A Hamiltonian treatment of stimulated Brillouin scattering in nanoscale integrated waveguides

We present a multimode Hamiltonian formulation for the problem of opto-acoustic interactions in optical waveguides. We establish a Hamiltonian representation of the acoustic field and then introduce a full system with a simple opto-acoustic coupling that includes both photoelastic/electrostrictive and radiation pressure/moving boundary effects. The Heisenberg equations of motion are used to obtain coupled mode equations for quantized envelope operators for the optical and acoustic fields. We show that the coupling coefficients obtained coincide with those established earlier, but our formalism provides a much simpler demonstration of the connection between radiation pressure and moving boundary effects than in previous work [C. Wolff et al, Physical Review A 92, 013836 (2015)].Comment: 39 pages: 20 pages for main article + 19 pages supplementary information; 3 figure

Strongly driven nonlinear quantum optics in microring resonators

We present a detailed analysis of strongly driven spontaneous four-wave mixing in a lossy integrated microring resonator side-coupled to a channel waveguide. A nonperturbative, analytic solution within the undepleted pump approximation is developed for a cw pump input of arbitrary intensity. In the strongly driven regime self- and cross-phase modulation, as well as multi-pair generation, lead to a rich variety of power-dependent effects; the results are markedly different than in the low power limit. The photon pair generation rate, single photon spectrum, and joint spectral intensity (JSI) distribution are calculated. Splitting of the generated single photon spectrum into a doublet structure associated with both pump detuning and cross-phase modulation is predicted, as well as substantial narrowing of the generated signal and idler bandwidths associated with the onset of optical parametric oscillation at intermediate powers. Both the correlated and uncorrelated contributions to the JSI are calculated, and for sufficient powers the uncorrelated part of the JSI is found to form a quadruplet structure. The pump detuning is found to play a crucial role in all of these phenomena, and a critical detuning is identified which divides the system behaviour into distinct regimes, as well as an optimal detuning strategy which preserves many of the low-power characteristics of the generated photons for arbitrary input power.Comment: 18 pages, 10 figure

Surface - lattice resonances in 2d arrays of spheres: multipolar interactions and a mode analysis

We present a multipolar model of surface - lattice resonances (SLRs) in 2d arrays of spheres including the electric dipole, magnetic dipole, and electric quadrupole moments of the spheres. We identify SLRs of dipolar and multipolar character, show the importance of non-resonant multipoles in their description, and discuss the sensitivity of SLRs to illumination conditions. We link SLRs to an excitation of modes supported by the array, and we propose a simplified model of the mode dispersion relations that explains the sensitivity of SLRs and the band gap in mode dispersion found at low frequencies. Finally we discuss the resonant features associated with a direct coupling to a mode which can occur in addition to the diffractive coupling signalled by SLRs.Comment: 20 pages, 17 figure

Why you should not use the electric field to quantize in nonlinear optics

We show that using the electric field as a quantization variable in nonlinear optics leads to incorrect expressions for the squeezing parameters in spontaneous parametric down-conversion and conversion rates in frequency conversion. This observation is related to the fact that if the electric field is written as a linear combination of bosonic creation and annihilation operators one cannot satisfy Maxwell's equations in a nonlinear dielectric.Comment: This version corrects a minor typo from the published version in Optics Letters. Eq. 22 should have an \epsilon_0 that is lacking in the OL versio