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Physical Review A

Photon-pair generation in lossy coupled-resonator optical waveguides via spontaneous four-wave mixing

Mohsen Kamandar Dezfouli, Marc M. Dignam

Published Mar 16, 2017• 4 citations
Publisher

Abstract

We theoretically model pair generation and evolution via the nonlinear process of spontaneous four-wave mixing in a coupled-resonator optical waveguide in a photonic crystal slab. Using the adjoint master equation for a system of lossy coupled cavities, we calculate a symmetrized second-order coherence function to determine pair detection probability. We find that the scattering loss can have as large an effect on pair generation as waveguide dispersion. In particular, the wave-vector dependence of the loss can shift the frequency of the maximum detection probability and therefore cannot, in general, be ignored or treated via a simple overall loss factor.

DOI
10.1103/physreva.95.033815

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We theoretically model pair generation and evolution via the nonlinear process of spontaneous four-wave mixing in a coupled-resonator optical waveguide in a photonic crystal slab. Using the adjoint master equation for a system of lossy coupled cavities, we calculate a symmetrized second-order coherence function to determine pair detection probability. We find that the scattering loss can have as large an effect on pair generation as waveguide dispersion. In particular, the wave-vector dependence of the loss can shift the frequency of the maximum detection probability and therefore cannot, in general, be ignored or treated via a simple overall loss factor.
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We employ a quasimode representation of the adjoint master equation to study nonlinear pair-generation dynamics via spontaneous four-wave mixing in coupled-cavity systems in the presence of scattering loss. Perturbative analytic solutions for signal and idler photon-number operators are derived, which enable us to examine the effect of scattering loss on pair-generation dynamics. In particular, for a simple three-mode system, we show that any loss mismatch for the signal and idler photons increases the probability of finding unpaired photons. While decreasing the loss rates for signal and idler photons increases the pair signal brightness, it also results in higher generation rates for multiple pairs in the system, which can result in lower operational signal-to-noise ratios.
We develop a general Hamiltonian treatment of spontaneous four-wave mixing in a microring resonator side-coupled to a channel waveguide. The effect of scattering losses in the ring is included, as well as parasitic nonlinear effects including self- and cross-phase modulation. A procedure for computing the output of such a system for arbitrary parameters and pump states is presented. For the limit of weak pumping an expression for the joint spectral intensity of generated photon pairs, as well as the singles-to-coincidences ratio, is derived.
We investigate theoretically the temporal evolution of a squeezed state in lossy coupled-cavity systems. We present a general formalism based upon the tight-binding approximation and apply this to a two-cavity system as well as to a coupled-resonator optical waveguide in a photonic crystal. We derive analytical expressions for the number of photons and the quadrature noise in each cavity as a function of time when the initial excited state is a squeezed state in one of the cavities. We also analytically evaluate the time-dependent cross correlation between the photons in different cavities to evaluate the degree of quantum entanglement. We demonstrate that loss in such coupled-cavity systems cannot be treated using simple exponential factors. Finally, we also derive approximate analytic expressions for the maximum photon number, maximum squeezing, and maximum entanglement for cavities far from the initially excited cavity in a lossless coupled-resonator optical waveguide.