[Paper Review] Time-resolved resonance and linewidth of an ultrafast switched GaAs/AlAs microcavity

Philip J. Harding, Allard P. Mosk+4 more|ArXiv.org|Jan 24, 2009

Photonic and Optical Devices29 references3 citations

TL;DR

This study demonstrates ultrafast, time- and frequency-resolved switching of a GaAs/AlAs microcavity using pump-probe spectroscopy, revealing a double-exponential relaxation of both resonance energy and linewidth due to distinct carrier recombination times in the λ-slab and GaAs mirrors. The key finding is that the relaxation time in the mirrors approaches the cavity photon storage time, enabling nonlinear effects and revealing an optimal Q-factor for maximizing reflectivity modulation depth at a given carrier density.

ABSTRACT

We explore a planar GaAs/AlAs photonic microcavity using pump-probe spectroscopy. Free carriers are excited in the GaAs with short pump pulses. The time-resolved reflectivity is spectrally resolved short probe pulses. We show experimentally that the cavity resonance and its width depend on the dynamic refractive index of both the lambda-slab and the lambda/4 GaAs mirrors. We clearly observe a double exponential relaxation of both the the cavity resonance and its width, which is due to the different recombination timescales in the lambda-slab and the mirrors. In particular, the relaxation time due to the GaAs mirrors approaches the photon storage time of the cavity, a regime for which nonlinear effects have been predicted. The strongly non-single exponential behavior of the resonance and the width is in excellent agreement to a transfer-matrix model taking into account two recombination times. The change in width leads to a change in reflectivity modulation depth. The model predicts an optimal cavity Q for any given induced carrier density, if the modulation depth is to be maximized.

Motivation & Objective

• To investigate the dynamic response of a GaAs/AlAs microcavity under ultrafast carrier excitation.
• To resolve the time- and frequency-dependent shifts and broadening of the cavity resonance due to free-carrier effects.
• To determine how recombination dynamics in the λ-slab and mirrors govern the resonance and linewidth evolution.
• To identify the optimal initial Q-factor that maximizes reflectivity modulation depth under carrier-induced refractive index changes.
• To assess the role of broadening mechanisms—wavevector spreading, spatial inhomogeneity, and kinetic broadening—on the observed linewidth evolution.

Proposed method

• Time- and frequency-resolved pump-probe spectroscopy with sub-100 fs temporal and sub-10 meV spectral resolution was used to measure reflectivity dynamics.
• A transfer-matrix model incorporating two distinct recombination times (τ_gm for mirrors, τ_gc for λ-slab) was applied to simulate the cavity response.
• The model included free-carrier absorption, spatial inhomogeneity, wavevector spreading, and a time-dependent photon storage time τ_ph(t) derived from the dynamic refractive index.
• Theoretical calculations of the resonance shift and linewidth were compared to experimental data to validate the double-exponential relaxation model.
• Modulation depth was calculated as a function of initial Q₀ and carrier density N₀ to identify the optimal Q for maximum depth.
• Theoretical curves assumed a constant τ_ph for comparison, but the best agreement with data was found when τ_ph was allowed to vary dynamically.

Experimental results

Research questions

• RQ1 How do the resonance energy and linewidth of a GaAs/AlAs microcavity evolve dynamically after ultrafast carrier excitation?
• RQ2 What causes the observed double-exponential relaxation in the cavity resonance and linewidth, and how do the recombination times in the λ-slab and mirrors contribute?
• RQ3 To what extent do broadening mechanisms such as wavevector spreading, spatial inhomogeneity, and kinetic broadening affect the measured linewidth over time?
• RQ4 How does the time-dependent photon storage time τ_ph(t) influence the observed cavity response, and why does assuming a constant τ_ph yield better agreement with data than a time-varying one?
• RQ5 What is the optimal initial Q-factor Q₀ for maximizing reflectivity modulation depth at a given carrier density N₀?

Key findings

• The cavity resonance and linewidth exhibit double-exponential relaxation, with distinct time constants of 14.7 ± 0.5 ps (GaAs mirrors) and 38.0 ± 0.5 ps (λ-slab), confirming two distinct recombination pathways.
• The relaxation time in the GaAs mirrors (14.7 ps) approaches the cavity photon storage time (62.9 ps), placing the system in a regime where nonlinear effects are predicted and now experimentally accessible.
• The time-resolved linewidth increases due to free-carrier absorption, wavevector spreading, and kinetic broadening, with all mechanisms contributing across all probe delays.
• Theoretical modeling shows that assuming a constant photon storage time τ_ph yields the best agreement with experimental data, contrary to expectations of dynamic τ_ph dependence.
• An optimal initial Q₀ of approximately 300 is predicted to maximize modulation depth at a carrier density of 2.58 × 10¹⁹ cm⁻³, with the maximum decreasing for Q₀ > 300 due to increased sensitivity to broadening.
• For lower carrier densities (e.g., one order of magnitude lower), the optimal Q₀ shifts to ~5000, indicating a strong dependence of optimal performance on carrier density.