It is known that light can be slowed down in the vicinity of resonances in dispersive materials.5 In order to reduce the group velocity (vg) of light coherently, there are primarily two major approaches employing either electronic or optical resonances. In the electronic scheme, drastic slowing down and complete stopping of light pulses can be accomplished by converting optical signals into electronic coherences.6-9 The use of electronic states to coherently store the optical information, however, imposes severe constraints in the scheme, including narrow bandwidth, limited working wavelengths and strong temperature dependence. While promising steps have been taken towards slowing light in solidstate media and semiconductor nanostructures operating at room temperature,10 it still remains a great challenge to implement such schemes on-a-chip incorporating optoelectronic devices.9 Besides, only a few special and delicate electronic resonances available in nature possess the required properties. As a result, there has been great interest in pursuing alternative approaches utilizing optical resonances in photonic structures, such as microcavities,11photonic crystals,12 semiconductor waveguide ring resonators,13etc. In 2007, researchers in UK proposed a tapered structure based on metamaterial with negative refractive index.14 Theoretically, this structure should be able to slow light to a standstill. The material would halt each frequency of light, and hence color, at slightly different places, to make so called “trapped rainbow” (see Fig. 9.1), which opened a new and attractive approach to stopping light.
It is known that light can be slowed down in the vicinity of resonances in dispersive materials.5 In order to reduce the group velocity (vg) of light coherently, there are primarily two major approaches employing either electronic or optical resonances. In the electronic scheme, drastic slowing down and complete stopping of light pulses can be accomplished by converting optical signals into electronic coherences.6-9 The use of electronic states to coherently store the optical information, however, imposes severe constraints in the scheme, including narrow bandwidth, limited working wavelengths and strong temperature dependence. While promising steps have been taken towards slowing light in solidstate media and semiconductor nanostructures operating at room temperature,10 it still remains a great challenge to implement such schemes on-a-chip incorporating optoelectronic devices.9 Besides, only a few special and delicate electronic resonances available in nature possess the required properties. As a result, there has been great interest in pursuing alternative approaches utilizing optical resonances in photonic structures, such as microcavities,11photonic crystals,12 semiconductor waveguide ring resonators,13etc. In 2007, researchers in UK proposed a tapered structure based on metamaterial with negative refractive index.14 Theoretically, this structure should be able to slow light to a standstill. The material would halt each frequency of light, and hence color, at slightly different places, to make so called “trapped rainbow” (see Fig. 9.1), which opened a new and attractive approach to stopping light.
A global web of optical fibers forms the backbone of the Internet. This network relies on routers that switch the transmitted pulses from one fiber to another, so that information ends up at the desired destination. Currently, data traffic at major interconnections requires routers to first convert the travelling optical pulse into an electrical one, perform a switching operation, and then convert the electrical pulse back to its original form. This process can slow-down systems by a factor of 1000. Until now, the prime difficulty in designing an all-optical network router was finding a means to temporarily store or buffer the packets of information. Researchers have recently proposed a variety of methods for completely stopping light. Unfortunately, inherent limitations prevent their deployment. For instance, previous approaches employed ultra cold or hot gases1 and did not use solid-state materials. Other methods stored the data pulses as acoustical disturbances, which still travelled slowly down the fiber2. We have proposed3 a light-guiding structure that does not require cryogenic temperatures and can efficiently bring an optical pulse to a complete halt. In this approach, light travels inside an engineered solid-state meta-material (MM), that has a negative refractive index. This material was developed4 in 2001 and the scheme is conceptually simple. The device we envisioned is a three-layer waveguiding heterostructure, in which the middle MM layer is surrounded by two regular dielectrics. The center portion tapers from wide to narrow. Because the power-flow direction inside theMM layer is opposite to the one in the dielectric regions, the guided electromagnetic waves are markedly slowed. Figure 1 shows the propagation of a monochromatic ( f = 1THz) p-polarized magnetic-field component. The light enters the device from the wide end and stops at the prearranged critical thickness. Because of theMM’s anomalous frequency dispersion, the longest (red) wavelength components stop at the Figure 1. A white light beam hits the tapered negative refractive index layer (shown in white), which is surrounded by two regular dielectric layers (shown in blue and green). Upon entering the structure, each frequency component, or color, of the beam stops at different thicknesses, forming a trapped rainbow.
Research into slow light began theoretically in 1880 with the paper [1] of H A Lorentz, who is best known for his work on relativity and the speed of light. Experimental work started some 60 years later with the work of S L McCall and E L Hahn [2] who explored non-linear self-induced transparency in ruby. This field of research has burgeoned in the last 10 years, starting with the work of L Vestergaard Hau and coworkers on slow light via electromagnetically induced transparency in a Bose–Einstein condensate [3]. Many groups are now able to slow light down to a few metres per second or even stop the motion of light entirely [4]. Today, slow light – or more often `slow and fast light' – has become its own vibrant field with a strongly increasing number of publications. In broad scope, slow light research can be categorized in terms of the sort of physical mechanism used to slow down the light. One sort of slow light makes use of material dispersion. This dispersion can be the natural dispersion of the ordinary refractive index or can be the frequency dependence of some nonlinear optical process, such as electromagnetically induced transparency, coherent population oscillations, stimulated light scattering, or four-wave mixing processes. The second sort of slow light makes use of the wavelength dependence of artificially structured materials, such as photonic crystals, optical waveguides, and collections of microresonators. Material systems in which slow light has been observed include metal vapours, rare-earth-doped materials, Raman and Brillioun gain media, photonic crystals, microresonators and, more recently, metamaterials. A common feature of all of these schemes is the presence of a sharp single resonance or multiple resonances produced by an atomic transition, a resonance in a photonic structure, or in a nonlinear optical process. Current applications of slow light include a series of attractive topics in optical information processing, such as optical data storage, optical memories, quantum information devices, and optical communication systems in which the use of slow light will allow all-optical processing with less wasted heat. To implement these applications, devices such as buffers, memories, interferometers and switches that utilize slow light need to be developed. Future challenges include the need for improved coupling of light into slow light modes, overcoming propagation losses, and mitigating the influence of large dispersion of the group velocity. The collection of papers in this special issue of Journal of Optics features a broad spectrum of articles that highlight actual developments in many of the material types and schemes described above. It represents therefore an excellent up to date snapshot of the current state of the field of slow light research. References [1] Lorentz H A 1880 Uber die Beziehung zwischen der Fortpflanzung des Lichtes und der Körperdichte Wiedemann Ann. 9 641–64 [2] McCall S L and Hahn E L 1967 Self-induced transparency by pulsed coherent light Phys. Rev. Lett. 18 908–11 [3] Vestergaard Hau L, Harris S E, Dutton Z and Behroozi C H 1999 Nature 397 594 [4] Philips D F, Fleischhauer A, Mair A, Walsworth R L and Lukin M D 2001 Storage of light in atomic vapor Phys. Rev. Lett. 86 783–6
There is a wide variety of proposals for implementations of slow-light effects, and many of them are described in the various chapters of this book. The physical implementations vary from system to system, and so do the mathematical formalisms used to describe the specific physical systems. However, it is also possible that one has two completely different physical slow-light systems, yet the mathematical framework describing the slowing and stopping of light is very similar. In this chapter, we present an example falling into this category. The two physically different slow-light systems are (1) semiconductor multiple quantum wells (QWs) (more specifically: Bragg-spaced multiple QWs, or BSQWs [1-16]) and (2) optical resonators (more specifically: side-coupled integrated spaced sequence of resonators with two waveguide channels, or two-channel SCISSORs [17,18]). In Figure 13.1, BSQWs are schematically shown as a sequence of thin semiconductor QWs, spaced by a distance a with a dielectric of refractive index nb between the wells. SCISSORs are sequences of ring-shaped dielectric optical microresonators coupled to two waveguides (Figure 13.2). Clearly, these are very different physical systems, and so onemay wonder in which sense slow-light concepts (i.e., the concepts for delaying, stopping, storing, and releasing light) can be similar or almost identical in these systems. The answer to this question lies in the fact that both systems can be viewed as physical realizations of one-dimensional resonant photonic bandgap structures (RPBGs). RPBGs differ from conventional (nonresonant) photonic bandgap structures in that each unit cell in the photonic lattice exhibits an optical resonance with a resonance frequency that is identical or at least close to the Bragg frequency characterizing the optical lattice. In QWs, the optical resonance is taken to be the heavy-hole exciton resonance, while in SCISSORs we take one of the optical resonances of the microrings.
Recently there has been a considerable interest in metamaterial waveguide structures capable of dramatically slowing down or, even, completely stopping light. Here, we shall explain in some detail the working principle behind the deceleration and/or stopping of light in metamaterial structures, and review the various, metamaterial-enabled, methods that have been proposed thus far towards achieving such a goal. Further, we will concisely describe how one can construct zero-loss metamaterials over a continuous and broad (but not infinite) range of frequencies, which is an essential prerequisite for any slow-light system. Moreover, it will be explained that inside such waveguide structures light can in principle be stopped (zero group velocity, vg = 0) even in the presence of losses. By nature, metamaterialenabled schemes for stopping/storing light invoke solid-state materials and, as such, are not subject to low-temperature or atomic coherence limitations. Furthermore, these methods simultaneously allow for broad bandwidth operation, since they do not rely on group index resonances; large delay-bandwidth products, since a wave packet can, in principle, be completely stopped and buffered indefinitely; and (for the case, in particular, where a negative-index metamaterial is used) high, almost 100%, in/out-coupling efficiencies. Thus, we conclude that these methods for trapping photons, which can be realised using existing technology, could open the way to a multitude of hybrid optoelectronic devices to be used in 'quantum information' processing, communication networks and signal processors and may conceivably herald a new realm of combined metamaterials and slow light research.
Frontiers in Guided Wave Optics and Optoelectronics 84 absorption is much too high to render the group effect useful.An exciting breakthrough happened in the early nineties when it was shown that group velocities of few tens of meters per second were possible with nonlinear resonance interactions (Hau et al., 1999).Two important features of nonlinear resonances make this possible: substantially reduced absorption, or even amplification, of radiation at a resonance, and sharpness of such resonances; the sharper a resonance, the higher dn/dω and so the stronger the enhancement of group index, and hence the greater the pulse is delayed.Widely ranging applications for slow light have been proposed, of which those for telecommunication systems and devices (optical delay lines, optical buffers, optical equalizers and signal processors) are currently of most interest (Gauthier, 2005).The essential demand of such devices is compatibility with existing telecommunication systems, that is they must be of wide enough bandwidth (≥10 GHz) and able to be integrated seamlessly into such systems.Of the various nonlinear resonance mechanisms and media, which allow sufficiently long induced delays, stimulated Brillouin and Raman scattering (SBS and SRS) in optical fiber are deemed to be among the best candidates.Currently SBS is the most actively investigated and many experimental and theoretical papers on pulse delaying via SBS in optical fiber have been published in the last few years, see the review paper (Thevenaz, 2008) and references therein.In this process the pulse to be delayed is a frequency down-shifted (Stokes) pulse.This is transmitted through an optical fiber through which continuous wave (CW) pump radiation is sent in the opposite direction to prime the delay process.It is supposed that the Stokes pulse is amplified by parametric coupling with the pump wave and a material (acoustic) wave in the medium (Kroll, 1965), and the amplification is characterised by a resonant-type gain profile.The dispersion of refractive index associated with this profile (which is similar to that in Fig. 1) can then be used to increase the group index for optical pulses at the Stokes frequency (Zeldovich, 1972).Along with obvious device compatibility, there are several other advantages of the SL via SBS approach for optical communications systems: slow-light resonance can be created at any wavelength by changing the pump wavelength; use of optical fibre allows for long interaction lengths and thus low powers for the pump radiation, the process runs at room temperature, it uses off the shelf telecom equipment, and SBS works in the entire transparency range of fibers and in all types of fiber.Currently a main obstacle to applications of this approach is the narrow SBS gain spectral bandwidth, (Thevenaz, 2008), which is typically ≈ 120-200 MHz in silica fiber in the spectral range of telecom optical radiation (~1.3-1.6 μm) (Agrawal, 2006).This chapter reviews our ongoing work on the physical mechanisms that give rise to pulse delay in SBS.In section 2 the theoretical background of the SBS phenomenon is given and the main working equations describing this nonlinear interaction are presented.In section 3 ways by which the SBS spectral bandwidth may be increased are addressed.Waveguide induced spectral broadening of SBS in optical fibre is considered as a means of increasing the bandwidth to the multi-GHz range.An alternative way widely discussed in the literature, (Thevenaz, 2008), is based on spectral broadening of the pump radiation.However it is shown through analytic analysis of the SBS equations converted to the frequency domain that pump radiation broadening by any reasonable amount has only a negligible effect on increasing the SBS bandwidth.Importantly in this section we show that, irrespective of the nature of the broadening considered, the SBS gain bandwidth remains www.intechopen.
The two-level atom can, for good reason, be considered the basic material structure for the study of quantum optics [1]. The two-level atom has played a fundamental role in studies of physical processes, including self-induced transparency (SIT), photon echoes, optical nutation, saturation spectroscopy, and, most recently, slow- and fast-light research. This latter field has recently been the subject of great activity, as researchers have learned how to utilize various physical processes to exert control over the velocity of propagation of light pulses through material systems [2]. This interest stems both from the intellectual intrigue in situations in which the velocity of light can be speeded up or slowed down by many orders of magnitude and the promise that such techniques might be useful for applications in fields such as telecommunications and optical computing [3‐6]. Most of the recent work in this field has made use of the process of electromagnetically induced transparency (EIT) to induce a narrow transparency region in an otherwise highly absorbing optical material [7, 8]. The rapid variation of the refractive index n associated with this transparency window then leads to a strong modification of the group velocity n g in accordance with the standard relation