Topology optimization of multi-track ring resonators and 2D microcavities for nonlinear frequency conversion

Abstract

We exploit recently developed topology-optimization techniques to design complex, wavelength-scale resonators for enhancing various nonlinear χ (2) and χ (3) frequency conversion processes.In particular, we demonstrate aperiodic, multi-track ring resonators and 2D slab microcavities exhibiting long lifetimes Q 10 4 , small modal volumes V (λ/2n) 3 , and among the largest nonlinear overlaps (a generalization of phase matching in largeetalon waveguides) possible, paving the way for efficient, compact, and wide-bandwdith integrated nonlinear devices. OCIS codes:190 [4][5][6], and quantum information processing [7][8][9]. A well-known approach for lowering the power requirements of such nonlinear devices is that of employing optical resonators which confine light for long times (dimensionless lifetimes Q) in small volumes V [10-21]. Although microcavity resonators designed for on-chip, infrared applications promise some of the smallest confinement factors available, their implementation is highly limited by the difficult task of identifying wavelength-scale (V ∼ λ 3 ) structures supporting long-lived, resonant modes at widely separated wavelengths and satisfying rigid frequency-matching and mode-overlap constraints [15,22]. Recently, we proposed a computational framework based on largescale topology-optimization (TO) techniques that enables automatic discovery of multilayer and grating structures exhibiting some of the largest SHG figures of merit ever predicted [23].In this letter, we extend our TO formulation to allow the possibility of more sophisticated nonlinear processes and apply it to the problem of designing rotationally symmetric and slab microresonators that exhibit high-efficiency second harmonic generation (SHG) and * Corresponding author: zinlin@g.harvard.edu sum/difference frequency generation (SFG/DFG). In particular, we demonstrate multi-track ring resonators and proof-of-principle two-dimensional slab cavities supporting multiple, resonant modes (even several octaves apart) that would be impossible to design "by hand". Our designs ensure frequency matching, long radiative lifetimes, and small (wavelength-scale) modal confinement while also simultaneously maximizing the nonlinear modal overlap (or "phase matching") necessary for efficient NFC. For instance, we discover topology-optimized concentric ring cavities exhibiting SHG efficiencies as high as P 2 /P 2 1 = 1.3 × 10 25 χ (2) 2 [W −1 ] even with low operational Q ∼ 10 4 , a performance that is on a par with recently fabricated 60µm-diameter, ultrahigh Q ∼ 10 6 AlN microring resonators [21] (P 2 /P 2 1 ∼ 1.13 × 10 24 χ (2) 2 [W −1 ]); essentially, our topology-optimized cavities not only possess the smallest possible modal volumes ∼ (λ/n) 3 , but can also operate over wider bandwidths by virtue of their increased nonlinear modal overlap.As reviewed in Refs. 23-25, a typical topology optimization problem seeks to maximize or minimize an objective function f , subject to certain constraints g, over a set of free variables or degrees of freedom (D...

Doubly resonant χ(2) nonlinear photonic crystal cavity based on a bound state in the continuum

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Poles of the scattering matrix: an inverse method for designing photonic resonators

“…The challenge of designing structures with multiple Fano resonances for harmonic generation is better suited for an inverse design approach [3,10,28]. Inverse methods aim to optimize an objective functional by iteratively solving Maxwell's equations for a variety of material topologies [9].…”

“…Inverse methods aim to optimize an objective functional by iteratively solving Maxwell's equations for a variety of material topologies [9]. They have been used to design ring resonators [28], fibers [10], and gratings [3] for nonlinear frequency conversion [10,28]. However, the need to solve Maxwell's equations iteratively is computationally expensive and time consuming, limiting the variety of structures that can be considered.…”

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