Theoretical investigation of defects in photonic crystals in the presence of dielectric losses (original) (raw)
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In this paper, the characteristic matrix method is employed to theoretically investigate the propagation of electromagnetic waves through one-dimensional defective lossy photonic crystals (PCs) composed of negative index materials (NIMs) and positive index materials (PIMs). We consider symmetric and asymmetric geometric structures with two different types of NIM defect layers at the center of the structure. The effects of the polarization and the angle of incidence on the defect modes in the transmission spectra of both structures are investigated. The results show that the number of the defect modes within the photonic band gap (PBG) depends on the type of the NIM defect layer and is independent of the geometrical structure.
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We introduce an analytical model to investigate the localized defect modes associated with a defect cell inserted in a one-dimensional photonic crystal for both transverse electric (TE) and transverse magnetic (TM) polarizations, at an arbitrary angle of incidence. The defect cell, which is made of two dielectric constituents, leads to the appearance of several localized defect modes within the photonic band gaps. We develop an analytical approach based on the both transfer matrix and Green's function methods to determine the number and frequency of the defect modes that can be controlled easily by varying the parameter values of the constituent layers of the photonic crystal. The method demonstrates that the electric field amplitude depends on the defect cell position in the photonic crystal while the defect mode frequency is independent of it. This method is useful for photonic band gap engineering and designing the photonic-based devices.
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We present a three-dimensional finite-difference time-domain analysis of localized defect modes in an optically thin dielectric slab that is patterned with a two-dimensional array of air holes. The symmetry, quality factor, and radiation pattern of the defect modes and their dependence on the slab thickness are investigated.
Accurate model of electromagnetic wave propagation in unidimensional photonic crystals with defects
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Complete vectorial studies of electromagnetic wave propagation in complex media are difficult and computationally intensive. A mathematical continuous model can simplify some of such difficulties. Using this technique, we have modeled the propagation of electromagnetic plane waves through a semiinfinite photonic crystal with defects. The model is exact in the sense that the only approximations are the numerical accurate solution of ordinary differential equations and the simulation of defects by a high frequency sinusoidal continuous variation of the main crystal period.
Transmission through photonic crystals with multiple line defects at oblique incidence
Journal of the Optical Society of America B Optical Physics, 2008
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Electrical modeling of photonic crystal defects
Microwave and Optical Technology Letters, 2012
A transmission line model of a planar photonic crystal (PC) waveguide is presented here. Electrical characteristics of single and multiple point defects in a PC waveguide are investigated. It is shown that a point defect in the waveguide can be modeled as a reactance connected across the transmission line. Investigation shows that depending on the size and refractive index, a point defect can be inductive or capacitive and its reactance can vary over a wide range. A double defect behaves as a bandpass filter. V