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Journal of Physics D Applied Physics

Investigation of the transient Kerr effect in a nonlinear photonic crystal microcavity

Chao Li, Jun-Fang Wu

Published Mar 18, 2013• 5 citations
Publisher

Abstract

We present an analytical model and numerical experiments to investigate the dynamic features of the transient Kerr effect (TKE) in an optical period, which is much shorter than the time scale in the case of a pulse pump as commonly proposed. It is found that under the influence of the TKE, the sum of transmission and reflection rate can be far below unity even for a nonlinear photonic crystal structure without any absorption or radiation loss. However, this does not contradict the energy conservation principle. The physical origin for this novel phenomenon is revealed.

DOI
10.1088/0022-3727/46/15/155105

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We present an analytical model and numerical experiments to investigate the dynamic features of the transient Kerr effect (TKE) in an optical period, which is much shorter than the time scale in the case of a pulse pump as commonly proposed. It is found that under the influence of the TKE, the sum of transmission and reflection rate can be far below unity even for a nonlinear photonic crystal structure without any absorption or radiation loss. However, this does not contradict the energy conservation principle. The physical origin for this novel phenomenon is revealed.
We investigate the response of photonic crystal (PC) atoms with Kerr nonlinearity to the excitation of ultrashort optical pulses. Surprisingly, it is found that PC atoms with sharp resonant peaks in frequency spectrum (or with large quality factors) can respond to ultrashort pulses very rapidly when Kerr nonlinearity is introduced. More interestingly, the response time under high-power densities can be even shorter than the duration of the pump pulse. It is revealed that the nonlinearity induced broadening of dynamical frequency spectrum is responsible for the ultrafast response time, implying the possibility of ultrafast all-optical switching.
Optical bistable responses in AlGaAs-based photonic crystal cavities with Al fractions of 0.16 and 0.27 under a stationary condition are studied. An analysis of the experimental results with a one-dimensional etalon model indicates that the bistable response is primarily driven by optical nonlinearities that stem from a heat generation in two-photon absorption and in free-carrier absorption. A free-carrier plasma effect is not influential, which is a major difference from the case of Si photonic crystal cavities. The accumulation of heat enables the phase or index to significantly change. An estimate indicates that a highQQQ-factor is advantageous for driving bistability exclusively by the Kerr effect.
Pair generation in time-varying media is commonly attributed to time reflection at temporal boundaries or to amplification inside momentum k gaps. Here we show that these two processes are connected by the time domain Stokes phenomenon. A finite duration photonic time crystal (PTC) slab provides the necessary Stokes connection between the incident vacuum mode, transient k gap amplification, and time boundary scattering. With Kerr nonlinearity, the otherwise unbounded amplification is arrested, spawning Kerr stabilized k gap solitons. When these solitons cross the exit boundary of the time slab, Stokes induced mode conversion produces a secondary pair generation process, yielding four spatially separated and entangled pulse branches. Detection of a backward propagating light pulse therefore heralds its forward propagating partner. We further propose combined Hanbury Brown Twiss and Hong Ou Mandel measurements to test their nonclassical correlations. These results reveal a link between asymptotic Stokes physics and quantum temporal scattering in PTCs, and suggest a route toward ultrafast heralded quantum light sources.