Characterization of defect modes in one-dimensional photonic crystals: An analytic approach (original) (raw)
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Defect Mode Properties and Origin in one Dimensional Photonic Crystal
The properties and origin of defect modes in the one dimensional photonic crystal (PC) with a central defect has been studied. Two types of photonic crystals, each having single defect, namely, symmetric and asymmetric PCs are considered. It is found that a defect mode arise at central wavelength for asymmetric PC, whereas two defect modes arise in the vicinity of central wavelength for symmetric PC. These two defect modes can be fixed to a single central defect by increasing the width of the defect layer. But the intensities of these defect modes are found to be different from the intensities of defect modes for asymmetric case. The origin of these defect modes can be explained using impedance matching condition. The propagation characteristics of the proposed structure are analyzed by using the transfer matrix method.
Journal of Electromagnetic Waves and Applications, 2013
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.
Spatial and frequency domain effects of defects in 1D photonic crystal
Optical and Quantum Electronics, 2007
The aim of this paper is to present the analysis of influence of defects in 1D photonic crystal (PC) on the density of states and simultaneously spontaneous emission, in both spatial and frequency domains. In our investigations we use an analytic model of 1D PC with defects. Our analysis reveals how presence of a defect causes a defect mode to appear. We show that a defect in 1D PC has local character, being negligible in regions of PC situated far from the defected elementary cell. We also analyze the effect of multiple defects, which lead to photonic band gap splitting.
Defect modes caused by twinning in one-dimensional photonic crystals
Journal of the Optical Society of America B, 2004
Propagation of electromagnetic waves in a one-dimensional photonic crystal with a twin-defect-a periodicity break where one half of the photonic structure is a mirror image of the other one-is studied using a transfermatrix method. This work is done in the general framework of photonic structures composed of isotropic materials exhibiting both dielectric and magnetic properties. Both polarizations of electromagnetic waves impinging at oblique incidence on the structure are considered. We derive analytical expressions for the frequency of defect modes and for the enhancement of the electromagnetic field inside the defect. In particular, we discuss possibilities of tuning of defect levels for a photonic crystal structure with a two-layer elementary cell.
Single and coupled degenerate defect modes in two-dimensional photonic crystal band gaps
Physical Review A, 2009
We investigate the formation and coupling of defect modes in two-dimensional photonic crystal ͑PC͒ band gaps associated with degenerate edges. Using a method based on Green's functions and perturbation theory, we derive a condition for the degeneracy of a defect mode in a PC band gap. We show that the interaction between multiple degenerate defects splits this degeneracy and provide a semi-analytic model for the splitting using a 4 ϫ 4 tight-binding matrix. We observe that the structure of this tight-binding matrix is related to the overlap and corresponding symmetry of the defect modes. We confirm our analysis by comparing with numerical results.
Transmission Properties of 1D Defect Metallic-Dielectric Photonic Crystals
2016
In this study, we have theoretically investigated transmission properties of transverse electric fields at visible region frequencies in one dimensional defect Metallic-Dielectric photonic crystals. We examined the effect of photonic crystals thickness, layer numbers, layer refractive indexes and defects on transparency. We use OptiFDTD software for simulations. OptiFDTD software uses finite-different time-domain method.
Properties of defect modes in geometrically chirped one-dimensional photonic crystals
Optical Materials, 2011
The variation of the transmission coefficient with defect mode frequency in a geometrically chirped photonic crystal with central defect layer has been investigated theoretically using transfer matrix method and validated experimentally by fabricating and characterizing such photonic crystals. The defect mode frequency is extracted by modeling the defect layer as a Fabry-Perot resonant cavity with mirrors replaced by two geometrically chirped photonic crystals. It is shown that the structural asymmetry of the chirped photonic crystals with respect to the central defect layer affects the width of the photonic band gap and also induces coupling variation between the eigenmodes of the defect layer and those at the band edges of the constituent photonic crystals. This leads to variation in the defect mode transmittance across the photonic band gap and introduces notches at positions where the eigenmodes of the band edges have maximum transmission.
Localized defect modes in a two-dimensional triangular photonic crystal
Physical Review B, 1998
By using a finite-difference time-domain numerical method based on introducing an oscillating dipole at a proper position in a two-dimensional photonic crystal consisting of an array of dielectric cylinders, we numerically solve the inhomogeneous wave equation discretized in both space and time to calculate the eigenfrequency and the eigenfunction of a localized defect mode. We study the spatial distribution of the electric field and the radiated power associated with the defect modes produced by introducing a defect cylinder into an otherwise periodic two-dimensional triangular photonic crystal. We have obtained excellent agreement for the defect mode of A 1 symmetry created by removing a single cylinder from the center of the region of cylinders arrayed in a triangular lattice with the experimental result of Smith et al. ͓J. Opt. Soc. Am. B 10, 314 ͑1993͔͒. We have also examined systems in which defect states are introduced by varying the radius of a single cylinder and when both the dielectric strength and the radius of the defect cylinder are changed. The calculated values of the donor and acceptor levels associated with the exponentially decaying defect modes of A 1 symmetry induced by changing the radius are in good quantitative agreement with the nondegenerate donor and acceptor levels obtained by the supercell method within the plane-wave approach reported recently by Feng et al. ͓Jpn.