Stimulated Brillouin scattering in nanoscale silicon step-index waveguides: A general framework of selection rules and calculating SBS gain

Optics Express

Volumn 21, Issue 25, 2013, Pages 31402-31419

  Qiu, Wenjun ^a   Rakich, Peter T ^b   Shin, Heedeuk ^b   Dong, Hui ^c   Soljačić, Marin ^a   Wang, Zheng ^c  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b Yale University   (United States)

^c The University of Texas at Austin   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHEMICAL BONDS; MOLECULAR ORBITALS; SILICON; WAVE FUNCTIONS; WAVEGUIDES;

FORWARD-AND-BACKWARD; GAIN COEFFICIENTS; MODAL CONFINEMENT; NANO-SCALE WAVEGUIDES; RADIATION PRESSURE; SILICON WAVEGUIDE; STEP-INDEX WAVEGUIDES; STIMULATED BRILLOUIN SCATTERING (SBS);

STIMULATED BRILLOUIN SCATTERING;

EID: 84890487411     PISSN: None     EISSN: 10944087     Source Type: Journal    
DOI: 10.1364/OE.21.031402     Document Type: Article

References (60)

1. R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, "Stimulated Brillouin scattering and coherent generation of intense hypersonic waves," Phys. Rev. Lett. 12, 592-595 (1964).
2. P. Dainese, P. Russell, N. Joly, J. Knight, G. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, "Stimulated Brillouin scattering from multi-ghz-guided acoustic phonons in nanostructured photonic crystal fibres," Nat. Phys. 2, 388-392 (2006).
3. A. Kobyakov, M. Sauer, and D. Chowdhury, "Stimulated Brillouin scattering in optical fibers," Adv. Opt. Photonics 2, 1-59 (2010).
4. M. S. Kang, A. Nazarkin, A. Brenn, and P. S. J. Russell, "Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial raman oscillators," Nat. Phys. 5, 276-280 (2009).
5. R. Pant, C. G. Poulton, D.-Y. Choi, H. Mcfarlane, S. Hile, E. Li, L. Thevenaz, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, "On-chip stimulated Brillouin scattering," Opt. Express 19, 8285-8290 (2011).
6. M. Tomes and T. Carmon, "Photonic micro-electromechanical systems vibrating at x-band (11-ghz) rates," Phys. Rev. Lett. 102, 113601 (2009).
7. A. Byrnes, R. Pant, E. Li, D. 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, 18845-18854 (2012).
8. Z. Yu and S. Fan, "Complete optical isolation created by indirect interband photonic transitions," Nat. Photonics 3, 91-94 (2009).
9. M. S. Kang, A. Butsch, and P. S. J. Russell, "Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre," Nat. Photonics 5, 549-553 (2011).
10. 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).
11. Z. Zhu, D. J. Gauthier, and R. W. Boyd, "Stored light in an optical fiber via stimulated Brillouin scattering," Science 318, 1748-1750 (2007).
12. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
13. K. Y. Song, M. Herráez, and L. Thévenaz, "Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering," Opt. Express 13, 82-88 (2005).
14. K. Y. Song, K. S. Abedin, K. Hotate, M. G. Herráez, and L. Thévenaz, "Highly efficient Brillouin slow and fast light using As2Se3 chalcogenide fiber," Opt. Express 14, 5860-5865 (2006).
15. R. Pant, M. D. Stenner, M. A. Neifeld, and D. J. Gauthier, "Optimal pump profile designs for broadband sbs slow-light systems," Opt. Express 16, 2764-2777 (2008).
16. R. Pant, A. Byrnes, C. G. Poulton, E. Li, D. Choi, S. Madden, B. Luther-Davies, and B. J. Eggleton, "Photonicchip- based tunable slow and fast light via stimulated Brillouin scattering," Opt. Lett. 37, 969-971 (2012).
17. T. Kurashima, T. Horiguchi, and M. Tateda, "Distributed-temperature sensing using stimulated Brillouin scattering in optical silica fibers," Opt. Lett. 15, 1038-1040 (1990).
18. A. Schliesser, R. Riviere, G. Anetsberger, O Arcizet, and T. J. Kippenberg, "Resolved-sideband cooling of a micromechanical oscillator," Nat. Phys. 4, 415-419 (2008).
19. G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, "Observation of spontaneous Brillouin cooling," Nat. Phys. 8, 203-207 (2012).
20. 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).
21. H. O. Hill, B. S. Kawasaki, and D. C. Johnson, "CW Brillouin laser," Appl. Phys. Lett. 28, 608-609 (1976).
22. I. V. Kabakova, R. Pant, D. Choi, S. Debbarma, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, "Narrow linewidth Brillouin laser based on chalcogenide photonic chip," Opt. Lett. 38, 3208-3211 (2013).
23. Y. R. Shen, N. Bloembergen, "Theory of stimulated Brillouin and Raman scattering," Phys. Rev. 137, A1787- A1805 (1965).
24. R. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2009).
25. G. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2006).
26. J. Botineau, E. Picholle, and D. Bahloul, "Effective stimulated Brillouin gain in singlemode optical fibres," Electron. Lett. 31, 2032-2034 (1995).
27. J. Wang, Y. Zhu, R. Zhang, and D. J. Gauthier, "FSBS resonances observed in a standard highly nonlinear fiber," Opt. Express 19, 5339-5349 (2011).
28. A. H. McCurdy, "Modeling of stimulated Brillouin scattering in optical fibers with arbitrary radial index profile," J. Lightwave Technol. 23, 3509 (2005).
29. X. Huang and S. Fan, "Complete all-optical silica fiber isolator via stimulated Brillouin scattering," J. Lightwave Technol. 29, 2267-2275 (2011).
30. M. S. Kang, A. Brenn, and P. S. J. Russell, "All-optical control of gigahertz acoustic resonances by forward stimulated interpolarization scattering in a photonic crystal fiber," Phys. Rev. Lett. 105, 153901 (2010).
31. P. T. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, "Giant enhancement of stimulated Brillouin scattering in the subwavelength limit," Phys. Rev. X 2, 011008 (2012).
32. H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson III, A. Starbuck, Z. Wang, and P. T. Rakich, "Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides," Nat. Commun. 4, 1944 (2013).
33. R. Van Laer, D. Van Thourhout, and R. Baets, "Strong stimulated Brillouin scattering in an on-chip silicon slot waveguide," in CLEO: Science and Innovations, San Jose, CA, 9-14 June 2013 .
34. P. T. Rakich, M. A. Popovi, M. Soljacic, and E. P. Ippen, "Trapping, corralling and spectral bonding of optical resonances through optically induced potentials," Nat. Photonics 1, 658-665 (2007).
35. M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, "Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces," Nat. Photonics 1, 416-422 (2007).
36. T. J. Kippenberg and K. J. Vahala, "Cavity optomechanics: Back-action at the mesoscale," Science 321, 1172-1176 (2008).
37. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, "Optomechanical crystals," Nature 462, 78-82 (2009).
38. G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, "Controlling photonic structures using optical forces," Nature 462, 633-636 (2009).
39. M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, "Modeling dispersive coupling andlosses of localized optical andmechanical modes in optomechanicalcrystals," Opt. Express 17, 20078-20098 (2009).
40. M. Li, W. H. P. Pernice, and H. X. Tang, "Tunable bipolar optical interactions between guided lightwaves," Nat. Photonics 3, 464-468 (2009).
41. J. Roels, I. D. Vlaminck, L. Lagae, B. Maes, D. V. Thourhout, and R. Baets, "Tunable optical forces between nanophotonic waveguides," Nat. Nanotechnol. 4, 510-513 (2009).
42. Q. Lin, J. Rosenberg, D. Chang, R. Camacho, M. Eichenfield, K. J. Vahala, and O. Painter, "Coherent mixing of mechanical excitations in nano-optomechanical structures," Nat. Photonics 4, 236-242 (2010).
43. D. Royer and E. Dieulesaint, Elastic Waves in Solids I: Free and Guided Propagation (Springer, 2000).
44. Z. Yu and S. Fan, "Complete optical isolation created by indirect interband photonic transitions," Nat. Photonics 3, 91-94 (2008).
45. P. T. Rakich, P. Davids, and Z. Wang, "Tailoring optical forces in waveguides through radiation pressure and electrostrictive forces," Opt. Express 18, 14439-14453 (2010).
46. M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, "Evanescent-wave bonding between optical waveguides," Opt. Lett. 30, 3042-3044 (2005).
47. P. T. Rakich, Z. Wang, and P. Davids, "Scaling of optical forces in dielectric waveguides: rigorous connection between radiation pressure and dispersion," Opt. Lett. 36, 217-219 (2011).
48. W. Qiu, P. Rakich, M. Soljacic, and Z. Wang, "Stimulated Brillouin scattering in slow light waveguides," arXiv1210.0738 (2012).
49. S. Chandorkar, M. Agarwal, R. Melamud, R. Candler, K. Goodson, and T. Kenny, "Limits of quality factor in bulk-mode micromechanical resonators," in IEEE 21st International Conference on Micro Electro Mechanical Systems, 2008. MEMS 2008 (2008), pp. 74-77.
50. E. Dieulesaint and D. Royer, Elastic Wvaes in Solids II: Generation, Acousto-Optic Interaction, Applications (Springer, 2000).
51. J. P. Gordon, "Radiation forces and momenta in dielectric media," Phys. Rev. A 8, 14-21 (1973).
52. P. W. Milonni and R. W. Boyd, "Momentum of light in a dielectric medium," Adv. Opt. Photonics, 2, 519-553 (2010).
53. S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, "Perturbation theory for Maxwell's equations with shifting material boundaries," Phys. Rev. E 65, 066611 (2002).
54. M. A. Hopcroft, W. D. Nix, and T. W. Kenny, "What is the Youngs Modulus of silicon?," J. Microelectromech. Syst. 19, 229-238 (2010).
55. L. S. Hounsome, R. Jones, M. J. Shaw, and P. R. Briddon, "Photoelastic constants in diamond and silicon," Phys. Status Solidi A 203, 3088-3093 (2006).
56. R. Shelby, M. Levenson, and P. Bayer, "Guided acoustic-wave Brillouin scattering," Phys. Rev. B 31, 5244-5252 (1985).
57. R. Shelby, M. Levenson, and P. Bayer, "Resolved forward Brillouin scattering in optical fibers," Phys. Rev. Lett. 54, 939-942 (1985).
58. R. Pant, A. Byrnes, C. G. Poulton, E. Li, D.-Y. Choi, S. Madden, B. Luther-Davies, and B. J. Eggleton, "Photonicchip- based tunable slow and fast light via stimulated Brillouin scattering," Opt. Lett. 37, 969-971 (2012).
59. 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).
60. 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).