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.
Highlights
On-chip, coherent light generation is of interest for many classical photonics applications, including light sources at wavelengths where gain media are underdeveloped, optical frequency comb generation [1, 2], and optical data stream wavelength conversion [3]
We present a general design approach for optical parametric oscillators (OPOs) based on degenerate-pump four-wave mixing (FWM) to achieve the maximum possible conversion efficiency
In order to arrive at an economical formalism to account fully for nonlinear loss, we introduce the nonlinear figure of merit (NFOM), or, more precisely our nonlinear loss sine σ3
Summary
On-chip, coherent light generation is of interest for many classical photonics applications, including light sources at wavelengths where gain media are underdeveloped, optical frequency comb generation [1, 2], and optical data stream wavelength conversion [3]. We develop a temporal coupled mode theory (CMT) model of the parametric oscillator, and normalize it with respect to linear losses, giving a very general representation of the OPO design problem, in terms of normalized pump power and the material nonlinear figure of merit (NFOM). In this context, we discuss OPO architectures that offer certain advantages over single-cavity designs
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