Design of sharp transmission filters using band-edge resonances in one-dimensional photonic crystal hetero-structures

Applied Physics B (Impact Factor: 1.78). 09/2009; 96(4):709-713. DOI: 10.1007/s00340-009-3662-1

ABSTRACT This paper presents a design of sharp transmission filters using band edge resonance effects in a hetero-structure composed
of one-dimensional photonic crystals with different periods. Assuming that the photonic crystals are made of identical pairs
of transparent materials, the band-edge resonance occurs when the periods are distributed in a geometrical progression with
a common ratio, r=r

, where r

is a known function of refractive-index modulation, incident angle and the polarization of light. The band-edge resonance
results in sharp resonant peaks in the transmission spectrum, with the full width at half maximum of the peaks increasing
with an increase in the number of unit cells in each photonic crystal. Furthermore, if M photonic crystals are used to construct the hetero-structure, M−1 resonant peaks with the spacing between kth (1<k<M) and (k−1)th peaks equal to the band gap of the kth photonic crystal form in the transmission spectrum.

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    ABSTRACT: In this paper, we investigate by theoretical analysis a way to enlarge the frequency range of band gap in one-dimensional heterostructure photonic crystal (PC) made of two PCs alternate stacked by conventional and double negative index material. The numerical results by scattering matrix method (SMM) show that, for the proposed PC with appropriate parameters, there is an omnidirectional photonic band gap (OBG), which is insensitive to incident angle and polarization. The thickness ratio of layers in the second PC is the inverse and identical of that in the first PC, respectively. Two PCs form the PC heterostructures. Moreover, we demonstrate the existence of OBG and notable enlargement of the frequency range of the OBG in proposed PC heterostructure. The reason is that the pass band of one of the two PCs falls into the forbidden band of another PC. Decreasing the thickness of layers but not changing the thickness ratio of layers in the second PC, the frequency range of OBG keeps invariant. However, with the increasing of thickness of layers, the frequency range of OBG gets narrow.
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