Design of triply-resonant microphotonic parametric oscillators based on Kerr nonlinearity

Abstract

We propose optimal designs for triply-resonant optical parametric oscillators (OPOs) based on degenerate four-wave mixing (FWM) in microcavities. We show that optimal designs in general call for different external coupling to pump and signal/idler resonances. We provide a number of normalized performance metrics including threshold pump power and maximum achievable conversion efficiency for OPOs with and without two-photon (TPA) and free-carrier absorption (FCA). We find that the maximum achievable conversion efficiency is bound to an upper limit by nonlinear and free-carrier losses independent of pump power, while linear losses only increase the pump power required to achieve a certain conversion efficiency. The results of this work suggest unique advantages in on-chip implementations that allow explicit engineering of resonances, mode field overlaps, dispersion, and wavelength-and mode-selective coupling. We provide universal design curves that yield optimum designs, and give example designs of microring-resonator-based OPOs in silicon at the wavelengths 1.55 μm (with TPA) and 2.3 μm (no TPA) as well as in silicon nitride (Si(3)N(4)) at 1.55 μm. For typical microcavity quality factor of 10(6), we show that the oscillation threshold in excitation bus can be well into the sub-mW regime for silicon microrings and a few mW for silicon nitride microrings. The conversion efficiency can be a few percent when pumped at 10 times of the threshold. Next, based on our results, we suggest a family of synthetic "photonic molecule"-like, coupled-cavity systems to implement optimum FWM, where structure design for control of resonant wavelengths can be separated from that of optimizing nonlinear conversion efficiency, and where furthermore pump, signal, and idler coupling to bus waveguides can be controlled independently, using interferometric cavity supermode coupling as an example. Finally, consideration of these complex geometries calls for a generalization of the nonlinear figure of merit (NFOM) as a metric for performance in nonlinear photonic systems, and shows different efficiencies for single and multi-cavity geometries, as well as for standing and traveling wave excitations.

A compact, integrated silicon device for the generation of spectrally filtered, pair-correlated photons

“…This process can also be stimulated, in which case input power at the signal frequency increases the output power of the idler frequency, which can be used for parametric oscillation [22][23][24][25]. However, it is only through the spontaneous process that the correlated photon pairs needed for quantum applications can be generated.…”

Four-wave mixing in silicon coupled-cavity resonators with port-selective, orthogonal supermode excitation

“…Optimum design of an optical parametric oscillator calls for unequal coupling of the waveguide(s) to the three resonances that interact via FWM [8,9]. Also, in parametric wavelength conversion and/or amplification of an optical data stream, to maximally utilize a CW pump, we suggest that a narrow-linewidth pump resonance should be used to minimize the needed pump power, while high bit-rate data streams require widelinewidth signal and idler resonances to accommodate the modulated signals.…”

“…Unlike a single-ring resonator, a triple-ring resonator does not require careful design of waveguide cross-section dimension to minimize dispersion for phase matching-the three supermodes of the same longitudinal order in triple cavities automatically satisfy it as long as the rings are identical and couplings are small. However, since the three modes have different mode profiles, their effective overlap volume for FWM is four times as large as that of a single microring [9]. This efficiency reduction may serve as a necessary trade off for the additional flexibility in design.…”

“…The little transmission dips E (A, C) show that "signal (pump) bus" couples weakly to pump (signal/idler) resonance. [9] in a silicon microcavity with nonlinear loss included. Critical coupling and perfect phase matching are assumed.…”

“…A few ratios of free carrier and photon lifetime are used. [9], which is the in-bus pump power normalized to the oscillation threshold power with optimum coupling when nonlinear loss can be neglected. This oscillation threshold power scales quadratically with intrinsic cavity loss rate and linearly with nonlinear interaction mode volume.…”