?^(2) and ?^(3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities

Abstract

We derive general conditions for 100% frequency conversion in any doubly resonant nonlinear cavity, for both second-and third-harmonic generation via χ (2) and χ (3) nonlinearities. We find that conversion efficiency is optimized for a certain "critical" power depending on the cavity parameters, and assuming reasonable parameters we predict 100% conversion using milliwatts of power or less. These results follow from a semi-analytical coupled-mode theory framework which is generalized from previous work to include both χ (2) and χ (3) media as well as inhomogeneous (fully vectorial) cavities, analyzed in the high-efficiency limit where down-conversion processes lead to a maximum efficiency at the critical power, and which is verified by direct finite-difference time-domain (FDTD) simulations of the nonlinear Maxwell equations. Explicit formulas for the nonlinear coupling coefficients are derived in terms of the linear cavity eigenmodes, which can be used to design and evaluate cavities in arbitrary geometries.

Unconventional photon blockade in doubly resonant microcavities with second-order nonlinearity

“…-and fulfilling a doubly resonant condition -i.e. possessing two confined modes at fundamental and second-harmonic frequencies [21][22][23], respectively. Since the scheme proposed in Ref.…”

Radiative heat transfer in nonlinear Kerr media

“…The real and imaginary parts of the nonlinear coefficient α are given by the overlap integral α = 3 4 ω 0 ε 0 χ (3) |E| 4 /( ε|E| 2 ) 2 of the linear cavity fields E and lead to SPM and TPA, respectively. 34 In addition to radiation coming from the external bath ∼ s + , Eq. (1) includes a stochastic Langevin source Dξ(t) given by the product of a normalized "diffusion coefficient" D, relating amplitude fluctuations to dissipation from the internal (phonon) reservoir, and a time-dependent stochastic process ξ(t) whose form and properties can be derived from very general statistical considerations 16,35,36 .…”

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

“…The fundamental assumption of TCMT (accurate for weak nonlinearities) is that any such system, regardless of geometry, can be accurately described by a few sets of geometry-specific parameters [41]. These include the frequencies ω ck and corresponding lifetimes τ k (or quality factors Q k = ω ck τ k /2) of the cavity modes, as well as nonlinear coupling coefficients α kk and β k , determined by overlap integrals between the cavity modes (and often derived from perturbation theory [23]). Note that, in general, the total decay rate (1/τ k ) of the modes consist of decay into the input or output channel (1/τ sk ), as well as external (e.g., absorption or radiation) losses with decay rate 1/τ ek , so that 1/τ k = 1/τ sk + 1/τ ek .…”

“…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].…”

“…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.…”