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Advances in Optics and Photonics

Slow light in various media: a tutorial

Jacob B. Khurgin

Published Mar 23, 2010• 204 citations
Publisher

Abstract

I consider the physical basics of slow light propagation in atomic media, photonic structures, and optical fibers. I show similarities and differences between all of the above media and develop set of criteria that are then used to compare different media. Special attention is given to dispersion of group velocity and loss, which are shown to limit the bandwidth and delay capacity of all the slow light schemes.

DOI
10.1364/aop.2.000287

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I consider the physical basics of slow light propagation in atomic media, photonic
structures, and optical fibers. I show similarities and differences between all of
the above media and develop set of criteria that are then used to compare different
media. Special attention is given to dispersion of group velocity and loss, which are
shown to limit the bandwidth and delay capacity of all the slow light schemes.
Transparency (EIT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 15.7 Coupled Photonic Resonator Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 15.8 Dispersion Limitation of Nonlinear Photonic SL Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 15.9 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 Recent years have seen a great increase in interest in the regime of light propagation with reduced group velocity, commonly referred to as slow light (SL). Startingwith the pioneeringwork performed in the late 1990s [1] a great effort had been directed at both understanding the basic physics of SL phenomena and applying it to various practical tasks-optical communications, signal processing, photonic switching, and many others.
The group velocity at which light pulses propagate through a dispersive material system is very different from the vacuum speed of light c, One refers to light as being "slow" for v g << c (Boyd & Gauthier, 2009) or "fast" for v g > c or v g <0 (Stenner et al, 2003 ).For v g <0, the pulse envelope appears to travel backward in the material (Gehring et al, 2006), and hence it is sometimes referred to as "backward light."The subject of slow light has caused keen interest in the past decade or more, and it is possible to control the group velocity of light pulses in the dispersive materials.Interest in slow and fast light dates back to the early days of the 20th century.Sommerfeld and Brillouin (Sommerfeld & Brillouin, 1960) were intrigued by the fact that theory predicts that v g can exceed c, which leads to apparent inconsistencies with Einstein's special theory of relativity.Experimental investigations of extreme propagation velocities were performed soon after the invention of the laser (Faxvog and et al, 1970).In 1999, Harris's group research work greatly stimulated researchers' interests, which showed that light could be slowed down to 17m/s.The result was obtained in ultra cold atom clouds with the use of electromagnetically induced transparency (EIT), which induces transparency in a material while allowing it to retain strong linear and nonlinear optical properties (Hau et al, 1999).Slow light can also be obtained through the use of the optical response of hot atomic vapors (Philips et al, 2001).These early research works require hard conditions and the slow light cannot operate in room temperature.Recently, researchers found ways to realize slow light operating in room temperature and solid-state materials, which are more suited for many practical applications, namely slow light via stimulated Brillouin scattering(SBS), slow light via coherent population oscillations (CPO), tunable time delays based on group velocity dispersion or conversion/ dispersion(C/D), slow light in fiber Bragg gratings and so on.In this chapter, we describe some of the physical mechanisms that can be used to induce slow and fast light effects in room-temperature solids (Bigelow et al, 2003) and some of the exotic propagation effects that can thereby be observed.We also survey some applications of slow and fast light within the fields of quantum electronics and photonics. Fundamentals of slow and fast lightSlow and fast light refer to the group velocity of a light wave.The group velocity is the velocity most closely related to the velocity at which the peak of a light pulse moves through an optical dispersive material (Milonni, 2005), and is given by the standard result www.intechopen.comRecent Progress in Optical Fiber Research 82where n is the refractive (phase) index and ω is the angular frequency of the carrier wave of the light field.One refers to light as being slow light for v g << c, fast light for for v g > c, and backwards light for v g <0 or v g is negative.Extreme values of the group velocity invariably rely on the dominance of the second contribution to the group index of Equation ( 1).This contribution of course results from the frequency dependence of the refractive index, and for this reason extreme values of the group velocity are usually associated with the resonant or near-resonant response of material systems.According to this theory, slow light is expected in the wings of an absorption line and fast light is expected near line center, and the spatial dispersion, that is, the non-locality in space of the medium response, is another mechanism that can lead to slow light, as has been predicted (Kocharovskaya et al,2001) and observed (Strekalov et al, 2001).We catalogue the main methods to realize slow light in room temperature solid, namely slow light via stimulated Brillouin scattering(SBS), slow light via coherent population oscillations (CPO), tunable time delays based on group velocity dispersion or conversion/ dispersion(C/D), slow light in fiber Bragg gratings and so on.We will describe CPO and SBS slow light in more details.
Fast or slow light propagation means that the group velocity of a quasi-monochromatic light pulse propagating in a resonant medium can be significantly faster or slower than the light speed in a vacuum. Since the end of the last century and the beginning of this century, studies on this subject have attracted a great deal of interest. Remarkable progress has been achieved, based on various nonlinear optical interactions in resonant media. The fundamental research on this subject can enrich our understanding of special relativity and causality in physics. On the other hand, those mechanisms and techniques developed for fast and slow light propagation have provided the potential for many future applications, such as optical buffers and variable delay lines for optical networks, optical computing, optical telecommunications, optical data storage, and signal processing.
We present an analysis of the propagation of light pulses through materials possessing extreme values of the group velocity. We begin with an analysis of the behaviour that occurs upon propagation through materials possessing simple Lorentzian gain or absorption lines or materials possessing sharp dips in gain or absorption features. We also describe how more complicated lineshapes can be used to tailor the dispersion of a slow-light system. We furthermore present an analysis of fundamental limitations to how many pulse widths a pulse of light can be delayed or advanced. We show how these mechanisms lead to different limits for slow and fast propagation media.
Properties of periodic dielectric media have attracted a big interest in the last two decades due to numerous exciting physical phenomena that cannot occur in homogeneous media. Due to their strong dispersive properties, the speed of light can be significantly slowed down in periodic structures. When light velocity is much smaller than the speed of light in a vacuum, we describe this phenomena as slow light. In this thesis, we analyze important properties of slow light enhancement and limitations in periodic structures. We analyze quantitatively and qualitatively different technologies and significant structures with numerical and analytical methods. By analyzing different structures, we show very general properties for limitation and enhancement in the slow light regime. Inherent imperfections of fabricated structures such as a material loss and structural disorder have a strong influence on slowly propagating light. By means of perturbative analysis, we address the effect of small imperfections in periodic structures. From our analysis, we find very universal behavior in a slow light regime for all periodic structures. Even if losses are very small the dispersion is severely affected in the vicinity of the band edge. The minimum attainable group velocity will depend on the amount of imperfections. Since imperfections are inherited as part of any periodic structure it is necessary to take them into account when we are interested in slow light applications. Slowly propagating light gives rise to longer interaction time in the periodic media. Due to this reason, weak light-matter interaction is enhanced. The enhancement due to slow light has been studied for loss and gain. By introducing gain/loss, dispersive properties, in the slow light region, are severely influenced. The minimum attainable group velocity is strongly dependent on the amount of introduced loss/gain that will result in limitation of enhancement. Therefore, small amounts of gain/loss will provide great enhancement. While for a large amount of gain/loss slow, light is heavily jeopardized, hence no enhancement will occur.