Effects of disorder in two-dimensional photonic crystal waveguides

Abstract

The effects of randomness on the guiding properties of waveguides embedded in disordered twodimensional photonic crystals composed of a finite cluster of circular cylinders of infinite length are investigated for TM-polarized radiation. Different degrees of disorder in the radius, filling fraction, refractive index and position are considered for both straight and 90• bent guides. The crystals exhibit similar sensitivity to refractive index and radius disorder, with a degree of disorder from 15%-20% yielding little substantial change in the guiding properties. A smaller range of position disorder is also considered. For strong disorder in radius and refractive index the guide effectively closes. These results were obtained by a Monte Carlo simulation method, and the performance of this method is analyzed. The method requires at least 10 realizations in some cases for convergence to commence; substantially more realizations are required for moderate and strong disorder to achieve accurate results.

Localisation and disorder in the design of 2D photonic crystal devices

“…These may be modelled by the addition to the desired cylinder parameters of random variables drawn from suitable distributions. The effects of such disorder may then be studied using a Monte Carlo approach [8]. We consider an ensemble of pc waveguides in which the th cylinder of a realisation has radius 0.3d and refractive index n = 3.0 + ξ , where ξ is a random variable uniformly distributed in the range [−Q, Q].…”

Local density of states of chiral Hall edge states in gyrotropic photonic clusters

“…In our calculation the radii of cylinders have been uniformly distributed in the range [0.13d, 0.2d] which corresponds to a 35% degree of disorder from the initial value a = 0.2d. In such strong radial disorder guiding is no longer taking place in conventional photonic crystal waveguides 30 .…”

Scattering of plane waves by slabs of dielectric photonic crystal with line defects

“…A typical feature of these modes is that the EM field remains trapped within the defect region(s), e.g., see refs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and references therein. The localized defect modes have been intensively studied, both theoretically and experimentally, since about ten years.…”

“…Two-dimensional PCs, which are composed of rods arranged to a periodic lattice, and which show defects of various types have been used in a very wide frequency range for a large number of applications from integrated optics to powerful vacuum electron devices. In particular, defect modes have successfully been employed for filtering and coupling (e.g., [9,11,[15][16][17]), waveguiding and bending (e.g., [2,10,[18][19][20][21]), and splitting/combining (e.g., [12,[22][23][24]) of EM radiation. They have also been used as mirrors [7], resonant cavities [13,25,26], and fibers [14,27].…”