We demonstrate the generation of slow and fast light (SFL) in a linear and passive three-beam interferometer. Such propagation regimes occur for narrowband pulses with center frequency close to the transmission minima. A model that fully describes SFL effects in this system is developed and an analytical approximate expression for the group delay at the minima is derived. We demonstrate that slow light is not possible if the length difference between adjacent branches of the interferometer is a constant. If a small length detuning ($\ensuremath{\xi}$) in one of the branches is introduced, slow light at one of the two minima can be obtained as long as $\ensuremath{\xi}$ exceeds a critical value. Simultaneously, tunneling, superluminal, or normal regime is sustained at the other minimum, depending on the system's length. A proof-of-model experiment is performed in the radiofrequency range using coaxial cables and $1\ifmmode\times\else\texttimes\fi{}3$ power splitters. The possible realization and performance of such a system in the optical range is also discussed. This system is proposed as a simple alternative to active systems and photonic band-gap structures for sustaining both slow and fast light.
We demonstrate the generation of slow and fast light (SFL) in a linear and passive three-beam interferometer. Such propagation regimes occur for narrowband pulses with center frequency close to the transmission minima. A model that fully describes SFL effects in this system is developed and an analytical approximate expression for the group delay at the minima is derived. We demonstrate that slow light is not possible if the length difference between adjacent branches of the interferometer is a constant. If a small length detuning (\ensuremathξ) in one of the branches is introduced, slow light at one of the two minima can be obtained as long as \ensuremathξ exceeds a critical value. Simultaneously, tunneling, superluminal, or normal regime is sustained at the other minimum, depending on the system's length. A proof-of-model experiment is performed in the radiofrequency range using coaxial cables and 1\ifmmode×\else\texttimes\fi3 power splitters. The possible realization and performance of such a system in the optical range is also discussed. This system is proposed as a simple alternative to active systems and photonic band-gap structures for sustaining both slow and fast light.
In this work, we explore the generation of slow and fast light (SFL) in a linear and passive three-beam interferometer for center pulse frequency close to the transmission minima. We show that the group delay can be tuned from subluminal to superluminal values by simply changing the length of one of the interferometer's arms. Some figures of merit of this three-beam interferometer as an SFL system are discussed, namely fractional delay and pulse distortion. We build our interferometers using 50-Ω coaxial cables and 1x3 power splitters in order to perform the experiments in the radiofrequency range, where a full frequency-domain characterization of them can be performed with a vector network analyzer. Together with the frequency domain results, we present direct measurement of the group delay in time domain. Fractional delays of ±25% were measured for a train of sinusoidally modulated wavepacket with 300 kHz repetition rate. Additionally, a Lithium Niobate interferometer operative in the optical range (1.55 μm) was simulated and discussed. This system is proposed as an alternative to active systems and photonic band-gap structures for sustaining both slow and fast light, with special emphasis in sensing purposes.
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.
We propose and demonstrate a method for manipulation of group velocity from slow-to-fast light (SFL) in a two-beam Mach–Zehnder interferometer in radio frequency (RF) regime. The subluminal, superluminal, and tunneling propagation regimes occur in a narrow frequency band around the resonance frequency of the interferometer where destructive interference occurs. Importantly, the group velocity at the resonance frequency can be controlled by simply adjusting the transmission magnitude of the signals from the two beams, without changing the length of the interferometer. Models that fully describe the SFL effects in the microwave interferometer system are developed and closed-form expressions for the prediction of group delays at the resonance frequency are obtained. The simple and effective method is verified through numerical calculations and experimental measurements. We also demonstrate that the proposed method applies to a microwave cavity interferometer. A proof-of-concept experiment is performed using a custom open-ended coaxial cable resonator (OE-CCR). Positive and negative group delays are experimentally measured when the resonator is set at different coupling states.
An analytical approach is reported that describes previously observed fast-light regimes in linear and passive Mach-Zehnder interferometers (MZI) where the optical path difference is due to a different length of the branches. Approximate expressions are developed for the transmission coefficient and group delay spectral functions valid for frequencies close to the transmission minima ${\ensuremath{\omega}}_{\mathrm{min}}$, where these regimes occur. It is found that the group delay at ${\ensuremath{\omega}}_{\mathrm{min}}$ verifies a simple scaling law. We demonstrate that slow light cannot arise in this system, and that tunneling and superluminal regimes appear only for low-loss devices, where the attenuation drives the change in the propagation regimes. The propagation of a sinusoidally modulated pulse train through the MZI is described, and relevant figures of merit, which are intrinsic to the system and universal for any operative spectral range, are determined. The theoretical approach is illustrated by simulations of a silicon-based interferometer designed for advancing pulses at 1.55 \ensuremath{\mu}m. Also, previously reported experimental results in the radiofrequency range are interpreted in the framework of the model.
In this work, we demonstrate the existence of abnormal pulse propagation regimes in linear and passive multiple-beam interferometers, where the group velocity can be tuned from subluminal to superluminal values by simply changing the length of one of the interferometer's arms. Experiments are performed in the radiofrequency range by using coaxial transmission lines. The interferometers group delay is characterized both in the frequency and in the time domain. Group velocities of 2c and tunnelling with negative group velocity of -0.11c were measured for electromagnetic wave packets of 2 μs width travelling through a Mach-Zehnder interferometer. In a 4-beam interferometer, the group velocity of a 5 μs wide pulse was reduced to only 0.3c (compared to the usual value of 0.67c). The system is scalable to other frequency ranges and its implementation for narrowband optical pulses could be feasible by means of micromachining technologies. A scaling approach for advancing/delaying optical pulses at 1.55 μm is discussed. These systems are proposed as an alternative for controlling the group velocity without the need of using photonic crystals or periodically microstructuring, doping or using non-linear media.
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.