CN104568383B - Multi-mold sound wave lightguide fiber temperature and strain sensitivity evaluation method - Google Patents

Abstract

The invention discloses a multi-mold sound wave lightguide fiber temperature and strain sensitivity evaluation method. According to the method, a power formula of the beat spectrum peak (i, j) in a Brillouin beat spectrum is obtained according to power formulas of the ith Brillouin peak and the jth Brillouin peak in a Brillouin gain spectrum, and the power formulas need to contain acousto-optic effective areas corresponding to different acoustic molds in optical cables; when the optical cables are located on a linear strain region under the indoor temperature, Taylor expansion is conducted on the power formulas at the position with the strain being 0 in the mode that the high-order term is ignored, and power-strain coefficients of the beat spectrum peak (i, j) are worked out; when the optical cables are in the loose state, Taylor expansion is conducted on the beat spectrum power formula at the position where T=T0 in the mode that the high-order term is ignored, and power-temperature coefficients of the beat spectrum peak (i, j) are worked out. By means of the multi-mold sound wave lightguide fiber temperature and strain sensitivity evaluation method, the high-sensitivity optical cables used for an optical time domain reflection (OTDR) technique based on Brillouin beat spectrum detection can be screened out, and the method is used for guiding designing of high-strain and high-temperature-sensitivity multi-mold sound wave lightguide fibers.

Description

Method for evaluating temperature and strain sensitivity of multimode acoustic waveguide optical fiber

Technical Field

The invention relates to the field of optical fiber sensing based on Brillouin scattering, in particular to a method for evaluating the temperature and strain sensitivity of a multimode acoustic waveguide optical fiber.

Background

The frequency shift and power of the Brillouin scattering light are both related to strain and temperature, and continuous distributed measurement of the strain and the temperature can be realized by measuring the frequency shift and the power of backward spontaneous Brillouin scattering light generated when the pulse light is transmitted in the optical fiber. Multimode acoustic waveguide fiber, which is an optical fiber with complex refractive index distribution and multiple acoustic modes, has a Brillouin Gain Spectrum (BGS) with multiple peaks, and the Brillouin Gain Spectrum (BGS) has a Beat effect to form a Brillouin Beat Spectrum (BBS). In the prior art, a new optical time domain reflectometry (BBS-OTDR) Distributed fiber sensing technology based on Brillouin beat spectrum detection is proposed, and fast Distributed measurement of temperature and strain on a fiber is successfully achieved by only measuring the power of a beat spectrum (y.lu, z.qin, p.lu, d.zhou, l.chen, and x.bao, "Distributed strain and temperature measurement by mass bright wave reflected spectrum," IEEE photon. In the optical time domain reflection distributed optical fiber sensing technology based on the Brillouin beat spectrum detection, if a multimode acoustic waveguide optical fiber with higher strain and temperature sensitivity is selected,

the performance of the sensing system can be effectively improved.

However, no method for calculating the strain and temperature sensitivity of the multimode acoustic waveguide fiber based on the detection technology exists at present.

Disclosure of Invention

The present invention is directed to a method for evaluating the temperature and strain sensitivity of a multimode acoustic waveguide fiber to select a multimode acoustic waveguide fiber with higher strain and temperature sensitivity.

The invention adopts the following technical scheme for solving the technical problems:

the method for evaluating the temperature and the strain sensitivity of the multimode acoustic waveguide fiber comprises the following steps:

step one, calculating and obtaining the effective refractive index n of the optical fiber according to the known refractive index distribution of the multimode acoustic waveguide optical fiber_eff；

Step two, obtaining a power formula of a beat peak (i, j) in the Brillouin beat spectrum according to power formulas of the ith Brillouin peak i and the jth Brillouin peak j in the Brillouin gain spectrum of the multimode acoustic waveguide fiber

Wherein, P_P(0) α is the attenuation coefficient of the optical fiber, z is the position from the initial end of the fiber, K is the Boltzmann constant, c is the speed of light in vacuum, W is the incident pulse width, T is the temperature, λ is the incident wavelength, p₁₂Is the photoelastic coefficient of the fiber, as strain, k_i(, T) is the Poisson ratio function of the fiber where the ith acoustic mode is excited, k_j(, T) is the Poisson ratio function of the fiber where the jth acoustic mode is excited, E_i(, T) is a function of the Young's modulus of the fiber at which the ith acoustic mode is excited, E_j(, T) is a function of the Young's modulus of the fiber at which the jth acoustic mode is excited,is the acousto-optic effective area function corresponding to the ith acoustic mode,the function of the acousto-optic effective area corresponding to the jth acoustic mode is shown, wherein i and j are integers which are more than 0;

step three, when the optical fiber is in a linear strain area and the temperature T is room temperature T₀And (3) performing Taylor expansion on the power formula obtained in the step two at the position where the strain is 0, and calculating to obtain a power-strain coefficient C of the beat frequency peak (i, j)_p(i,j)，

Wherein,

wherein n is_eff(，T₀) Is equal to room temperature T at temperature T₀Effective refractive index function with respect to strain, E_iYoung's modulus of the fiber where the ith acoustic mode is excited, E_jYoung's modulus of the fiber where the jth acoustic mode is excited, E_i(，T₀) For the ith acoustic mode at a temperature T equal to room temperature T₀Young's modulus function of time with respect to strain, E_j(，T₀) For the jth acoustic mode at a temperature T equal to room temperature T₀Young's modulus function of time with respect to strain, k_iIs the Poisson's ratio, k, of the fiber where the ith acoustic mode is excited_jIs the Poisson's ratio, k, of the fiber where the jth acoustic mode is excited_i(，T₀) For the ith acoustic mode at a temperature T equal to room temperature T₀Poisson's ratio function of time versus strain, k_j(，T₀) The jth acoustic mode is at a temperature T equal to room temperature T₀As a function of poisson's ratio with respect to strain,the acousto-optic effective area corresponding to the ith acoustic mode in the optical fiber,the acousto-optic effective area corresponding to the jth acoustic mode in the optical fiber,for the ith acoustic mode at a temperature T equal to room temperature T₀As a function of the acousto-optic effective area for strain,for the jth acoustic mode at a temperature T equal to room temperature T₀Acousto-optic effective area function with respect to strain;

step four, when the optical fiber is in a relaxed state, the temperature T is room temperature T₀And (3) performing Taylor expansion on the power formula obtained in the step two, and calculating to obtain a power-temperature coefficient C of the beat frequency peak (i, j)_pT(i,j)，

Wherein,

wherein n is_eff(0, T) is an effective refractive index function with respect to temperature T in the relaxed state of the fiber, E_i(0, T) is a function of the Young's modulus of the ith acoustic mode in the relaxed state of the fiber with respect to temperature T, E_j(0, T) is a Young's modulus function of the jth acoustic mode in the relaxed state of the fiber with respect to temperature T, k_i(0, T) is the Poisson's ratio function of the ith acoustic mode in the relaxed state of the fiber with respect to temperature T, k_j(0, T) is a Poisson's ratio function of the jth acoustic mode in a fiber relaxed state with respect to temperature T,is an acousto-optic effective area function of the ith acoustic mode in the relaxed state of the optical fiber and with respect to the temperature T,is the acousto-optic effective area function of the jth acoustic mode in the fiber relaxed state with respect to temperature T.

As a further optimized solution of the method for evaluating the temperature and strain sensitivity of the multimode acoustic waveguide fiber according to the present invention, the fiber is strained when the fiber is in a relaxed state, which is 0.

As a further optimized scheme of the method for evaluating the temperature and the strain sensitivity of the multimode acoustic waveguide fiber, n in the first step_effIs obtained by finite element analysis.

The method for evaluating the temperature and the strain sensitivity of the multimode acoustic waveguide optical fiber is used as the method for evaluating the temperature and the strain sensitivity of the multimode acoustic waveguide optical fiberScheme for further optimization of said method, said T₀＝300K。

As a scheme for further optimizing the method for evaluating the temperature and the strain sensitivity of the multimode acoustic waveguide optical fiber, the power formula in the second step is determined by the effective refractive index, the Young modulus, the Poisson ratio and the acousto-optic effective area of the optical fiber, and the effective refractive index, the Young modulus, the Poisson ratio and the acousto-optic effective area of the optical fiber are all functions of strain and temperature.

Compared with the prior art, the invention adopting the technical scheme has the following technical effects: according to the refractive index distribution of the known multimode acoustic waveguide fiber, the strain and the temperature coefficient of the beat frequency peak of the multimode acoustic waveguide fiber are directly derived and calculated theoretically, so that the high-sensitivity fiber based on the BBS-OTDR technology can be screened and used for guiding the design of the multimode acoustic waveguide fiber with high strain and temperature sensitivity.

Drawings

FIG. 1 is a plot of the refractive index profile of a Large Effective Area Fiber (LEAF) according to an embodiment of the present invention.

Fig. 2a is a BGS diagram of LEAF according to an embodiment of the present invention.

FIG. 2b is a BBS diagram of LEAF according to an embodiment of the present invention.

Fig. 3 is a graph of the distribution of three acoustic modes and a polynomial fit for LEAF in accordance with an embodiment of the present invention.

FIG. 4 is a plot of the fundamental optical mode distribution and polynomial fit of a LEAF according to an embodiment of the present invention.

Detailed Description

The technical scheme of the invention is further explained in detail by combining the attached drawings:

a method for evaluating temperature and strain sensitivity of a multimode acoustic waveguide fiber, comprising the steps of:

1) from the known refractive index profile of the optical fiber, the effective refractive index n of the optical fiber can be obtained by finite element analysis according to the eigenequation of the solution mode_eff。

2) According to the power formula of the brillouin peak in spontaneous brillouin BGS:

wherein z is the position from the initial end of the fiber, P_P(0) For the incident optical power, α is the fiber attenuation coefficient, α ═ 0.2dB/km is the fiber attenuation coefficient at 1.55 μm, c is the speed of light in vacuum, W is the incident pulse width, S is the scattering trapping factor:

wherein, α_BIs the Brillouin loss coefficient, λ is the incident wavelength, K is the Boltzmann constant, T is the temperature, P₁₂Is the photoelectric expansion coefficient, V_aIs the longitudinal speed of sound, ρ is the density, A^aoThe acousto-optic effective area; acousto-optic effective area corresponding to ith acoustic mode in optical fiberAcousto-optic effective area corresponding to jth acoustic modeRespectively as follows:

wherein f (r) is the optical fundamental mode distribution of the optical fiber, ξ_i(r) is the ith acoustic mode distribution, ξ_j(r) is the j th acoustic mode distribution, r is the radius of the optical fiber, i and j are integers more than 0, and f (r) and ξ can be obtained by solving the eigen equation of the optical mode and the acoustic mode_i(r) and ξ_j(r) distribution along the fiber radius r, and polynomial fitting is performed to obtain an analytical expression within a certain range.

Longitudinal sound velocity V corresponding to ith sound mode_aiLongitudinal sound velocity V corresponding to jth sound mode_ajCan be expressed as:

wherein E is_iYoung's modulus of the fiber where the ith acoustic mode is excited, E_jIs the Young's modulus, k, of the fiber where the jth acoustic mode is excited_iIs the Poisson's ratio, k, of the fiber where the ith acoustic mode is excited_jIs the Poisson's ratio, p, of the fiber where the jth acoustic mode is excited_iDensity, p, of the fiber where the i-th acoustic mode is excited_jIs the density of the fiber where the jth acoustic mode is excited.

3) Obtaining the power P of the beat peak (i, j) in the BBS according to the formula (1)_BBS(i,j)Can be expressed as:

wherein, P_BiIs the peak power, P, of the ith Brillouin peak in BGS_BjIs the peak power, P, of the jth Brillouin peak in BGS_P(0) α is the attenuation coefficient of the optical fiber, z is the position from the initial end of the fiber, K is the Boltzmann constant, c is the speed of light in vacuum, W is the incident pulse width, T is the temperature, λ is the incident wavelength, P is the optical fiber attenuation coefficient₁₂Is the photoelectric expansion coefficient, is the strain,the acousto-optic effective area corresponding to the ith acoustic mode in the optical fiber,the acoustic-optical effective area corresponding to the jth acoustic mode in the optical fiber;

as can be seen from equation (8), since n_eff、E_i、E_j、k_i、k_j、Andare both functions of strain and temperature T, and can be expressed as n_eff(，T)、E_i(，T)、E_j(，T)、k_i(，T)、k_j(，T)、Andequation (8) can therefore be expressed as:

wherein, P_P(0) α is the attenuation coefficient of the optical fiber, z is the position from the initial end of the fiber, K is the Boltzmann constant, c is the speed of light in vacuum, W is the incident pulse width, T is the temperature, λ is the incident wavelength, P is the optical fiber attenuation coefficient₁₂Is the coefficient of photoelectric expansion, strain, k_i(, T) is the Poisson ratio function of the fiber where the ith acoustic mode is excited, k_j(, T) is the Poisson ratio function of the fiber where the jth acoustic mode is excited, E_i(, T) is a function of the Young's modulus of the fiber at which the ith acoustic mode is excited, E_j(, T) Young's modulus function of the fiber where the jth acoustic mode is excited,is the acousto-optic effective area function corresponding to the ith acoustic mode,an acousto-optic effective area function corresponding to the jth acoustic mode;

4) in the linear strain region and at room temperature T₀Lower (T ═ T)₀300K), taylor expansion is performed on equation (9) at 0, and ignoring higher order terms, equation (9) can be expressed as:

wherein, P_BBS(i,j)(z,,T₀) Shows the strain at a fiber position z, the temperature T₀The beat peak power in time. P_BBS(i,j)(z,0,T₀) Representing a strain of 0 and a temperature T at fiber position z₀The beat peak power in time. Thus the power-strain coefficient C of the beat peak (i, j)_p(i,j)Comprises the following steps:

wherein:

wherein n is_eff(，T₀) Is equal to room temperature T at temperature T₀Effective refractive index function with respect to strain, E_iYoung's modulus of the fiber where the ith acoustic mode is excited, E_jYoung's modulus of the fiber where the jth acoustic mode is excited, E_i(，T₀) For the ith acoustic mode at a temperature T equal to room temperature T₀Young's modulus function of time with respect to strain, E_j(，T₀) For the jth acoustic mode at a temperature T equal to room temperature T₀Young's modulus function of time with respect to strain, k_iIs the Poisson's ratio, k, of the fiber where the ith acoustic mode is excited_jIs the Poisson's ratio, k, of the fiber where the jth acoustic mode is excited_i(，T₀) For the ith acoustic modeFormula (II) at a temperature T equal to room temperature T₀Poisson's ratio function of time versus strain, k_j(，T₀) The jth acoustic mode is at a temperature T equal to room temperature T₀As a function of poisson's ratio with respect to strain,the acousto-optic effective area corresponding to the ith acoustic mode in the optical fiber,the acousto-optic effective area corresponding to the jth acoustic mode in the optical fiber,for the ith acoustic mode at a temperature T equal to room temperature T₀As a function of the acousto-optic effective area for strain,for the jth acoustic mode at a temperature T equal to room temperature T₀An acousto-optic effective area function with respect to strain;

5) when the optical fiber is in a relaxed state (═ 0), the pair of equations (9) is represented by T ═ T₀Taylor expansion is performed and higher order terms are ignored. The following can be obtained:

wherein, P_BBS(i,j)(z,0, T) represents the beat peak power at fiber position z at which strain is 0 and temperature T. Δ T is the amount of temperature change. Thus the power-temperature coefficient C of the beat peak (i, j)_pT(i,j)Comprises the following steps:

wherein,

wherein n is_eff(0, T) is an effective refractive index function with respect to temperature T in the relaxed state of the fiber, E_i(0, T) is a function of the Young's modulus of the ith acoustic mode in the relaxed state of the fiber with respect to temperature T, E_j(0, T) is a Young's modulus function of the jth acoustic mode in the relaxed state of the fiber with respect to temperature T, k_i(0, T) is the Poisson's ratio function of the ith acoustic mode in the relaxed state of the fiber with respect to temperature T, k_j(0, T) is a Poisson's ratio function of the jth acoustic mode in a fiber relaxed state with respect to temperature T,is an acousto-optic effective area function of the ith acoustic mode in the relaxed state of the optical fiber and with respect to the temperature T,is the acousto-optic effective area function of the jth acoustic mode in the fiber relaxed state with respect to temperature T.

A Large Effective Area Fiber (LEAF) is a multimode acoustic waveguide Fiber, and the refractive index profile of the LEAF is shown in fig. 1, where Δ (%) is the relative refractive index difference. The effective refractive index n of the LEAF can be obtained by finite element analysis_effIs 1.461. Figure 2a shows BGS for LEAF. FIG. 2b shows BBS of LEAF. Wherein, peak (1,2) in BBS is obtained by beating peak 1 and peak 2 in BGS, and peak (1,3) is obtained by beating peak 1 and peak 3 in BGS. The invention will now be specifically described by taking peak (1,2) as an example.

FIG. 3 is a graph of the distribution of three acoustic modes and a polynomial fit of LEAF according to an embodiment of the present invention, where the fitting expression isWherein a is_ilIs a polynomial fitting coefficient, r is the fiber radius, l is the polynomial order (integer), and N is the maximum order and is a positive integer. Table 1 is a polynomial fitting coefficient table of distribution of three acoustic modes in the LEAF according to the embodiment of the present invention, where i ═ 1 represents a fitting coefficient of a 1 st acoustic mode, i ═ 2 represents a fitting coefficient of a 2 nd acoustic mode, and i ═ 3 represents a fitting coefficient of a 3 rd acoustic mode. When i is 1, the polynomial fitting maximum order area takes N6. When i is 2, the polynomial fitting maximum order area takes N7. When i is 3, the polynomial fitting maximum order area takes N as 8.

FIG. 4 is a plot of the optical fundamental mode distribution and a polynomial fit of a LEAF according to an embodiment of the present invention, the fit being expressed asWherein b is_lFor polynomial fit coefficients, the maximum fit coefficient is taken to be N-6. Table 2 is a polynomial fitting coefficient table of the distribution of optical fundamental modes in the LEAF according to the embodiment of the present invention, and when i is 1,2, or 3, the three acousto-optic effective areas of the LEAF can be obtained by using formula (4). Formula (12) The partial derivative term of the middle acousto-optic effective area to the strain can be expressed as:

the temperature-dependent partial derivative term of the acousto-optic effective area in equation (15) can be expressed as:

where k is the Poisson's ratio of the fiber, α_CTypical value of the expansion coefficient of the optical fiber is 5.7 × 10^-7/K，r₀For the initial effective radius, 12 μm was chosen in our calculation, since both the optical and acoustic modes tend to 0 at r-12 μm. The values of equations (12f, 12g) and (15f, 15g) can be obtained by equations (16) and (17), polynomial fitting, and equations (4) and (5). Table 3 is a table of typical parameters and their partial derivatives with respect to temperature strain for single mode optical mode fibers used in embodiments of the present invention. Wherein the parameters in table 3 are represented: the refractive index n, young's modulus E, poisson's ratio k of the fiber, in this example calculation, when i takes different values, we take the same value for young's modulus and poisson's ratio because they differ very little.₀These parameters are expressed in terms of strain 0 and temperature T₀The value of time. The power-strain coefficient of the beat peak (1,2) can be obtained according to the parameter values in table 3, and the formula (11) and the formulas (12 a-12 g). Similarly, the power-temperature coefficient of the beat peak (1,2) can be obtained by using the formula (14) and the formulas (15a to 15 g). The power-strain and power-temperature coefficients of peak (1,3) can be obtained in a similar way. The calculated results were compared with experimental values (Y.Lu, Z.Qin, P.Lu, D.ZHou, L.Chen, and X.Bao, "Distributed structured and structured measurement by Brillouin bed at spread," IEEEPhoton.Technol.Lett., vol.25, No.11, pp.1050-1053,2013.), as shown in Table 4, which is a table comparing the theoretical derivation results with the experimental results of the examples of the present invention. Wherein C is_p(1,2)Power strain of peak (1,2)Coefficient, C_p(1,3)Is the power strain coefficient of peak (1,3), C_pT(1,2)Is the power temperature coefficient of peak (1,2), C_pT(1,3)The power temperature coefficient of peak (1,3) is shown in units inside brackets. The theoretical calculation result of the invention is consistent with the experimental result.

TABLE 1

TABLE 2

TABLE 3

TABLE 4

Claims (5)

1. A method for evaluating temperature and strain sensitivity of a multimode acoustic waveguide fiber, comprising the steps of:

step one, calculating and obtaining the effective refractive index n of the optical fiber according to the known refractive index distribution of the multimode acoustic waveguide optical fiber_eff；

Step two, obtaining a power formula of a beat peak (i, j) in the Brillouin beat spectrum according to power formulas of the ith Brillouin peak i and the jth Brillouin peak j in the Brillouin gain spectrum of the multimode acoustic waveguide fiber

$\begin{array}{c}{P}_{BBS(i,j)}=2\·\frac{P_p\left(0\right)n_{eff}^5\exp (-2\mathrm{\α}z){\mathrm{\π}}^2{\mathrm{Kp}}_{12}^{2}cW\·T}{3{\mathrm{\λ}}^2}\\ \·\sqrt{\frac{(1+k_i(\mathrm{\ϵ},T\left)\right)(1-2k_i(\mathrm{\ϵ},T\left)\right)}{(1-k_i(\mathrm{\ϵ},T\left)\right)E_i(\mathrm{\ϵ},T)A_i^{ao}(\mathrm{\ϵ},T)}}\sqrt{\frac{(1+k_j(\mathrm{\ϵ},T\left)\right)(1-2k_j(\mathrm{\ϵ},T\left)\right)}{(1-k_j(\mathrm{\ϵ},T\left)\right)E_j(\mathrm{\ϵ},T)A_j^{ao}(\mathrm{\ϵ},T)}}\end{array};$

Wherein, P_P(0) α is the attenuation coefficient of the optical fiber, z is the position from the initial end of the fiber, K is the Boltzmann constant, c is the speed of light in vacuum, W is the incident pulse width, T is the temperature, λ is the incident wavelength, p₁₂Is the photoelastic coefficient of the fiber, as strain, k_i(, T) is the Poisson ratio function of the fiber where the ith acoustic mode is excited, k_j(, T) is the Poisson ratio function of the fiber where the jth acoustic mode is excited, E_i(, T) is a function of the Young's modulus of the fiber at which the ith acoustic mode is excited, E_j(, T) is a function of the Young's modulus of the fiber at which the jth acoustic mode is excited,is the acousto-optic effective area function corresponding to the ith acoustic mode,the function of the acousto-optic effective area corresponding to the jth acoustic mode is shown, wherein i and j are integers which are more than 0;

step three, when the optical fiber is in a linear strain area and the temperature T is room temperature T₀And (3) performing Taylor expansion on the power formula obtained in the step two at the position where the strain is 0, and calculating to obtain a power-strain coefficient C of the beat frequency peak (i, j)_p(i,j)，

$C_{p\mathrm{\ϵ}(i,j)}={\mathrm{\Δn}}_{eff\mathrm{\ϵ}}+{\mathrm{\ΔE}}_{i\mathrm{\ϵ}}+{\mathrm{\ΔE}}_{j\mathrm{\ϵ}}+{\mathrm{\Δk}}_{i\mathrm{\ϵ}}+{\mathrm{\Δk}}_{j\mathrm{\ϵ}}+{\mathrm{\ΔA}}_{i\mathrm{\ϵ}}^{ao}+A_{j\mathrm{\ϵ}}^{ao};$

Wherein,

${\mathrm{\Δn}}_{eff\mathrm{\ϵ}}=\frac{5}{n_{eff}}\[\frac{\∂n_{eff}(\mathrm{\ϵ},T_0)}{\∂\mathrm{\ϵ}}\]{|}_{\mathrm{\ϵ}=0};$

${\mathrm{\ΔE}}_{i\mathrm{\ϵ}}=-\frac{1}{2E_i}\[\frac{\∂E_i(\mathrm{\ϵ},T_0)}{\∂\mathrm{\ϵ}}\]{|}_{\mathrm{\ϵ}=0};$

${\mathrm{\ΔE}}_{j\mathrm{\ϵ}}=-\frac{1}{2E_j}\[\frac{\∂E_j(\mathrm{\ϵ},T_0)}{\∂\mathrm{\ϵ}}\]{|}_{\mathrm{\ϵ}=0};$

${\mathrm{\Δk}}_{i\mathrm{\ϵ}}=\frac{k_i(k_i-2)}{(1-k_i)(1+k_i)(1-2k_i)}\[\frac{\∂k_i(\mathrm{\ϵ},T_0)}{\∂\mathrm{\ϵ}}\]{|}_{\mathrm{\ϵ}=0};$

${\mathrm{\Δk}}_{j\mathrm{\ϵ}}=\frac{k_j(k_j-2)}{(1-k_j)(1+k_j)(1-2k_j)}\[\frac{\∂k_j(\mathrm{\ϵ},T_0)}{\∂\mathrm{\ϵ}}\]{|}_{\mathrm{\ϵ}=0};$

${\mathrm{\ΔA}}_{i\mathrm{\ϵ}}^{ao}=-\frac{1}{2A_i^{ao}}\[\frac{\∂A_i^{ao}(\mathrm{\ϵ},T_0)}{\∂\mathrm{\ϵ}}\]{|}_{\mathrm{\ϵ}=0};$

${\mathrm{\ΔA}}_{j\mathrm{\ϵ}}^{ao}=-\frac{1}{2A_j^{ao}}\[\frac{\∂A_j^{ao}(\mathrm{\ϵ},T_0)}{\∂\mathrm{\ϵ}}\]{|}_{\mathrm{\ϵ}=0};$

wherein n is_eff(，T₀) Is equal to room temperature T at temperature T₀Effective refractive index function with respect to strain, E_iYoung's modulus of the fiber where the ith acoustic mode is excited, E_jYoung's modulus of the fiber where the jth acoustic mode is excited, E_i(，T₀) For the ith acoustic mode at a temperature T equal to room temperature T₀Young's modulus function of time with respect to strain, E_j(，T₀) For the jth acoustic mode at a temperature T equal to room temperature T₀Young's modulus function of time with respect to strain, k_iIs the Poisson's ratio, k, of the fiber where the ith acoustic mode is excited_jIs the Poisson's ratio, k, of the fiber where the jth acoustic mode is excited_i(，T₀) For the ith acoustic mode at a temperature T equal to room temperature T₀Poisson's ratio function of time versus strain, k_j(，T₀) The jth acoustic mode is at a temperature T equal to room temperature T₀As a function of poisson's ratio with respect to strain,the acousto-optic effective area corresponding to the ith acoustic mode in the optical fiber,the acousto-optic effective area corresponding to the jth acoustic mode in the optical fiber,for the ith acoustic mode at a temperature T equal to room temperature T₀As a function of the acousto-optic effective area for strain,for the jth acoustic mode at a temperature T equal to room temperature T₀Acousto-optic effective area function with respect to strain;

step four, when the optical fiber is in a relaxed state, the temperature T is room temperature T₀And D, performing Taylor expansion on the power formula obtained in the step two, and calculating to obtain beat frequencyPower-temperature coefficient of peak (i, j) C_pT(i,j)，

$C_{pT(i,j)}={\mathrm{\Δn}}_{effT}+{\mathrm{\ΔE}}_{iT}+{\mathrm{\ΔE}}_{jT}+{\mathrm{\Δk}}_{iT}+{\mathrm{\Δk}}_{jT}+{\mathrm{\ΔA}}_{iT}^{ao}+{\mathrm{\ΔA}}_{jT}^{ao}+1/T_0;$

Wherein,

${\mathrm{\Δn}}_{effT}=\frac{5}{n_{eff}}\[\frac{\∂n_{eff}(0,T)}{\∂T}\]{|}_{T=T_0};$

${\mathrm{\ΔE}}_{iT}=-\frac{1}{2E_i}\[\frac{\∂E_i(0,T)}{\∂T}\]{|}_{T=T_0};$

${\mathrm{\ΔE}}_{jT}=-\frac{1}{2E_j}\[\frac{\∂E_j(0,T)}{\∂T}\]{|}_{T=T_0};$

${\mathrm{\Δk}}_{iT}=\frac{k_i(k_i-2)}{(1-k_i)(1+k_i)(1-2k_i)}\[\frac{\∂k_i(0,T)}{\∂T}\]{|}_{T=T_0};$

${\mathrm{\Δk}}_{jT}=\frac{k_j(k_j-2)}{(1-k_j)(1+k_j)(1-2k_j)}\[\frac{\∂k_j(0,T)}{\∂T}\]{|}_{T=T_0};$

${\mathrm{\ΔA}}_{iT}^{ao}=-\frac{1}{2A_i^{ao}}\[\frac{\∂A_i^{ao}(0,T)}{\∂T}\]{|}_{T=T_0};$

${\mathrm{\ΔA}}_{jT}^{ao}=-\frac{1}{2A_j^{ao}}\[\frac{\∂A_j^{ao}(0,T)}{\∂T}\]{|}_{T=T_0};$

wherein n is_eff(0, T) is an effective refractive index function with respect to temperature T in the relaxed state of the fiber, E_i(0, T) is a function of the Young's modulus of the ith acoustic mode in the relaxed state of the fiber with respect to temperature T, E_j(0, T) is a Young's modulus function of the jth acoustic mode in the relaxed state of the fiber with respect to temperature T, k_i(0, T) is the Poisson's ratio function of the ith acoustic mode in the relaxed state of the fiber with respect to temperature T, k_j(0, T) is a Poisson's ratio function of the jth acoustic mode in a fiber relaxed state with respect to temperature T,is an acousto-optic effective area function of the ith acoustic mode in the relaxed state of the optical fiber and with respect to the temperature T,is the acousto-optic effective area function of the jth acoustic mode in the fiber relaxed state with respect to temperature T.

2. The method of claim 1, wherein the strain is present when the fiber is at 0 in a relaxed state.

3. The method of claim 1, wherein n in step one is the same as n in step one_effIs obtained by finite element analysis.

4. The method of claim 1, wherein T is the temperature and strain sensitivity of the multimode acoustic waveguide fiber₀＝300K。

5. The method as claimed in claim 1, wherein the power formula in the second step is determined by the effective refractive index, young's modulus, poisson's ratio of the optical fiber and the acousto-optic effective area of the optical fiber, and the effective refractive index, young's modulus, poisson's ratio and the acousto-optic effective area of the optical fiber are all functions of strain and temperature.