Abstract

We review recent progress in inducing and harnessing stimulated Brillouin scattering (SBS) in integrated photonic circuits. Exciting SBS in a chip-scale device is challenging due to the stringent requirements on materials and device geometry. We discuss these requirements, which include material parameters, such as optical refractive index and acoustic velocity, and device properties, such as acousto-optic confinement. Recent work on SBS in nano-photonic waveguides and micro-resonators is presented, with special attention paid to photonic integration of applications such as narrow-linewidth lasers, slow- and fast-light, microwave signal processing, Brillouin dynamic gratings, and nonreciprocal devices.

© 2013 Optical Society of America

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H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
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J. Li, H. Lee, and K. J. Vahala, “Microwave synthesizer using an on-chip Brillouin oscillator,” Nat. Commun. 4, 2097 (2013).
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Y. G. Lu, Z. G. Qin, P. Lu, D. P. Zhou, L. Chen, and X. Y. Bao, “Distributed strain and temperature measurement by Brillouin beat spectrum,” IEEE Photon. Technol. Lett. 25, 1050–1053 (2013).
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D. P. Zhou, W. H. Li, L. Chen, and X. Y. Bao, “Distributed temperature and strain discrimination with stimulated Brillouin scattering and Rayleigh backscatter in an optical fiber,” Sensors 13, 1836–1845 (2013).
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M. Santagiustina, S. Chin, N. Primerov, L. Ursini, and L. Thévenaz, “All-optical signal processing using dynamic Brillouin gratings,” Sci. Rep. 3, 1594 (2013).
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G. Wang, L. Zhan, J. Liu, T. Zhang, J. Li, L. Zhang, J. Peng, and L. Yi, “Watt-level ultrahigh-optical signal-to-noise ratio single-longitudinal-mode tunable Brillouin fiber laser,” Opt. Lett. 38, 19–21 (2013).
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H. G. Winful, “Chirped Brillouin dynamic gratings for storing and compressing light,” Opt. Express 21, 10039–10047 (2013).
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I. V. Kabakova, R. Pant, D.-Y. Choi, S. K. Debbarma, B. Luther-Davies, S. Madden, and B. J. Eggleton, “Narrow linewidth Brillouin laser based on chalcogenide photonic chip,” Opt. Lett. 38, 3208–3211 (2013).
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Y. Antman, N. Primerov, J. Sancho, L. Thevenaz, and A. Zadok, “Variable delay using stationary and localized Brillouin dynamic gratings,” Proc. SPIE 8273, 82730C (2012).
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W. Li, M. Li, and J. Yao, “A narrow-passband and frequency-tunable microwave photonic filter based on phase-modulation to intensity-modulation conversion using a phase-shifted fiber Bragg grating,” IEEE Trans. Microwave Theor. Tech. 60, 1287–1296 (2012).
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H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Phys. Rev. Lett. 109, 033901 (2012).
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L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
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J. Sancho, N. Primerov, S. Chin, Y. Antman, A. Zadok, S. Sales, and L. Thevenaz, “Tunable and reconfigurable multi-tap microwave photonic filter based on dynamic Brillouin gratings in fibers,” Opt. Express 20, 6157–6162 (2012).
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Y. K. Dong, H. Y. Zhang, L. Chen, and X. Y. Bao, “2  cm spatial-resolution and 2  km range Brillouin optical fiber sensor using a transient differential pulse pair,” Appl. Opt. 51, 1229–1235 (2012).
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K. H. Tow, Y. Leguillon, P. Besnard, L. Brilland, J. Troles, P. Toupin, D. Mechin, D. Tregoat, and S. Molin, “Relative intensity noise and frequency noise of a compact Brillouin laser made of As38Se62 suspended-core chalcogenide fiber,” Opt. Lett. 37, 1157–1159 (2012).
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X. Liu and X. Y. Bao, “Brillouin spectrum in LEAF and simultaneous temperature and strain measurement,” J. Lightwave Technol. 30, 1053–1059 (2012).
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K. Y. Song, “Effects of induced birefringence on Brillouin dynamic gratings in single-mode optical fibers,” Opt. Lett. 37, 2229–2231 (2012).
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S. Afshar V, M. A. Lohe, W. Q. Zhang, and T. M. Monro, “Full vectorial analysis of polarization effects in optical nanowires,” Opt. Express 20, 14514–14533 (2012).
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W. C. Jiang, X. Lu, J. Zhang, and Q. Lin, “High-frequency silicon optomechanical oscillator with an ultralow threshold,” Opt. Express 20, 15991–15996 (2012).
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C. Husko and B. J. Eggleton, “Energy efficient nonlinear optics in silicon: are slow-light structures more efficient than nanowires?” Opt. Lett. 37, 2991–2993 (2012).
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A. Byrnes, R. Pant, E. Li, D.-Y. Choi, C. G. Poulton, S. Fan, S. Madden, B. Luther-Davies, and B. J. Eggleton, “Photonic chip based tunable and reconfigurable narrowband microwave photonic filter using stimulated Brillouin scattering,” Opt. Express 20, 18836–18845 (2012).
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J. Li, H. Lee, T. Chen, and K. J. Vahala, “Characterization of a high coherence, Brillouin microcavity laser on silicon,” Opt. Express 20, 20170–20180 (2012).
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C. G. Poulton, R. Pant, A. Byrnes, S. Fan, M. J. Steel, and B. J. Eggleton, “Design for broadband on-chip isolator using stimulated Brillouin scattering in dispersion-engineered chalcogenide waveguides,” Opt. Express 20, 21235–21246 (2012).
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Y. G. Lu, X. Y. Bao, L. Chen, S. R. Xie, and M. Pang, “Distributed birefringence measurement with beat period detection of homodyne Brillouin optical time-domain reflectometry,” Opt. Lett. 37, 3936–3938 (2012).
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S. Li, M.-J. Li, and R. S. Vodhanel, “All-optical Brillouin dynamic grating generation in few-mode optical fiber,” Opt. Lett. 37, 4660–4662 (2012).
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T. F. S. Büttner, I. V. Kabakova, D. D. Hudson, R. Pant, E. Li, and B. J. Eggleton, “Multi-wavelength gratings formed via cascaded stimulated Brillouin scattering,” Opt. Express 20, 26434–26440 (2012).
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S. Levy, V. Lyubin, M. Klebanov, J. Scheuer, and A. Zadok, “Stimulated Brillouin scattering amplification in centimeter-long directly written chalcogenide waveguides,” Opt. Lett. 37, 5112–5114 (2012).
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X. Y. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors 12, 8601–8639 (2012).
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Figures (32)

Figure 1
Figure 1

Illustration of the processes involved in stimulated Brillouin scattering. A pump and Stokes wave interfere to compress or expand the material, either by electrostriction or by radiation pressure. This excites a moving density wave, which changes the refractive index periodically via the photoelastic effect or by directly moving the waveguide boundaries. This moving index grating reflects the pump, downshifting it to the Stokes frequency.

Figure 2
Figure 2

Timeline of major advances in SBS theory and experiment, showing the milestones in the different platforms used for harnessing SBS. Photo of L. Brillouin reprinted from AIP Emilio Segre Visual Archives, Leon Brillouin Collection. Photo of L. Mandelstam is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. Figure from [51] copyright 2011, Optical Society of America. Figure from [55] reprinted by permission from Nature Publishing Group, Macmillan Publishers Ltd: Nat. Commun. 4, 1944 (2013), www.nature.com. Figure from [74] reprinted with permission from E. P. Ippen and R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972), http://dx.doi.org/10.1063/1.1654249. Copyright 1972, AIP Publishing LLC. Figure from [2] reprinted with permission from K. O. Hill et al., Appl. Phys. Lett. 28, 608–609 (1976), http://dx.doi.org/10.1063/1.88583. Copyright 1976, AIP Publishing LLC. Figure from [75] reprinted by permission from Nature Publishing Group, Macmillan Publishers Ltd: Nat. Phys. 2, 388–392 (2006), www.nature.com. Figure from [76] reprinted with permission from I. S. Grudinin, A. B. Matsko, and L. Maleki, Phys. Rev. Lett. 102, 043902 (2009). Copyright 2009 by the American Physical Society; http://link.aps.org/doi/10.1103/PhysRevLett.102.043902. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society. Figure from [52] reprinted by permission from Nature Publishing Group, Macmillan Publishers Ltd: Nat. Photonics 6, 369–373 (2012), www.nature.com.

Figure 3
Figure 3

Traveling-wave and resonator waveguide geometries for harnessing SBS in a photonic chip. Figure from [51] copyright 2011, Optical Society of America. Figure from [55] reprinted by permission from Nature Publishing Group, Macmillan Publishers Ltd: Nat Commun 4, 1944 (2013), www.nature.com. Figure from [75] reprinted by permission from Nature Publishing Group, Macmillan Publishers Ltd: Nat. Phys. 2, 388–392 (2006), www.nature.com. Reprinted with permission from [6]. Copyright 2012 Society of Photo-Optical Instrumentation Engineers. Figure from [76] reprinted with permission from I. S. Grudinin, A. B. Matsko, and L. Maleki, Phys. Rev. Lett. 102, 043902 (2009). Copyright 2009 by the American Physical Society; http://link.aps.org/doi/10.1103/PhysRevLett.102.043902. Figure from [83] reprinted with permission from M. Tomes and T. Carmon, Phys. Rev. Lett. 102, 113601 (2009). Copyright 2009 by the American Physical Society; http://link.aps.org/doi/10.1103/PhysRevLett.102.113601. Figure from [62] reprinted by permission from Nature Publishing Group, Macmillan Publishers Ltd: Nat. Commun. 4, 1994 (2013), www.nature.com. Figure from [52] reprinted by permission from Nature Publishing Group, Macmillan Publishers Ltd: Nat. Photonics 6, 369–373 (2012), www.nature.com.

Figure 4
Figure 4

Optical and acoustic dispersion showing the momentum conservation for backward (upper) and forward (down) SBS.

Figure 5
Figure 5

Acoustic-optic confinement η regimes for an optical guiding device for different contrasts between the core (Vcore) and cladding (Vcladding) acoustic velocity and its impact on the Brillouin gain. For VcoreVcladding acousto-optic overlap reduces due to radiating acoustic mode, while large acousto-optic overlap occurs for VcoreVcladding due to acoustic guidance and for VcoreVcladding (acoustic mode leakage regime) due to large acoustic impedance mismatch and thus large leakage time [98]. Copyright 2013, Optical Society of America.

Figure 6
Figure 6

Backscattered SBS process using the generator (top) and amplifier (bottom) configuration. In the generator configuration spontaneous pump scattering from thermally generated phonons results in generation of efficient Stokes signal in the backward direction, which beats with the pump to generate a traveling index grating. At large pump powers, the grating generated from beating between pump and scattered Stokes becomes stronger, resulting in stimulated pump scattering. In the amplifier configuration, pump and Stokes stimulate the acoustic wave causing Stokes amplification due to pump scattering.

Figure 7
Figure 7

SBS in chalcogenide (As2Se3) fiber showing (a) efficient slow-and fast-light light in a 5 m long fiber resulting in a group-index change of 2.2 with only 60 mW of CW pump power [23] and (b) formation of multiple Hill gratings in a 10 cm long fiber due to the multiple Stokes lines, generated by a pulsed pump with average pump power 20mW (peak power 40W) [135]. (a) Copyright 2006, Optical Society of America. (b) Copyright 2012, Optical Society of America.

Figure 8
Figure 8

Schematic of a suspended silicon nanowire used in [54] and individual contribution of the radiation pressure and electrostriction induced forces to FSBS gain factor for two different acoustic modes (E2, E5) and the giant SBS enhancement for mode E2 due to coherent addition of the two effects. The displacement and direction of forces on walls of the device are also shown [54]. The nanowire has a cross section of 300nm×280nm [54]. Reprinted with permission from P. T. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, Phys. Rev. X 2, 011008 (2012). Copyright 2012 by the American Physical Society; http://link.aps.org/doi/10.1103/PhysRevX.2.011008.

Figure 9
Figure 9

Schematic of the chalcogenide photonic chip along with calculated optical and acoustic modes in the rib waveguide [58]. On-chip SBS was generated using a pump, which gets backscattered from the acoustic phonons resulting in SBS at large pump powers. Copyright 2013, Optical Society of America.

Figure 10
Figure 10

Characterization of on-chip SBS using the SBS generation process: (a) backscattered spectrum showing generation of strong Stokes signal at large pump powers and (b) transmitted pump power and Stokes signal power variation with input pump power demonstrating that above a threshold power the Stokes signal increases while the output pump power starts to roll off [51]. Copyright 2011, Optical Society of America.

Figure 11
Figure 11

Characteristics of SBS in a chalcogenide photonic chip: (a) measured (o) Brillouin gain profile and a Lorentzian fit (--) to it and (b) ratio of output to input Stokes power [o, measured; --, exponential fit using Eq. (11)] versus CW pump power, demonstrating an exponential increase [51]. Copyright 2011, Optical Society of America.

Figure 12
Figure 12

Schematic of the hybrid photonic–phononic device used in the demonstration of FSBS in silicon: (a) device geometry showing a suspended silicon nanowire embedded in a silicon nitride membrane with air slots, which act as feedback elements for the acoustic modes, (b) cross section of silicon nanowire, (c) scanning electron microscope image of the device showing five air slot sections, and (d) zoomed version of one section of the device [55]. Reprinted by permission from Nature Publishing Group, Macmillan Publishers Ltd: Nat. Commun. 4, 1944 (2013), www.nature.com.

Figure 13
Figure 13

Spectral response for the first-order Stokes and anti-Stokes FSBS resonance for a device with a membrane width of 0.8 μm at different pump powers [55]. Reprinted by permission from Nature Publishing Group, Macmillan Publishers Ltd: Nat. Commun. 4, 1944 (2013), www.nature.com.

Figure 14
Figure 14

Device design and calculated modes for silica-based wedge resonator with a diameter of 1 mm [52]: (a) top view, (b) side view of the resonator for different wedge angles, and (c) calculated optical modes for different wedge angles at different wavelengths demonstrating the normal dispersion introduced by different wedge angles. Reprinted by permission from Nature Publishing Group, Macmillan Publishers Ltd: Nat. Photonics 6, 369–373 (2012), www.nature.com.

Figure 15
Figure 15

Effect of the pump wavelength on Brillouin lasing threshold for wedge resonators with different diameters, demonstrating that the threshold is minimum for the pump wavelength for which the Brillouin shift equals the FSR of the resonator [52]. Reprinted by permission from Nature Publishing Group, Macmillan Publishers Ltd: Nat. Photonics 6, 369–373 (2012), www.nature.com.

Figure 16
Figure 16

Multi-order Stokes generation on a silica wedge resonator and its application for microwave generation [60]: (a) first- and third-order Stokes in a silica wedge resonator and (b) phase noise for different microwave tones generated by using a 1/N frequency divider with the 21.7 GHz tone generated upon optical detection of signal in (a). Reprinted by permission from Nature Publishing Group, Macmillan Publishers Ltd: Nat. Commun. 4, 2097 (2013), www.nature.com.

Figure 17
Figure 17

(a) Principle of cascaded SBS in a chalcogenide photonic chip where the cleaved facets give rise to a FP cavity generating forward and backward propagating pump and Stokes, which generate higher-order Stokes and anti-Stokes at higher pump powers, and (b) measured spectrum in the pump incident direction showing generation of multi-order Stokes as the pump power is increased and anti-Stokes signal generation due to the four-wave mixing between the co-propagating pump and Stokes [50]. Copyright 2011, Optical Society of America.

Figure 18
Figure 18

Photonic-chip-based Brillouin laser: (a) principle of Brillouin ring laser where only the backscattered Stokes is recirculated in the ring while the pump is circulated only once before it is removed by an optical circulator, (b) pump power versus the Stokes power showing the lasing threshold and a slope efficiency of 30%, and (c) measured Brillouin ring laser linewidth (100kHz) demonstrating a 15 times reduction compared to the pump linewidth (1.55 MHz) and 350 times reduction compared to the Brillouin gain bandwidth (34MHz) [153]. Copyright 2013, Optical Society of America.

Figure 19
Figure 19

Principle of Brillouin slow-light demonstrating pulse delay when the pump was turned on. A probe pulse centered at the Stokes (anti-Stokes) frequency ωs (ωas) experiences large positive (negative) index slope resulting in slow- (fast-) light [57]. Copyright 2012, Optical Society of America.

Figure 20
Figure 20

Group-index measurements for (a) slow-light and (b) fast-light regime using SBS in a photonic chip [57]. Copyright 2012, Optical Society of America.

Figure 21
Figure 21

Tunable pulse delay for the SBS slow- and fast-light in a chalcogenide photonic chip using a nearly Gaussian pulse with a pulsewidth of (a) 25 ns and (b) 100 ns, and (c) comparison of the experimental and theoretical delay, obtained using Eq. (13) [57]. Copyright 2012, Optical Society of America.

Figure 22
Figure 22

Schematic showing the operation of BDG in a chalcogenide photonic chip where the dynamic grating written using pumps at frequencies ωP and ωS in the x-polarization is read using a probe at frequency ωpry in y-polarization [59]. Copyright 2013, Optical Society of America.

Figure 23
Figure 23

Experimental setup to realize BDG in a photonic chip. EDFA, erbium-doped fiber amplifier; IM, intensity modulator; C1,2, circulator; FPC, fiber polarization controller; FBG, fiber Bragg grating; OSA, optical spectrum analyzer.

Figure 24
Figure 24

Characterization of the BDG: (a) writing process using CW pumps in x-polarization centered at a wavelength of 1550 nm and (b) reading process using a probe located around 1525 nm [59]. Copyright 2013, Optical Society of America.

Figure 25
Figure 25

Effect of power Pp1 in pump1 on the grating reflectivity. (a) Read signal spectrum for different Pp1 while power in pump2 is kept fixed (8mW) and (b) read signal showing an exponential increase as expected for the SBS process: measured (o) and exponential fit (--) [59]. Copyright 2013, Optical Society of America.

Figure 26
Figure 26

Dependence of the read signal on the frequency of (a) pump2, showing that the read signal follows the Brillouin gain profile as expected, and (b) probe frequency [59]. Copyright 2013, Optical Society of America.

Figure 27
Figure 27

Principle of a photonic-chip-based MPF where the phase modulation of a laser by the microwave signal generates two equal amplitude out-of-phase sidebands, which cancel each other on detection. Application of SBS gain to a small portion of the phase modulated spectrum on one side (upper or lower sideband) results in the detection of the part of the microwave signal that sees the SBS gain, resulting in a band-pass filter response [56,61]. Copyright 2012, Optical Society of America.

Figure 28
Figure 28

Characterization of on-chip SBS microwave photonic band-pass filter: (a) tuning response over 2–12 GHz and (b) bandwidth and amplitude stability over the tuning range [61]. Copyright 2012, Optical Society of America.

Figure 29
Figure 29

SBS pump profile tailoring to reconfigure the band-pass response of the MPF: (a),(c) calculated response for single- and dual-pump configuration and (b),(d) measured filter response for single- and dual-pump configuration demonstrating 3 dB bandwidth increase from 20 to 40 MHz and shape factor improvement from 2 to 3.5 [61]. Copyright 2012, Optical Society of America.

Figure 30
Figure 30

Schematic of nonreciprocal processes, for (a) BSBS and (b) FSBS. In each case two pumps create an acoustic grating, which then drives transitions in the signal in one direction but not another.

Figure 31
Figure 31

(a) Dispersion curve, describing the transitions between two modes of a suspended silica fiber. (b) Optical and acoustic powers in the pump and signal as a result of SBS-driven mode conversion. Complete conversion in the signal from mode 2 to mode 1 is achieved over a length of 12m [185]. Copyright 2008 IEEE. Reprinted, with permission, from H. Xinpeng and F. Shanhui, J. Lightwave Technol. 29, 2267–2275 (2011).

Figure 32
Figure 32

(a) Schematic of on-chip isolation: two pumps are input to different modes and used to drive the transition of the signal to the higher-order mode, which is then filtered out. (b) Photo-induced perturbation of the refractive index can be used to adjust the isolation bandwidth. (c) Contour map of achievable isolation as a function of total input power [190]. Copyright 2012, Optical Society of America.

Tables (1)

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Table 1. Optical and Elastic Parameters for Commonly Used Optical Materials

Equations (17)

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νB=2nVaλp.
G=gBIPL,
gB=η4πn8p122λp3cρνBΔνB.
η=|E2ρ˜dA|2E2dA|ρ˜|2dA.
Epz+ncEpt=α2Ep+ig2Esρ,
Esz+ncEst=α2Es+ig2Epρ*,
ρt+(ΓB2iΔω)ρ=ig1EpEs*,
g1=γeΩB2Va2cn,
g2=γeωp4cnρ,
Es(ω,L)=Es(ω,0)ejk(ω)L,
k(ω)=gBIpΓB22(ω(ωpΩB)+jΓB2),
Ps(ω,L)=Ps(ω,0)egBPpAeffL
Pth=π2n2VeffgBλPλSQpQs,
Vg(ω)=cn+ωdndω,
τgd(ω)=dϕdω=Re[d(k(ω)L)dω]=GΓB14δω2ΓB2(1+4δω2ΓB2)2.
τgd(ωS)=GΓB=gBIpLΓB=LΔngc.
ΔνBνBx=Δnnx=ΔλBDGλP,

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