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Journal of the Optical Society of America B

Slowing light with Fabry-Perot resonator arrays

Joyce K. S. Poon, Philip Chak, John M. Choi, Amnon Yariv

Published Oct 1, 2007• 27 citations
Publisher

Abstract

We analyze the transmission of light through coupled-resonator optical waveguides in the form of evanescently coupled Fabry-Perot resonator arrays. We develop a transfer matrix method to calculate the amplitude and phase responses of the arrays. We also discuss the inclusion of optical gain in the system to compensate for losses in these structures. Owing to the compact length along the propagation direction in evanescently coupled arrays, large slowing factors of the order of 102-103 can be achieved even with a weak index contrast of ∼0.1%. The large slowing factor, coupled with weak index contrast, makes this structure a promising candidate for artificial slow light system.

DOI
10.1364/josab.24.002763

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We analyze the transmission of light through coupled-resonator optical waveguides in the form of evanescently coupled Fabry-Perot resonator arrays. We develop a transfer matrix method to calculate the amplitude and phase responses of the arrays. We also discuss the inclusion of optical gain in the system to compensate for losses in these structures. Owing to the compact length along the propagation direction in evanescently coupled arrays, large slowing factors of the order of 102-103 can be achieved even with a weak index contrast of ∼0.1%. The large slowing factor, coupled with weak index contrast, makes this structure a promising candidate for artificial slow light system.
The optical buffer is a key component in all-optical information processing systems. Recently a number of schemes that use slow light propagation in various media and structures have been proposed as means toward implementation of all-optical buffers. We rigorously analyze the similarities and differences in approaches that use electromagnetically induced transparency (EIT) and coupled resonant structures (CRS). We introduce the figure of merit, finesse, that is common to both approaches and obtain fundamental limitations on bit rates and storage capacities of optical buffers. We show that at very low bit rates and storage capacities EIT outperforms CRS, but at rates of 10 Mbits/s and above the EIT medium becomes quite inefficient, and the situation is reversed. Two types of CRS based on high-index-contrast fiber gratings and high-index semiconductor-air photonic crystals and (or) microring resonators are found to hold promise for applications in the 1-1000-Gbits/s range, but only if the losses can be drastically reduced.
In this paper, we demonstrate the relation between the amount of slowing and the amount of insertion loss in an optical slow wave structure when the material used has finite absorption. The delay properties are calculated as a function of wavelength for a single Fabry-Perot resonator and a delay line consisting of multiple coupled resonators. In all of these delay lines, if the amount of delay increases, the insertion loss of the line likewise increases. For low material loss, the normalized increase in delay is equal to the normalized increase in insertion loss. We also compare a coupled resonator delay line to a simple waveguide made of the same material and with the same amount of delay. The simple waveguide always has less insertion loss than the coupled resonator line because of the unavoidable reflection from the coupled resonator line. Even in the case of an asymmetric mirror delay line with zero reflection at the input, the simple waveguide has less insertion loss.
Ability to tune the group velocity of a light pulse is of great importance for optical communication applications and realization of quantum information processing. Tunability of group velocity can be achieved by using either optical or electronic resonances. Tunability of an optical resonance depends on the change in refractive index of the cavity material. However, since electro-optical coefficients of non-engineered materials are quite small, the tuning range of optical resonances by electric field is narrow. This makes tuning by electric field impractical for most applications. Quantum dot (QD) coupled to a photonic crystal cavity is a useful hybrid system exhibiting nonlinear features. In this work, we analyze the use of quantum dot - optical cavity hybrid systems to engineer nonlinear waveguides susceptible to electric fields. We start by theoretically analyzing the optical pulse propagation at low-photon number excitation limit in a periodically arranged strongly coupled quantum dot - photonic crystal system. A one dimensional periodic array of evanescently coupled photonic cavities (coupled resonator optical waveguides, CROWs) containing non-interacting quantum dots allows us to tune the group velocity and the bandwidth of the pulse by adjusting the cavity/QD coupling. Tunable group velocity can be achieved by applying an external electric field which will result in a significant decrease in the cavity/QD coupling because of DC Stark effect. We also show that, using this approach, light pulses can be slowed down or stored by compressing the pulse bandwidth adiabatically and reversibly. Adiabatic bandwidth compression can be achieved by slowly decreasing the coupling strength when the light pulse is inside the coupled resonator optical waveguide. The energy splitting and the coupling constant after applying electric field is calculated by using perturbation theory for two level systems. With our approach, nonlinear materials highly susceptible to electric fields can be engineered in low-excitation regime.