沟道型折射率多模光纤的前向布里渊散射效应及其温度响应

张泽霖; 路元刚; 谢有文; 黄剑; 周朗; ZHANG Zelin; LU Yuangang; XIE Youwen; HUANG Jian; ZHOU Lang

Transactions of Nanjing University of Aeronautics & Astronautics

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FBS Effect and Temperature Dependence in Trench‑Assisted Multimode Fiber PDF

- ORCID：
ZHANG Zelin ^1,2
- ORCID：
LU Yuangang ^1,2
- ORCID：
XIE Youwen ^1,2
- ORCID：
HUANG Jian ^1,2
- ORCID：
ZHOU Lang ^1,2

1. Key Laboratory of Space Photoelectric Detection and Perception of Ministry of Industry and Information Technology， College of Astronautics， Nanjing University of Aeronautics and Astronautics， Nanjing 211106， P. R. China； 2. College of Science， Nanjing University of Aeronautics and Astronautics， Nanjing 211106， P. R. China

CLC： TN29

Updated：2020-12-16

DOI：http://dx.doi.org/10.16356/j.1005-1120.2020.S.012

Abstract

We propose the trench-assisted multimode fiber （TA-OM4） as a novel sensing fiber in forward Brillouin scattering （FBS）-based temperature sensor， due to its higher temperature sensitivity， better bending resistance and lower propagation loss， compared with the single mode fiber （SMF） and other sensing fibers. The FBS effect and acousto-optic interaction in TA-OM4 are the first time to be demonstrated and characterized at 1 550 nm theoretically and experimentally. A 2.0 km long TA-OM4 is put into an oven to measure its temperature sensitivity， which can reach up to 80.3 kHz/℃， exceeding 53% of SMF （52.4 kHz/℃）. The simulated and experimental results verify that the TA-OM4 may be a good candidate as the sensing fiber for the FBS-based temperature sensor.

Keywords

forward Brillouin scattering; acousto-optic interaction; optic-fiber sensor; temperature sensitivity; multimode fiber

0 Introduction

Stimulated Brillouin scattering （SBS） in optical fiber is a phenomenon caused by the interaction between a light wave and an acoustic wave， which is widely studied and employed in the field of distributed sensing^［

1-2］. Backward Brillouin scattering induces high frequency shifts around 10 GHz which can be utilized in Brillouin optical time-domain sensors and Brillouin laser. However， the forward Brillouin scattering （FBS） have much lower frequency shift of several hundreds of mega Hertz， which can be used in several applications， such as temperature sensing， opto-mechanical chemical sensors， optical frequency comb and opto-mechanical laser^{［Reference 3-6}3-6］.

Recently， the temperature sensors based on FBS have been proposed using the silica single mode fiber （SMF）， high nonlinear fiber （HNLF） and photonics crystal fiber （PCF）^［

7-9］. However， the lower temperature sensitivity of SMF may limit its measurement accuracy. Compared with SMF， although the HNLF and PCF have slightly lager temperature sensitivities， their disadvantages of bad bending resistance， high cost and large propagation loss which are 5.4 dB/km of PCF and 0.76 dB/km of HNLF， respectively， can compromise their sensing performance for future FBS-based temperature sensors in complex engineering application^{［Reference 8-9}8-9］. Fortunately， the trench-assisted multimode fiber （TA-OM4）， due to its low propagation loss （0.24 dB/km） which is similar to that of SMF （0.20 dB/km）， excellent bending resistance and high backward stimulated Brillouin scattering （BSBS） and modulation instability （MI） threshold， has been a good candidate as the sensing fiber in BSBS-based temperature sensors^{［Reference 10

Baidu Scholar}10］. However， the characteristic of FBS process in TA-OM4 at 1 550 nm and its applications in FBS-based temperature sensors have not been reported.

In this paper， we theoretically and experimentally investigate the acousto-optic interaction caused by FBS and FBS spectrum in TA-OM4. Furthermore， we have found that the largest strain coefficient in TA-OM4 is about 4.0 kHz/με， which is so small that the frequency shift of FBS is not sensitive to make acceptable strain measurement. Therefore， we only focus on its temperature dependence of FBS in this paper. Compared with the temperature response of FBS in SMF， we experimentally measure the FBS temperature response of TA-OM4. The highest temperature dependence of TA-OM4 is linear with a coefficient of 80.3 kHz/℃， which is 53% larger than that of SMF （52.4 kHz/℃）. The simulated and experimental results show that the TA-OM4 may be a good candidate as the sensing fiber in FBS-based temperature sensors.

1 FBS Resonances in TA‑OM4

1.1 Theoretical description of FBS in optical fiber

The acoustic modes responsible for FBS are radial dilatational modes （R_0，_m） and mixed torsional-radial modes （TR_2，_m）. The FBS is a typical opto-acoustic interaction， which can be described as the coupling amplitude equations between optical field E （r， z， t） and acoustic wave for the displacement vector U （r， z， t） ^［

11］

\frac{\partial^{2} E}{\partial z^{2}} - \frac{n_{e f f}^{2}}{c^{2}} \frac{\partial^{2} E}{\partial t^{2}} = \frac{1}{ε_{0} c^{2}} \frac{\partial^{2} P^{N L}}{\partial t^{2}}

(1)

\frac{\partial^{2} U}{\partial z^{2}} + Γ \frac{\partial U}{\partial t} + {V_{s}}^{2} \nabla \times (\nabla \times U) - {V_{l}}^{2} \nabla (\nabla \cdot U) = \frac{F}{ρ_{0}}

(2)

where P^NL is the total nonlinear polarization， c the light velocity in vacuum， n_eff the effective refractive index， ε₀ the vacuum permittivity， V_l the longitudinal acoustic velocity of the fiber， ρ₀ the density of fused silica， V_s shear sound velocity of the fiber， and Γ the acoustic damping parameter. $F = ε_{0} [1 / 2 γ_{12} \nabla (E \cdot E) + γ_{44} (E \cdot \nabla) E]$ is the electrostrictive driving term， and γ₁₂ and γ₄₄ are both the elements of the electrostrictive tensor for fused silica. By employing the finite element analysis （FEA） method and solving Eq.（1）， we obtain the optical field E（r）. Moreover， by solving Eq.（2） with the appropriate boundary conditions， we difine the normalized displacement distribution U_m（r） in terms of Bessel functions J_n（z）， where n is the order of Bessel functions. By using $ρ_{m} (r) = - ρ_{0} \nabla U_{m} (r)$ ， we obtain the density vibration caused by FBS.

For the radial dilatational R_0，_m modes， the boundary condition corresponding to the free fiber surface can be written as

(1 - α^{2}) J_{0} (y) - α^{2} J_{2} (y) = 0

(3)

where α is the ratio between shear sound velocity and longitudinal acoustic velocity， and y_m the mth zero of Eq.（3）. Furthermore， the central frequency of the mth acoustic mode can be expressed as

f_{m} = \frac{y_{m} V_{l}}{π d}

(4)

where d is the cladding diameter of optical fiber.

Similar to the Kerr effect in fiber， the opto-mechanical coefficient can be used to quantify the opto-acoustic interaction caused by FBS， which can be expressed as^［

6，12-13］

γ_{O M}^{(m)} = \frac{k_{0}}{2 π n_{n e f f}^{2} c ρ_{0}} \frac{Q_{E}^{(m)} Q_{p}^{(m)}}{Γ_{m} f_{m}}

(5)

where Γ_m is the linewidth of the mth resonant peak induced by FBS. The $Q_{E}^{(m)}$ and $Q_{p}^{(m)}$ are the electrostrictive overlap and photo-elastic overlap， which determines the efficiency of stimulation of acoustic modes and describes the modification of the effective index by acoustic modes^［

13-14］， respectively. By solving Eqs.（1）—（5）， the acoustic field distribution and FBS resonances can be obtained next.

1.2 Simulation and FBS spectrum in TA‑OM4

For TA-OM4， the diameters of the fiber core and cladding are 50 and 125 μm， respectively. The refractive index profile is given in Fig.1. The refractive index profile shows a quasi-quadratic distribution in the central region and has a trench-index profile around the fiber core^［

10］. The three highest linear polarization （LP） modes are respectively LP₀₁， LP₁₁ and LP₂₁， and the corresponding intensity ratio of these three LP modes I₀₁∶I₁₁∶I₂₁， is 1∶0.14∶0.006. Considering the highest intensity ratio of LP₀₁， the tiny coupling efficiency between LP₀₁ and other high-order modes and the single mode condition of most optical components^{［Reference 15

Baidu Scholar}15］， it is enough to investigate the FBS process of TA-OM4 corresponding to the fundamental mode LP_01.

Fig.1 Refractive index profile of TA-OM4 and calculated three LP optical modes with the highest intensity

By solving Eqs.（1）and（2）， three excited acoustic modes are found and displayed in Fig.2. As it shown in Fig.2（a）， taking R_0，4 mode as an example， the R_0，_m modes are the radial dilatational modes， which have the most efficient scattering efficiency and are independent of angular coordinate φ. Especially， the R_0，_mmodes can induce refractive index changes so that the pure phase modulation will be also induced. Other acoustic modes are TR_2，_m acoustic modes， which are the mixed torsional-radial modes. As it shown in Figs.2（b）and（c）， different from R_0，_m modes， the TR_2，_m modes are doubly degenerated， which vary sinusoidally with angular coordinate 2φ. Furthermore， the scattering efficiency of TR_2，_m modes is much lower than that of R_0，_m modes. For the TR_2，_m （90°/0°） mode， its induced birefringent axes are parallel to the birefringent axes of TA-OM4， which does not induce the depolarized scattering but the polarized scattering and also cause pure phase modulation. For the TR_2，_m （45°/ $-$ 45°） mode， the mode pattern is rotated by 45°. In this case pure phase modulation will not occur， and the depolarized scattering is induced^［

16］.

Fig.2 Normalized transverse profile of acoustic modes excited by LP₀₁ optical mode in TA-OM4

Generally， the overlap between optical modes and acoustic modes determines the shape of FBS resonances. Taking four acoustic modes （R_0，1 to R_0，4） as examples， the 2D mode profiles of longitudinal optical fundamental mode LP₀₁ and four acoustic modes are displayed in Fig.3.

Fig.3 2-D profiles of optical mode LP₀₁ and acoustic modes R_0,1 to R_0,4

In order to experimentally investigate the FBS process in TA-OM4， we also measure the FBS spectrum by using a coherent detection， which is shown in Fig.4. The light source （NKT Photonics） is a 1 550 nm single-wavelength semiconductor laser with linewidth 5 kHz. The pump light propagating through the isolator （ISO） is split into two branches by a 50/50 coupler. The upper branch used as the pump light is amplified by an erbium-doped fiber amplifier （EDFA， Amonics）. A narrow bandpass filter （BPF， AOS Photonics） with 3.5 GHz bandwidth is used to eliminate the amplified spontaneous emission （ASE） noise induced by EDFA. A variable attenuator （VA） is utilized to adjust the input power level to protect fiber components. The pump light is launched into 2.0 km long TA-OM4 （YOFC） to obtain the FBS signal which beats with the reference light. Finally， a 1.6 GHz bandwidth photodetector （PD， Thorlabs PDB480） is utilized to detect the beat signal， which is analyzed by an electrical spectrum analyzer （ESA， Tektronix RSA5126B） and used to obtain the FBS spectrum.

Fig.4 Experimental setup of measuring the FBS spectrum of TA-OM4

In our experiment， the incident light power is 11.2 mW. The measured FBS spectrum is shown in Fig.5. The measured FBS spectrum includes two parts. One part is from the R_0，_m modes and the other is from the TR_2，_m modes. However， due to the random change of polarization states along the TA-OM4， the FBS intensities induced by TR_2，_m modes are much lower than those of R_0，_m modes. As it shown in Fig.5， we can find that the fourth resonant peak with the highest intensity locates at 173.1 MHz. By solving Eq.（5）， we obtain the calculated opto-mechanical coefficient of R_0，4 mode as 5.25 （W∙km）^-1， which is slightly higher than that of SMF 5 （W∙km）^-1［

6］. In Fig.6， two adjacent resonant peaks generated by R_0，_m modes have equivalent frequency interval of 47.5 MHz， which can be verified by solving Eq.（4）. It is obvious that， whatever resonant peaks intensity and frequency shift， the calculated and experimental results are in good agreement. The largest difference of normalized intensity between calculated and experimental results are less than 5%， which are from the error of the estimated fiber parameters.

Fig.5 The measured FBS spectrum of TA-OM4

Fig.6 Measured (green) and calculated (red) normalized FBS resonant intensity in TA-OM4 induced by R_0,_m modes

2 Temperature Response in TA‑OM4

In order to evaluate whether the TA-OM4 can be used as the novel sensing fiber in FBS-based temperature sensors， we put both TA-OM4 and SMF into an oven to measure their temperature sensitivities of R_0，_m modes， and results are shown in Fig.7. Seven different temperatures between $-$ 10 ℃ to 50 ℃ are measured with a temperatures step of 10 ℃. It is obvious that the temperature sensitivities increase linearly with an increase in m value of R_0，_m modes， whose trends are in accordance with that in Ref.［

17］. The observed temperature coefficient of R_0，12 in TA-OM4 can reach 80.3 kHz/℃， which is 53% larger than that of SMF （52.4 kHz/℃）.

Fig.7 Measured temperature sensitivities of TA-OM4 and SMF versus different R_0,_m modes， respectively

Furthermore， we also obtain the temperature sensitivities of spectral peaks corresponding to R_0，4 （f₄=173.1 MHz） mode in TA-OM4 and R_0，5 （f₅=222.9 MHz） mode in SMF， which exhibit the highest resonance intensity of all peaks. In Fig.8， the calibration temperature coefficient of TA-OM4 （ $α_{T A ⁃ O M 4}$ ） can reach 31.9 kHz/℃， which is much 41% larger than that of SMF （ $α_{S M F} =$ 22.6 kHz/℃）.

Fig.8 Temperature sensitivities of R_0,4 mode in TA-OM4 and R_0,5 mode in SMF

3 Conclusions

FBS processes in TA-OM4 are theoretically and experimentally investigated and the acousto-optic interaction of TA-OM4 at 1 550 nm are characterized and demonstrated. We experimentally measure the FBS spectrum， which is in good agreement with simulated results. The temperature sensitivities of R_0，_m modes in TA-OM4 are also measured， which exceed 40% of SMF. The calculated and experimental results demonstrate that the TA-OM4 could be a good sensing fiber in FBS-based temperature sensors， with advantages of high temperature sensitivity， good bending resistance and low propagation loss.

Contributions Statement

Mr. ZHANG Zelin contributed to simulation by doing experiment and writing the manuscript. Prof. LU Yuangang designed and guided the study， and gave key opinions on the core issues. Mr. XIE Youwen and Mr.HUANG Jian conducted some related works about the experiments. Ms. ZHOU Lang conducted some related works about the simulation.

Acknowledgements

This work was supported in part by the National Natural Foundation of China （Nos.61875086， 61377086）， the Aerospace Science Foundation of China （No.2016ZD52042）， and Nanjing University of Aeronautics and Astronautics Ph.D. short-term visiting scholar project （No.190901DF08）.

Conflict of Interest

The author declare no competing interests.

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