Abstract

Optical bistability and self-pulsation (SP) in silicon microring resonators (MRRs) are experimentally observed. The waveforms and frequencies of SP can be controlled by changing input light power and its wavelength, and the region of SP can be modulated readily by applying a reverse voltage on the PN junction embedded in the MRR. These phenomena are theoretically studied by adopting the coupled-mode theory and linear stability analysis method for differential equations, with theoretical results fitting well with the experimental ones.

© 2014 Optical Society of America

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References

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2013 (2)

L. Zhang, Y. Fei, T. Cao, Y. Cao, Q. Xu, and S. Chen, “Multibistability and self-pulsation in nonlinear high-Q silicon microring resonators considering thermo-optical effect,” Phys. Rev. A 87, 053805 (2013).
[Crossref]

X. Sun, X. Zhang, C. Schuck, and H. X. Tang, “Nonlinear optical effects of ultrahigh-Q silicon photonic nanocavities immersed in superfluid helium,” Science Reports 3, 1436 (2013).

2012 (4)

2010 (4)

2009 (2)

A. de Rossi, M. Lauritano, S. Combrié, Q. V. Tran, and C. Husko, “Interplay of plasma-induced and fast thermal nonlinearities in a GaAs-based photonic crystal nanocavity,” Phys. Rev. A 79, 043818 (2009).
[Crossref]

I. S. Grudinin and K. J. Vahala, “Thermal instability of a compound resonator,” Opt. Express 17, 14088–14097 (2009).
[Crossref]

2006 (1)

2005 (3)

2003 (1)

T. Kuwayama, M. Ichimura, and E. Arai, “Interface recombination velocity of silicon-on-insulator wafers measured by microwave reflectance photoconductivity decay method with electric field,” Appl. Phys. Lett. 83, 928–930 (2003).
[Crossref]

2002 (1)

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705–713 (2002).
[Crossref]

1997 (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Absil, P. P.

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705–713 (2002).
[Crossref]

Ang, K. W.

T. Y. Liow, K. W. Ang, Q. Fang, J. F. Song, Y. Z. Xiong, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Silicon modulators and germanium photodetectors on SOI: monolithic integration, compatibility, and performance optimization,” IEEE J. Sel. Top. Quantum Electron. 16, 307–315 (2010).
[Crossref]

Arai, E.

T. Kuwayama, M. Ichimura, and E. Arai, “Interface recombination velocity of silicon-on-insulator wafers measured by microwave reflectance photoconductivity decay method with electric field,” Appl. Phys. Lett. 83, 928–930 (2003).
[Crossref]

Baets, R.

Bienstman, P.

T. Van Vaerenbergh, M. Fiers, P. Mechet, T. Spuesens, R. Kumar, G. Morthier, B. Schrauwen, J. Dambre, and P. Bienstman, “Cascadable excitability in microrings,” Opt. Express 20, 20292–20308 (2012).
[Crossref]

T. Van Vaerenbergh, M. Fiers, J. Dambre, and P. Bienstman, “Simplified description of self-pulsation and excitability by thermal and free-carrier effects in semiconductor microcavities,” Phys. Rev. A 86, 063808 (2012).
[Crossref]

Bogaerts, W.

Borselli, M.

Cao, T.

L. Zhang, Y. Fei, T. Cao, Y. Cao, Q. Xu, and S. Chen, “Multibistability and self-pulsation in nonlinear high-Q silicon microring resonators considering thermo-optical effect,” Phys. Rev. A 87, 053805 (2013).
[Crossref]

S. Chen, L. Zhang, Y. Fei, and T. Cao, “Bistability and self-pulsation phenomena in silicon microring resonators based on nonlinear optical effects,” Opt. Express 20, 7454–7468 (2012).
[Crossref]

Cao, Y.

L. Zhang, Y. Fei, T. Cao, Y. Cao, Q. Xu, and S. Chen, “Multibistability and self-pulsation in nonlinear high-Q silicon microring resonators considering thermo-optical effect,” Phys. Rev. A 87, 053805 (2013).
[Crossref]

Chen, S.

L. Zhang, Y. Fei, T. Cao, Y. Cao, Q. Xu, and S. Chen, “Multibistability and self-pulsation in nonlinear high-Q silicon microring resonators considering thermo-optical effect,” Phys. Rev. A 87, 053805 (2013).
[Crossref]

S. Chen, L. Zhang, Y. Fei, and T. Cao, “Bistability and self-pulsation phenomena in silicon microring resonators based on nonlinear optical effects,” Opt. Express 20, 7454–7468 (2012).
[Crossref]

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

H. A. Haus, M. A. Popovic, M. R. Watts, C. Manolatou, B. E. Little, and S. T. Chu, “Optical resonators and filters,” in Optical Microcavities, K. Vahala, ed. (World Scientific, 2004).

Claps, R.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, 071115 (2005).
[Crossref]

Combrié, S.

A. de Rossi, M. Lauritano, S. Combrié, Q. V. Tran, and C. Husko, “Interplay of plasma-induced and fast thermal nonlinearities in a GaAs-based photonic crystal nanocavity,” Phys. Rev. A 79, 043818 (2009).
[Crossref]

Dambre, J.

T. Van Vaerenbergh, M. Fiers, P. Mechet, T. Spuesens, R. Kumar, G. Morthier, B. Schrauwen, J. Dambre, and P. Bienstman, “Cascadable excitability in microrings,” Opt. Express 20, 20292–20308 (2012).
[Crossref]

T. Van Vaerenbergh, M. Fiers, J. Dambre, and P. Bienstman, “Simplified description of self-pulsation and excitability by thermal and free-carrier effects in semiconductor microcavities,” Phys. Rev. A 86, 063808 (2012).
[Crossref]

de Rossi, A.

A. de Rossi, M. Lauritano, S. Combrié, Q. V. Tran, and C. Husko, “Interplay of plasma-induced and fast thermal nonlinearities in a GaAs-based photonic crystal nanocavity,” Phys. Rev. A 79, 043818 (2009).
[Crossref]

Dimitropoulos, D.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, 071115 (2005).
[Crossref]

Dumon, P.

Fang, Q.

T. Y. Liow, K. W. Ang, Q. Fang, J. F. Song, Y. Z. Xiong, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Silicon modulators and germanium photodetectors on SOI: monolithic integration, compatibility, and performance optimization,” IEEE J. Sel. Top. Quantum Electron. 16, 307–315 (2010).
[Crossref]

Fei, Y.

L. Zhang, Y. Fei, T. Cao, Y. Cao, Q. Xu, and S. Chen, “Multibistability and self-pulsation in nonlinear high-Q silicon microring resonators considering thermo-optical effect,” Phys. Rev. A 87, 053805 (2013).
[Crossref]

S. Chen, L. Zhang, Y. Fei, and T. Cao, “Bistability and self-pulsation phenomena in silicon microring resonators based on nonlinear optical effects,” Opt. Express 20, 7454–7468 (2012).
[Crossref]

Fiers, M.

T. Van Vaerenbergh, M. Fiers, P. Mechet, T. Spuesens, R. Kumar, G. Morthier, B. Schrauwen, J. Dambre, and P. Bienstman, “Cascadable excitability in microrings,” Opt. Express 20, 20292–20308 (2012).
[Crossref]

T. Van Vaerenbergh, M. Fiers, J. Dambre, and P. Bienstman, “Simplified description of self-pulsation and excitability by thermal and free-carrier effects in semiconductor microcavities,” Phys. Rev. A 86, 063808 (2012).
[Crossref]

Fomin, A. E.

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Foster, M. A.

Gaeta, A. L.

Gorodetsky, M. L.

Grover, R.

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705–713 (2002).
[Crossref]

Grudinin, I. S.

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

H. A. Haus, M. A. Popovic, M. R. Watts, C. Manolatou, B. E. Little, and S. T. Chu, “Optical resonators and filters,” in Optical Microcavities, K. Vahala, ed. (World Scientific, 2004).

Ho, P.-T.

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705–713 (2002).
[Crossref]

Husko, C.

A. de Rossi, M. Lauritano, S. Combrié, Q. V. Tran, and C. Husko, “Interplay of plasma-induced and fast thermal nonlinearities in a GaAs-based photonic crystal nanocavity,” Phys. Rev. A 79, 043818 (2009).
[Crossref]

Ibrahim, T. A.

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705–713 (2002).
[Crossref]

Ichimura, M.

T. Kuwayama, M. Ichimura, and E. Arai, “Interface recombination velocity of silicon-on-insulator wafers measured by microwave reflectance photoconductivity decay method with electric field,” Appl. Phys. Lett. 83, 928–930 (2003).
[Crossref]

Ilchenko, V. S.

Itabashi, S.

Jalali, B.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, 071115 (2005).
[Crossref]

Jhaveri, R.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, 071115 (2005).
[Crossref]

Johnson, F. G.

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705–713 (2002).
[Crossref]

Johnson, T. J.

Kou, R.

Kumar, R.

Kuwayama, T.

T. Kuwayama, M. Ichimura, and E. Arai, “Interface recombination velocity of silicon-on-insulator wafers measured by microwave reflectance photoconductivity decay method with electric field,” Appl. Phys. Lett. 83, 928–930 (2003).
[Crossref]

Kwong, D. L.

T. Y. Liow, K. W. Ang, Q. Fang, J. F. Song, Y. Z. Xiong, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Silicon modulators and germanium photodetectors on SOI: monolithic integration, compatibility, and performance optimization,” IEEE J. Sel. Top. Quantum Electron. 16, 307–315 (2010).
[Crossref]

Laine, J.-P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Lauritano, M.

A. de Rossi, M. Lauritano, S. Combrié, Q. V. Tran, and C. Husko, “Interplay of plasma-induced and fast thermal nonlinearities in a GaAs-based photonic crystal nanocavity,” Phys. Rev. A 79, 043818 (2009).
[Crossref]

Levy, J. S.

Li, M.

Liow, T. Y.

T. Y. Liow, K. W. Ang, Q. Fang, J. F. Song, Y. Z. Xiong, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Silicon modulators and germanium photodetectors on SOI: monolithic integration, compatibility, and performance optimization,” IEEE J. Sel. Top. Quantum Electron. 16, 307–315 (2010).
[Crossref]

Lipson, M.

Little, B. E.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

H. A. Haus, M. A. Popovic, M. R. Watts, C. Manolatou, B. E. Little, and S. T. Chu, “Optical resonators and filters,” in Optical Microcavities, K. Vahala, ed. (World Scientific, 2004).

Lo, G. Q.

T. Y. Liow, K. W. Ang, Q. Fang, J. F. Song, Y. Z. Xiong, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Silicon modulators and germanium photodetectors on SOI: monolithic integration, compatibility, and performance optimization,” IEEE J. Sel. Top. Quantum Electron. 16, 307–315 (2010).
[Crossref]

Luo, L. W.

Manolatou, C.

H. A. Haus, M. A. Popovic, M. R. Watts, C. Manolatou, B. E. Little, and S. T. Chu, “Optical resonators and filters,” in Optical Microcavities, K. Vahala, ed. (World Scientific, 2004).

Mechet, P.

Morthier, G.

Nishi, H.

Painter, O.

Park, S.

Pernice, W. H. P.

Poitras, C. B.

Popovic, M. A.

H. A. Haus, M. A. Popovic, M. R. Watts, C. Manolatou, B. E. Little, and S. T. Chu, “Optical resonators and filters,” in Optical Microcavities, K. Vahala, ed. (World Scientific, 2004).

Preston, K.

Priem, G.

Salem, R.

Schrauwen, B.

Schuck, C.

X. Sun, X. Zhang, C. Schuck, and H. X. Tang, “Nonlinear optical effects of ultrahigh-Q silicon photonic nanocavities immersed in superfluid helium,” Science Reports 3, 1436 (2013).

Shinojima, H.

Song, J. F.

T. Y. Liow, K. W. Ang, Q. Fang, J. F. Song, Y. Z. Xiong, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Silicon modulators and germanium photodetectors on SOI: monolithic integration, compatibility, and performance optimization,” IEEE J. Sel. Top. Quantum Electron. 16, 307–315 (2010).
[Crossref]

Spuesens, T.

Sun, X.

X. Sun, X. Zhang, C. Schuck, and H. X. Tang, “Nonlinear optical effects of ultrahigh-Q silicon photonic nanocavities immersed in superfluid helium,” Science Reports 3, 1436 (2013).

Tang, H. X.

X. Sun, X. Zhang, C. Schuck, and H. X. Tang, “Nonlinear optical effects of ultrahigh-Q silicon photonic nanocavities immersed in superfluid helium,” Science Reports 3, 1436 (2013).

W. H. P. Pernice, M. Li, and H. X. Tang, “Time-domain measurement of optical transport in silicon micro-ring resonators,” Opt. Express 18, 18438–18452 (2010).
[Crossref]

Tran, Q. V.

A. de Rossi, M. Lauritano, S. Combrié, Q. V. Tran, and C. Husko, “Interplay of plasma-induced and fast thermal nonlinearities in a GaAs-based photonic crystal nanocavity,” Phys. Rev. A 79, 043818 (2009).
[Crossref]

Tsuchizawa, T.

Turner-Foster, A. C.

Vahala, K. J.

Van, V.

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705–713 (2002).
[Crossref]

Van Thourhout, D.

Van Vaerenbergh, T.

T. Van Vaerenbergh, M. Fiers, P. Mechet, T. Spuesens, R. Kumar, G. Morthier, B. Schrauwen, J. Dambre, and P. Bienstman, “Cascadable excitability in microrings,” Opt. Express 20, 20292–20308 (2012).
[Crossref]

T. Van Vaerenbergh, M. Fiers, J. Dambre, and P. Bienstman, “Simplified description of self-pulsation and excitability by thermal and free-carrier effects in semiconductor microcavities,” Phys. Rev. A 86, 063808 (2012).
[Crossref]

Watanabe, T.

Watts, M. R.

H. A. Haus, M. A. Popovic, M. R. Watts, C. Manolatou, B. E. Little, and S. T. Chu, “Optical resonators and filters,” in Optical Microcavities, K. Vahala, ed. (World Scientific, 2004).

Wiederhecker, G. S.

Woo, J. C. S.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, 071115 (2005).
[Crossref]

Xiong, Y. Z.

T. Y. Liow, K. W. Ang, Q. Fang, J. F. Song, Y. Z. Xiong, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Silicon modulators and germanium photodetectors on SOI: monolithic integration, compatibility, and performance optimization,” IEEE J. Sel. Top. Quantum Electron. 16, 307–315 (2010).
[Crossref]

Xu, Q.

L. Zhang, Y. Fei, T. Cao, Y. Cao, Q. Xu, and S. Chen, “Multibistability and self-pulsation in nonlinear high-Q silicon microring resonators considering thermo-optical effect,” Phys. Rev. A 87, 053805 (2013).
[Crossref]

Yamada, K.

Yu, M. B.

T. Y. Liow, K. W. Ang, Q. Fang, J. F. Song, Y. Z. Xiong, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Silicon modulators and germanium photodetectors on SOI: monolithic integration, compatibility, and performance optimization,” IEEE J. Sel. Top. Quantum Electron. 16, 307–315 (2010).
[Crossref]

Zhang, L.

L. Zhang, Y. Fei, T. Cao, Y. Cao, Q. Xu, and S. Chen, “Multibistability and self-pulsation in nonlinear high-Q silicon microring resonators considering thermo-optical effect,” Phys. Rev. A 87, 053805 (2013).
[Crossref]

S. Chen, L. Zhang, Y. Fei, and T. Cao, “Bistability and self-pulsation phenomena in silicon microring resonators based on nonlinear optical effects,” Opt. Express 20, 7454–7468 (2012).
[Crossref]

Zhang, X.

X. Sun, X. Zhang, C. Schuck, and H. X. Tang, “Nonlinear optical effects of ultrahigh-Q silicon photonic nanocavities immersed in superfluid helium,” Science Reports 3, 1436 (2013).

Appl. Phys. Lett. (2)

D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, 071115 (2005).
[Crossref]

T. Kuwayama, M. Ichimura, and E. Arai, “Interface recombination velocity of silicon-on-insulator wafers measured by microwave reflectance photoconductivity decay method with electric field,” Appl. Phys. Lett. 83, 928–930 (2003).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

T. Y. Liow, K. W. Ang, Q. Fang, J. F. Song, Y. Z. Xiong, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Silicon modulators and germanium photodetectors on SOI: monolithic integration, compatibility, and performance optimization,” IEEE J. Sel. Top. Quantum Electron. 16, 307–315 (2010).
[Crossref]

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8, 705–713 (2002).
[Crossref]

J. Lightwave Technol. (1)

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FIMMWAVE, Photon Design Ltd., http://www.photond.com/products/fimmwave.htm .

Supplementary Material (1)

» Media 1: MOV (3486 KB)     

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Figures (8)

Fig. 1.
Fig. 1. Schematic of the measurement setup. The laser is amplified by EDFA and its polarization is controlled by PC, single-mode tapered fiber is used to couple the light into and out of the chip with coupling loss of about 5dB/facet. A DC power is used to adjust the free-carrier lifetime. Inset: SEM image of silicon MRR before fabricated PN junction. CW laser, tunable continuous-wave laser; EDFA, erbium-doped fiber amplifier; PC, polarization controller; PD, photodetector; OSA, optical spectrum analyzer.
Fig. 2.
Fig. 2. Measured spectra of optical transmission of the silicon MRR (without GSG probe) at various input power levels. The quoted input power refers to the power at the bus waveguide before coupling into the MRR. Inset: zoom-in views of optical spectra for lower input powers. The laser wavelength is swept from shorter wavelength to longer wavelength.
Fig. 3.
Fig. 3. Real-time waveforms at different input wavelength with fixed input power 10 dBm. (a) λ=1544.5nm (Δλ=610pm); (b) λ=1544.9nm (Δλ=1010pm). The movie of the dynamical process when sweeping the input wavelength from short to long can be found by clicking the hyperlink (Media 1).
Fig. 4.
Fig. 4. (a) Frequency of output oscillation with input wavelength detuning at different input power. (b) Duty ratio of output oscillating waveforms with input wavelength detuning at different input power. The input power is 8, 9, 10, and 11 dBm, respectively.
Fig. 5.
Fig. 5. Theoretical predicted boundaries of BI and SP at the map of input power and input wavelength detuning. The black circles denote the measured BI boundaries with the upper and lower solid lines representing the 1 dB power measurement tolerance. Insets: the numerical solutions of the used model showing the output dynamical waveforms at different input wavelength detunings with fixed input power at 10 mW. The wavelength detuning is 600 and 1000 pm, respectively, which is marked by red circles.
Fig. 6.
Fig. 6. (a) Experimental measured input power data of BI boundaries at different input wavelength detunings. The higher (lower) BI branch points marked by black circles (red rectangles) were measured by increasing (decreasing) the input power gradually. Two solid curves are the predicted BI boundaries. (b) One example of the relationship between output power and input power. Black: for input power increasing from lower to higher; Red: for input power decreasing from higher to lower. The power in horizontal and vertical coordinates has not excluded additional optical losses induced by couplers and polarization controller.
Fig. 7.
Fig. 7. Frequency and duty ratio of SP versus input wavelength detuning with input power fixed at 10 mW.
Fig. 8.
Fig. 8. (a) Experimental results of optical spectra at different input power with reverse voltage of 1V. Inset: Zoom-in views of the spectra at lower input power. (b) Comparison between the experimental measurements (black circles and green triangles) and numerical results of the regions of BI (two pink-dotted lines). The green triangles mark the resonant wavelength before stimulating BI, while the black circles denote the BI boundary wavelength.

Tables (1)

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Table 1. Parameter Values Used in Calculation

Equations (1)

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1τcar=SH+W+2(Hh)WHS,

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