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

Abstract

We develop a general framework of evaluating the Stimulated Brillouin Scattering (SBS) gain coefficient in optical waveguides via the overlap integral between optical and elastic eigen-modes. This full-vectorial formulation of SBS coupling rigorously accounts for the effects of both radiation pressure and electrostriction within micro- and nano-scale waveguides. We show that both contributions play a critical role in SBS coupling as modal confinement approaches the sub-wavelength scale. Through analysis of each contribution to the optical force, 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 how the optical force distribution and elastic modal profiles jointly determine the magnitude and scaling of SBS gains in both forward and backward SBS processes. We further apply this method to the study of intra- and inter-modal SBS processes, and demonstrate that the coupling between distinct optical modes are necessary to excite elastic modes with all possible symmetries. For example, we show that strong inter-polarization coupling can be achieved between the fundamental TE- and TM-like modes of a suspended silicon waveguide.

Simultaneous Guidance of Surface Acoustic and Surface Optical Waves in Phoxonic Crystal Slabs

“…As numerous attempts have been devoted to slow down light or sound in the PTC [43] or PNC [44,45] structures, it can be inferred that by finely tuning the geometrical parameters, the improvement of simultaneously slow sound and light can be realized in this kind of PXC structure. We believe the PXC surface waveguides can be adopted to study the optomechanical/acousto-optical interaction between the photonic and phononic guided modes [46][47][48]. The development of the waveguides supporting the propagation of slow photons and phonons at the same time may result in the enhancement of the photon-phonon interaction.…”

Guided-wave Brillouin scattering in air

“…nonchiral) and therefore f kl = 0 when k = l. Using to represent k = l and ⊥ to represent k = l, and following Refs. [13,24,25], the Brillouin gain for gases can therefore be written as:…”

Transformation-optics simulation method for stimulated Brillouin scattering

“…However, there is a limitation to simply implementing the nonlinear coupling terms as weak contributions to standard differential equations: a computation solving the electromagnetic wave equation in Eulerian coordinates is not by default able to account for the movement of the geometry, arising from the existence of displacements (which are in turn computed in a Lagrangian frame). This invariably leads to wrong results, especially at the nanoscale, where the effect of (moving) interfaces can play a dominant role [6,7,9]. The obstacle could be avoided by performing a time-domain study instead, but it is in practice undesirable, because of the wildly different time scales of the optical and mechanical periods.…”

“…These effects are so dramatic as to be 2 to 4 orders of magnitude larger than traditional theories predict (5 in the case of forward SBS) [6]. Naturally, new theoretical tools have been developed to study and describe these phenomena both in waveguides and various resonant structures [6][7][8], which are understood to be due to a combination of surface electrostriction and radiation pressure. In hindsight, it is unsurprising that these effects only become predominant at the nanoscale, where the surface-to-volume ratio * roberto.zecca@duke.edu of particles and waveguides is so high.…”

“…While it has been known and experimented upon for several decades, recent years have seen a renewed interest in SBS and related effects, which already enable many devices, ranging from powerful sources and amplifiers to platforms for the study of slow light [4] and nonreciprocity [5], and show great promise for future applications. There has been a growing body of literature on the previously unknown gain enhancements that can be achieved by specifically tailored nanostructures [6][7][8][9]. In particular, it has been proven by theory and experiment [10] that when waveguide geometries reach the nanoscale, previously unexpected, giant Brillouin gain enhancements occur.…”