FDTD modeling of anisotropic nonlinear optical phenomena in silicon waveguides

Optics Express

Volumn 18, Issue 20, 2010, Pages 21427-21448

  Dissanayake, Chethiya M ^a   Premaratne, Malin ^a   Rukhlenko, Ivan D ^a   Agrawal, Govind P ^b  

^a MONASH UNIVERSITY   (Australia)

^b UNIVERSITY OF ROCHESTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; FINITE DIFFERENCE TIME DOMAIN METHOD; NONLINEAR OPTICS; NUMERICAL ANALYSIS; OPTICAL PROPERTIES; PHASE MODULATION; PHOTONIC DEVICES; POLARIZATION; WAVEGUIDES;

ANISOTROPIC OPTICAL PROPERTIES; COMPUTATIONALLY EFFICIENT; CROSS-PHASE MODULATIONS; FDTD MODEL; FDTD MODELING; LONGITUDINAL OPTICAL; NON-LINEAR OPTICAL; NONLINEAR EFFECT; NOVEL DEVICES; NUMERICAL SIMULATORS; OPTICAL PHENOMENA; POLARIZATION DEPENDENCE; POLARIZATION EFFECT; REALISTIC CONDITIONS; SILICON PHOTONICS; SILICON WAVEGUIDE; SINGLE MODE; SLOWLY VARYING ENVELOPE APPROXIMATION; THIRD-ORDER;

THREE DIMENSIONAL;

EID: 77958020651     PISSN: None     EISSN: 10944087     Source Type: Journal    
DOI: 10.1364/OE.18.021427     Document Type: Article

References (79)

1. H. Iwai and S. Ohmi, "Silicon integrated circuit technology from past to future," Microelectron. Reliab. 42, 465-491 (2002).
2. S. E. Thompson and S. Parthasarathy, "Moore's law: The future of Si microelectronics," Mater. Today 9, 20-25 (2006).
3. M. Schulz, "The end of the road for silicon?" Nature 399, 729-730 (1999).
4. B. Jalali, "Can silicon change photonics?" Phys. Status Solidi (a) 2, 213-224 (2008).
5. R. A. Soref, "The past, present, and future of silicon photonics," IEEE J. Sel. Top. Quantum Electron. 12, 1678-1687 (2006).
6. G. T. Reed and A. P. Knight, Silicon Photonics: An Introduction (Wiley, Hoboken, NJ, 2004).
7. L. Pavesi and D. J. Lockwood, Eds., Silicon Photonics (Springer, New York, 2004).
8. B. Jalali, S. Yegnanarayanan, T. Yoon, T. Yoshimoto, I. Rendina, and F. Coppinger, "Advances in silicon-on-insulator optoelectronics," IEEE J. Sel. Top. Quantum Electron. 4, 938-947 (1998).
9. B. Jalali and S. Fathpour, "Silicon Photonics," J. Lightwave Technol. 24, 1460-4615 (2006).
10. R. Claps, D. Dimitropoulos, and B. Jalali, "Stimulated Raman scattering in silicon waveguides," Electron. Lett. 38, 1352-1354 (2002).
11. M. Dinu, F. Quochi, and H. Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett. 82, 2954-2956 (2003).
12. E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood, Jr., "Self-phase-modulation in submicron silicon-on-insulator photonic wires," Opt. Express 14, 5524-5534 (2006).
13. I.-W. Hsieh, X. Cheng, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, "Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides," Opt. Express 14, 12380-12387 (2006).
14. I.-W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M.Jr. Osgood, S. J. McNab, and Y. A. Vlasov, "Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires," Opt. Express 15, 1135-1146 (2007).
15. T. Liang, L. Nunes, T. Sakamoto, K. Sasagawa, T. Kawanishi, M. Tsuchiya, G. Priem, D. V. Thourhout, P. Dumon, R. Baets, and H. Tsang, "Ultrafast all-optical switching by cross-absorption modulation in silicon wire waveguides," Opt. Express 13, 7298-7303 (2005). (Pubitemid 41338455)
16. Q. Lin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, "Ultrabroadband parametric generation and wavelength conversion in silicon waveguides," Opt. Express 14, 4786-4799 (2006).
17. Y.-H Kuo, H. Rong, V. Sih, S. Xu, M. Paniccia, and O. Cohen, "Demonstration of wavelength conversion at 40 Gb/s data rate in silicon waveguides," Opt. Express 14, 11721-11726 (2006). (Pubitemid 44826858)
18. H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J.-I. Takahashi, and S.-I. Itabashi, "Four-wave mixing in silicon wire waveguides," Opt. Express 13, 4629-4637 (2005).
19. R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, "Anti-Stokes Raman conversion in silicon waveguides," Opt. Express 11, 2862-2872 (2003).
20. V. Raghunathan, R. Claps, D. Dimitropoulos, and B. Jalali, "Parametric Raman wavelength conversion in scaled silicon waveguides," J. Lightwave Technol. 23, 2094-2102 (2005).
21. Ö. Boyraz and B. Jalali, "Demonstration of a silicon Raman laser," Opt. Express 12, 5269-5273 (2004).
22. H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, "An all-silicon Raman laser," Nature 433, 292-294 (2005).
23. R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, "Observation of stimulated Raman amplification in silicon waveguides," Opt. Express 11, 1731-1739 (2003).
24. Q. Xu, V. R. Almeida, and M. Lipson, "Demonstration of high Raman gain in a submicrometer-size silicon-on-insulator waveguide," Opt. Lett. 30, 35-37 (2005).
25. T. K. Liang, L. R. Nunes, M. Tsuchiya, K. S. Abedin, T. Miyazaki, D. Van Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H. K. Tsang, "High speed logic gate using two-photon absorption in silicon waveguides," Opt. Commun. 265, 171-174 (2006).
26. C. Manolatou and M. Lipson, "All-optical silicon modulators based on carrier injection by two-photon absorption," J. Lightwave Technol. 24, 1433-1439 (2006).
27. D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, "Ultrafast all-optical modulation via two-photon absorption in silicon-on-insulator waveguides," Electron. Lett. 41, 320-321 (2005).
28. R. Dekker, A. Driessen, T. Wahlbrink, C. Moormann, J. Niehusmann, and M. Först, "Ultrafast Kerr-induced all-optical wavelength conversion in silicon waveguides using 1.55 mm femtosecond pulses," Opt. Express 14, 8336-8346 (2006). (Pubitemid 44331051)
29. R. Espinola, J. Dadap, R. Osgood, Jr., S. McNab, and Y. Vlasov, "C-band wavelength conversion in silicon photonic wire waveguides," Opt. Express 13, 8336-8346 (2005).
30. R. Salem, G. E. Tudury, T. U. Horton, G. M. Carter, and T. E. Murphy, "Polarization-insensitive optical clock recovery at 80 Gb/s using a silicon photodiode," IEEE Photon. Technol. Lett. 17, 1968-1970 (2005). (Pubitemid 41488313)
31. O. Boyraz, P. Koonath, V. Raghunathan, and B. Jalali, "All optical switching and continuum generation in silicon waveguides," Opt. Express 12, 4094-4102 (2004).
32. I.-W. Hsieh, X. Chen, X. Liu, J. I. Dadap, N. C. Panoiu, C.-Y. Chou, F. Xia, W. M. Green, Y. A. Vlasov, and R. M. Osgood, "Supercontinuum generation in silicon photonic wires," Opt. Express 15, 15242-15249 (2007).
33. E. K. Tien, N. S. Yuksek, F. Qian, and O. Boyraz, "Pulse compression and modelocking by using TPA in silicon waveguides," Opt. Express 15, 6500-6506 (2007).
34. L. Yin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, "Optical switching using nonlinear polarization rotation inside silicon waveguides," Opt. Lett. 34, 476-478 (2009).
35. B. A. Daniel and G. P. Agrawal, "Vectorial nonlinear propagation in silicon nanowire waveguides: Polarization effects," J. Opt. Soc. Am. B 27, 956-965 (2010).
36. I. D. Rukhlenko, I. L. Garanovich, M. Premaratne, A. A. Sukhorukov, G. P. Agrawal, and Yu. S. Kivshar, "Polarization rotation in silicon waveguides: Analytical modeling and applications," IEEE Photonics Journal 2, 423-435 (2010).
37. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, Boston, 2005).
38. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1999).
39. K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
40. R. M. Joseph and A. Taflove, "FDTD Maxwell's equations models for nonlinear electrodynamics and optics," IEEE Trans. Antennas Propag. 45, 364-374 (1997).
41. P. M. Goorjian, A. Taflove, R. M. Joseph, and S. C. Hagness, "Computational modeling of femtosecond optical solitons from Maxwell's equations," IEEE J. Quantum Electron. 28, 2416-2422 (1992).
42. F. L. Teixeira, "Time-domain finite-difference and finite-element methods for Maxwell equations in complex media," IEEE Trans. Antennas Propag. 56, 2150-2166 (2008).
43. J. Schneider and S. Hudson, "A finite-difference time-domain method applied to anisotropic material," IEEE Trans. Antennas Propag. 41, 994-999 (1993).
44. R. Holland, "Finite-difference solution of Maxwell's equations in generalized nonorthogonal coordinated," IEEE Trans. Nucl. Sci. NS-30, 4589-4591 (1983).
45. L. X. Dou and A. R. Sebak, "3D FDTD method for arbitrary anisotropic materials," Microwave Opt. Technol. Lett. 48, 2083-2090 (2006).
46. D.-X. Xu, P. Cheben, D. Dalacu, A. Delâge, S. Janz, B. Lamontagne, M.-J. Picard, and W. N. Ye, "Eliminating the birefringence in silicon-on-insulator ridge waveguides by use of cladding stress," Opt. Lett. 29, 2384-2386 (2004).
47. J. Pastrnak and K. Vedam, "Optical anisotropy of silicon single crystals," Phys. Rev. B 3, 2567-2571 (1971).
48. T. Chu, M. Yamada, J. Donecker, M. Rossberg, V. Alex, and H. Riemann, "Optical anisotropy in dislocation-free silicon single crystals," Microelectron. Eng. 66, 327-332 (2003).
49. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, Boston, 2003).
50. E. B. Graham and R. E. Raab, "Light propagation in cubic and other anisotropic crystals," Proc. R. Soc. London, Ser. A 430, 593-614 (1990).
51. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, New York, 1991).
52. R. M. Osgood, Jr., N. C. Panoiu, J. I. Dadap, X. Liu, X. Chen, I. Hsieh, E. Dulkeith, W. M. J. Green, and Y. A. Vlasov, "Engineering nonlinearities in nanoscale optical systems: Physics and applications in dispersion-engineered silicon nanophotonic wires," Adv. Opt. Photonics 1, 162-235 (2009).
53. Q. Lin, O. J. Painter, and G. P. Agrawal, "Nonlinear optical phenomena in silicon waveguides: Modeling and applications," Opt. Express 15, 16604-16644 (2007).
54. B. Jalali, V. Raghunathan, D. Dimitropoulos, and Ö. Boyraz, "Raman-based silicon photonics," IEEE J. Sel. Top. Quantum Electron. 12, 412-421 (2006).
55. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, Boston, 2007).
56. I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, "Analytical study of optical bistability in silicon-waveguide resonators," Opt. Express 17, 22124-22137 (2009).
57. I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, "Analytical study of optical bistability in silicon ring resonators," Opt. Lett. 35, 55-57 (2010).
58. V. R. Almeida and M. Lipson, "Optical bistability on a silicon chip," Opt. Lett. 29, 2387-2389 (2004).
59. Q. Xu and M. Lipson, "Carrier-induced optical bistability in silicon ring resonators," Opt. Lett. 31, 341-343 (2006).
60. R. F. Tinder, Tensor Properties of Solids (Morgan & Claypool Publishers, San Rafael, 2008).
61. J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, "Anisotropic nonlinear response of silicon in the near-infrared region," Appl. Phys. Lett. 91, 071113(1-3) (2007).
62. B. Tatian, "Fitting refractive-index data with the Sellmeier dispersion formula," Appl. Opt. 23, 4477-4485 (1984).
63. C. Dissanayake, I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, "Raman-mediated nonlinear interactions in silicon waveguides: Copropagating and counterpropagating pulses," IEEE Photonics Technol. Lett. 21, 1372-1374 (2009).
64. L. Yin, Q. Lin, and G. P. Agrawal, "Soliton fission and supercontinuum generation in silicon waveguides," Opt. Lett. 32, 391-393 (2007).
65. H. H. Li, "Refractive index of silicon and germanium and its wavelength and temperature derivatives," J. Phys. Chem. Ref. Data 9, 561-658 (1980).
66. J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, "Optical solitons in a silicon waveguide," Opt. Express 15, 7682-7688 (2007).
67. N. C. Panoiu, X. Chen, and R. M. Osgood, Jr., "Modulation instability in silicon photonic nanowires," Opt. Lett. 31, 3609-3611 (2006).
68. H. Garcia and R. Kalyanaraman, "Phonon-assisted two-photon absorption in the presence of a dc-field: The nonlinear Franz-Keldysh effect in indirect gap semiconductors," J. Phys. B 39, 2737-2746 (2006).
69. P. H. Wendland and M. Chester, "Electric field effects on indirect optical transitions in silicon," Phys. Rev. 140, A1384-A1390 (1965).
70. M. Cardona and G. Güntherodt, Light Scattering in Solids II, M. Cardona and G. Güntherodt, Eds. (SpringerVerlag, New York, 1982).
71. X. Chen, N. C. Panoiu, and R. M. Osgood, Jr., "Theory of Raman-mediated pulsed amplification in silicon-wire waveguides," IEEE J. Quantum Electron. 42, 160-170 (2006).
72. Y. Okawachi, M. A. Foster, J. E. Sharping, A. L. Gaeta, Q. Xu, and M. Lipson, "All-optical slow-light on a photonic chip," Opt. Express 14, 2317-2322 (2006).
73. H. K. Tsang and Y. Liu, "Nonlinear optical properties of silicon waveguides," Semicond. Sci. Technol. 23, 064007(1-9) (2008).
74. R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, "Influence of nonlinear absorption on Raman amplification in silicon-on-insulator waveguides," Opt. Express 12, 2774-2780 (2004).
75. A. Liu, H. Rong, R. Jones, O. Cohen, D. Hak, and M. Paniccia, "Optical amplification and lasing by stimulated Raman scattering in silicon waveguides," J. Lightwave Technol. 24, 1440-1455 (2006).
76. S. Afshar and T. M. Monro, "A full vectorial model for pulse propagation in emerging waveguides with subwave-length structures part I: Kerr nonlinearity," Opt. Express 17, 2298-2318 (2009).
77. G. W. Rieger, K. S. Virk, and J. F. Young, "Nonlinear propagation of ultrafast 1.5 mm pulses in high-index-constrast silicon-on-insulator waveguides," Appl. Phys. Lett. 84, 900-902 (2004).
78. N. Suzuki, "FDTD analysis of two-photon absorption and free-carrier absorption in Si high-contrast waveguides," J. Lightwave Technol. 25, 2495-2501 (2007).
79. I. D. Rukhlenko, C. Dissanayake, and M. Premaratne, "Visualization of electromagnetic-wave polarization evolution using the Poincaré sphere," Opt. Lett. 35, 2221-2223 (2010).