Abstract

Nonlinear Bragg scattering, also known as wavelength exchange, is a non-degenerate four-wave-mixing process which has attracted considerable interest as means of noise-free quantum frequency translation [1, 2]. In elementary Bragg scattering two strong pumps at frequencies ω_p1 and ω_p2 = ω_p1 + Δ mediate the sinusoidal exchange of energy between a weak signal at ω₀ and an idler at ω₁ = ω₀ + Δ. The process is efficient only when phase-matched, which imposes a strict restriction to the choice of interacting frequencies: only a single signal frequency exists that can be phase-matched for fixed pump frequencies. Here we consider a cascade of Bragg scattering processes, and show that efficient exchange of energy between a signal and an n^th order idler at ω_n = ω₀ + nΔ is possible even if none of the elementary steps are phase-matched. Such exchange occurs when the sum of the individual phase-mismatches accumulated along the cascade vanishes, which is equivalent to the direct phase-matching of a higher-order χ^{(2n + 1)} nonlinear process mimicked by the cascade [3]. The possibility to phase-match different orders of the cascade for fixed pump frequencies relaxes the phase-matching requirements for Bragg scattering [4]. We also discuss the intimate link between phase-matched Bragg scattering cascades and interactions of solitons with weak linear waves.

© 2013 IEEE