Anomalous group velocity at the high energy range of a 3D photonic nanostructure

Abstract

Abstract:We report on a study of electromagnetic waves propagation in thin periodically ordered photonic nanostructures in the spectral range where the light wavelength is on the order of the lattice parameter. The vector KKR method we use allows us to determine the group index from finite photonic structures including extinction providing confirmation of recently emerged results. We show that for certain frequencies the group velocity of opal slabs can either be superluminal or approach zero depending on the crystal thickness and the unavoidable presence of losses. In some cases, group velocity can be negative. Such behavior can be clearly attributed to the finite character of the three-dimensional structure and reproduces previously reported experimental observations. Calculations show that contrary to the predictions of extraordinary group velocity reductions for infinite periodic structures, the group velocity of real opals may exhibit strong fluctuations at the high energy range. Hence, a direct identification between the calculated anomalous group velocities, for an actual opal film, and the predicted propagating low dispersion modes for an ideal infinite ordered structure seems difficult to establish. 49-77 (1998). 14. K. Ohtaka, "Scattering theory of low-energy photon diffraction," J. Phys. C: Solid State 13(4), 667-680 (1980). 15. A. Modinos, "Scattering of electromagnetic waves by a plane of spheres-formalism," Physica A 141(2-3), 575-588 (1987) ©2010 Optical Society of America

Anomalous group velocity at the high energy range of real 3D photonic nanostructures

“…For convergence reasons, the values of the code parameter, LMAX, that controls the cut-off value of the angular momentum in the spherical-wave expansion of the electric fields is taken as LMAX = 9. For all calculations shown in this paper, the code parameter, RMAX, of the plane wave expansion of the electric field, is taken as RMAX = 26; meaning that we use the first 41 reciprocal-lattice vectors [8,17,23].…”

“…The frequency dependence of both, the phase delay introduced to the forwardly transmitted beam, and the group index, strongly depend on the index contrasts between the nanospheres and the surrounding medium [23]. While for very low dielectric contrasts the phase increases linearly with frequency, for higher index contrasts phase becomes a more complex function with either positive or negative slopes.…”

Propagació i generació de llum en nanoestructures fotòniques

“…Per a extincions més grans els comportaments se suavitzen i no s'assoleixen velocitats de grup tant petites com les que es podrien esperar, fins i tot per a un òpal format per una apilament de fins a 200 plans [111]. En el rang d'energies altes d'una estructura periòdica finita en 3D, els aspectes reals com les imperfeccions i efectes finits, ja no poden ser considerats una pertorbació menor, sinó que són determinants i dominen la propagació de la llum [Bot09b,Dor07a,Eng06].…”

“…For greater extinctions the oscillations smooth and group velocity does not attain the expected low values, even for thick opals formed by 200 [111] layers. In the high energy range of a finite 3D periodic structure, real aspects like imperfections and finite effects, may no longer be considered as a minor perturbation, since they come to dominate light propagation [Bot09b,Dor07a,Eng06].…”

“…Poden ser invertits i infiltrats modificant-ne les propietats, especialment en aquest interval; o bé poden ser manipulats per crear estructures encara més complexes [Bla06]. A més, s'ha descobert que, a energies altes, aquestes estructures presenten unes propietats complexes que donen lloc a comportaments físics nous, com ara la velocitat de grup anòmala, descrita en el Capítol 4 [Bot09b]. En particular, la reducció de la velocitat de grup afavoreix la interacció entre la radiació i la matèria i pot donar lloc a aplicacions interessants en el camp de l'òptica no lineal [Slu03].…”