The slow-light effect, which implies reduction of the group velocity of light by many orders of magnitude, is considered to be one of the most exciting discoveries in quantum optics of the last decade. The physics underlying the effect is related to an extremely steep dispersion of the medium in a very narrow region of its transparency, while all the manifestations of the effect are usually reduced just to a small pulse delay. Perhaps this is the reason why, after the discovery of the slow-light effect, some of the simplest nonlinear phenomena associated with a retarded optical response have been implicitly revised and assigned to reduction of the light group velocity. In this lecture, a few examples of common inconsistencies in the area of the slow-light physics will be presented.
The slow-light effect, which implies reduction of the group velocity of light by many orders of magnitude, is considered to be one of the most exciting discoveries in quantum optics of the last decade. The physics underlying the effect is related to an extremely steep dispersion of the medium in a very narrow region of its transparency, while all the manifestations of the effect are usually reduced just to a small pulse delay. Perhaps this is the reason why, after the discovery of the slow-light effect, some of the simplest nonlinear phenomena associated with a retarded optical response have been implicitly revised and assigned to reduction of the light group velocity. In this lecture, a few examples of common inconsistencies in the area of the slow-light physics will be presented.
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.
As evidenced by this book, there has been a flurry of activity over the last decade on tailoring the dispersive properties of optical materials [1]. What has captured the attention of the research community were some of the early results on creating spectral regions of large normal dispersion [2-4]. Large normal dispersion results in extremely small group velocities, where the group velocity is the approximate speed at which a pulse of light propagates through a material. We denote the group velocity by υg = c/ng, where c is the speed of light in vacuum and ng is known as the group index. In the early experiments, described in greater detail in Chapter 1, a dilute gas of atoms is illuminated by a control or coupling beamwhose frequency is tuned precisely to an optical transition of an atom. This control field modifies the absorption and dispersion properties of another atomic transition that shares a common energy level. A narrow transparencywindow is created on this second transition-a process known as electromagnetically induced transparency (EIT)—and within this window, υg takes on extremely small values. Many experiments have now observed υg ∼ 1 m/s or less, implying ng > 108. This result is remarkable, considering the fact that the refractive index n of a material rarely exceeds 3 in the visible part of the spectrum.What are the implications of such large group indices? What applications are enabled by this basic science discovery?
The propagation of light in dispersive media is a subject of fundamental as well as practical importance. In recent years attention has focused in particular on how refractive index can vary with frequency in such a way that the group velocities of optical pulses can be much greater or much smaller than the speed of light in vacuum, or in which the refractive index can be negative. Treating these topics at an introductory to intermediate level, Fast Light, Slow Light and Left-Handed Light focuses on the basic theory and describes the significant experimental progress made during the past decade. The book pays considerable attention to the fact that superluminal group velocities are not in conflict with special relativity and to the role of quantum effects in preventing superluminal communication and violations of Einstein causality. It also explores some of the basic physics at the opposite extreme of very slow group velocities as well as stopped and regenerated light, including the concepts of electromagnetically induced transparency and dark-state polaritons. Another very active aspect of the subject discussed concerns the possibility of designing metamaterials in which the refractive index can be negative and propagating light is left-handed in the sense that the phase and group velocities are in opposite directions. The last two chapters are an introduction to some of the basic theory and consequences of negative refractive index, with emphasis on the seminal work carried out since 2000. The possibility that "perfect" lenses can be made from negative-index metamaterials-which has been perhaps the most controversial aspect of the field-is introduced and discussed in some detail.
The propagation of light in dispersive media is a subject of fundamental as well as practical importance. In recent years attention has focused in particular on how refractive index can vary with frequency in such a way that the group velocities of optical pulses can be much greater or much smaller than the speed of light in vacuum, or in which the refractive index can be negative. Treating these topics at an introductory to intermediate level, Fast Light, Slow Light and Left-Handed Light focuses on the basic theory and describes the significant experimental progress made during the past decade. The book pays considerable attention to the fact that superluminal group velocities are not in conflict with special relativity and to the role of quantum effects in preventing superluminal communication and violations of Einstein causality. It also explores some of the basic physics at the opposite extreme of very slow group velocities as well as stopped and regenerated light, including the concepts of electromagnetically induced transparency and dark-state polaritons. Another very active aspect of the subject discussed concerns the possibility of designing metamaterials in which the refractive index can be negative and propagating light is left-handed in the sense that the phase and group velocities are in opposite directions. The last two chapters are an introduction to some of the basic theory and consequences of negative refractive index, with emphasis on the seminal work carried out since 2000. The possibility that "perfect" lenses can be made from negative-index metamaterials-which has been perhaps the most controversial aspect of the field-is introduced and discussed in some detail.
One of the key issues when dealing with slow light is the inevitable effect of dispersion, the result of which is to broaden a pulse upon propagation. Moreover, the dispersion tends to increase when the group velocity, the speed at which the pulse propagates, decreases. To see this, we note that if we write the group velocity vg ≡ c/ng, where ng is the group index, then we find that ng = n+ωdn/dω. Since for the materials we are interested in, the refractive index does not vary strongly in magnitude, and slow light is obtained when the derivative dn/dω is large and positive. However, as the variations in the magnitude of n itself are limited, the large derivative can only be maintained over a narrow bandwidth ∝ (dn/dω)−1. Therefore, a large delay implies a narrow bandwidth, and hence a limited pulse width. Here we discuss how to avoid this limit by using nonlinear effects in the form of gap solitons. Though this argument is quite simple, it can be made rigorous using the Kramers-Kronig relations. In this way it can be shown that the achievable delay in a linear, two-port device is subject to a limitation of the product of the delay and the bandwidth (Lenz et al., 2001).