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Acta Physica Sinica

Influence of gain on propagation properties of slow light in one-dimensional periodic structures

Yun Shen, Fu Ji-Wu, Guoping Yu

Published Jan 1, 2014• 0 citations
Publisher

Abstract

Recently, studies by Jure Grgic et al. (Phys. Rev. Lett. 108 183903, 2012) show that in a periodic structure, the large gain can be eventually turned to decreasing the effect of slow light on the structure. In this paper, one-dimensional periodic structures are taken as an instance, and the influences of gain on slow light are further investigated. It is shown that different influences can exhibit in the finite-length and infinite-length one-dimensional periodic structures. For the infinite-length structures, the addition of gain can decrease the slow light effect, whereas for finite-lengh structures, the compensation of gain can, to a certain degree, increase the slow light effect. Our results verify a feasible way in the application of such a periodic structure, as a slow-light device, and especially as the tunable slow-light devices, in the high-density integration of optical circuits.

DOI
10.7498/aps.63.174202

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Recently, studies by Jure Grgic et al. (Phys. Rev. Lett. 108 183903, 2012) show that in a periodic structure, the large gain can be eventually turned to decreasing the effect of slow light on the structure. In this paper, one-dimensional periodic structures are taken as an instance, and the influences of gain on slow light are further investigated. It is shown that different influences can exhibit in the finite-length and infinite-length one-dimensional periodic structures. For the infinite-length structures, the addition of gain can decrease the slow light effect, whereas for finite-lengh structures, the compensation of gain can, to a certain degree, increase the slow light effect. Our results verify a feasible way in the application of such a periodic structure, as a slow-light device, and especially as the tunable slow-light devices, in the high-density integration of optical circuits.
Properties of periodic dielectric media have attracted a big interest in the last two decades due to numerous exciting physical phenomena that cannot occur in homogeneous media. Due to their strong dispersive properties, the speed of light can be significantly slowed down in periodic structures. When light velocity is much smaller than the speed of light in a vacuum, we describe this phenomena as slow light. In this thesis, we analyze important properties of slow light enhancement and limitations in periodic structures. We analyze quantitatively and qualitatively different technologies and significant structures with numerical and analytical methods. By analyzing different structures, we show very general properties for limitation and enhancement in the slow light regime. Inherent imperfections of fabricated structures such as a material loss and structural disorder have a strong influence on slowly propagating light. By means of perturbative analysis, we address the effect of small imperfections in periodic structures. From our analysis, we find very universal behavior in a slow light regime for all periodic structures. Even if losses are very small the dispersion is severely affected in the vicinity of the band edge. The minimum attainable group velocity will depend on the amount of imperfections. Since imperfections are inherited as part of any periodic structure it is necessary to take them into account when we are interested in slow light applications. Slowly propagating light gives rise to longer interaction time in the periodic media. Due to this reason, weak light-matter interaction is enhanced. The enhancement due to slow light has been studied for loss and gain. By introducing gain/loss, dispersive properties, in the slow light region, are severely influenced. The minimum attainable group velocity is strongly dependent on the amount of introduced loss/gain that will result in limitation of enhancement. Therefore, small amounts of gain/loss will provide great enhancement. While for a large amount of gain/loss slow, light is heavily jeopardized, hence no enhancement will occur.
Light showing extremely slow propagation (known as "slow light") can produce various effects such as compression of optical signals, buffering, convolution integral calculation, beam forming, enhancement of optical absorption, gain, non-linearity, and so on. To generate such light, very large material and structural dispersions are used. Photonic crystal waveguides are good candidates for many device applications since they can easily generate slow light at room temperature. This paper discusses the potential of slow light devices while explaining some critical issues, such as the delay-band product and the dispersion compensation.
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.
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.
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.
One of the key issues when dealing with slow light is the inevitable effect of dispersion, the result of which is to broaden a pulse upon propagation. Moreover, the dispersion tends to increase when the group velocity, the speed at which the pulse propagates, decreases. To see this, we note that if we write the group velocity vg ≡ c/ng, where ng is the group index, then we find that ng = n+ωdn/dω. Since for the materials we are interested in, the refractive index does not vary strongly in magnitude, and slow light is obtained when the derivative dn/dω is large and positive. However, as the variations in the magnitude of n itself are limited, the large derivative can only be maintained over a narrow bandwidth ∝ (dn/dω)−1. Therefore, a large delay implies a narrow bandwidth, and hence a limited pulse width. Here we discuss how to avoid this limit by using nonlinear effects in the form of gap solitons. Though this argument is quite simple, it can be made rigorous using the Kramers-Kronig relations. In this way it can be shown that the achievable delay in a linear, two-port device is subject to a limitation of the product of the delay and the bandwidth (Lenz et al., 2001).