Emergence of semi-localized Anderson modes in a disordered photonic crystal as a result of overlap probability - Condensed Matter > Other Condensed MatterReport as inadecuate




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Abstract: In this paper we study the effect of positional randomness on transmissionalproperties of a two dimensional photonic crystal as a function of a randomnessparameter $\alpha$ $\alpha=0$ completely ordered, $\alpha=1$ completelydisordered. We use finite-difference time-domain~FDTD method to solve theMaxwell-s equations in such a medium numerically. We consider two situations:first a $90\degr$ bent photonic crystal wave-guide and second a centrallypulsed photonic crystal micro-cavity. We plot various figures for each casewhich characterize the effect of randomness quantitatively. More specifically,in the wave-guide situation, we show that the general shape of the normalizedtotal output energy is a Gaussian function of randomness withwavelength-dependent width. For centrally pulsed PC, the output energy curvesdisplay extremum behavior both as a function of time as well as randomness. Weexplain these effects in terms of two distinct but simultaneous effects whichemerge with increasing randomness, namely the creation of semi-localized modesand the shrinking and eventual destruction of the photonic band-gaps.Semi-localized i.e. Anderson localized modes are seen to arise as asynchronization of internal modes within a cluster of randomly positioneddielectric nano-particles. The general trend we observe shows a sharp change ofbehavior in the intermediate randomness regime i.e. $\alpha \approx 0.5$which we attribute to a similar behavior in the underlying overlap probabilityof nano-particles



Author: A. R. Hashemi, M. Hosseini-Farzad, Afshin Montakhab

Source: https://arxiv.org/







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