Slow light through tightly coupled light waves and acoustic waves in nanoscale waveguides

Abstract

We develop a general framework of evaluating slow-light performance using Stimulated Brillouin Scattering (SBS) in optical waveguides via the overlap integral between optical and elastic eigen-modes. We show that spatial symmetry of the optical force dictates the selection rules of the excitable elastic modes. By applying this method to a rectangular silicon waveguide, we demonstrate the spatial distributions of optical force and elastic eigen-modes jointly determine the magnitude and scaling of SBS gain coefficient in both forward and backward SBS processes. We further apply this method to inter-modal SBS process, and demonstrate that the coupling between distinct optical modes is necessary to excite elastic modes with all possible symmetries. INTRODUCTIONStimulated Brillouin Scattering (SBS) is a third order nonlinear process in which two optical modes are coupled through an elastic mode 1,2 . In a waveguide system, the interference of pump and Stokes waves generates a time-varying optical force at the beat frequency. The optical force, while at resonance with an elastic mode at the phase-matching wavevector, excites the mechanical vibration of the waveguide, which can in turn scatter light between the pump and Stokes waves. Since its discovery, SBS has been extensively studied with a variety of applications in efficient phonon generation [3,4 , optical frequency conversion [5][6][7] , slow light [8][9][10][11] , and signal processing techniques 12,13 .The optical force that mediates SBS includes electrostriction force and radiation pressure 14,15 . Electrostriction is an intrinsic material nonlinearity, which arises from the tendency of materials to become compressed in the region of high optical intensity. In previous studies, electrostriction is treated as a bulk nonlinearity with only electrostriction body force taken into account 1,2 . We find that the discontinuities of optical intensities and photoelastic constants can generate electrostriction pressure on material boundaries. Radiation pressure is another boundary nonlinearity, which arises from the interaction of light with the material boundaries with discontinuous dielectric constant 16,17 . For nanoscale structures, radiation pressure is radically enhanced, enabling a variety of optomechanics applications [18][19][20][21][22][23] . Within nanoscale waveguides, the distributions of electrostriction force and radiation pressure are quite different. The interplay between these two effects creates new degree of freedoms of tailoring SBS process.In translationally invariant waveguides, SBS can be categorized into forward SBS (FSBS) and backward SBS (BSBS). In FSBS, the pump and Stokes waves propagate in the same direction, generating translationally invariant optical forces, which excite standing elastic modes 6 . In BSBS, the pump and Stokes waves propagate in the counter directions, generating translationally varying optical forces, which excite traveling elastic modes. SBS can also occur between distinct optical modes [24][25][26][27][28] . I...