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Physical Review A

Microcavity-quality-factor enhancement using nonlinear effects close to the bistability threshold and coherent population oscillations

Yannick Dumeige, Alejandro M. Yacomotti, P. Grinberg, Kamel Bencheikh, Élodie Le Cren, Juan Ariel Levenson

Published Jun 21, 2012• 13 citations
Publisher

Abstract

We analytically show that inserting a driven, two-level system inside a microcavity can improve its optical properties. In this approach, the strong dispersion induced by a pump via population oscillations increases the cavity lifetime experienced by a slightly detuned probe. We further predict that if the cavity is pumped through a resonant channel, optical absorptive or dispersive bistability can be combined with the population-oscillation-induced steep material dispersion to obtain a strong quality-factor enhancement. Moreover, differential amplification coming from the nonlinear feature of the pump transfer function can be used to drastically increase the probe transmission beyond intrinsic characteristics of the resonator. The $Q$-factor enhancement and the differential amplification can be advantageously combined with a frequency pulling effect to stabilize or readjust the microcavity resonance frequency.

DOI
10.1103/physreva.85.063824

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We analytically show that inserting a driven, two-level system inside a microcavity can improve its optical properties. In this approach, the strong dispersion induced by a pump via population oscillations increases the cavity lifetime experienced by a slightly detuned probe. We further predict that if the cavity is pumped through a resonant channel, optical absorptive or dispersive bistability can be combined with the population-oscillation-induced steep material dispersion to obtain a strong quality-factor enhancement. Moreover, differential amplification coming from the nonlinear feature of the pump transfer function can be used to drastically increase the probe transmission beyond intrinsic characteristics of the resonator. The QQQ-factor enhancement and the differential amplification can be advantageously combined with a frequency pulling effect to stabilize or readjust the microcavity resonance frequency.
Summary form only given. Optical microcavities with high quality factors Q are of great interest in integrated micro- and nanophotonics. Their narrow resonance and long photon lifetime (τcav) can be used in fundamental physics, sensing applications, microwave signal optical processing or for optical delay line and memory miniaturization [1]. Considering a Lorentzian resonance profile, the quality factor and the photon lifetime of a microcavity with a resonant angular frequency ωο = 2·πε/λ0reads: Q = ω0τcab= nG(ω0)LF/λ0, (1) where ngis the group index of the material constituting the microcavity, F is the finesse and L is the cavity round-trip length. The usual method to obtain ultra-high quality factors consists in optimizing the manufacturing process to reach high finesse values. Following this approach record quality factors up to 1011have been measured in millimetric CaF2 whispering gallery mode (WGM) resonators [2]. Otherwise, Eq. (1) shows that for a given finesse, the use of resonators made with slow-light materials displaying high group indices can also increase the quality factor. This method has already been successfully implemented in bulky resonators including a highly dispersive slow-light medium [3]. We have recently demonstrated that this approach can be applied to solid-state optical micro-resonators [4]. The slow-light effect was introduced thanks to population oscillations in an Er3+doped WGM fluoride glass microsphere (diameter 100 μm). Since the lifetime of the4I13/2level is very long (T ≈ 10 ms) strong group index up to 106can be obtained. Using a cavity-ring-down method (see Fig. 1) in a pump probe configuration, we have measured a photon lifetime of 2.5 ms at 1530 nm corresponding to a quality factor of 3 × 1012[4].
Summary form only given. We implement coherent population oscillation and carrier-induced nonlinear refractive index in a semiconductor active nanocavity to strongly increase the photonic lifetime and manipulate its optical response.The so-called photonic crystal L3 cavity, given by three missing holes in a 2D photonic crystal (2D-PhC), is an emblematic illustration of a nanocavity with strong light confinement due to high-Q resonance and small mode volume [1]. Strong electronic confinement can also be achieved provided the cavity contains active semiconductor nanostructures such as quantum wells (QWs) or dots. These two effects lead to the enhancement of the light-matter interaction and, potentially, to a modification of photonic, electronic and thermal characteristic times. Thus, semiconductor 2D-PhC L3 nanocavities are excellent candidates for the implementation of advanced nonlinear photonic interactions. In this work we study the combined effects of both coherent population oscillation (CPO) and carrier-induced nonlinear dephasing in the photon lifetime of a L3 cavity incorporating 4 InGaAsP/InGaAs QWs. The CPO induces a decrease of the group velocity through a strong dispersion of the refractive index (i.e. slow light effect) while the nonlinear phase shift, if implemented close to the bistability threshold, ends up with a strong slowing down of the optical response. The resulting cavity lifetime strongly depends on the control parameters. It is then possible to actively control the photon lifetime of the nanocavity, to enhance its quality factor, to achieve differential amplification under the slow-light regime and to benefit from frequency pulling During this presentation we will discuss theoretically [1] all these aspects with respect to the role of CPO and dynamical nonlinear responses. We will further present recent experimental results [2] demonstrating the enhancement by two orders of magnitude of the cavity lifetime together with the frequency pulling effect.Γ
Optical Kerr nonlinearity is central to optical bistability in high-Q microcavities. Here, we show that optical Kerr nonlinearities in Fabry Perot resonators can also result in self-focusing effects, that can substantially modify the Q-factors of the resonators. For the studied cavities, up to five-fold increase in Q-factors is predicted, attributed to reduction of sidewall leakage, confirmed via simulations performed on curved cavities. We also show that for high Q-factor cavities, the higher-order Kerr effect can become relevant already at modest input intensities scaling inversely with Q-factor for a particular n2/n4 ratio. We investigate numerically the role of higher-order Kerr effect on optical bistability responses and find that its inclusion can shift the bistability threshold to higher input intensities than predicted by the standard n2-only model.
Optical microcavities and metallic nanostructures have been shown to significantly modulate the dynamics and spectroscopic response of molecular systems. We present a study of the nonlinear optics of a model consisting of NNN anharmonic multilevel systems (e.g., Morse oscillators) undergoing collective strong coupling with a resonant infrared microcavity. We find that, under experimentally accessible conditions, molecular systems in microcavities may have nonlinear phenomena significantly intensified due to the high quality of polariton resonances and the enhanced microcavity electromagnetic energy density relative to free space. Particularly large enhancement of multiphoton absorption happens when multipolariton states are resonant with bare molecule multiphoton transitions. In particular, our model predicts two-photon absorption cross-section enhancements by several orders of magnitude relative to free space when the Rabi splitting ${\mathrm{\ensuremath{\Omega}}}_{R}$ is approximately equal to the molecular anharmonic shift $2\mathrm{\ensuremath{\Delta}}$. Our results provide rough upper bounds to resonant nonlinear-response enhancement factors as relaxation to dark states is treated phenomenologically. Notably, ensembles of two-level systems undergoing strong coupling with a cavity (described by the Tavis-Cummings model) show no such optical nonlinearity enhancements, highlighting the rich phenomenology afforded by multilevel anharmonic systems. Similar conclusions are expected to hold for excitonic systems that share features with our model (e.g., molecular dyes with accessible ${S}_{0}\ensuremath{\rightarrow}{S}_{1}\ensuremath{\rightarrow}{S}_{2}$ transitions) and strongly interact with a UV-visible cavity.