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arXiv:1506.00689 · Physical Review A

Slow-light transmission in one-dimensional periodic structures

Óscar del Barco, M. Ortuño

Published Feb 26, 2010• 5 citations
arXivHTMLPDF

Abstract

We have analyzed the transmission properties of pulses through one-dimensional periodic structures in order to systematically explore the best conditions to achieve the maximum delay with the minimum possible distortion. In the absence of absorption and no layer variation, the transmission coefficient ${t}_{N}$ can be well approximated by a sum of Lorentzian resonances. The ratio between their width ${\ensuremath{\Gamma}}_{\mathrm{r}}$ and their separation $\ensuremath{\Delta}{\ensuremath{\omega}}_{\mathrm{r}}$ is a crucial parameter to characterize the distortion of the transmitted pulse. For typical values of the parameters used in telecommunications and high index of refraction contrasts ${n}_{2}/{n}_{1}$, the distortion of the transmitted pulse is unacceptably large for frequencies near the edge of the transmission window. We estimate fractional delays achievables in terms of the central frequency used and the pulse bandwidth.

DOI
10.1103/physreva.81.023833

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Paradoxically, slow light promises to increase the speed of telecommunications in novel photonic structures, such as coupled resonators [1] and photonic crystals [2,3]. Apart from signal delays, the key consequence of slowing light down is the enhancement of light-matter interactions. Linear effects such as refractive index modulation scale linearly with slowdown in photonic crystals [3], and nonlinear effects are expected to scale with its square [4]. By directly observing the spatial compression of an optical pulse, by factor 25, we confirm the mechanism underlying this square scaling law. The key advantage of photonic structures over other slow light concepts is the potentially large bandwidth, which is crucial for telecommunications [5]. Nevertheless, the slow light previously observed in photonic crystals [2,3,6,7] has been very dispersive and featured narrow bandwidth. We demonstrate slow light with a bandwidth of 2.5 THz and a delay-bandwidth product of 30, which is an order of magnitude larger than any reported so far.
We study analytically pulse distortion in linear slow light systems, and provide some useful limits on these devices. Additionally, we also show that the contributions of phase and amplitude broadening can be de-coupled and quantified. It is observed that phase broadening is generally smaller than amplitude broadening in conventional slow light media (lorentzian gain profile) except for very large fractional delays, where it becomes larger. Upon these expressions, we may envisage new strategies to minimize the distortion in the delaying of pulses, depending on the specific application and the required fractional delay. To overcome the residual distortion, we show that nonlinear systems can lead to a resharpening of the pulses and a re-generation of the filtered frequencies.
We analytically study the linear propagation of arbitrarily shaped light pulses through an absorbing medium with a narrow transparency window or through a resonant amplifying medium. We point out that, under certain general conditions, the pulse acquires a nearly Gaussian shape, irrespective of its initial shape and of the spectral profile of the line. We explicitly derive in this case the pulse parameters, including its skewness, responsible for a deviation of the delay of the pulse maximum from the group delay. We illustrate our general results by analyzing the slow-light experiments having demonstrated the largest fractional pulse delays.
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.
Ultra-slow light and complete transmission properties in one-dimensional Cantor photonic crystals are presented. In contrast to traditional dielectric photonic crystals, the proposed structure has large group delay, slower group velocity, and a high quality factor within the same layers and materials. This study shows that larger than 1 μs group delay and slower than 1 m/s group velocity are achieved in the fifth-order Cantor photonic crystal with 52.75 μm length. This ultra-slow-light structure is very promising for application in advanced slow-light devices. A high quality factor of 109 and multiband filters with complete transmission can also be obtained by using this approach.
Pulse propagation through 1-dimensional stratified media is studied. The general features of pulse propagation in relation to the delay or advancement of the pulse are discussed. It is shown that in a lossless system with spatial symmetry the reflected and the transmitted pulses have the same delay or advancement. The phase times and the explicit output pulse profiles for an input Gaussian pulse are calculated. While recalling recent results for a variety of systems (resonant absorbers or heterogeneous medium in a Fabry-Perot cavity, a slab of negative index medium, a left-handed/right-handed periodic structure, etc.), new results involving coupled waveguides and a high finesse cavity containing an electromagnetically induced transparency (EIT) medium are presented. Calculations clearly show that for pulses with a carrier tuned at the resonance of the stratified media, one generally has subluminal propagation. Alternatively, in stop gaps or away from the resonances one ends up with superluminal transit. In the case of the EIT cavity it is shown that the large dispersion offered by the intracavity medium can lead to substantial superluminality (ng≃−106) with peak transmission as high as 20%. This is in sharp contrast to large signal attenuation for usual superluminal transit. Note also that EIT, to the best of the authors knowledge, has so far been used to achieve only slow light.