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Journal of Applied Physics

Enhanced visible light generation in an active microcavity via third-harmonic conversion beyond the non-depletion approximation

Rong Yu, Chunling Ding, Jiangpeng Wang, Duo Zhang

Published Dec 26, 2017• 2 citations

Abstract

We explore the possibility of using an active doubly resonant microtoroid resonator to produce high-efficiency third-harmonic generation (THG) by exploiting optical third-order nonlinearity. In a microresonator, the active fundamental mode is coherently driven with a continuous-wave input laser at the telecommunication wavelength (1550 nm), and then, the visible THG signal (517 nm) is monitored via an individual bus waveguide. We thoroughly compare our results with those obtained from the conventional passive (i.e., loss) microtoroid resonator by a systematic analysis and detailed numerical simulations based on the Heisenberg-Langevin equations of motion. It is shown that the achievable THG spectrum features an ultralow critical input power. The THG power transmission can be significantly enhanced by about three orders of magnitude at a low input power of 0.1 μW as compared with the obtained results in the passive microtoroid resonator THG system. Moreover, the THG efficiency can reach up to 100% with optical critical input power as low as a few microwatts. In turn, the analytical expressions of the critical intracavity intensity of the light in the microcavity, the critical input pump power, and the maximum THG efficiency are obtained. The enhanced THG power transmission and high conversion efficiency are attributed to a gain-induced loss compensation in the microtoroid resonator, reducing the effective loss felt by the resonator photons. With state-of-the art technologies in the field of solid-state resonators, including but not limited to microtoroids, the proposed THG scheme is experimentally realizable.

DOI: 10.1063/1.5010243

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A numerical investigation is made of third harmonic generation (THG) under conditions of two-photon resonance between the fundamental frequency and a selected transition in the atoms of a medium. It is shown that under conditions of coherent interaction between the pump pulse and the medium, a THG efficiency of ∼20% or higher may be achieved. In this case, THG in the form of high-power ultrashort pulses may be obtained. It is shown that experimental observation of similar effects in specific media should not present particular difficulties.

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We calculate the spectrum of third-harmonic generation (THG) for multimode fundamental input fields. We consider input fields from (1) a laser with gain on several cavity modes, (2) pulses with short temporal duration, and (3) frequency-modulated input fields. The effects of phase modulation in the nonlinear medium on the spectrum of the THG field are considered. Using the estimates by Miles and Harris [IEEE J. Quantum Electron. QE-9, 470 (1973)] for the nonlinear susceptibilities ${\mathrm{\ensuremath{\chi}}}^{(3)}$(-3\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega}) and ${\mathrm{\ensuremath{\chi}}}^{(3)}$(-\ensuremath{\omega};\ensuremath{\omega},-\ensuremath{\omega},\ensuremath{\omega}) in alkali-metal vapors, we find that phase modulation can profoundly affect the efficiency and the spectrum of the THG. Generally, the self-phase modulation of the fundamental will tend to reduce the phase matching of an intense fundamental field and the third harmonic and thereby lower the conversion efficiency. New frequencies not contained in the set of frequencies ${\mathrm{\ensuremath{\omega}}}_{1\mathit{i}}$+${\mathrm{\ensuremath{\omega}}}_{1\mathit{j}}$+${\mathrm{\ensuremath{\omega}}}_{1\mathit{k}}$, where {${\mathrm{\ensuremath{\omega}}}_{1\mathit{i}}$} are frequencies in the fundamental laser spectrum, are created even at relatively low conversion due to phase modulation. Effects of cross phase modulation are also studied.

We describe a theoretical analysis of the nonlinear dynamics of third-harmonic generation $(\ensuremath{\omega}\ensuremath{\rightarrow}3\ensuremath{\omega})$ via Kerr $({\ensuremath{\chi}}^{(3)})$ nonlinearities in a resonant cavity with resonances at both $\ensuremath{\omega}$ and $3\ensuremath{\omega}$. Such a doubly resonant cavity greatly reduces the required power for efficient harmonic generation, by a factor of $\ensuremath{\sim}V∕{Q}^{2}$, 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 resonance), and how to excite the different stable solutions (and especially the high-efficiency solutions) by specially modulated input pulses.

The linear and nonlinear susceptibilities for resonant third-harmonic generation in an Mg-Kr system using the3s^{2}-3s3dtwo-photon resonance at 431 nm are presented. The Mg-Kr system is shown to be a suitable low-loss medium because of its small one-photon and two-photon absorption cross section. A detailed quantitative analysis up to a power conversion efficiency of1.2 \cdot 10^{-4}was carried out. The phase-matching curves and the intensity dependence are in excellent agreement with a nonstationary modification of the theory of resonant third-harmonic generation in high density, phase-matched systems recently presented by Puell et al. [4].

A lot of experimental and theoretical studies of a system in cavity quantum electrodynamics (cavity QED), which consists of two spatially separated quantum emitters strongly coupled to a single optical cavity mode, have recently attracted much interest in the quantum optics community for various quantum information applications. Here, we propose a method for high-order harmonic generation in a photonic crystal microcavity coupled to single semiconductor quantum dots (QDs). The system is coherently driven by a bichromatic laser consisting of the control and signal fields at low input power (a few nanowatts) and the cavity output power via the cavity loss channel is monitored. Via numerical simulations, we thoroughly explore the difference of the generated high-order harmonic spectra between two QDs, one QD, and zero QDs in microcavity. The results clearly indicate that harmonic generation can be significantly enhanced via collective coherent coupling in the case of two spatially separated QDs coupled to the same photonic crystal microcavity mode. In addition, we present a study of the carrier-envelope phase (CEP) effect on high-order harmonic spectra, which may provide the insight of CEP effect in a new regime. Beyond this, our obtained results also apply to other classes of single-mode cavity-QED setup incorporating two-level atoms or comparable solid-state emitters.