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Journal of Optics

The slowing of light in one-dimensional hybrid periodic and non-periodic photonic crystals

Naim Ben Ali, Jihene Zaghdoudi, M. Kanzari, Robert Kuszelewicz

Published Mar 31, 2010• 20 citations
Publisher

Abstract

Studied in the present paper are the transmission properties, the group velocity, the total phase, the phase time and the slowing-down factor of one-dimensional periodic photonic bandgap structures. The effects of the periodicity and non-periodicity of photonic structures and of the number of layers on the slowing down of light in these structures are also discussed. The group velocity of non-periodic (Fibonacci, Thue–Morse and Cantor) and hybrid (periodic/non-periodic) photonic bandgap structures are studied and compared to those of periodic structures. We show that the slowing-down factors at the edge of the bandgaps are higher for the hybrid (periodic/non-periodic) multilayer systems. The proposed structures have been modelled using the transfer matrix method.

DOI
10.1088/2040-8978/12/4/045402

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Studied in the present paper are the transmission properties, the group velocity, the total phase, the phase time and the slowing-down factor of one-dimensional periodic photonic bandgap structures. The effects of the periodicity and non-periodicity of photonic structures and of the number of layers on the slowing down of light in these structures are also discussed. The group velocity of non-periodic (Fibonacci, Thue–Morse and Cantor) and hybrid (periodic/non-periodic) photonic bandgap structures are studied and compared to those of periodic structures. We show that the slowing-down factors at the edge of the bandgaps are higher for the hybrid (periodic/non-periodic) multilayer systems. The proposed structures have been modelled using the transfer matrix method.
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.
In this work, we investigate the possibility of superluminal and negative delay times for electromagnetic wave propagation in a linear and passive periodic structure consisting of alternating isotropic and anisotropic media. This phenomenon is due to the birefringence of the anisotropic layers of the structure. By adjusting the orientations of these layers, the delay times of transmitted waves can be controlled from subluminality to superluminality and vice versa. Numerical results indicate that the apparent superluminal propagation of light occurs inside the photonic band-gaps when the principal axes of the anisotropic layers are parallel or perpendicular to the fixed axes. For other orientations of these layers, tunneling and superluminal regimes appear inside the photonic bandgaps and in the allowed bands for frequencies close to the transmission minima. The effect of the number of unit cells of the photonic crystal structure on the propagation of light with superluminal and negative delay times is also investigated. We show that the structure exhibits the Hartman effect in which the tunneling delay time of the electromagnetic wave through the photonic band-gap of the structure converges asymptotically to a finite value with increasing the number of layers. The Green's function approach has been used to derive the transmission and reflection coefficients, the density of states, and the delay times of electromagnetic waves propagating through the structure. The control of the magnitude and the sign of the delay time of light propagation represent a key point in slow and fast light technologies. The proposed structure in this study represents a new system for controlling the delay times of wave propagation without a need of active or non-linear media as well as lossy or asymmetric periodic structures.
Features of the propagation and slowing down of short light pulses (duration of ~0.1–2 ps) in one-dimensional resonant photonic crystals with various types of unit cells containing several quantum wells are discussed. It is established that the use of structures with a complex unit cell makes it possible to reduce the group velocity of exciton-polaritons along with the conservation of the width of the transparency window. The calculations show the possibility of the slowing down of a light pulse by a factor of 50 as compared to a pulse propagating in vacuum. The predicted delay time of the pulse is 2 ps at a damping of only 3–5 times.
Group velocity and dispersion property of slow light in one-dimensional photonic crystal with different defect layer thicknesses are studied. It is found that the increase of defect layer thickness will induce the decrease of group velocity, which is an advantage to the design of optical buffer. However, the dispersion slope is increased, inducing a limited factor to keep the shape of ultra-short pulses. Then the effect of slight violation of defect layer thicknesses, refractive index and incident angle on the slow light is studied. The result shows that these influences are smaller at the first gap which is useful for the practical uses.
A driving force in the rapidly developing field of photonic crystals has been the photonic bandgap, a range of energies where the propagation of light is completely forbidden. The photonic bandgap allows the design of photonic lattices that localize, guide and bend light at sub-micron length scales, providing opportunities for the creation of miniature optical devices and integrated optical circuits to help drive the revolution in photonics. A less well known attribute of photonic crystals is their theoretical ability to slow light to a velocity of zero. This phenomenon can be achieved at the high and low energy edges of photonic stopgaps where the photonic bands are flat and light exists as a standing wave commensurate with the photonic lattice and travels at a group velocity of zero, referred to as “slow photons” herein. It has been shown theoretically that the probability of harvesting slow photons scales inversely with their group velocity. This means that a number of well known photon driven processes and devices in chemistry and physics can be enhanced by capturing this unique property of slow photons. In this paper we will look at slow photons mainly through the eye of chemistry and highlight some recent developments in this exciting and emerging field that demonstrate the potential of slow photons in materials chemistry and nanochemistry.