Emergence of semi-localized Anderson modes in a disordered photonic crystal as a result of overlap probability*
- 76 Downloads
In this paper we study the effect of positional randomness on transmissional properties of a two dimensional photonic crystal as a function of a randomness parameter α (α = 0 completely ordered, α = 1 completely disordered). We use finite-difference time-domain (FDTD) method to solve the Maxwell’s equations in such a medium numerically. We consider two situations: first a 90° bent photonic crystal wave-guide and second a centrally pulsed photonic crystal micro-cavity. We plot various figures for each case which characterize the effect of randomness quantitatively. More specifically, in the wave-guide situation, we show that the general shape of the normalized total output energy is a Gaussian function of randomness with wavelength-dependent width. For centrally pulsed PC, the output energy curves display extremum behavior both as a function of time as well as randomness. We explain these effects in terms of two distinct but simultaneous effects which emerge with increasing randomness, namely the creation of semi-localized modes and the shrinking (and eventual destruction) of the photonic band-gaps. Semi-localized (i.e. Anderson localized) modes are seen to arise as a synchronization of internal modes within a cluster of randomly positioned dielectric nano-particles. The general trend we observe shows a sharp change of behavior in the intermediate randomness regime (i.e. α ≈ 0.5) which we attribute to a similar behavior in the underlying overlap probability of nano-particles.
KeywordsPhotonic Crystal Output Energy Randomness Factor FDTD Method Random Laser
Unable to display preview. Download preview PDF.
- 1.J.D. Joannopoulos, S.G. Johnson, R.D. Meade, J.N. Winn, Photonic Crystals: Molding the Flow of Light, 2nd edn. (Princeton University Press, 2008) Google Scholar
- 2.J.M. Lourtioz, H. Benisty, V. Berger, J.M. Gérard, D. Maystre, A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices (Springer, 2005) Google Scholar
- 10.A. Taflove, S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd edn. (Artech House, 2005) Google Scholar
- 27.C.M. Briskina, L.E. Li, Laser Phys. 12, 724 (2002) Google Scholar
- 33.T.N. Langtry, L.C. Botten, A.A. Asatryan, M.A. Byrne, A. Bourgeois, in Proc. of 11th Computational Techniques and Applications Conference CTAC-2003, edited by J. Crawford, A.J. Roberts (2004), Vol. 45, pp. C744–C758, http://anziamj.austms.org.au/V45/CTAC2003/Lang/home.html
- 35.P. Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena, 2nd edn. (Springer, 2006) Google Scholar