140 research outputs found
Exact modelling of the long wavelength properties of the fundamental mode in microstructured optical fibres
Local density of states of chiral Hall edge states in gyrotropic photonic clusters
We have constructed the Green's tensor for two-dimensional gyrotropic photonic clusters and have calculated their optical local density of states (LDOS). For clusters that support the chiral Hall edge states we calculate the LDOS as a function of wavele
Modes of symmetric composite defects in two-dimensional photonic crystals
We consider the modal fields and resonance frequencies of composite defects in two-dimensional photonic crystals (PCs). Using an asymptotic method based on Green's functions, we show that the coupling matrices for the composite defect can be represented as circulant or block-circulant matrices. Using the properties of these matrices, specifically that their eigenvectors are independent of the values of the matrix elements, we obtain modal properties such as dispersion relations, modal cutoff, degeneracy, and symmetry of the mode fields. Using our formulation, we investigate defects arranged on the vertices of regular polygons as well as PC ring resonators with defects arranged on the edges of polygons. Finally, we discuss the impact of band-edge degeneracies on composite-defect modes
Defect modes in otherwise perfect photonic crystal and photonic crystal fibres
Many of the applications of photonic crystals and photonic crystal fibres require the periodic structure tohave some type of defect. In photonic crystal fibers a point defect defines the fiber core, whereas in photonic crystals a line defect acts as a waveguide, and point defects act as cavities. The modeling of these defects usually either makes use of periodic boundary conditions, by which the defect is replicated periodically, or models a photonic cyrstal of finite extent. HOwever, some applications, for example the cut-off behaviour of a defect mode where the field extends very widely, require methods that can model a defect in an otherwise infinite and perfectly periodic structure. Here we present such a method. It combines the method of fictitious sources with averaging over the Brillouin zone, and we apply it to study the long wavelength behavior of the fundamental mode of photonic crystal fibers
Engineering cavity modes in photonic crystal double-heterostructures
We present results from a new method that allows us to design the mode fields for 3D photonic crystal heterostructure cavities, in the domain where the perturbation used to create the cavity is weak. The method, based on a perturbation treatment from solid-state physics, enables the rapid computation of the main features of 3D cavity modes for an arbitrary perturbation and is several orders of magnitude faster than direct numerical methods. We use this method to study optimal confinement of resonant states in these structures. © 2010 Optical Society of America
Anderson Localization of Classical Waves in Weakly Scattering Metamaterials
We study the propagation and localization of classical waves in
one-dimensional disordered structures composed of alternating layers of left-
and right-handed materials (mixed stacks) and compare them to the structures
composed of different layers of the same material (homogeneous stacks). For
weakly scattering layers, we have developed an effective analytical approach
and have calculated the transmission length within a wide region of the input
parameters. When both refractive index and layer thickness of a mixed stack are
random, the transmission length in the long-wave range of the localized regime
exhibits a quadratic power wavelength dependence with the coefficients
different for mixed and homogeneous stacks. Moreover, the transmission length
of a mixed stack differs from reciprocal of the Lyapunov exponent of the
corresponding infinite stack. In both the ballistic regime of a mixed stack and
in the near long-wave region of a homogeneous stack, the transmission length of
a realization is a strongly fluctuating quantity. In the far long-wave part of
the ballistic region, the homogeneous stack becomes effectively uniform and the
transmission length fluctuations are weaker. The crossover region from the
localization to the ballistic regime is relatively narrow for both mixed and
homogeneous stacks. In mixed stacks with only refractive-index disorder,
Anderson localization at long wavelengths is substantially suppressed, with the
localization length growing with the wavelength much faster than for
homogeneous stacks. The crossover region becomes essentially wider and
transmission resonances appear only in much longer stacks. All theoretical
predictions are in an excellent agreement with the results of numerical
simulations.Comment: 19 pages, 16 figures, submitted to PR
Coupled waveguide modes in hexagonal photonic crystals
We investigate the modes of coupled waveguides in a hexagonal photonic crystal. We find that for a substantial parameter range the coupled waveguide modes have dispersion relations exhibiting multiple intersections, which we explain both intuitively and using a rigorous tight-binding argument. © 2010 Optical Society of America
Coupled photonic crystal waveguides in hexagonal lattices
We investigate the dispersion curves of coupled waveguides in hexagonal lattices. We show that hexagonal PCW lattices have coupling coefficients that change magnitude and sign along the BZ. It is also shown that the modes of these structures no longer form odd and even modes but are superposed in a more general sense. © 2010 OSA /FiO/LS 2010
Two-dimensional local density of states in two-dimensional photonic crystals
We calculate the two-dimensional local density of states (LDOS) for two-dimensional photonic crystals composed of a finite cluster of circular cylinders of infinite length. The LDOS determines the dynamics of radiation sources embedded in a photonic crystal. We show that the LDOS decreases exponentially inside the crystal for frequencies within a photonic band gap of the associated infinite array and demonstrate that there exist "hot" and "cold" spots inside the cluster even for wavelengths inside a gap, and also for wavelengths corresponding to pass bands. For long wavelengths the LDOS exhibits oscillatory behavior in which the local density of states can be more than 30 times higher than the vacuum level. © 2001 Optical Society of America
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