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Publication# Doubly resonant second-harmonic generation of a vortex beam from a bound state in the continuum

Jean-François Carlin, Matteo Galli, Nicolas Grandjean, Romuald Houdré, Momchil Minkov, Jun Wang

2020

Journal paper

2020

Journal paper

Abstract

Second-harmonic generation in nonlinear materials can be greatly enhanced by realizing doubly resonant cavities with high quality factors. However, fulfilling such doubly resonant condition in photonic crystal (PhC) slab cavities is a long-standing challenge, because of the difficulty in engineering photonic bandgaps around both frequencies. Here, by implementing a second-harmonic bound state in the continuum (BIC) and confining it with a heterostructure design, we show the first doubly resonant PhC slab cavity with $2.4 \times {10^{- 2}}\;{{\rm W}^{- 1}}$ intrinsic conversion efficiency under continuous-wave excitation. We also report the confirmation of highly normal-direction concentrated far-field emission pattern with radial polarization at the second harmonic frequency. These results represent a solid verification of previous theoretical predictions and a cornerstone achievement, not only for nonlinear frequency conversion but also for vortex beam generation and prospective nonclassical sources of radiation.

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Photonic crystal

A photonic crystal is an optical nanostructure in which the refractive index changes periodically. This affects the propagation of light in the same way that the structure of natural crystals give

Nonlinear optics

Nonlinear optics (NLO) is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization density P responds non-linearly to the electric field

Resonance

Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the

Momchil Minkov, Vincenzo Savona

We optimize a photonic crystal slab for the generation of second harmonic. The optimization consists in two steps. In the first step a regular photonic crystal, consisting in a triangular lattice of circular holes in a dielectric slab, is optimized by allowing for holes of three alternating radii, with the objective of obtaining a high-frequency bandgap doubly resonant with the fundamental one. The second step consists in modeling a L3 defect cavity in such a photonic crystal where, by further varying the radii and positions of a few neighboring holes, doubly resonant modes at the fundamental and second harmonic frequencies are obtained, with maximal Q-factors and field overlap. The structure emerging from this optimization procedure has Q-factors of 3400 for the fundamental mode and of 430 for the doubly resonant one. Due to the localized nature of those modes and hence their large field overlap, efficient second-harmonic generation is expected in a material with a chi((2)) non-linearity.

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We fabricate and experimentally characterize an H0 photonic crystal slab nanocavity with a design optimized for maximal quality factor, Q = 1.7 x 10(6). The cavity, fabricated from a silicon slab, has a resonant mode at lambda = 1.59 mu m and a measured Q-factor of 400 000. It displays nonlinear effects, including high-contrast optical bistability, at a threshold power among the lowest ever reported for a silicon device. With a theoretical modal volume as small as V = 0.34(lambda/n)(3), this cavity ranks among those with the highest Q/V ratios ever demonstrated, while having a small footprint suited for integration in photonic circuits. (C) 2014 AIP Publishing LLC.

It is shown that noncentrosymmetric materials with bulk second-order nonlinear susceptibility can be used to generate strongly antibunched radiation at an arbitrary wavelength, solely determined by the resonant behavior of suitably engineered coupled microcavities. The proposed scheme exploits the unconventional photon blockade of a coherent driving field at the input of a coupled cavity system, where one of the two cavities is engineered to resonate at both fundamental and second harmonic frequencies, respectively. Remarkably, the unconventional blockade mechanism occurs with reasonably low quality factors at both harmonics, and does not require a sharp doubly resonant condition for the second cavity, thus proving its feasibility with current semiconductor technology.