https://orcid.org/0000-0002-4331-9236
Figures
Abstract
This study investigates temperature sensing based on slow light generation via stimulated Brillouin scattering in an M-shaped few-mode fiber. The temperature-dependent properties of four optical modes (LP01, LP11, LP21, and LP02) over a range from –20 °C to 80 °C are analyzed using the full-vectorial finite element method. Results show that the effective refractive index and Brillouin frequency shift of all modes increase with temperature, while the effective mode areas of all modes decrease. The LP02 mode exhibits exceptional temperature sensitivity, showing a significant rise in slow light time delay from 0 ns to 514.9 ns, along with a growth in the pulse broadening factor. In contrast, the LP01 mode maintains the largest time delay across the temperature range but shows less temperature-induced variation. The results demonstrate a trade-off between slow light enhancement (time delay) and signal distortion (pulse broadening). This study confirms that the LP02 mode in the M-shaped few-mode fiber is highly suitable for developing sensitive fiber-optic temperature sensors, providing a theoretical foundation for optimizing slow light applications in sensing.
Citation: Li L-J, Hou S-L (2026) Temperature sensing based on slow light via stimulated Brillouin scattering in M-shaped few-mode fiber. PLoS One 21(2): e0342177. https://doi.org/10.1371/journal.pone.0342177
Editor: Amit Kumar Goyal, Manipal Academy of Higher Education, INDIA
Received: October 31, 2025; Accepted: January 19, 2026; Published: February 13, 2026
Copyright: © 2026 Li, Hou. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All relevant data are within the manuscript and its Supporting Information files.
Funding: The funders (National Natural Science Foundation of China (No. 61665005), Provincial Special Scientific Research of Department of Education of Shaanxi (No. 23JK0423), and Science and Technology Research Program of Shangluo University (No. 23SKY033)) provided financial support only. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
1. Introduction
Driven by breakneck AI progress and an explosion in computing needs—including soaring demand for massive-scale computing clusters—the backbone network, as the foundational communications infrastructure, demands a significant expansion in bandwidth capacity [1–3]. Space Division Multiplexing (SDM), a pivotal innovation, transcends the limitations of traditional optical fibers, offering a potent solution for substantially boosting the capacity of transmission systems [4–6]. Among the various SDM approaches, M-shaped few-mode fibers (M-FMFs) have attracted significant research interest due to their potential for high-capacity, weakly-coupled mode-division multiplexing transmission, which positions them as a key focus in next-generation optical communication research.
Slow light is a physical phenomenon in which the group velocity of light is significantly reduced as it propagates through specific media [7,8]. This effect has found important applications in fields such as optical communication and optical fiber sensing. Several methods have been developed to generate slow light, including optical parametric amplification (OPA) [9], stimulated Brillouin scattering (SBS) [10], and stimulated Raman scattering (SRS) [11]. Among these, SBS has proven to be a particularly effective technique, owing to advantages such as a widely tunable wavelength range, relatively simple system requirements, and excellent compatibility with standard communication systems [12].
Stimulated Brillouin scattering is one of the major nonlinear effects induced by the interaction between light waves and acoustic waves [13]. When light propagates through a fiber, acoustic waves are excited by the electrostriction force induced by pump light and a fraction of the acoustic-waves-backscattered light which undergoes a frequency downshift (Stokes) or upshift (anti-Stokes). While extensively studied in single-mode fibers (SMFs), research on SBS-based slow light in few-mode fibers (FMFs) is comparatively less developed [14,15]. In FMFs, the Brillouin gain spectrum (BGS) reveals greater complexity due to multimodal interactions, wherein intramodal SBS typically dominates over intermodal processes [16]. This unique characteristic has spurred significant interest in utilizing FMFs for advanced Brillouin sensing applications, such as multi-parameter detection [17–20] and high-precision temperature measurement [21–23]. However, most prior work has focused on experimental BGS characterization or sensor demonstration. A systematic and parametric understanding of how temperature influences fundamental fiber properties—such as the effective mode area and modal refractive indices—within a specific FMF geometry remains elusive. Consequently, the quantitative relationship between these temperature-dependent parameters and key slow light performance metrics, including time delay and Brillouin threshold, remains largely unexplored. This knowledge gap consequently obstructs the rational design and performance optimization of FMF-based slow-light devices and sensors.
To bridge this knowledge gap, this work presents a foundational and comparative theoretical investigation into the temperature-dependent parametric properties of an M-FMF for SBS slow light generation. We develop an analytical model to quantify how variations in temperature affect key fiber parameters, such as the effective refractive index and effective mode area, and how these changes consequently govern the slow light performance for the supported LP01, LP11, LP21, and LP02 modes. The core objective is to establish a detailed parametric framework that elucidates the underlying physical dependencies specific to the M-FMF geometry. The findings aim to provide critical insights and a solid theoretical foundation for the future design and performance optimization of M-FMF-based slow light devices and high-sensitivity temperature sensors.
2. Theoretical analysis
Suppose the pump light is copolarized with the signal light, the three-wave coupled equations in the M-FMF are indicated as follows [24,25] (Critical parameters, including the Brillouin linewidth and acoustic damping, are treated as fixed; pump depletion is neglected. These simplifications, while necessary for this comparative study, mean the presented time delays represent intrinsic upper bounds under ideal gain conditions. Quantitative system-level predictions will require future models that incorporate these dynamic parameters).
where ,
, and
are described as [26,27]
,
, and
, here
,
, and
are the amplitudes of the i-th pump wave, the j-th Stokes wave and the k-th acoustic wave, respectively.
is the group index without SBS,
is light velocity in vacuum,
is loss coefficient of fiber,
is the full-width at half maximum bandwidth (FWHM) of Brillouin resonance,
is the detuning of angular frequency,
and
are the coupling coefficients of pump-Stokes and acousto-optic wave, separately.
The acoustic field is treated within an effective medium approximation. A detailed analysis of acoustic mode confinement and its temperature-dependent loss, while important for exact quantitative predictions, is beyond the scope of this comparative study focused on relative optical-mode sensitivity. The Brillouin frequency shift (BFS) of the k-th acoustic mode for an optical mode pair is expressed as [27]
Where is the effective index of the i-th optical mode,
is the velocity,
is propagation constant of the k-th acoustic wave.
The SBS effect happens when the input power is higher than Brillouin threshold, which is represented as [28]
where is the effective length of M-FMF,
is the real length,
is the effective mode area in which the SBS effect occurs, and it is given by [29]
Here and
are the electric-field distributions of the j-th Stokes and i-th pump wave, separately.
The difference between the transmitting time of a pulse without and with SBS is defined as time delay, which is taken the form [24]
where is Brillouin gain,
is the pump power,
is Brillouin gain coefficient,
, here
,
is FWHM which is assumed to be 35MHz [27],
is the photo-elastic coefficient,
represents the overlap integral and is given by
. The modal distributions of both optical mode and acoustic mode determine the value of overlap integral which reflects the SBS efficiency.
The pulse broadening factor is expressed as [24]
and
denote the pulse width of input and output Gaussian signals, respectively. Eq. (6) indicates that pulse broadening factor is greater than unity.
In the simulation, the variations of the refractive index and acoustic velocity of M-FMF with the temperature are indicated as follows [30,31]
Where is the change of temperature, and the room temperature is 20 °C.
is the doping concentration of GeO2 in the core.
3. Resluts and analysis
3.1. Mode distribution
A FMF with an M-shaped core refractive index profile is proposed for investigating the generation of SBS-based tunable slow light. Fig 1 illustrates the cross-sectional structure of the proposed M-FMF. The radius of the first and second core layers is 4 μm and 6 μm, respectively, with corresponding refractive indices of 1.454 and 1.4557 at 20 °C (at the wavelength of 1550 nm). The refractive index of the cladding is 1.444 under the same condition. Due to the fiber structure, only the LP01, LP11, LP21, and LP02 modes are supported in the proposed fiber and the other modes are cut off. In our simulation, only intramodal SBS and the changes caused by the peak value of the Brillouin main gain of each mode are taken into account.
The electric-field distributions of the four optical modes in the M-FMF at temperatures of 20 °C and 80 °C are depicted in Fig 2. It can be seen that the light of the four optical modes is mainly concentrated in the core region. Moreover, at 80 °C, the optical field distributions of the four modes are significantly reduced compared to those at 20°C. This demonstrates that the confinement of light within the optical fiber core is enhanced. At identical temperatures, the fundamental optical mode LP01 depicted in Figs 2(a) and (e) exhibits the tightest confinement to the M-FMF core, followed by the LP11 mode (Figs 2(b) and (f)), and the LP21 mode (Figs 2(c) and (g)), while the LP02 mode (Figs 2(d) and (h)) demonstrates the weakest confinement.
3.2. Effective mode area
The systematic analysis presented above reveals the fundamental thermo-optic governing principles behind the slow light performance in the proposed M-FMF. The core mechanism, as established in Eq. (7), is the temperature-induced increase in the material refractive index, which elevates both the core refractive index and the core-cladding index contrast. This directly leads to the observed increase in the effective refractive index for all supported modes (LP01, LP11, LP21, and LP02) within the –20 °C to 80 °C range, as shown in Fig 3(a). Notably, at any given temperature, the effective refractive index
decreases in the order of LP01, LP11, LP21, and LP02. This hierarchy is intrinsically linked to the mode field distribution and confinement. A more critical consequence of this enhanced index contrast is the significant reduction in the effective mode area
with rising temperature, as evidenced in Fig 3(b). The strengthened fiber confinement compresses the optical field more tightly within the core. It is particularly noteworthy that the higher-order LP02 mode exhibits a dramatically larger variation in effective mode area (from 700.1 μm2 to 90.7 μm2) compared to the fundamental and lower-order modes. This distinct behavior stems from its field profile being more susceptible to changes in the waveguide boundary conditions imposed by the thermo-optic effect.
These parametric changes—increased and decreased
—have a direct and profound impact on the SBS slow light characteristics. According to SBS theory, the Brillouin gain is inversely proportional to
. Therefore, the substantial reduction in
, especially for the LP02 mode, leads to a markedly enhanced SBS process. This is conclusively demonstrated in Fig 7 of Section 3.6, where the time delay and pulse broadening factor for the LP02 (and LP21) mode increase actively with temperature, while those for the LP01 and LP11 modes show a slight decrease. The LP01 mode maintains the largest time delay across the temperature range, indicating its SBS effect remains the strongest, consistent with its smallest
and highest
.
3.3. Brillouin gain spectrum
Fig 4 shows the Brillouin gain spectra of different modes in the M-FMF. This illustration demonstrates the temperature-dependent Brillouin frequency shift and the concurrent appearance of the Brillouin gain peak. Notably, it is found that BFS values of the four modes increase within the temperature range from –20 °C to 80 °C. Table 1 lists the specific BFS values obtained under different temperatures. This behavior arises because the BFS depends on both the effective refractive index and the effective acoustic velocity of the mode. As the temperature increases, the effective acoustic velocity gradually rises, thereby leading to an increase in the BFS. This temperature-induced shift in the BFS directly modifies the Brillouin gain spectrum, as quantitatively shown in Fig 4. Consequently, the alteration of the gain spectrum profile changes the steep dispersion slope experienced by a probe signal tuned near the gain peak, which is the fundamental mechanism for generating slow light. Therefore, the change in BFS ultimately governs the temperature-dependent tunability of the slow light time delay. The simulated results of this direct impact—the variation of slow light time delay with temperature—are explicitly presented and analyzed in Fig 7(a) of Section 3.6.
The Brillouin gain peak of the LP02 mode increases with temperature, indicating that its SBS effect in the FMF is strengthened as temperature rises, in contrast, the LP01, LP11, and LP21 modes exhibit opposite temperature-dependent trends. Under identical conditions, among these three modes, the LP01 mode shows the highest Brillouin gain peak intensity, followed by LP11, with LP21 displaying the lowest value. When the temperature increases from –20 °C to 80 °C, the Brillouin gain peak of the LP01 (LP11, LP21) mode decreases from 1.812 × 10-11 m/W (1.068 × 10-11 m/W, 8.516 × 10-12 m/W) to 1.621 × 10-11 m/W (8.676 × 10-12 m/W, 7.356 × 10-12 m/W), that of the LP11 mode decreases from 1.068 × 10-11 m/W to 8.676 × 10-12 m/W, and that of LP21 mode decreases from 8.516 × 10-12 m/W to 7.356 × 10-12 m/W, while the LP02 mode increases from 7.90 × 10-12 m/W to 1.026 × 10-11 m/W. The average changes in Brillouin gain peak for the LP01, LP11, LP21, and LP02 modes are respectively 1.91 × 10-12 m/W, 2.004 × 10-12 m/W, 1.16 × 10-12 m/W, and 2.36 × 10-12 m/W, with the LP02 mode exhibits the largest variation. This indicates that the LP02 mode demonstrates greater sensitivity to temperature changes compared to other modes.
3.4. Overlap integral
In the process of SBS in the M-FMF, the acousto-optic overlap integral is related to the coupled acoustic mode and optical mode. Fig 5 shows temperature-dependence curves of the acousto-optic overlap integral of different modes in the FMF. We observe that the overlap integrals of the LP01, LP11, and LP21 modes decrease with increasing temperature, which can be explained by the weakened ability of the fiber core to confine light, due to special structure of the M-type optical fiber. However, the LP02 mode exhibits opposite characteristic. The LP02 mode exhibits a markedly different temperature-dependent trend in coupling efficiency, SBS threshold, and slow light parameters compared to the LP01 and LP11 modes. This is attributed to its unique higher-order field structure, characterized by a ring-shaped intensity profile. This profile results in a distinct overlap with the acoustic phonon field and makes its effective mode area particularly sensitive to temperature-induced alterations in the M-FMF’s refractive index profile. Consequently, the SBS gain and the resulting nonlinear phase shift for the LP02 mode show a stronger and non-monotonic dependence on temperature, as reflected in its time delay and broadening factor. When the temperature increases from –20 °C to 80 °C, the coupling integral of the LP01 mode decreases from 0.897 to 0.819, that of the LP11 mode decreases from 0.536 to 0.445, and that of the LP21 mode decreases from 0.436 to 0.385, while the LP02 mode increases from 0.406 to 0.542.
3.5. Brillouin threshold
The Brillouin properties of the spatial modes in the M-FMF differ slightly, and the simulation results based on Equation (3) are presented in Fig 6, showing the Brillouin threshold for each mode at varying temperatures. Fig 6 shows that the Brillouin threshold of the LP02 mode decreases with temperature, particularly exhibiting a significant drop between –20 °C and 20 °C. In contrast, the Brillouin thresholds of the LP01, LP11, and LP21 modes change minimally with temperature. The reduction in effective mode area and the enhancement of the SBS effect lead to a decrease in the Brillouin threshold required for SBS occurrence. Furthermore, over the entire temperature range of –20 °C to 80 °C, the LP01 mode has the smallest Brillouin threshold, indicating that it is the most prone to the SBS effect among the four modes. Specifically, within –20 °C to 5 °C, the LP02 mode has the largest Brillouin threshold, followed by the LP21 and LP11 modes. Within 5 °C to 80 °C, the LP21 mode exhibits the highest threshold. As the temperature increases from –20 °C to 80 °C, the Brillouin threshold of the LP02 mode decreases from 930.5 mW to 92.7 mW, and that of LP21 mode decreases from 228.6 mW to 198.3 mW, while the LP01 mode increases from 57.8 mW to 61.7 mW and the LP11 mode increases from 135.7 mW to 150.0 mW. The average variation of Brillouin threshold for the LP02 mode is the largest among the four modes, reaching 701.9 mW. This indicates that the LP02 mode is more sensitive to temperature variations, which is consistent with the conclusion in Section 3.3.
3.6. Time delay of slow light
The temperature-dependent slow light characteristics presented in Fig 7 reveal a distinct, mode-selective behavior within the M-FMF, which forms the core of our parametric study. From Fig 7(a-b), a key finding is the divergent response between mode groups: the time delay and pulse broadening factor for the higher-order LP02 (and LP21) modes increase significantly with temperature, whereas those for the fundamental LP01 and lower-order LP11 modes exhibit a moderate decrease. This fundamental divergence can be directly traced to the thermo-optic effect governing the fiber properties, as established earlier. The rising temperature increases the core-cladding refractive index contrast, which more strongly confines the optical field of higher-order modes (evidenced by their drastically reduced in Fig 3(b)), thereby enhancing their SBS gain and consequent slow light effect. Conversely, the more stable confinement of the fundamental LP01 mode leads to its consistently dominant, yet slightly decreasing, SBS interaction across the temperature range.
This study provides a complementary perspective by quantitatively investigating the temperature-dependent evolution of key properties for the LP02 and other supported modes, and establishing how this evolution governs their SBS time delay—a direct performance metric for slow light-based sensors. The observed switch in the mode exhibiting the minimum time delay (from LP02 below 5°C to LP21 above 5°C) highlights the intricate and temperature-dependent relationship between modal confinement strength and SBS efficiency. The LP02 mode, with its pronounced temperature sensitivity (exhibiting a time delay change from 0 ns to 514.9 ns), is identified as a prime candidate for high-sensitivity temperature sensing. This marked response suggests the potential for achieving very high thermal resolution in sensor applications. Conversely, the relatively stable LP01 and LP11 modes (LP01 time delay change from 825.7 ns to 774.0 ns) are well-suited to act as stable reference channels in a multi-parameter sensor. Their low thermal sensitivity can be leveraged to compensate for common-mode noise or to measure other parameters, such as strain, with minimized thermal cross-sensitivity. Most importantly, the opposing temperature-dependent trends between the LP01/LP11 and LP02/LP21 mode groups inherently enable a differential or ratio metric sensing scheme. This approach can effectively isolate the temperature signal from other interfering perturbations, thereby enhancing measurement accuracy and enabling robust multi-parameter discrimination.
The sensitivity of the time delay to temperature (at 80 °C) for different pump power is shown in Fig 7(c). As can be seen, the time delay varies linearly with pump power. As mentioned above, compared with the LP11 and LP21 modes, the LP02 mode exhibits superior sensitivity. At a pump power of 0.3W, the sensitivities are 5.805 ns/°C for LP01, 2.388 ns/°C for LP11, 1.805 ns/°C for LP21, and 3.862 ns/°C for LP02. At 1 W, they increase to 19.350 ns/°C for LP01, 7.960 ns/°C for LP11, 6.018 ns/°C for LP21, 12.873 ns/°C for LP02, respectively. These results indicate that the time delay sensitivity can be effectively enhanced by increasing the pump power.
Within the framework of this foundational theoretical investigation, it is crucial to appropriately contextualize the presented performance metrics. Our analysis, based on numerical simulations under idealized conditions, establishes the theoretical upper bounds for intrinsic material and waveguide responses—such as the maximum achievable time delay (514.9 ns for the LP02 mode) and its intrinsic temperature sensitivity (12.873 ns/°C at 1 W of pump power). These parameters define the fundamental physical limits imposed by the M-FMF design; they are essential prerequisites for, yet distinct from, final system-level benchmarks. While indicators like the delay-bandwidth product (which is more pertinent to communication buffers than to the quasi-static sensing targeted here), signal-to-noise ratio, and ultimate sensing resolution are vital for evaluating a complete sensor system, their rigorous quantification inherently lies beyond the primary scope of this work. Such practical metrics are highly system-dependent, being influenced by experimental implementation details—including laser noise, detection electronics, and environmental shielding—as well as by challenges such as long-term stability and cross-sensitivity to strain or other perturbations. Consequently, a comprehensive evaluation of these practical benchmarks constitutes the logical and essential next step. This will be pursued through the construction and characterization of an experimental prototype based on the design principles elucidated here (e.g., utilizing the highly sensitive LP02 mode or a differential sensing scheme), with the primary goal of validating the practical potential of M-FMF-based slow-light temperature sensing.
3.7. Output wave
The variations in the output signal waves for the four modes at a wavelength of 1550 nm as a function of temperature are depicted in Fig 8. In this figure, a noticeable time delay and broadening of the output signals are observed compared to the input signal wave, which has an input pulse width of 200 ns. As shown, the output waves of all four modes exhibit varying degrees of broadening, and the time delay varies significantly with temperature, particularly for the LP02 mode. This indicates that LP02 mode is more sensitive to temperature variations, which agrees with the conclusion in Section 3.6. Simulation results show that the pulse broadening factor increases with the time delay. Additionally, time delay is consistently associated with pulse distortion, implying that any increase in time delay degrades pulse quality due to greater distortion.
4. Conclusion
This study investigates temperature sensing characteristics based on slow light generation via SBS in the M-FMF. Through theoretical analysis and numerical simulations, we examine how temperature variations affect the effective mode area, Brillouin gain spectrum, overlap integral, and slow light time delay for four modes: LP01, LP11, LP21, and LP02. The results reveal that as the temperature increases, the slow light time delay of the LP02 mode increases significantly, along with an increase in the pulse broadening factor, indicating its high sensitivity to temperature. In contrast, the LP01 mode exhibits the largest time delay and the strongest slow light performance throughout the tested temperature range. This work provides foundational insights by establishing a comparative theoretical framework. It identifies the LP02 mode as the most promising candidate for sensing due to its superior overlap integral and thermo-optic response, thereby laying a necessary theoretical foundation for practical M-FMF temperature sensors. The logical next steps are to build an experimental prototype for validation and to develop more comprehensive models that incorporate dynamic effects, such as pump depletion and temperature-dependent acoustic damping, to enable precise system-level prediction.
Supporting information
S1 Data. Raw datasets.
The Excel files contain the raw data analyzed in the manuscript.
https://doi.org/10.1371/journal.pone.0342177.s001
(XLSX)
References
- 1. Lu X. Space division multiplexing technology: Principles, applications, and future prospects. AEI. 2025;16(3):6–11.
- 2. Tu J, Li C. Review of Space Division Multiplexing Fibers. Acta Optics Sinca. 2021;41(1):0106003.
- 3. Fang J, Hu J, Zhong Y, Kong A, Ren J, Wei S, et al. 3D waveguide device for few-mode multi-core fiber optical communications. Photon Res. 2022;10(12):2677.
- 4. Richardson DJ, Fini JM, Nelson LE. Space-division multiplexing in optical fibres. Nature Photon. 2013;7(5):354–62.
- 5. Pei L, Wang J, Zheng J, Ning T, Xie Y, He Q, et al. Research on specialty and application of space-division multiplexing fiber. Infrared and Laser Engineering. 2018; 47(10): 42–53.
- 6. Zhao Y, Ning Y, Zhao Z, Yu X, Zhang J. Key technologies of multi-dimensional multiplexed optical network. Optical Communication Technology. 2020;44(10):1–5.
- 7. Hau LV, Harris SE, Dutton Z, Behroozi CH. Light speed reduction to 17 metres per second in an ultracold atomic gas. Nature. 1999;397(6720):594–8.
- 8. Kash MM, Sautenkov VA, Zibrov AS, Hollberg L, Welch GR, Lukin MD, et al. Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas. Phys Rev Lett. 1999;82(26):5229–32.
- 9. Dahan D, Eisenstein G. Tunable all optical delay via slow and fast light propagation in a Raman assisted fiber optical parametric amplifier: A route to all optical buffering. Opt Express. 2005;13(16):6234–49. pmid:19498636
- 10. Ippen EP, Stolen RH. Stimulated Brillouin scattering in optical fibers. Applied Physics Letters. 1972;21(11):539–41.
- 11. Sharping J, Okawachi Y, Gaeta A. Wide bandwidth slow light using a Raman fiber amplifier. Opt Express. 2005;13(16):6092–8. pmid:19498618
- 12. Zhang L, Zhan L, Qian K, Liu J, Shen Q, Hu X, et al. Superluminal propagation at negative group velocity in optical fibers based on Brillouin lasing oscillation. Phys Rev Lett. 2011;107(9):093903. pmid:21929244
- 13. Li A, Hu Q, Shieh W. Characterization of stimulated Brillouin scattering in a circular-core two-mode fiber using optical time-domain analysis. Opt Express. 2013;21(26):31894–906. pmid:24514785
- 14. Song KY, Kim YH. Characterization of stimulated Brillouin scattering in a few-mode fiber. Opt Lett. 2013;38(22):4841–4. pmid:24322146
- 15. Song KY, Kim YH, Kim BY. Intermodal stimulated Brillouin scattering in two-mode fibers. Opt Lett. 2013;38(11):1805–7. pmid:23722750
- 16. Srinivasan B, Agrawal GP, Venkitesh D. Role of the modal composition of pump in the multi-peak Brillouin gain spectrum in a few-mode fiber. Optics Communications. 2021;494:127052.
- 17. Guo Y, Liu Y, Wang Z, Yao Z. Dual resonance and dual-parameter sensor of few-mode fiber long period grating. Acta Optica Sinca. 2018; 38(09): 87–92.
- 18. Li X-J, Cao M, Tang M, Mi Y-A, Tao H, Gu H, et al. Inter-mode stimulated Brillouin scattering and simultaneous temperature and strain sensing in M-shaped few-mode fiber. Acta Phys Sin. 2020;69(11):114203.
- 19. Li Y, Lu X, Su Y, Zhou D, Ren F. A spatial-division multiplexed multi-parameter Brillouin sensor based on an etched weakly-coupled few-mode heterogeneous multi-core fiber. Sensor Review. 2025;45(6):885–97.
- 20. Li Y, Ren F, Zhou D. Simultaneous temperature and strain sensing in a weakly-coupled polarization-maintaining few-mode fiber based on the intramodal SBS. SR. 2025;45(3):348–58.
- 21. Jing Z, Yongqian L. Temperature sensing characteristics based on coreless- few mode-coreless optical fiber structure. Journal of Applied Optics. 2022;43(1):167–70.
- 22. Yang L, Wang X, Wu T, Lin H, Luo S, Chen Z, et al. Deep learning-based multimode fiber distributed temperature sensing. Sensors (Basel). 2025;25(9):2811. pmid:40363250
- 23. Zhang X, Cao H, He J, Wang L, Li Y, Kang J, et al. Optical fiber multimode interference sensors using spatial multiplexing. Optics Communications. 2025;577:131383.
- 24. Zhu Z, Gauthier DJ, Okawachi Y, Sharping JE, Gaeta AL, Boyd RW, et al. Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber. J Opt Soc Am B. 2005;22(11):2378.
- 25. Damzen MJ, Vlad V, Mocofanescu A, Babin V. Stimulated Brillouin Scattering. CRC Press. 2003.
- 26. Wei-Wei Ke, Xiao-Jun Wang, Xuan Tang. Stimulated Brillouin Scattering Model in Multi-Mode Fiber Lasers. IEEE J Select Topics Quantum Electron. 2014;20(5):305–14.
- 27. Minardo A, Bernini R, Zeni L. Experimental and numerical study on stimulated Brillouin scattering in a graded-index multimode fiber. Opt Express. 2014;22(14):17480–9. pmid:25090563
- 28. Lambin Iezzi V, Loranger S, Harhira A, Kashyap R, Saad M, Gomes A, et al. Stimulated Brillouin scattering in multi-mode fiber for sensing applications. 2011 7th International Workshop on Fibre and Optical Passive Components, 2011. 1–4.
- 29. Ward B, Mermelstein M. Modeling of inter-modal Brillouin gain in higher-order-mode fibers. Opt Express. 2010;18(3):1952–8. pmid:20174024
- 30. Weng Y, Ip E, Pan Z, Wang T. Single-end simultaneous temperature and strain sensing techniques based on Brillouin optical time domain reflectometry in few-mode fibers. Opt Express. 2015;23(7):9024–39. pmid:25968738
- 31. Dong Y, Ren G, Xiao H, Gao Y, Li H, Xiao S, et al. Simultaneous temperature and strain sensing based on m-shaped single mode fiber. IEEE Photon Technol Lett. 2017;29(22):1955–8.