Cascaded forward Brillouin scattering to all Stokes orders

Abstract

View the article online for updates and enhancements. AbstractInelastic scattering processes such as Brillouin scattering can often function in cascaded regimes and this is likely to occur in certain integrated opto-acoustic devices. We develop a Hamiltonian formalism for cascaded Brillouin scattering valid for both quantum and classical regimes. By regarding Brillouin scattering as the interaction of a single acoustic envelope and a single optical envelope that covers all Stokes and anti-Stokes orders, we obtain a compact model that is well suited for numerical implementation, extension to include other optical nonlinearities or short pulses, and application in the quantum-optics domain. We then theoretically analyze intra-mode forward Brillouin scattering (FBS) for arbitrary waveguides with and without optical dispersion. In the absence of optical dispersion, we find an exact analytical solution. With a perturbative approach, we furthermore solve the case of weak optical dispersion. Our work leads to several key results on intra-mode FBS. For negligible dispersion, we show that cascaded intra-mode FBS results in a pure phase modulation and discuss how this necessitates specific experimental methods for the observation of fiber-based and integrated FBS. Further, we discuss how the descriptions that have been established in these two classes of waveguides connect to each other and to the broader context of cavity opto-mechanics and Raman scattering. Finally, we draw an unexpected striking similarity between FBS and discrete diffraction phenomena in waveguide arrays, which makes FBS an interesting candidate for future research in quantum-optics.

Quantum theory of continuum optomechanics

“…This keeps our approach general and simplifies the representation of the interacting fields, especially for situations with strongly nonlinear dynamics. For example, this approach avoids the need to treat cascaded forward-scattering with an infinite number of photon fields, similar to the approach taken in [32].…”

Shaping nonlinear optical response using nonlocal forward Brillouin interactions

“…When considering non-zero GVD, the modulation experienced by the light in waveguide B will no longer be purely phase modulated and will exhibit some residual intensity modulation [28]. We numerically demonstrate the effect of GVD by keeping the second order term of the optical dispersion operator in equation (A5) in both waveguides A and B , where we have used a piecewise linear approximation.…”

“…In the absence of strong optical dispersion, an FSBS process enables light to be cascaded to multiple optical frequencies [13,25,27,28], and we describe the optical fields in each waveguide as a sum of discrete tones with field amplitude a n , and spaced by frequency Ω such that w w -=W n n 1…”

“…In the presence of GVD, the output field will no longer be purely phase modulated, and will exhibit residual amplitude modulation (RAM) [28] (discussed further in appendix F).…”

Spectral photonic lattices with complex long-range coupling

“…Broken TRS is of considerable importance in topological physics, but is challenging to implement in optics, requiring for example a periodic modulation of the lattice [2]. Photonic lattice systems utilizing dimensions other than space potentially allow greater freedom to realize these novel features and explore their effects; for instance, discretized spectral components of optical waves can couple to each other driven by nonlinear frequency conversion [3], photon-phonon interactions [4,5], and fast modulation of optical resonators [6]. Temporal lattices have also been studied extensively, particularly in the contexts of quantum simulation and parity-time symmetry [7,8].…”