Cavity-enhanced second harmonic generation via nonlinear-overlap optimization

Abstract

We describe an approach based on topology optimization that enables automatic discovery of wavelength-scale photonic structures for achieving high-efficiency second-harmonic generation (SHG). A key distinction from previous formulation and designs that seek to maximize Purcell factors at individual frequencies is that our method not only aims to achieve frequency matching (across an entire octave) and large radiative lifetimes, but also optimizes the equally important nonlinear--coupling figure of merit $\bar{\beta }$, involving a complicated spatial overlap-integral between modes. We apply this method to the particular problem of optimizing micropost and grating-slab cavities (one-dimensional multilayered structures) and demonstrate that a variety of material platforms can support modes with the requisite frequencies, large lifetimes $Q>10^4$, small modal volumes $\sim (\lambda /n{)}^3$, and extremely large $\bar{\beta }\gtrsim 10^{-2}$, leading to orders of magnitude enhancements in SHG efficiency compared to state of the art photonic designs. Such giant $\bar{\beta }$ alleviate the need for ultra-narrow linewidths and thus pave the way for wavelength-scale SHG devices with faster operating timescales and higher tolerance to fabrication imperfections.

References in corpus (10)

• High Quality factor photonic crystal nanobeam cavities
• Second-Harmonic Generation in Silicon Nitride Ring Resonators
• Naturally-phasematched second harmonic generation in a whispering gallery mode resonator
• Visible-to-telecom quantum frequency conversion of light from a single quantum emitter
• Integrated high quality factor lithium niobate microdisk resonators
• Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power
• Chi2 and chi3 harmonic generation at a critical power in inhomogeneous doubly resonant cavities
• Second harmonic generation in phase matched aluminum nitride waveguides
• Bloch-wave engineering of quantum dot-micropillars for cavity quantum electrodynamics experiments
• Sub-micron diameter micropillar cavities with high Quality factors and ultra-small mode volumes