Investigation of stimulated Brillouin scattering in As2S3 photonic crystal fibers at the mid-infrared waveband
doi: 10.37188/CO.EN.2022-0003
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Abstract:
Stimulated Brillouin scattering in As2S3 photonic crystal fibers was investigated at wavelengths of 2 μm to 6 μm by the finite element method. The numerical results indicate that the proposed photonic crystal fiber can maintain single-mode operation when the air filling factor is less than 0.6. The Brillouin frequency shift is mainly influenced by the pump wavelength and fiber structure. The Brillouin frequency shift decreases by 4.16 GHz when the pump wavelength is increased from 2 μm to 6 μm, while the Brillouin frequency shift changes by the order of megahertz when the rate of air filling increases from 0.5 to 0.6. The FWHM of the Brillouin gain spectrum depends on the phonon lifetime, and the FWHM of the Brillouin gain spectrum is nine times wider at a pump wavelength of 2 μm than that at a pump wavelength of 6 μm. The maximum Brillouin gain of the proposed fibers with air filling fractions of 0.5 and 0.6 are 2.413×10−10 m/W and 2.429×10−10 m/W, respectively. The Brillouin threshold is positively correlated with the pump wavelength for the same effective fiber length, and is 27.8% and 19.6% larger at a pump wavelength of 6 μm than that at 2 μm with air fill factors of 0.5 and 0.6, respectively. The numerical results are of great significance for the design and fabrication of optical devices or optical sensors based on the proposed fibers in the mid-infrared band.
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Key words:
- stimulated Brillouin scattering /
- mid-infrared /
- photonic crystal fiber /
- fiber optics
摘要:通过有限元方法研究了As2S3光子晶体光纤在2 μm至6 μm波段的受激布里渊散射。数值结果表明,当空气占空比小于0.6时,所提出的光子晶体光纤可保持单模工作。布里渊频移主要受泵浦波长和光纤结构的影响,泵浦波长从2 μm增加到6 μm时,布里渊频移减小了4.16 GHz;而当空气占空比由0.5增加到0.6时,布里渊频移变化量仅为兆赫兹量级。布里渊增益谱的半高全宽取决于声子寿命,泵浦波长为2 μm时布里渊增益谱的半高全宽是泵浦波长为6 μm时的9倍。在空气填充率为0.5和0.6的情况下,提出的光子晶体光纤的最大布里渊增益分别为2.413×10−10 m/W和2.429×10−10 m/W。在光纤有效长度相同的条件下,布里渊阈值与泵浦波长正相关,在空气填充率为0.5和0.6的光子晶体光纤中,使用6 μm泵浦时的布里渊阈值比使用2 μm时分别增大了27.8%和19.6%。这些数值结果对于中红外波段设计和制造基于所提出光纤的光学设备或光学传感器具有重要意义。
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1. Introduction
Capacity expansion through dense wavelength division multiplexing[1-3], frequency division multiplexing[4-5], time division multiplexing[6-7] and space division multiplexing[8-9] in the conventional 1.55 μm telecom band has been extensively investigated. These technologies utilize a limited spectrum to achieve high-speed, high-capacity information transmission, and they will be more efficient if their available spectrum can be further extended. For this reason, a series of studies have been conducted to find new communication windows outside the 1.55 μm telecommunication waveband[10-11]. In addition to communication purposes, optical fibers operating in the infrared band have many potential applications in chemistry, stress and temperature sensing[12-15]. Several commonly used materials for the fabrication of optical fibers operating in the mid-infrared spectrum range include chalcogenide[16-18], tellurite[19], high germania-doped[20] and fluoride[21] glasses. The main advantages of these glasses over the widely used silica glasses are that they have lower losses in the mid-infrared band, while chalcogenide glasses have higher nonlinear coefficients.
Chalcogenide glass such as As2S3 with low optical loss and high nonlinearity is a good candidate for optical communication and optical sensing in the mid-infrared waveband. As2S3 bulk samples transmit light in the 0.6−12 μm spectrum range while the transparency window for As2S3 fiber is significantly narrower at 1−6 μm[12]. The definition of the infrared wavelength range varies with the applicable discipline or application scenario. In this paper, we consider 0.7−2 µm as near-infrared, 2−15 µm as mid-infrared, and 15 µm−1 mm as far-infrared. To date, several studies of Stimulated Brillouin Scattering (SBS) based on As2S3 materials have been reported where SBS in various As2S3 fibers were explored experimentally and theoretically. Kenta et al.[22] studied SBS in a multimode As2S3 fiber using a Nd:YAG pulsed laser operated at 1.064 μm. Xu et al.[17] numerically analyzed SBS in As2S3 suspended-core Microstructured Optical Fibers (MOFs), then the circumstances when the holes of the MOFs were filled with trichloromethane, ethanol and water were further investigated. SBS-induced slow light in an As2S3 fiber is also a promising application. Florea et al.[18] demonstrated for the first time that by using a slow-light generation in single mode As2S3 fiber, they could obtain a delay of 19 ns in 10 m of fiber with only 31 mW of launched power, then a temperature sensor using SBS-based slow light was proposed by Mbaye et al.[23]. Experimental characterization of SBS at 2 μm in an As2S3 step-index fiber was reported by Deroh et al.[10]. When pumping at 2 μm, the Brillouin Frequency Shift (BFS) from the As2S3 step-index fiber is around 6.2 GHz , which is almost the same as the BFS from the As2S3 Photonic Crystal Fiber (PCF) proposed in this paper.
We report novel As2S3 PCFs with square arranged air holes. The SBS of the proposed fibers at mid-infrared waveband were theoretically investigated and their mode contributions were analyzed. The BFS, Brillouin threshold and Brillouin Gain Spectrum (BGS) were simulated by the finite element method. This work is of great significance for the design and fabrication of optical devices or optical sensors at the mid infrared waveband.
2. Model and theory
Fig. 1. shows the cross section of the proposed PCF which is made entirely of pure As2S3 with square arranged air holes. The cladding consists of two layers of square air holes and three layers of regular octagonal air holes arranged in a square lattice across the cross section. There is an absence of square air holes in the center, which serves as the core of the PCF. Unlike the popular circular air holes, the use of square and octagonal air holes allows the fiber core to be square so that a square optical mode can be obtained. In Fig. 1, D describes the circular diameter of the octagonal air holes, Λ is the pitch of the air holes and A is the edge length of the square and octagonal air holes. In this work, the side lengths of the square air holes and the regular octagonal air holes are fixed to 3 μm and the diameter of the cladding is 125 μm. We define the factor D/Λ as the Air Filling Fraction (AFF) to identify PCFs with different structural parameters.
The refractive index of As2S3 as a function of wavelength which is derived from the Sellmeier equation[24] as
n2As2S3=1+1.8983678λ2λ2−0.0225+1.9222979λ2λ2−0.0625+0.8765134λ2λ2−0.1225+0.1188704λ2λ2−0.2025+0.9569903λ2λ2−750, (1) where λ is the wavelength in microns and
nAs2S3 is the refractive index of As2S3. The other material properties such as density ρ, Young’s modulus Y, Poisson’s ratio νp and the Photo-elastic tensor of As2S3 are shown in Table 1[25].Physical property As2S3 Density ρ(kg/m3) 3210 Young modulus Y(GPa) 16.2 Poisson ratio vp 0.285 Photo-elastic tensor p11 0.25 Photo-elastic tensor p12 0.24 Photo-elastic tensor p44 0.005 By relationship
VI=√(1−vp)Y(1+vp)(1−2vp)ρ [26], the longitudinal acoustic velocity Vl of As2S3 is 2554.66 m/s.In our proposed PCF, because of the influence of air holes on the cladding, the cladding’s effective refractive index is lower than that of the core, which forms a total internal reflection waveguide structure. According to the optical waveguide theory, the normalized frequency is determined by[27]:
V=2πλpreff√n2As2S3−n2FSM, (2) where λp is the pump wavelength, reff is the effective core radius and
nFSM is the refractive index of the fundamental space filling mode (FSM). It is well known that the normalized frequency is an important parameter to determine the cut-off condition. When the normalized frequency is lower than 2.405, the high-order optical modes in the fiber are cut off.SBS is a typical third order nonlinear optical phenomenon. Its characteristic is that the energy of the pump wave is transferred to a Stokes wave through an acoustic wave. The acoustic wave is driven by the electrostrictive force generated by the beating between the pump and Stokes waves. The acoustic waves periodically modulate the refractive index of the medium to obtain characteristics similar to those of fiber Bragg gratings. However, unlike fiber Bragg gratings, since the acoustic wave moves along the fiber, the Doppler effect will creat a red shift in the reflected wave.
The spatial distribution of acoustic modes can be obtained from the wave equation[28]
∇2tu(x,y)+(4π2f2BV2l−β2α)u(x,y)=0, (3) where
u(x,y) is the spatial distribution of the acoustic mode and βa denotes the propagation constant of the acoustic wave. Here, βa satisfies the phase matching condition βa=2β0 for backward SBS,β0=2πneff/λ is the propagation constant of the optical mode, neff is the effective refractive index of the optical mode. The BFS of each acoustic mode corresponds to its acoustic frequencyfB . Since the longitudinal acoustic waves play a dominant role in PCF, the transverse acoustic waves are not taken into account. Therefore the simulation in this paper is valid only for longitudinal acoustic modes.When the attenuation of an acoustic wave with time t follows
exp(−t/τ) , the BGS has a Lorentzian spectral profile which is expressed as[29]gB(f)=∑igB,i(ΔfB/2)2(f−fB,i)2+(ΔfB/2)2, (4) gB,i=4πn8effp212Iicλ3pρ0fBΔfB, (5) where
gB,i is the peak value of the Brillouin gain for each acoustic mode andΔfB is the Full Width at Half Maximum (FWHM) of the gain spectrum which is related to the phonon lifetimeτ byΔfB=(2πτ)−1 . For As2S3, the phonon lifetime is 1.33 ns at a pump wavelength of 1.064 μm, and the phonon lifetime of the acoustic wave in an SBS is proportional to the square of the pump wavelength[30]. The overlap integral Ii is introduced to characterize the interaction strength between acoustic modes and optical modes. Ii can be expressed by the integral on the fiber cross section as[29]Ii=(∬|E(x,y)|2ui(x,y)dxdy)2∬|E(x,y)|4dxdy∬|ui(x,y)|2dxdy, (6) where E(x, y) and ui(x, y) are the spatial distribution of the optical and ith-order acoustic mode, respectively.
In SBS, the effective optical mode area is another key factor. It has a significant effect on the Brillouin gain and Brillouin threshold. Both the core size and
nFSM will affect Aeff significantly. Aeff is obtained usingAeff=(∬|E(x,y)|2dxdy)2∬|E(x,y)|4dxdy, (7) Pth=AeffCgBLeff, (8) where Pth and Leff is the Brillouin threshold power and the effective fiber length, respectively. Note that, C in Eq. (8) changes with different types of fiber, e.g. in standard single-mode fibers C equals 21[29]. However, in the As2S3 PCF proposed in this paper, the value of C needs to be further explored. Nevertheless, we can compare the relative Brillouin thresholds for PCFs with different AFFs or at different pumping wavelengths.
3. Results and discussion
Five PCFs with different structures of varying air hole pitches were calculated, and their AFFs were 0.5, 0.6, 0.7, 0.8 and 0.9, respectively. Fig. 2 shows the simulated results of Fundamental Optical Modes (FOMs) with different AFFs at pump wavelengths of 2 μm, 4 μm and 6 μm, respectively. Since the PCF core is a square area, the distribution of the FOM approximates a square when the four regular octagonal air holes closest to the center are aligned.
PCFs with larger AFFs have a better ability to confine optical waves and their optical fields are more concentrated. The core sizes of PCFs with different AFFs are significantly different. PCFs with larger AFFs have smaller core sizes, which has the largest impact on their effective mode areas. Their effective mode areas vary linearly with the pump wavelength due to the fact that light with a longer wavelength is less likely to be confined in the core and is negatively correlated with the AFF as shown in Fig. 3 (Color online).
To determine the condition of single mode transmission, the refractive index of the FSM was also calculated to obtain the normalized frequency. Fig. 4(a) (Color online) is the spatial distribution of the FSM which is the fundamental solution of Maxwell’s wave equation in the cladding. Fig. 4(b) (Color online) is the refractive index of FSM with different AFFs versus the pump wavelength.
Then, the normalized frequency can be obtained using Eq. (2) as shown in Fig. 5 (Color online). The dashed line in the figure corresponds to the normalized frequency of 2.405, which is the dividing line between single-mode operation and multimode operation. Only those below the dashed line, i.e. PCFs with AFFs less than 0.6, can maintain single-mode operation in the 2 μm to 6 μm waveband.
The effective refractive index of FOMs with different AFFs is shown in Fig. 6 (Color online). As the pump wavelength increases, the effective refractive index of FOMs decreases, which is a joint effect of their waveguide properties and material dispersion. When the PCF has a large AFF, the effect of the PCF structure on the change in the effective refractive index is more obvious when the pump wavelength is changed.
In single-mode fibers, the BGS will have multiple peaks due to their higher-order acoustic modes, but in multimode fibers, the BGS becomes more complex under the influence of higher-order optical modes. The mode composition of the pump and Stokes pair will also have an impact on the BGS. Therefore, in this paper, only SBS in single-mode PCF was discussed.
The propagation constants of the acoustic modes are obtained using the phase-matching condition and Eq. (3) are solved by the finite element method. Fig. 7 (Color online) shows the spatial distributions of the acoustic modes at various pump wavelengths with AFFs of 0.5 and 0.6. For each situation, three acoustic modes with the largest overlap integral for different pump wavelengths and AFF are illustrated. All the acoustic modes shown in Fig. 7 belong to the symmetric L0m-like acoustic modes group since the overlap integrals between the antisymmetric acoustic modes and FOMs are almost zero and their contributions to SBS are negligible.
Fig. 8 (Color online) illustrates the BGS of the PCF with an AFF of 0.5 at a pump wavelength of 6 μm. The primary peak of the BGS is mainly generated by the interaction between the acoustic mode and FOM while the higher-order acoustic modes have higher frequencies to bring some distortion to the edge of the primary peak. The Brillouin gain generated by the L01-like acoustic mode is 14.7 dB and 19.4 dB greater than that generated by the L02-like acoustic mode and L03-like acoustic mode, respectively. The FWHM of the BGS is 3.8 MHz and the BFS corresponding to the L01-like acoustic mode is 7.21 MHz and 16.6 MHz smaller than that corresponding to the L02-like and L03-like acoustic modes, respectively.
When using shorter pump wavelength, for example, Fig. 9 (Color online) presents the BGS in PCF with an AFF of 0.5 at 2 μm pumping wavelength. The BFS generated by the L01-like acoustic mode are only 2.3 MHz and 4.1 MHz smaller than that generated by the L02-like and L03-like acoustic modes, and the frequency difference between them is too small to be separated in the BGS at an FWHM of 33.9 MHz for each gain peak. The Brillouin gain generated by the L01-like acoustic mode is 13.8 dB and 25.9 dB greater than that generated by the L02-like acoustic mode and L03-like acoustic mode, respectively. Therefore, the BGS in single-mode PCF is generated by the interaction between the L01-like acoustic mode and the FOM, while the effect of higher-order acoustic modes on the BGS is almost negligible.
The BGS of PCFs with AFFs of 0.5 and 0.6 at different pump wavelengths are shown in Fig. 10(a) (Color online) and Fig. 10(b) (Color online), respectively. Since the acoustic frequencies are lower and have higher phonon lifetimes when pumped with longer wavelengths, the gain spectra are correspondingly narrower, which is evident in Fig. 10. The FWHM of the BGS is nine times wider at a pump wavelength of 2 μm than that at a pump wavelength of 6 μm. Since the effect of structure on BFS is not very drastic, the BFSs differences of PCF with different AFFs are megahertz orders of magnitude at each pump wavelength which is relatively small. In the 2 μm to 6 μm waveband studied in this paper, the maximum Brillouin gain of PCFs with AFFs of 0.5 and 0.6 are 2.413×10−10 m/W and 2.429×10−10 m/W, respectively.
The relative Brillouin threshold was estimated using Eq. (8) as shown in Fig. 11. The relative Brillouin thresholds obtained by normalization can be used to compare the Brillouin thresholds at PCFs with different AFFs or at different pump wavelengths. The PCF with an AFF of 0.6 has a significantly lower Brillouin threshold than the PCF with an AFF of 0.5 owing to its smaller area of optical modes. For a particular fiber structure, the Brillouin threshold is smaller when using shorter pump wavelengths than when using longer pump wavelengths. When the same effective length of fiber is available, the Brillouin thresholds are 27.8% and 19.6% larger at a pump wavelength of 6 μm than that at a pump wavelength of 2 μm in the proposed fibers with AFFs of 0.5 and 0.6, respectively.
4. Conclusion
In summary, an As2S3 PCF was proposed. Its single-mode conditions were explored and its SBS properties including BFS, Brillouin gain coefficients, BGS and Brillouin threshold were investigated. According to our calculations, among our proposed fibers, only those with AFFs of 0.5 and 0.6 can realize single mode transmission in the 2 μm to 6 μm waveband. The contribution of higher-order acoustic modes to the BGS in single-mode PCF is weak, and only the L01-like acoustic mode is feasible. The maximum Brillouin gain coefficients in the PCFs with AFFs of 0.5 and 0.6 at the pump wavelengths of 2 μm to 6 μm are 2.413×10−10 m/W and 2.429×10−10 m/W, respectively. This work has implications for the design and fabrication of SBS-based all-optical devices in the mid-infrared waveband.
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Table 1. Material parameters of As2S3
Physical property As2S3 Density ρ(kg/m3) 3210 Young modulus Y(GPa) 16.2 Poisson ratio vp 0.285 Photo-elastic tensor p11 0.25 Photo-elastic tensor p12 0.24 Photo-elastic tensor p44 0.005 -
[1] GUAN X, SHI W, RUSCH L A. Ultra-dense wavelength-division multiplexing with microring modulator[J]. Journal of Lightwave Technology, 2021, 39(13): 4300-4306. doi: 10.1109/JLT.2021.3070515 [2] LUBANA A, KAUR S, MALHOTRA Y. Performance optimization of a super-dense wavelength division multiplexing system employing a Raman + erbium–ytterbium doped fiber hybrid optical amplifier[J]. Journal of Optical Technology, 2021, 88(6): 308-314. doi: 10.1364/JOT.88.000308 [3] MA Z Y, WU Q Q, LI Q H, et al. Ultra-dense wavelength division multiplexing passive optical network[J]. Laser &Optoelectronics Progress, 2021, 58(5): 0500006. (in Chinese) [4] ZHANG CH J, GAO M Y, SHI Y, et al. Experimental comparison of orthogonal frequency division multiplexing and universal filter multi-carrier transmission[J]. Journal of Lightwave Technology, 2021, 39(22): 7052-7060. doi: 10.1109/JLT.2021.3113388 [5] XU X Y, YUE D W. Orthogonal frequency division multiplexing modulation techniques in visible light communication[J]. Chinese Optics, 2021, 14(3): 516-527. (in Chinese) doi: 10.37188/CO.2020-0051 [6] ZHU K, ZHOU B, WU H, et al. Multipath distributed acoustic sensing system based on phase-sensitive optical time-domain reflectometry with frequency division multiplexing technique[J]. Optics and Lasers in Engineering, 2021, 142: 106593. doi: 10.1016/j.optlaseng.2021.106593 [7] WU SH Z, WEN H Q, CHEN X H. Method for reducing the influence of crosstalk on quasi-distributed sensing network with time-division multiplexing fibre Bragg gratings[J]. Journal of Physics:Conference Series, 2021, 1754: 012212. doi: 10.1088/1742-6596/1754/1/012212 [8] PEI L, LI ZH Q, WANG J SH, et al. Review on gain equalization technology of fiber amplifier using space division multiplexing[J]. Acta Optica Sinica, 2021, 41(1): 0106001. (in Chinese) doi: 10.3788/AOS202141.0106001 [9] PUTTNAM B J, RADEMACHER G, LUÍS R S. Space-division multiplexing for optical fiber communications[J]. Optica, 2021, 8(9): 1186-1203. doi: 10.1364/OPTICA.427631 [10] DEROH M, BEUGNOT J C, HAMMANI K, et al. Comparative analysis of stimulated Brillouin scattering at 2 µm in various infrared glass-based optical fibers[J]. Journal of the Optical Society of America B, 2020, 37(12): 3792-3800. doi: 10.1364/JOSAB.401252 [11] WANG X, ZHOU P, WANG X L, et al. Tunable slow light via stimulated Brillouin scattering at 2 μm based on Tm-doped fiber amplifiers[J]. Optics Letters, 2015, 40(11): 2584-2587. doi: 10.1364/OL.40.002584 [12] TAO G M, EBENDORFF-HEIDEPRIEM H, STOLYAROV A M, et al. Infrared fibers[J]. Advances in Optics and Photonics, 2015, 7(2): 379-458. doi: 10.1364/AOP.7.000379 [13] ALIMAGHAM F, WINTERBURN J, DOLMAN B, et al. Real-time bioprocess monitoring using a mid-infrared fibre-optic sensor[J]. Biochemical Engineering Journal, 2021, 167: 107889. doi: 10.1016/j.bej.2020.107889 [14] WANG H Y, BAKER C, CHEN L, et al. Stimulated Brillouin scattering in high-birefringence elliptical-core As2Se3-PMMA microfibers[J]. Optics Letters, 2021, 46(5): 945-948. doi: 10.1364/OL.418137 [15] CHEN X Y, YAN X, ZHANG X N, et al. Theoretical investigation of mid-infrared temperature sensing based on four-wave mixing in a CS2-filled GeAsSeTe microstructured optical fiber[J]. IEEE Sensors Journal, 2021, 21(9): 10711-10718. doi: 10.1109/JSEN.2021.3061654 [16] CARCREFF J, CHEVIRÉ F, GALDO E, et al. Mid-infrared hollow core fiber drawn from a 3D printed chalcogenide glass preform[J]. Optical Materials Express, 2021, 11(1): 198-209. doi: 10.1364/OME.415090 [17] XU Q, GAO W Q, LI X, et al. Investigation on optical and acoustic fields of stimulated Brillouin scattering in As2S3 suspended-core microstructured optical fibers[J]. Optik, 2017, 133: 51-59. doi: 10.1016/j.ijleo.2017.01.003 [18] FLOREA C, BASHKANSKY M, DUTTON Z, et al. Stimulated Brillouin scattering in single-mode As2S3 and As2Se3 chalcogenide fibers[J]. Optics Express, 2006, 14(25): 12063-12070. doi: 10.1364/OE.14.012063 [19] VANI P, VINITHA G, NASEER K A, et al. Thulium-doped barium tellurite glasses: structural, thermal, linear, and non-linear optical investigations[J]. Journal of Materials Science:Materials in Electronics, 2021, 32(18): 23030-23046. doi: 10.1007/s10854-021-06787-5 [20] DEROH M, BEUGNOT J C, KIBLER B, et al. . Stimulated Brillouin scattering in Germanium-doped-core optical fibers up to 98% mol doping level[C]. Proceedings of Specialty Optical Fibers 2018, Optica Publishing Group, 2018: SoTu3G. 2. [21] LAMBIN-IEZZI V, LORANGER S, SAAD M, et al. Stimulated Brillouin scattering in SM ZBLAN fiber[J]. Journal of Non-Crystalline Solids, 2013, 359: 65-68. doi: 10.1016/j.jnoncrysol.2012.10.004 [22] SHINKAWA K, ODA Y, MA Z T, et al. Transient stimulated brillouin scattering in multimode As2S3 glass fiber[J]. Japanese Journal of Applied Physics, 2009, 48(7R): 070215. [23] DIOUF M, TRICHLLI A, ZGHAL M. Stimulated Brillouin scattering-based slow light using singlemode As2S3 chalcogenide photonic crystal fiber for temperature sensing[C]. Proceedings of Frontiers in Optics 2019, Optica Publishing Group, 2019: JTu3A. 63. [24] RODNEY W S, MALITSON I H, KING T A. Refractive index of arsenic trisulfide[J]. Journal of the Optical Society of America, 1958, 48(9): 633-636. doi: 10.1364/JOSA.48.000633 [25] WIEDERHECKER G S, DAINESE P, MAYER ALEGRE T P. Brillouin optomechanics in nanophotonic structures[J]. APL Photonics, 2019, 4(7): 071101. doi: 10.1063/1.5088169 [26] TIMOSHENKO S P, GOODIER J N. Theory of Elasticity[M]. New York: McGraw-Hill, 1970. [27] DEMIR H, OZSOY S. Solid-core square-lattice photonic crystal fibers: comparative studies of the single-mode regime and numerical aperture for circular and square air-holes[J]. Optical and Quantum Electronics, 2011, 42(14): 851-862. [28] DASGUPTA S, POLETTI F, LIU SH, et al. Modeling brillouin gain spectrum of solid and microstructured optical fibers using a finite element method[J]. Journal of Lightwave Technology, 2011, 29(1): 22-30. doi: 10.1109/JLT.2010.2091106 [29] AGRAWAL G P. Nonlinear Fiber Optics[M]. 4th ed. Amsterdam: Academic Press, 2007. [30] OGUSU K, LI H P, KITAO M. Brillouin-gain coefficients of chalcogenide glasses[J]. Journal of the Optical Society of America B, 2004, 21(7): 1302-1304. doi: 10.1364/JOSAB.21.001302 期刊类型引用(0)
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