On guided waves in photonic crystal waveguides (original) (raw)
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On guided electromagnetic waves in photonic crystal waveguides
American Mathematical Society Translations: Series 2, 2010
The paper addresses the issue of existence of modes guided by linear defects in photonic crystals. Such modes can be created in spectral gaps of the bulk materials and are evanescent in the bulk.
SIAM Journal on Scientific Computing, 2013
This works deals with one dimensional infinite perturbation-namely line defects-in periodic media. In optics, such defects are created to construct an (open) waveguide that concentrates light. The existence and the computation of the eigenmodes is a crucial issue. This is related to a self-adjoint eigenvalue problem associated to a PDE in an unbounded domain (in the directions orthogonal to the line defect), which makes both the analysis and the computations more complex. Using a Dirichlet-to-Neumann (DtN) approach, we show that this problem is equivalent to one set on a small neighborhood of the defect. On contrary to existing methods, this one is exact but there is a price to be paid : the reduction of the problem leads to a nonlinear eigenvalue problem of a fixed point nature.
Excitation of radiative and evanescent defect modes in linear photonic crystal waveguides
Physical Review B, 2004
The dispersion of line-defect modes in silicon-on-insulator photonic crystal waveguides is explored by means of angle-and polarization-resolved micro-reflectance measurements. The frequency-wave vector range accessible to the experiments is greatly expanded by the use of attenuated total reflectance, in addition to the standard one, thereby allowing one to study both truly guided (evanescent) and quasi-guided (radiative) photonic modes. The presence of a supercell repetition in the direction perpendicular to the line defect leads to the simultaneous excitation of defect and bulk modes folded in a reduced Brillouin zone. The group-velocity dispersion of defect modes corresponding to different polarizations of light is fully determined.
Transmission through photonic crystals with multiple line defects at oblique incidence
Journal of the Optical Society of America B Optical Physics, 2008
Transmission through two-dimensional photonic crystals (PhCs) with several (non)periodic line defects, each being created by removing a single row of rods, are studied with the emphasis put on angular selectivity. Most of the observed features appear due to a hybrid mechanism, which is realized as a common effect of the splitting of a transmission peak being the result of peculiar coupling of individual defect-mode resonators, and the angle-dependent guided-wave cavity effect, which depends on the chosen dispersion. In the case of zero-order propagation, the role of periodic location of line defects is demonstrated. A rich variety of effects can be obtained in the angle domain within a rather narrow frequency range, which contains eigenfrequencies of defect modes. Peculiarities of the transmission peaks arising in the case of first-order propagation are considered in both angle and frequency domains. It is shown that the defect-mode related peaks can be close by to the peaks, which appear due to resonances within the pieces of PhC separated by line defects and their coupling. For the effects observed while two beams are propagating, the presence of multiple defects is rather critical than the periodicity of their location.
Modes of coupled photonic crystal waveguides
Optics Letters, 2004
We consider the modes of coupled photonic crystal waveguides. We find that the fundamental modes of these structures can be either even or odd, in contrast with the behavior in coupled conventional waveguides, in which the fundamental mode is always even. We explain this finding using an asymptotic model that is valid for long wavelengths.
Design of Photonic Crystals Devices with Defects
A powerful and efficient method based on the leaky mode propagation method and recently applied by the authors to model defect-free optical periodic structures, is used to characterize photonic bandgap structures incorporating multiple defects, having arbitrary shape and dimensions. The importance of the defect-mode characterization in photonic bandgap materials materials is due to the intensive use of defects for light localization to design very promising optical devices. In order to prove the usefulness of the method, design of an optical filters for dense wavelength division multipexing applications, has been carried out by the developed model.
Waveguide branches in photonic crystals
Journal of the Optical Society of America B, 2001
Theoretical and numerical analyses of waveguide branches in a photonic crystal are presented. Conditions for perfect transmission and zero reflection are discussed. Based upon these conditions, numerical simulations of electromagnetic-wave propagation in photonic crystals are performed to identify structures with near-complete transmission.
Defect-mode-like transmission and localization of light in photonic crystals without defects
2010
It is shown that far-and near-field effects, which are similar to those arising in transmission through finite-thickness photonic crystals ͑PCs͒ with structural defects, can be obtained in the conventional defect-free dielectric square-lattice PCs. Multiple narrow peaks of total transmission can appear within a frequency range, where the noncircular isofrequency dispersion contours of one type are quickly transformed for a higher-order Floquet-Bloch wave to the noncircular contours of the other type, leading to a frequency-domain passband being very narrow within a certain range of variation of the angles of incidence. In this regime, the mirror reflectance of the equivalent Fabry-Pérot resonator takes rather large values, which correspond to large values of Q factor and group index of refraction, strong field localization, and good isolation of the transmission peaks from each other. In some examples presented, Q factor exceeds 10 4 .
Guiding waves with photonic crystals
Optics Communications, 1999
We study a finite doped photonic crystal using a rigorous theory of diffraction. We exhibit a structure allowing to guide two bands of wavelengths in two different regions of the crystal. Rigorous numerical results are given showing the localization of the electromagnetic energy inside the crystal. Such a device could be of great use for the realization of filters. q
Practical and theoretical modal analysis of photonic crystal waveguides
Journal of Applied Physics, 2004
We present practical and theoretical, stage-by-stage analysis of light propagation around a 90°c orner in a two-dimensional photonic crystal waveguide. Using a series of different samples we quantify the coupling efficiency between the conventional ridge waveguide and the photonic crystal waveguide as well as the bending efficiency around the 90°corner. From this, the transmission spectra indicate nearly 90% bending efficiency. We compare the experimental results to the three-dimensional simulated band diagram and field distribution. The propagating defect modes are identified in detail and we show that efficient transmission around sharp bends in photonic crystal waveguides can be achieved for leaky modes above the light line with short photonic crystal sections.