Nonlinear harmonic generation and devices in doubly resonant Kerr cavities

Abstract

We describe a theoretical analysis of the nonlinear dynamics of third-harmonic generation ͑ → 3͒ via Kerr ͑ ͑3͒ ͒ nonlinearities in a resonant cavity with resonances at both and 3. Such a doubly resonant cavity greatly reduces the required power for efficient harmonic generation, by a factor of ϳV / Q 2 , where V is the modal volume and Q is the lifetime, and can even exhibit 100% harmonic conversion efficiency at a critical input power. However, we show that it also exhibits a rich variety of nonlinear dynamics, such as multistable solutions and long-period limit cycles. We describe how to compensate for self-and cross-phase modulation ͑which otherwise shifts the cavity frequencies out of resonance͒, and how to excite the different stable solutions ͑and especially the high-efficiency solutions͒ by specially modulated input pulses.

High-efficiency degenerate four-wave mixing in triply resonant nanobeam cavities

“…The frequency mismatch at which this bifurcation occurs is proportional to P m , so that, as P m → 0, the regime over which there exist high-efficiency steady states reduces to a single fixed point occurring at cp = 0. Beyond this bifurcation point, the system enters a limit-cycle regime (shaded regions) characterized by periodic modulations of the output signal in time [37,38,72]. Interestingly, we find that the average efficiency of the limit cycles (dashed lines)…”

“…Multistability complicates matters since, depending on the initial conditions, the system can fall into different stable solutions and in particular, simply turning on the source at the critical input power may result in an undesirable low-efficiency solution. One well-known technique that allows such a system to lock into the desired high-efficiency solutions is to superimpose a gradual exponential turn-on of the pump with a Gaussian pulse of larger amplitude [37]. We found that a single Gaussian pulse with a peak power of 4P crit 0 and a temporal width ∼τ m , depicted in the right inset of Fig.…”

“…Recent developments in nanofabrication are enabling fabrication of nanophotonic structures, e.g., waveguides and cavities that confine light over long times and small volumes [17][18][19][20][21], minimizing the power requirements of nonlinear devices [22,23] and paving the way for novel on-chip applications based on all-optical nonlinear effects [18,[24][25][26][27][28][29][30][31][32][33]. In addition to greatly enhancing light-matter interactions, the use of cavities can also lead to qualitatively rich dynamical phenomena, including multistability and limit cycles [34][35][36][37][38][39][40]. In this paper, we explore realistic microcavity designs that enable highly efficient degenerate four-wave mixing (DFWM) beyond the undepleted pump regime.…”

“…These include studies of χ (2) processes such as second harmonic generation [26,[47][48][49], sum and difference frequency generation [50], and optical parametric amplification [27,28,51], as well as χ (3) processes such as third harmonic generation [47,52], four-wave mixing [53][54][55], and optical parametric oscillators [22,[56][57][58]. Studies that go beyond the undepleted regime and/or employ resonant cavities reveal complex nonlinear dynamics in addition to highefficiency conversion [23,[37][38][39]41,59,60], but have primarily focused on ring-resonator geometries due to their simplicity and high degree of tunability [60]. Significant efforts are underway to explore similar functionality in wavelength-scale photonic components (e.g., photonic crystal cavities) [49,50], although high-efficiency conversion has yet to be experimentally demonstrated.…”

Radiative heat transfer in nonlinear Kerr media

“…Since nonlinear optical effects are generally weak in bulk materials, we focus on nanostructured resonant systems with strong effective nonlinear interactions 10,12 . Such systems are susceptible to universal descriptions based on the coupled-mode theory framework 13,14 , which we exploit to investigate the ways in which nonlinearities can enable interesting/designable radiative effects. In particular, we show that self-phase modulation (SPM) and two-photon absorption (TPA) effects lead to strong modifications of their emissivity, including thermal broadening and non-Lorentzian, asymmetric lineshapes.…”