Power limits and a figure of merit for stimulated Brillouin scattering in the presence of third and fifth order loss

Abstract

We derive a set of design guidelines and a figure of merit to aid the engineering process of on-chip waveguides for strong Stimulated Brillouin Scattering (SBS). To this end, we examine the impact of several types of loss on the total amplification of the Stokes wave that can be achieved via SBS. We account for linear loss and nonlinear loss of third order (two-photon absorption, 2PA) and fifth order, most notably 2PA-induced free carrier absorption (FCA). From this, we derive an upper bound for the output power of continuous-wave Brillouin-lasers and show that the optimal operating conditions and maximal realisable Stokes amplification of any given waveguide structure are determined by a dimensionless parameter ℱ involving the SBS-gain and all loss parameters. We provide simple expressions for optimal pump power, waveguide length and realisable amplification and demonstrate their utility in two example systems. Notably, we find that 2PA-induced FCA is a serious limitation to SBS in silicon and germanium for wavelengths shorter than 2200nm and 3600nm, respectively. In contrast, three-photon absorption is of no practical significance.

Impact of nonlinear loss on stimulated Brillouin scattering

“…It is attained for the optimal choice of waveguide length and pump power, both of which depend on F FCA . This interdependence is discussed in a separate paper [23]. In Fig.…”

“…These figures of merit must be greater than 1 in order for the Stokes wave to be amplified. The application of these figures of merit can result in upper bounds for the Stokes amplification; an investigation of the specific limits resulting from the presence of free carriers has been submitted separately as a rapid communication [23]. The layout of the manuscript is as follows: in Section II, we state the preliminaries of our analysis, we introduce the relevant equations of motion, define and apply the small-signal approximation for the Stokes wave and state the expressions for the effective nonlinear loss coefficients for the case of intra-mode forward and backward SBS.…”

Design of Partially Suspended Silicon Nitride Slot Waveguides for Efficient Forward Stimulated Brillouin Scattering

“…Furthermore, TPA also creates considerable free carriers, thereby TPA-induced FCA becomes the dominant mechanism of nonlinear losses in Si waveguides. The optical power coupling equations that include the nonlinear losses are as follows [30] dP p dz = −(α + βP p + γ P 2 p )P p − (2β + 4γ P p + γ P s + )P p P s (8) dP s dz = −(α + βP s + γ P 2 s )P s − (2β + 4γ P s + γ P p − )P p P s (9) where P p and P s are the pump and Stokes transmitted power, respectively. The coefficients α, β, γ and correspond to the linear loss, TPA loss, TPA-induced FCA loss and SBS gain.…”

Transformation-optics simulation method for stimulated Brillouin scattering

“…In this fashion, our method is able to predict configurations in which the combined contribution of elastic modes does not give rise to any gain, but instead result in net loss. Thus, our method expands the prediction capabilities of current theories, which by construction are only able to predict positive values of gain in optically lossless systems [6,7,9,22].…”