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Journal of Physics B Atomic Molecular and Optical Physics

Quantum theory for microcavity enhancement of second harmonic generation

Ying Wu, Xiaoxue Yang

Published May 25, 2001• 23 citations
Publisher

Abstract

We present a quantum theory to derive the analytical expression of microcavity enhancement for second harmonic generation. The expression explicitly gives the dependence of the enhancement on detunings and the Purcell factor of the relevant microcavity mode, and it is suitable for microcavities with any dimensions and arbitrary geometric shapes. The result for a one-dimensional microcavity agrees well with a recent microcavity-enhanced second harmonic generation experiment by Cao et al (2000 Appl. Phys. Lett. 76 538).

DOI
10.1088/0953-4075/34/11/319

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We present a quantum theory to derive the analytical expression of microcavity enhancement for second harmonic generation. The expression explicitly gives the dependence of the enhancement on detunings and the Purcell factor of the relevant microcavity mode, and it is suitable for microcavities with any dimensions and arbitrary geometric shapes. The result for a one-dimensional microcavity agrees well with a recent microcavity-enhanced second harmonic generation experiment by Cao et al (2000 Appl. Phys. Lett. 76 538).
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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.