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Journal of the Optical Society of America B

Analysis of optical ARMA architectures in the slow-light regime

Vishnupriya Govindan, Steve Blair

Published Oct 20, 2008• 0 citations
Publisher

Abstract

We study pulse propagation in the slow-light regime with positive and negative group delays in auto-regressive moving average (ARMA) filters, including the ring-enhanced Mach-Zehnder interferometer (REMZI) and side-coupled integrated spaced sequence of resonators (SCISSOR) optical architectures. Both architectures are optimized to maximize the delay-bandwidth product for a fixed output pulse-distortion level. In the negative-group-delay regime, absorption is incorporated in the rings. The REMZI architecture has the highest delay-bandwidth product in both the positive and negative-group-delay regimes due to greater efficiency in incorporating filter phase within the passband. We also explore the effects of pulse shape in the lossy regime and the limitations it poses in the amount of pulse advancement that is usable for practical applications.

DOI
10.1364/josab.25.00c116

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•Apr 21, 2015•0 citations
We study pulse propagation in the slow-light regime with positive and negative group delays in auto-regressive moving average (ARMA) filters, including the ring-enhanced Mach-Zehnder interferometer (REMZI) and side-coupled integrated spaced sequence of resonators (SCISSOR) optical architectures. Both architectures are optimized to maximize the delay-bandwidth product for a fixed output pulse-distortion level. In the negative-group-delay regime, absorption is incorporated in the rings. The REMZI architecture has the highest delay-bandwidth product in both the positive and negative-group-delay regimes due to greater efficiency in incorporating filter phase within the passband. We also explore the effects of pulse shape in the lossy regime and the limitations it poses in the amount of pulse advancement that is usable for practical applications.
In this paper, we propose and demonstrate the application of concepts from digital filter design to optimize artificial optical resonant structures to produce a nearly ideal nonlinear phase shift response. Multi-stage autoregressive moving average (ARMA) optical filters (ring resonator based Mach-Zehnder interferometer lattices) are designed and studied. The filter group delay is used as an alternate measure instead of finesse or quality factor to study the nonlinear sensitivity for multiple resonances. The nonlinearity of a 4-stage ARMA filter is 17 times higher than that of the intrinsic material. We demonstrate that the nonlinear sensitivity can be increased within the same bandwidth by allocating more in-band phase or using higher-order filter structures and that the nonlinear enhancement improves with increasing group delay. We also investigate some possible ways to pre-compensate the nonlinear response to reduce the occurrence of optical bistabilities. The impact of optical loss, including linear absorption and two-photon absorption, and fabrication tolerance are discussed in post-analysis.
We propose and demonstrate the application of concepts from digital filter design in order to optimize artificial optical resonant structures to produce a nearly ideal nonlinear phase shift response. Multistage autoregressive moving average (ARMA) optical filters (ring-resonator-based Mach-Zehnder interferometer lattices) are designed and studied. The filter group delay is used as a measure instead of finesse or quality factor to study the nonlinear sensitivity for multiple resonances. The nonlinearity of a four-stage ARMA filter is 17 times higher than that of the intrinsic material of the same group delay. We demonstrate that the nonlinear sensitivity can be increased within constant bandwidth by allocating more in-band phase or by using higher-order filter structures and that the nonlinear sensitivity enhancement improves with increasing group delay. We also investigate methods to precompensate the nonlinear response to reduce the occurrence of optical bistabilities. The effect of optical loss, including linear absorption and two-photon absorption, is discussed in postanalysis. In addition, we discuss how the improvement in nonlinear response scales with respect to various filter parameters.
An analytical approach is reported that describes previously observed fast-light regimes in linear and passive Mach-Zehnder interferometers (MZI) where the optical path difference is due to a different length of the branches. Approximate expressions are developed for the transmission coefficient and group delay spectral functions valid for frequencies close to the transmission minima ${\ensuremath{\omega}}_{\mathrm{min}}$, where these regimes occur. It is found that the group delay at ${\ensuremath{\omega}}_{\mathrm{min}}$ verifies a simple scaling law. We demonstrate that slow light cannot arise in this system, and that tunneling and superluminal regimes appear only for low-loss devices, where the attenuation drives the change in the propagation regimes. The propagation of a sinusoidally modulated pulse train through the MZI is described, and relevant figures of merit, which are intrinsic to the system and universal for any operative spectral range, are determined. The theoretical approach is illustrated by simulations of a silicon-based interferometer designed for advancing pulses at 1.55 \ensuremath{\mu}m. Also, previously reported experimental results in the radiofrequency range are interpreted in the framework of the model.
Under the constraint of fixed pulse distortion, we study the bandwidth-delay product and nonlinear phase shift performance of coupled-resonator slow-light waveguides with designs that produce maximally-flat transmission and maximally-flat group delay responses. Even though improvement in bandwidth-delay product can be obtained with increasing number of resonators, the nonlinear response fails to improve beyond a certain number of resonators due to the increased filter bandwidth necessary to maintain a fixed pulse distortion. However, as expected, the nonlinear response improves with resonator finesse and degrades with resonator loss.
This Thesis lies within the field of Slow and Fast Light (SFL) technologies, which are currently receiving much attention because of their interesting applications, ranging from optical information processing to enhanced precision sensing and interferometry. These technologies are based on systems that exhibit steep positive dispersion to propagate a light pulse at group velocity well below the speed of light in vacuum (slow light) or steep negative dispersion to achieve pulse propagation at superluminal or even at negative group velocity (fast light). SFL effects thus arise in a myriad of materials exhibiting spectral resonances. Current efforts in this field are mainly focused on the manipulation of material gain or absorption resonances by nonlinear optical processes (material SFL) or on the optimization of photonic band-gap structures, without substantial material dispersion, but where structural dispersion comes as a result of the coupling between the light wavelength and the characteristic length of the system (structural SFL). This Thesis focuses on the theoretical and experimental analysis of electromagnetic pulse propagation with abnormal group velocities in two kind of linear and passive devices. In the first part of the Thesis a new system exhibiting structural SFL is demonstrated. It deals with multiple-beam interferometers and provides a comprehensive study of the arising of SFL in this system devoid of photonic band gaps. A theoretical model that fully describes the allowed pulse propagation regimes and its performance in terms of both the interferometer's and the pulse characteristics is developed. Considering amplitude modulated pulses, the capabilities and limitations of SFL effects in this kind of system are retrieved by quantifying typical figures of merit like fractional delay, pulse distortion and Delay-Bandwidth Product. The theoretical framework is valid for any frequency region and the model predictions are probed by performing experiments in the radiofrequency range and through exact numerical simulations in the optical range. The simplest interferometer, with only two branches, is first considered since it is widely used in actual communication systems. It is analytically demonstrated that slow light cannot possibly be sustained and that the total attenuation drives the changes in the pulse propagation regimes. By increasing the number of branches, group delay tuning from slow to fast light regimes occurs if the optical length of one of the branches is slightly changed. In the second part of the Thesis, the ability of mono- and multilayer structures to speed up or slow down electromagnetic pulses is investigated, with special emphasis on their reflection properties. Namely, Distributed Bragg Reflectors (DBRs) and Fabry-Perot filters, common in today's communication systems, are examined. These structures were fabricated to operate in the microwave and in the radiofrequency range with the aim of confirming theoretical predictions. Experimental results of their frequency- and time-domain characterization are compared with simulations. An advantage of operating in these frequency ranges is that the transmission and reflection phase function can be measured with a two port vector network analyzer. Such a simple measurement of this key function that determines the pulse propagation regime cannot be directly performed in the optical range. Moreover, microstrip DBRs were designed and their potential application as a negative group-delay circuit to improve the efficiency of feedforward amplifiers, which are commonly used for cancelling inherent distortion in microwave amplifiers, is explored.