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Optics Express

Visualization of superluminal pulses inside a white light cavity using plane wave spatio temporal transfer functions

H. Yum, Y. J. Jang, Xiaohui Liu, M. S. Shahriar

Published Aug 2, 2012• 3 citations
Publisher

Abstract

In a white light cavity (WLC), the group velocity is superluminal over a finite bandwidth. For a WLC-based data buffering system we recently proposed, it is important to visualize the behavior of pulses inside such a cavity. The conventional plane wave transfer functions, valid only over space that is translationally invariant, cannot be used for the space inside WLC or any cavity, which is translationally variant. Here, we develop the plane wave spatio temporal transfer function (PWSTTF) method to solve this problem, and produce visual representations of a Gaussian input pulse incident on a WLC, for all times and positions.

DOI
10.1364/oe.20.018898

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In a white light cavity (WLC), the group velocity is superluminal over a finite bandwidth. For a WLC-based data buffering system we recently proposed, it is important to visualize the behavior of pulses inside such a cavity. The conventional plane wave transfer functions, valid only over space that is translationally invariant, cannot be used for the space inside WLC or any cavity, which is translationally variant. Here, we develop the plane wave spatio temporal transfer function (PWSTTF) method to solve this problem, and produce visual representations of a Gaussian input pulse incident on a WLC, for all times and positions.
It is well-known that a transfer function method is useful to predict the profile of a pulse after it propagates through an intracavity fast-light medium. However, by using this technique, a behavior of the pulse inside the medium cannot be determined. In this paper, we describe a new theoretical approach to deal with this constraint. In the new method, we find an analytical solution for a monochromatic field of infinite spatial and temporal extents, and add the waves with the weighted amplitude and with the tailored phase to embody a Gaussian input pulse moving toward the cavity. At different time frames, the sum of these waves produces a spatial profile of the pulse before, inside and after the cavity. In particular, the pulse profile can be visualized during a superluminal propagation through the intracavity fast-light medium with zero group index. This model allows us to understand the physical process behind the superluminal propagation through a white light cavity, which is significant to realize a high bandwidth data buffer system overcoming conventional delay bandwidth product(DBP) problem.
In this paper, we study theoretically the behavior of a pulse as it propagates through an intracavity fast-light medium. The method of using a transfer function to determine a pulse after it passes through a cavity is well known. However, this approach cannot be used to determine the behavior of the pulse inside the cavity. To circumvent this constraint, we use an approach that starts by finding a self-consistent solution for a monochromatic field of infinite spatial and temporal extents, and determine its amplitudes before, inside, and after the cavity. We then construct a Gaussian input pulse by adding a set of these waves, properly phased and weighted, to represent a moving pulse before the cavity. Adding these waves at various time intervals then yields the complete spatial profile everywhere, including before, inside and after the cavity. We first confirm the prediction of this model by analyzing the behavior of a pulse passing through an empty cavity, and comparing the prediction of the output with the one produced by the transfer function method. We then apply the technique to a cavity containing a fast-light medium. The resulting model allows us to visualize the behavior of the pulse as it propagates superluminally inside the cavity, and interferes with itself through multiple bounces. For a vanishing group index, an interference pattern is formed immediately after the pulse enters the cavity, with an output pulse emerging with no time delay or distortion. The results obtained here illustrates the physical mechanism behind pulse propagation through a white light cavity, a process we have proposed earlier for realizing a high bandwidth, long delay data buffering system
Recently, a tunable bandwidth white light cavity (WLC) was demonstrated by using an anomalously dispersive intra-cavity medium to adjust a cavity linewidth without reducing the cavity buildup factor [G.S. Pati et al., Phys. Rev. Lett. 99, 133601 (2007)]. In this paper, we show theoretically how such a WLC can be used to realize a distortion-free delay system for a data pulse. The system consists of two WLCs placed in series. Once the pulse has passed through them, the fast-light media in both WLCs are deactivated, so that each of these now acts as a very high reflectivity mirror. The data pulse bounces around between these mirrors, undergoing negligible attenuation per pass. The trapped pulse can be released by activating the fast-light medium in either WLC. Numerical simulations show that such a system can far exceed the delay-bandwidth constraint encountered in a typical data buffer employing slow light. We also show that the pulse remains virtually undistorted during the process.
Techniques to control dispersion in a medium have attracted much attention due\nto potential applications to devices such as ring laser gyroscopes, interferometric\ngravitational wave detectors, data buffers, phased array radars and quantum information\nprocessors. Of particular interest is an optical resonator containing a medium with an\nanomalous dispersion corresponding to fast-light, which behaves as a White Light\nCavity (WLC). A WLC can be tailored to improve the sensitivity of sensing devices as\nwell as to realize an optical data buffering system that overcomes the delay-bandwidth\nproduct of a conventional cavity.\nThis dissertation describes techniques to tailor the dispersion for fast-light in\nintracavity media. We present first a demonstration of fast-light in a photorefractive\ncrystal. When placed inside a cavity, such a medium could be used to enhance the\nbandwidth of a gravitational wave detector. We then describe how a superluminal laser\ncan be realized by adding anomalously dispersive medium inside a ring laser. We\nidentify theoretical conditions under which the sensitivity of the resonance frequency to a change in the cavity length is enhanced by as much as seven orders of magnitude. This\npaves the way for realizing a fast-light enhanced ring laser gyroscope, for example. This\nis followed by the development of a novel data buffering system which employs two\nWLC systems in series. In this system, a data pulse can be delayed an arbitrary amount\nof time, without significant distortion. The delay time is independent of the data\nbandwidth, and is limited only by the attenuation experienced by the data pulse as it\nbounces between two high-reflectivity mirrors. Such a device would represent a\nsignificant breakthrough in overcoming the delay-time bandwidth product limitation\ninherent in conventional data buffers.\nWe then describe our experimental effort to create a fiber-based WLC by using\nstimulated Brillouin scattering (SBS). Experimental results, in agreement with our\ntheoretical model presented here, show that the WLC effect is small under the conditions\nsupported by current fiber optic technology. We conclude that future efforts to induce a\nlarge WLC effect would require fibers with high Brillouin coefficient and low\ntransmission loss, as well as optical elements with very low insertion loss and high\npower damage thresholds.
Spectral reshaping and nonuniform phase delay associated with an electromagnetic pulse propagating in a temporally dispersive medium may lead to interesting observations in which the group velocity becomes superluminal or even negative. In such cases, the finite bandwidth of the superluminal region implies the inevitable existence of a cutoff distance beyond which a superluminal pulse becomes subluminal. In this paper, we derive a closed-form analytic expression to estimate this cutoff distance in abnormal dispersive media with gain. Moreover, the method of steepest descent is used to track the time-frequency dynamics associated with the evolution of the center of mass of a superluminal pulse to the subluminal regime. This evolution takes place at longer propagation depths as a result of the subluminal components affecting the behavior of the pulse. Finally, the analysis presents the fundamental limitations of superluminal propagation in light of factors such as the medium depth, pulse width, and the medium dispersion strength.