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Optics Express

Pulse propagation in the slow and stopped light regime

Tal A. Weiss, Yonatan Sivan

Published Jul 17, 2018• 5 citations
Publisher

Abstract

Electromagnetic pulse propagation in the slow light regime and near a zero group velocity point is relevant to a plethora of potential applications, and has analogies in numerous other wave systems. Unfortunately, the standard frequency-based formulation for pulse propagation is unsuitable for describing the dynamics in such regimes, due to the divergence of the dispersion coefficients. Moreover, in the presence of absorption, it is not clear how to interpret the propagation dynamics due to the drastic change induced by absorption upon the dispersion curves. As a remedy, we present an alternative momentum-based formulation, which is rapidly converging in these regimes, and naturally suitable for lossy and nonlinear media. It is specialized to a waveguide geometry which provides a significant simplification with respect to existing momentum-based schemes. Doing so, we provide a somewhat alternative, yet intuitive picture of the seeming enhanced absorption and nonlinear response in these regimes, and show that light-matter interactions are not enhanced in the slow/stopped light regimes.

DOI
10.1364/oe.26.019294

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Electromagnetic pulse propagation in the slow light regime and near a zero group velocity point is relevant to a plethora of potential applications, and has analogies in numerous other wave systems. Unfortunately, the standard frequency-based formulation for pulse propagation is unsuitable for describing the dynamics in such regimes, due to the divergence of the dispersion coefficients. Moreover, in the presence of absorption, it is not clear how to interpret the propagation dynamics due to the drastic change induced by absorption upon the dispersion curves. As a remedy, we present an alternative momentum-based formulation, which is rapidly converging in these regimes, and naturally suitable for lossy and nonlinear media. It is specialized to a waveguide geometry which provides a significant simplification with respect to existing momentum-based schemes. Doing so, we provide a somewhat alternative, yet intuitive picture of the seeming enhanced absorption and nonlinear response in these regimes, and show that light-matter interactions are not enhanced in the slow/stopped light regimes.
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.
We present a theoretical and numerical analysis of pulse propagation in a semiconductor photonic crystal waveguide with embedded quantum dots in a regime where the pulse is subjected to both waveguide and material dispersion. The group index and the transmission are investigated by finite-difference-time-domain Maxwell–Bloch simulations and compared to analytic results. For long pulses the group index (transmission) for the combined system is significantly enhanced (reduced) relative to slow light based on purely material or waveguide dispersion. Shorter pulses are strongly distorted and depending on parameters broadening or break-up of the pulse may be observed. The transition from linear to nonlinear pulse propagation is quantified in terms of the spectral width of the pulse.
Investigations of controlled modifications of dispersive properties of atomic media and of propagation of short laser pulses have recently become a dynamically developing field of theoretical and experimental researches. In this lecture a brief overview is presented of basic physical phenomena underlying modifications of a group velocity of a pulse propagating in an optically modified medium. In particular, the possibilities of slowing down this velocity to zero and of retrieving the stopped pulse are discussed.
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.
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 The propagation of light in dispersive media can be described by five different kinds of wave velocities [1-3]: • Phase velocity, which is the speed at which the zero crossings of the carrier wave move • Group velocity, at which the peak of a wave packet moves • Energy velocity, at which the energy is transported by the wave • Signal velocity, at which the half-maximum wave amplitude moves • Front velocity, at which the first appearance of a discontinuity moves Generally, all five velocities can differ from each other, although in a linear passive dispersive media, they coincide and are, usually, less than the light velocity in vacuum. Recently, experimental demonstrations [4-6] in variousmedia show that the group velocity of light canbe reducedby10-100million compared with its vacuum phase velocity. The physics is based on very steep frequency dispersion in the vicinity of narrow resonance of electromagnetically induced transparency (EIT) [7-11].