frequency signal with equal components differential regime of dual-drive Mach-Zehnder modulator has to be used. But in this case problem of not full suppression of initial carrier (one-frequency) radiation

Signal, containing only two spectral components, was obtained for a case of phase difference Δψ=180°. The career and the other side components were suppressed more than 20 dB. Signals, containing four spectral components, were obtained for a cases of phase difference Δψ=45° and Δψ=90°. In order to get four-frequency signal with equal components differential regime of dual-drive Mach-Zehnder modulator has to be used. But in this case problem of not full suppression of initial carrier (one-frequency) radiation may arise. Utilization of notch filter for

The questions of interaction between scanning two-frequency probing radiation and SMBS gain spectra are considered. If the laser

where 0 is initial laser frequency, is modulation rate, than the intensity of SMBS gain spectra signal will could define from the

The questions of interaction between scanning two-frequency probing radiation and SMBS

gain spectra are considered. If the laser wavelength is modulated by the frequency:

Frequency modulation allows sensitivity increasing of spectral photometric method at least in two orders with good SNR. Spectral resolution for derivative method is defined by frequency modulation rate . Time resolution defines by modulation frequency .

where ν0 is initial laser frequency, Δν is modulation rate, than the intensity of SMBS gain

During two-frequency probing SMBS gain spectra is exploring by two signals with central frequencies <sup>0</sup> *T* and <sup>0</sup> *<sup>T</sup>* . When

2

reflection) and its derivative by , correspondingly, *I*0 is source intensity. Selective amplifier, which is tuned to the frequency Ω or 2Ω, allowed signal recovering from SMBS GAIN

 

*<sup>t</sup> <sup>t</sup>* . <sup>2</sup>

(*ν*0) are SMBS gain spectra transmittance (the reverse value of

 

Interaction between frequency modulated laser radiation and SMBS gain spectra causes power amplitude modulation (AM) of receiving signal. Modulation rate of such signal is straight to *Q*-factor, and AM envelope follows linear-frequency modulation (LFM). When central laser wavelength is tuned to central peak of SMBS gain spectra and frequency deviation equals spectrum half

In work has been held modeling of signals processing for such system for direct and coherent detection. Usually in frequency ranging for extraction low frequency signal of telemetric frequencies which carries information of SMBS gain spectra properties within analyzing distance *R* in reception path received signal mixes with reference signal. In all cases measurement of subcarrier frequency increment *R c <sup>R</sup>* 2 is performed by means of registration diversity between subcarrier frequencies of transmitted and received

SMBS GAIN SPECTRA even with low gain and eliminate high level constant component <sup>0</sup>*T* <sup>0</sup> *I* of the signal.

( ) <sup>0</sup> nnn

Spectrum recovering accurate within constant component is accomplished by sequenced signal integration.

cos 0, 25 *t IT*

( ) ( ) ( ) ( ) (1) (2) <sup>2</sup> 00 0 0 0 0 *I t IT IT* =+DW-

**5.2. Two-frequency scanning for SMBS gain spectra characterization**

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

 

<sup>1</sup> <sup>0</sup> <sup>0</sup>

 

width, initial frequency of amplitude modulation is 0, and its frequency deviation is 2.

*<sup>t</sup>*

cos 0,25 cos 2 ..., <sup>2</sup>

<sup>0</sup> *T* ,*T* ,*T* are SMBS gain spectra transmittance (the reverse value of reflection) and its derivative by , correspondingly, *I*0 is source intensity. Selective amplifier, which is tuned to the frequency or 2, allowed signal recovering from

0 0

*t* cos*t* <sup>0</sup> , (23)

0 (2)

<sup>1</sup> cos <sup>2</sup>

 

<sup>2</sup> <sup>0</sup> <sup>0</sup>

  2

*t t t* (25)

DW+ cos 2 ..., *t* (24)

 

 

(1) *I t I*0*T* <sup>0</sup> *I*0*T t I T t* (24)

*t t* =+DW cos , (23)

nn

Figure 14. MZM output signal spectrum for the case of Δψ = 180 (*a* – dBm, *b* – W)

**4.2. Two-frequency scanning for SMBS gain spectra characterization** 

wavelength is modulated by the frequency:

(2) 0 (1)

where *<sup>T</sup>* (*ν*0), *<sup>T</sup>* (1)

/ 2 *<sup>T</sup>* modulation of sweeping frequencies is defined by:

(*ν*0), *<sup>T</sup>* (2)

where <sup>0</sup>

equation: 

may arise. Utilization of notch filter for purpose of carrier suppression will be discussed in 4.5.

purpose of carrier suppression will be discussed in 4.5.

spectra signal will could define from the equation:

nnn

**Figure 14.** MZM output signal spectrum for the case of Δψ=180° (*a* – dBm, *b* – W)

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

Interaction between frequency modulated laser radiation and SMBS gain spectra causes power amplitude modulation (AM) of receiving signal. Modulation rate of such signal is straight to *Q*-factor, and AM envelope follows linear-frequency modulation (LFM). When central laser wavelength is tuned to central peak of SMBS gain spectra and frequency deviation equals spectrum half width, initial frequency of amplitude modulation is Ω0, and its frequency deviation is 2ΔΩ [10].

In work has been held modeling of signals processing for such system for direct and coherent detection. Usually in frequency ranging for extraction low frequency signal of telemetric frequencies which carries information of SMBS gain spectra properties within analyzing distance *R* in reception path received signal mixes with reference signal. In all cases measure‐ ment of subcarrier frequency increment *ΔΩ<sup>R</sup>* =2*βR* / *c* is performed by means of registration diversity between subcarrier frequencies of transmitted and received signals. Simulation has shown that under matching the demands for scanning SMBS gain spectra and LFM chirp resolution of spatial measurements, more strict conditions are applied by SMBS gain spectra properties. That causes decrease of spatial resolution. In case of direct detection of double frequency reflected signal auto heterodyning is performed with spatial coincidence of mixing rays. In that case signal spectrum transfers to the zone with low noise level of photo detector. Range control is performed by measurement the reduplicated frequency changes of modulat‐ ing LFM chirp signal, and output signal frequency from intermediate amplifier of receiving system. SMBS gain spectra parameters control is performed by measurement of signal power level at that frequency. For short fibers, which require bands of receiving paths in the range 20-100 MHz, sensitivity increasing may total two orders [8].

In some works has been shown the possibility of using additional signals, which were none selectively influenced by testing SMBS gain spectra for increasing metrological properties of a system. In case of two-frequency source frequency modulation could be accomplished by two signals. The first confirms the demands for SMBS gain spectra scanning and LFM chirping, the second represents modulating signal with constant frequency within the limits of SMBS gain spectra with amplitude two orders less than the scanning signal amplitude. In that case measuring signal will contain two items. The first *U*<sup>1</sup> ≈*k*<sup>1</sup> *f* (*I*0, *T* , *R*)*ϕ*(*τ*) depends on SMBS gain spectra optical properties, gauging equipment parameters and etc. The second item *U*2, mostly is not under the influence of SMBS gain spectra, only from component *k*<sup>2</sup> *f* (*I*0, *T* , *R*). After normalization *U*1 regarding *U*2 for distance *R* (simultaneous signal selection) and assuming that *k*1=*k*2, we will get equation, which depends only on SMBS gain spectra properties *ϕ*(*τ*).

Thus, two-frequency SMBS gain spectra scanning allows system increasing performance both in direct detection mode and normalizing mode, because reference signal parameters are determined and are not the signals of spurious modulation [8].

#### **5.3. Multiple frequencies probing for SMBS gain spectra characterization**

Analysis has shown that the main demand for SMBS gain spectra high precision measurements is high synchronization of phase, frequency, amplitude and polarization of probe signals. Sometimes it is impossible to fulfill those conditions even with the use of digital frequency synthesizer and locked-in lasers. Therefore the task of getting two-frequency and two-band oscillations with multiple frequencies and high synchronization is of current importance. Let us consider such method based on amplitude-phase conversion (Il'in-Morozov's method [4]).

Method is based on phase commutation by 180° of amplitude modulated signal at the moment when its envelope has minimum value. The basic task of research is defining the form and parameters of modulating signal *S*(*t*) to receive an output two-frequency oscillation with suppressed carrier frequency ω0. Total suppression of side components with *n* ≥ 3 could be achieved with the use amplitude modulating oscillation *S*(*t*)=*S*0|sinΩt|. Than the resulting signal with amplitude modulation index *b* would have the following spectrum [8]:

$$\mathrm{e}(t) = \frac{2E\_0}{\pi} (1 - b) \sum\_{n} \frac{1}{n} \left\{ \cos \left( \alpha\_0 + n\Omega \right) t - \cos \left( \alpha\_0 - n\Omega \right) t \right\} + \frac{\pi E\_0 b}{4} \left\{ \cos \left( \alpha\_0 + \Omega \right) t - \cos \left( \alpha\_0 - \Omega \right) t \right\}.\tag{26}$$

Amplitude of spectral components will be defined by Fourier series indexes, and for *n*=1 *E*1=[2*E*0/π][1*b*]+[π*E*0*b*/4], for *n*≥3 *En*=[2*E*0/π*n*][1*b*]. When *b*opt=1 spectrum contains two useful components with frequencies ω0±Ω, and the spurious products are suppressed. When the modulation index varies between (0,7-1)*b*opt output signal nonlinear-distortions coefficient would be less than 1%.

Modulation signals given previously could be used for forming symmetric double band spectrum for multi frequency measurement systems. To realize them it is essential to solve equations set (25) for indexes, varying not only amplitude modulation index but also the value of phase commutation θ. Using the oscillation *S*(*t*)=*S*0|sinΩt| we will get the following equations for amplitudes of spectral components [8]:

$$E\_0 = \frac{E}{2}(1 + \cos\theta); E\_1 = E\left(\frac{1 - b}{\pi} + \frac{\pi b}{8}\right)(1 - \cos\theta);\tag{27}$$

Poly-harmonic Analysis of Raman and Mandelstam-Brillouin Scatterings and Bragg Reflection Spectra http://dx.doi.org/10.5772/59144 85

$$E\_n = \frac{E(1 - \cos \theta)}{\pi n} (1 - b) \text{ for n=3, 5, 7...},\\ E\_n = \frac{bE(1 + \cos \theta)}{1 - n^2} \text{ for n=2, 4, 6 \dots} \tag{28}$$

gain spectra with amplitude two orders less than the scanning signal amplitude. In that case measuring signal will contain two items. The first *U*<sup>1</sup> ≈*k*<sup>1</sup> *f* (*I*0, *T* , *R*)*ϕ*(*τ*) depends on SMBS gain spectra optical properties, gauging equipment parameters and etc. The second item *U*2, mostly is not under the influence of SMBS gain spectra, only from component *k*<sup>2</sup> *f* (*I*0, *T* , *R*). After normalization *U*1 regarding *U*2 for distance *R* (simultaneous signal selection) and assuming that *k*1=*k*2, we will get equation, which depends only on SMBS gain spectra properties *ϕ*(*τ*).

Thus, two-frequency SMBS gain spectra scanning allows system increasing performance both in direct detection mode and normalizing mode, because reference signal parameters are

Analysis has shown that the main demand for SMBS gain spectra high precision measurements is high synchronization of phase, frequency, amplitude and polarization of probe signals. Sometimes it is impossible to fulfill those conditions even with the use of digital frequency synthesizer and locked-in lasers. Therefore the task of getting two-frequency and two-band oscillations with multiple frequencies and high synchronization is of current importance. Let us consider such method based on amplitude-phase conversion (Il'in-Morozov's method [4]).

Method is based on phase commutation by 180° of amplitude modulated signal at the moment when its envelope has minimum value. The basic task of research is defining the form and parameters of modulating signal *S*(*t*) to receive an output two-frequency oscillation with suppressed carrier frequency ω0. Total suppression of side components with *n* ≥ 3 could be achieved with the use amplitude modulating oscillation *S*(*t*)=*S*0|sinΩt|. Than the resulting

{ ( ) ( ) } { ( ) ( ) } <sup>0</sup> <sup>0</sup>

Amplitude of spectral components will be defined by Fourier series indexes, and for *n*=1 *E*1=[2*E*0/π][1*b*]+[π*E*0*b*/4], for *n*≥3 *En*=[2*E*0/π*n*][1*b*]. When *b*opt=1 spectrum contains two useful components with frequencies ω0±Ω, and the spurious products are suppressed. When the modulation index varies between (0,7-1)*b*opt output signal nonlinear-distortions coefficient

Modulation signals given previously could be used for forming symmetric double band spectrum for multi frequency measurement systems. To realize them it is essential to solve equations set (25) for indexes, varying not only amplitude modulation index but also the value of phase commutation θ. Using the oscillation *S*(*t*)=*S*0|sinΩt| we will get the following

0 1 ( ) <sup>1</sup> (1 cos ); 1 cos ; 2 8

æ ö - =+ = + - ç ÷

p

p

*<sup>E</sup> b b <sup>E</sup> E E*

q

<sup>2</sup> <sup>1</sup> ( ) (1 ) cos cos cos cos .

*<sup>E</sup> E b et b nt nt t t <sup>n</sup>*

 w

0 0 0 0

= - å + W - - W + +W - -W (26)

p

ww

 q

è ø (27)

signal with amplitude modulation index *b* would have the following spectrum [8]:

*<sup>n</sup>* 4

w

equations for amplitudes of spectral components [8]:

p

would be less than 1%.

determined and are not the signals of spurious modulation [8].

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

**5.3. Multiple frequencies probing for SMBS gain spectra characterization**

Equations (26) (27) allows to define spectral distribution of resulting signal with any *b* and θ. However, from point of view of simple technical realization we should look for forming oscillations without phase commutation using synthesis of oscillations with complex harmonic composition with *k* components, for example [8]:

$$S(t) = \sum\_{k=1}^{n} S\_k \cos\left(2k\,\,\Omega\,\,t + \pi\right),\\E\_n = \frac{2E}{\pi} \left[\frac{1}{n} - \sum\_{k=1}^{n} \frac{mk}{2} \left(\frac{1}{n + 2k} + \frac{1}{n - 2k}\right)\right],\tag{29}$$

where *Sk* are the partial amplitudes, *En* are the equations for Fourier indexes of its spectrum, *mk* are partial indexes of amplitude modulation. Such approach of looking for forming oscillations will also allowed to take into account influence of real devices modulation characteristics nonlinearities on spectral distribution of output radiation, which are used to realize amplitude-phase conversion.

Differential frequency of two-frequency oscillation (25) when *b*opt=1 is defined by frequency Ω of phase commutation θ. Its stability unambiguously concerned with frequency stability of driving voltages and instabilities of commutations devices. Really achievable value of differential frequency's instability with thermo-stating of driving generators is 108 . During differential frequency's retuning, which is required in some types of measurements and rather simple realized with the use of amplitude phase conversion, minimum frequency shift is determined by modulators gain slope, and maximum frequency shift is determined by higher cutoff frequency of modulator and correlation between modulator and modulated frequencies [8].

Energy equality of side lobes and the effectiveness of their conversion are of great importance in multiple frequencies systems. Using the derived equations for the spectrums of output oscillations and taking into consideration properties of amplitude-phase conversion, i.e. using the additional power of amplitude modulation and phase commutation for forming the side lobes, we could determine, that power of the last one is nearly 60% of initial single frequency oscillation, and conversion index equals unit value without taking into account the loss in real modulators. Moreover multi frequency radiation allows any pair of formed frequencies using for differential analysis without retuning central laser frequency [8].

As it has been mentioned above retuning both laser frequency and difference frequency between spectral components either is very complex or is carried out nonlinearly. Simple way of SMBS gain spectra analysis could be realized with its multiple frequencies probing (fig.15).

If initial SMBS gain spectra probing by two-frequency signal with components *A*1 and *A*2 did not allowed the measurement of the central wavelength of SMBS gain spectra we should change the conditions of amplitude phase forming of probe signal. Solving the equation (25) with *E*3=0 and limiting to four components we will get multiple frequencies signal with *A*1, *A*2, *A*5 and *A*6. At that components *A*1, *A*2, *A*5 lie on the left slope and component *A*<sup>6</sup> lies on the right. It could be defined from phase characteristics. As far as *A*2>*A*6 what is evident from envelope analysis of that pair cutout by band pass filter we should change the parameters of amplitude phase conversion of probe signal one more time [10].

**Figure 15.** Multiple frequencies probing

At that components *A*1, *A*2, *A*<sup>5</sup> lie on the left slope and component *A*<sup>6</sup> lies on the right. It could be defined from phase characteristics. As far as *A*2>*A*<sup>6</sup> what is evident from envelope analysis of that pair cutout by band pass filter we should change the parameters of amplitude phase conversion of probe signal one more time. From equation (25) with *E*5=0 and limiting to four components will get multi frequency signal with *A*1, *A*2, *A*3 and *A*4, and with *А*2=*А*4, for example, what corresponds the tuning of that pair to the SMBS gain spectra central wavelength [10].

There are possible three types of analysis: analysis of each component alone (differential analysis), analysis of the envelope of each double frequency pair (integral-differential analy‐ sis), and the analysis of energy correlation of all components (integral analysis). All of these methods are possible and correspond to single, two-, and multiple frequencies probing of SMBS gain spectra with limited number of optical band pass filters which are conjugated with detuning frequency between spectral components [8].

In more complex way of searching the spectral center and half width we should solve an equation set with amplitude and phase coefficients. Process of multiple frequencies analysis of SMBS gain spectra consists on solving the following equations set [10]

$$\begin{bmatrix} \mathbf{D} \end{bmatrix} = \begin{bmatrix} \mathbf{A} \end{bmatrix} \times \begin{bmatrix} \mathbf{E} \end{bmatrix} \times \begin{bmatrix} \mathbf{E} \end{bmatrix}^\*,\tag{30}$$

where **[D]** is matrix of output photo detector currents value with frequencies *k*Ω; **[А]** is matrix describing required SMBS gain spectra components in band Δω; **[E]** is matrix describing spectrum of probe multiple frequencies oscillation with frequencies {ω0±*k*Ω}{Δω}, **[E]** is complex conjugate matrix with [E].

On the first step SMBS gain spectra is probing by two-frequency oscillation, amplitude of the components with *n*≥3 equals zero. At the same time hitting the SMBS gain spectra central peak is not required. From the analysis of photo detector components on frequency Ω we can define SMBS gain spectra slope, its steepness, frequency shift from central peak of reflection<sup>8</sup> . During the second step we use multi frequency oscillation, which component with *n*=3 does not equal zero. During the third step we use multi frequency oscillation, which component with *n*=3 equals zero, and component with *n*=5 does not equal zero. At the same time we analyze amplitudes of photo detector components with frequenciesΩ, 2Ω, 3Ω. As far as the amplitude of probe signal components is known and stable, as it has been shown before, we could with given precision define SMBS gain spectra, such as central wavelength, steepness, symmetry of the spectrum curve, and etc. At the third step varying the frequency Ω, number of compo‐ nents *n* and working filters with frequencies *k*Ω, we could optimize SMBS gain spectra analysis and tune the central frequency of probe laser to the reflection peak to take a tracking signal [8].

#### **5.4. Some remarks for SNR of spectra characterization**

*A*5 and *A*6. At that components *A*1, *A*2, *A*5 lie on the left slope and component *A*<sup>6</sup> lies on the right. It could be defined from phase characteristics. As far as *A*2>*A*6 what is evident from envelope analysis of that pair cutout by band pass filter we should change the parameters of amplitude

At that components *A*1, *A*2, *A*<sup>5</sup> lie on the left slope and component *A*<sup>6</sup> lies on the right. It could be defined from phase characteristics. As far as *A*2>*A*<sup>6</sup> what is evident from envelope analysis of that pair cutout by band pass filter we should change the parameters of amplitude phase conversion of probe signal one more time. From equation (25) with *E*5=0 and limiting to four components will get multi frequency signal with *A*1, *A*2, *A*3 and *A*4, and with *А*2=*А*4, for example, what corresponds the tuning of that pair to the SMBS gain spectra central wavelength [10].

There are possible three types of analysis: analysis of each component alone (differential analysis), analysis of the envelope of each double frequency pair (integral-differential analy‐ sis), and the analysis of energy correlation of all components (integral analysis). All of these methods are possible and correspond to single, two-, and multiple frequencies probing of SMBS gain spectra with limited number of optical band pass filters which are conjugated with

In more complex way of searching the spectral center and half width we should solve an equation set with amplitude and phase coefficients. Process of multiple frequencies analysis

where **[D]** is matrix of output photo detector currents value with frequencies *k*Ω; **[А]** is matrix describing required SMBS gain spectra components in band Δω; **[E]** is matrix describing

\*

**D AEE** = ´´ (30)

[ ] [ ][][] ,

of SMBS gain spectra consists on solving the following equations set [10]

phase conversion of probe signal one more time [10].

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

detuning frequency between spectral components [8].

**Figure 15.** Multiple frequencies probing

Let's consider some different situations with single, two-, and multiple frequencies probing of real selective structures with limited number of optical band pass filters which are conjugated with detuning frequency between spectral components [8]. SMBS gain spectra characterization from optical to the electrical field by single-sideband amplitude modulated radiation, in which the upper sideband is suppressed and single frequency probing is used in [6]. SMBS gain spectra characterization in single-mode optical fiber was presented in [7]. It is based on the use of advantages of single-sideband modulation and two-frequency probing radiation, which gives possibility of transfer the data signal's spectrum in the low noise region of a photo detector. Two-frequency scanning and multiple frequencies probing of SMBS gain spectra are discussed in sections 4.2-4.3 and were partly considered in [8]. SMBS gain spectra characteri‐ zation with two-frequency heterodyne and single frequency scanning was discussed in [4].

As we can see from [6,7] the needed bandwidth of photo detector is determined by Mandel‐ stam-Brillouin frequency shift and equal to 10-20 GHz. One version of signal processing may be realized on the envelope of differential frequency 2Δf [7]. So the needed bandwidth of photo detector is determined by Mandelstam-Brillouin gain and equal to 20-100 MHz. The same value of bandwidth is a feature of methods which are presented now and discussed in [8]. Additional advantage of method [4] is heterodyning. Applying of photo heterodyning allows significantly increase the system sensitivity under the condition of weak signals and receives information from frequency pushing of counter propagated signal spectrum [8].

If we don't go into details of the physical nature phenomena, the basic noises level of the radiance receivers is more than background noises level and determine the detect ability of receiving signal. The gain in SNR relative to single frequency measurements can be calculated as [63]

$$G = \bigcup\_{0}^{\mathcal{M}} S\left(f\right) df \left/ \int\_{f\_0 + \mathcal{M}}^{f\_0 - \mathcal{M}} S\left(f\right) df\right. \tag{31}$$

where *S*(*f*) – spectral density of radiance receiver noises, Δ*f* – bandwidth of photo receiver.

The gain will be determined by different nature and level of noise in different frequency regions (fig. 16)

**Figure 16.** To SNR gain remarks

There are current noises with distribution type 1/*f* and other powerful noises of low frequency nature for region {0...Δ*f*}for variants 2,4. There are thermal agitations and shot noises with low intension for region {*f*0 Δ*f*... *f*0+Δ*f*} for present methods and heterodyning 9. For little distance routes the gain in SNR can be mount to 1–2 orders. All these summaries are correct and for multiple frequencies probing [8]. The results are much closed to [53].

#### **5.5. Notch filters for suppressing of Rayleigh scattering**

The Raman scattering of light is known to be accompanied by the emergence of spectral components shifted in terms of frequency [15]. The number and the spectral positions of these lines depend on the structural characteristics of the scattering medium. It is known that the intensity of the anti-Stokes line is very low (30 dB weaker than the amplitude of elastic Rayleigh scattering); therefore, registration of the ratio of intensities of the Stokes and anti-Stokes components is a difficult task. In addition, the power of the probing radiation should not exceed several watts to avoid such nonlinear effects as the stimulated Raman scattering and the stimulated Mandelstam-Brillouin scattering. The principle of the SMBS distributed temperature sensors is based on the Landau-Placzek ratio where the temperature-insensitive Rayleigh signal provides a reference measurement of the fiber background losses and the temperature-sensitive Brillouin signal provides a measurement of the temperature [16]. It is estimated that the Rayleigh signal must be suppressed by at least 33 dB to reduce the effects of SRN to an acceptable level. In these circumstances, in order to achieve high accuracy of temperature measurement is required to choose the optimal method of Rayleigh scattering filtration and separation of the desired signal with minimal loss of information.

() () <sup>0</sup>

where *S*(*f*) – spectral density of radiance receiver noises, Δ*f* – bandwidth of photo receiver. The gain will be determined by different nature and level of noise in different frequency

There are current noises with distribution type 1/*f* and other powerful noises of low frequency nature for region {0...Δ*f*}for variants 2,4. There are thermal agitations and shot noises with low intension for region {*f*0 Δ*f*... *f*0+Δ*f*} for present methods and heterodyning 9. For little distance routes the gain in SNR can be mount to 1–2 orders. All these summaries are correct and for

The Raman scattering of light is known to be accompanied by the emergence of spectral components shifted in terms of frequency [15]. The number and the spectral positions of these lines depend on the structural characteristics of the scattering medium. It is known that the intensity of the anti-Stokes line is very low (30 dB weaker than the amplitude of elastic Rayleigh scattering); therefore, registration of the ratio of intensities of the Stokes and anti-Stokes components is a difficult task. In addition, the power of the probing radiation should not exceed several watts to avoid such nonlinear effects as the stimulated Raman scattering and the stimulated Mandelstam-Brillouin scattering. The principle of the SMBS distributed temperature sensors is based on the Landau-Placzek ratio where the temperature-insensitive

multiple frequencies probing [8]. The results are much closed to [53].

**5.5. Notch filters for suppressing of Rayleigh scattering**

*f f*

+D

<sup>=</sup> ò ò (31)

<sup>0</sup> 0

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

regions (fig. 16)

**Figure 16.** To SNR gain remarks

*f f f*

*G S f df S f df* D -D

> The separation of the relatively weak Brillouin signal from the Rayleigh has been reported using a bulk Fabry-Pérot interferometer (FPI) [54], which is lossy and expensive. A fiber Mach– Zehnder interferometer (MZI) has been demonstrated to achieve 27-dB Rayleigh rejection using a-switched fiber laser probe of 1.5-GHz bandwidth [55]. However, with a narrow-band source (20 MHz) and the resultant increased coherent Rayleigh noise, this is insufficient to achieve a temperature resolution of 1 °C. In [16] reports on the use of a narrow-band fiber Bragg grating filter (FBGF), which achieves recovery of the Brillouin signal by suppressing the Rayleigh signal. In this way, the Brillouin light path is subject to minimum attenuation and is frequency independent. Typically, the filter uses fiber Bragg gratings that produce narrowband signals of the Stokes and anti-Stokes components [14], which are then sent on different channels registration. However, this method makes great demands on the quality of lattices: a spectral width (which should be as much as possible), the reflection coefficient, losses, and so on. Unfortunately, even under optimal conditions, a significant portion of the desired signal is lost during filtration. So, FBG is more effective to suppress Rayleigh scattering, then to detail Stokes and anti-Stokes components.

> In [14,15] FBG with a spectral width of 0.5 nm reflection used to suppress the central Rayleigh line, which allowed to minimize the noise introduced by Rayleigh scattering without a substantial reduction in the integrated intensity of Raman shift lines. After filtering, the signal components of the SRS were separated by directional couplers with the appropriate wave‐ lengths and sent to pin-photodiodes. It was not possible in [16] to obtain a single grating that would provide rejection of Rayleigh line. Hence, the filter comprises two cascaded gratings separated with an isolator to prevent the formation of an étalon. The rating characteristics were all supplied to the following specifications: bandwidth 0.13 nm, reflectivity 0.98%. In this way the FBG offers minimum attenuation to the two Brillouin sidebands, which, therefore, pass relatively unaffected through the filter.

> We developed a new method of FBG writing on the basis of phase mask and restrictive object positioned between mask and fiber. Such optical scheme was realized and we got FBG, which allowed measurements of intensity of the Raman or Mandelstam-Brillouin scattering compo‐ nents in a wide spectral range with the minimum losses; the sensitivity of a conventional InGaAs photo-detector turned out to be sufficient for these measurements. This filter sup‐ pressed the central area of the spectrum at the wavelength of 1552,6 nm and transmitted the anti-Stokes and Stokes lines of the Raman or Brillouin scattering. The spectra of FBG for Rayleigh line filtration in SMBS gain spectra characterization, obtained by the spectrum analyzer 5240 FTB-S with a resolution of 2 pm, is shown on fig. 17.

**Figure 17.** Spectra of FBG filter

**Figure 18.** Setup for FBG recording

FBG for the experiments was manufactured by a given method of continuous recording with restrictive object in the setup, shown in Fig. 18, at the R&D Institute of Applied Electrody‐ namics, Photonics and Living Systems. The setup for FBG recording was made in Novosibrsk State University on the base of amplitude-modulated ultraviolet laser with the conversion of the second harmonic on the Ar+. Laser was focused on the core of the aged in hydrogen-doped germanium-silicon fiber (SMF-28).

#### **5.6. Discussion of results**

On the basis of two-frequency signal information structure investigation main principles of combined interaction of its instantaneous values of amplitude, phase and frequency with arbitrary contour has been defined. The numerical simulation in dual-drive MZM was carried out and different poly-harmonic spectrums were realized. Novel methods for multiple frequency characterization of stimulated SMBS gain spectrum in single-mode optical fiber are presented. This method is based on the usage of multiple frequencies probing radiation [8]. For conversion of the complex SMBS gain spectra from optical to the electrical field singlesideband modulation, direct or heterodyne detection are used. Determining of a multiple frequencies positions over the gain spectrum occurs through the amplitude modulation index of the envelope or the phase difference between envelopes of probing and passing components. The methods are 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 SMBS maximum gain coefficient. Measurement algorithm is realized on simple and stable experimental setup. Applying of photo heterodyning allows significantly increase the system sensitivity under the condition of weak signals and receives information from frequency pushing of counter propagated signal spectrum. We developed a new method of FBG writing on the basis of phase mask and restrictive object positioned between mask and fiber. Such optical scheme was realized and we got FBG, which allowed measurements of intensity of the Raman or Mandelstam-Brillouin scattering components in a wide spectral range with the minimum losses and deep suppression of Rayleigh scattering line.
