A new UTD for the electromagnetic plane wave scattering by a canonical circular cylinder with an impedance boundary condition

A UTD solution is developed for describing the scattering by a circular cylinder with an impedance boundary condition (IBC), when it is illuminated by an obliquely incident electromagnetic (EM) plane wave. The solution to this canonical problem will be crucial for the construction of a more general UTD solution valid for an arbitrary smooth convex surface with an IBC, when it is illuminated by an arbitrary EM ray optical field. The canonical solution is uniformly valid across the surface shadow boundary that is tangent to the surface at grazing incidence. This canonical solution contains cross polarized terms in the scattered fields, which arise from a coupling of the TEz and TMz waves at the impedance boundary on the cylinder. Here, z is the cylinder axis. Numerical results show very good accuracy for the simpler and efficient UTD solution, when compared to exact but very slowly convergent eigenfunction solution.

Plane-wave scattering-matrix theory of antennas and antenna-antenna interactions /

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Properties of the stochastic Gross-Pitaevskii equation: finite temperature Ehrenfest relations and the optimal plane wave representation

We present Ehrenfest relations for the high temperature stochastic Gross-Pitaevskii equation description of a trapped Bose gas, including the effect of growth noise and the energy cutoff. A condition for neglecting the cutoff terms in the Ehrenfest relations is found which is more stringent than the usual validity condition of the truncated Wigner or classical field method-that all modes are highly occupied. The condition requires a small overlap of the nonlinear interaction term with the lowest energy single particle state of the noncondensate band, and gives a means to constrain dynamical artefacts arising from the energy cutoff in numerical simulations. We apply the formalism to two simple test problems: (i) simulation of the Kohn mode oscillation for a trapped Bose gas at zero temperature, and (ii) computing the equilibrium properties of a finite temperature Bose gas within the classical field method. The examples indicate ways to control the effects of the cutoff, and that there is an optimal choice of plane wave basis for a given cutoff energy. This basis gives the best reproduction of the single particle spectrum, the condensate fraction and the position and momentum densities.

Absolute left-handed behaviors in a triangular elliptical-rod photonic crystal

In this paper we theoretically study the left-handed behaviors in a two-dimensional triangular photonic crystal made of elliptical rods in air. An absolute left-handed region is found in the second photonic band by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Typical left-handed behaviors such as negative refraction, flat superlensing and plano-concave lensing are demonstrated by the finite-difference time-domain simulations. These behaviors are also compared with the quasi-negative refraction and the resulted focusing effects in a square-lattice two-dimensional photonic crystal. (c) 2005 Optical Society of America

Scattering by two degenerate anisotropic modes in square-lattice dielectric photonic crystals

We systematically investigate the square-lattice dielectric photonic crystals that have been used to demonstrate flat slab imaging experimentally. A right-handed Bloch mode is found in the left-handed frequency region by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Using the multiple scattering theory, numerical simulations demonstrate that the left-handed mode and the right-handed mode are excited simultaneously by a point source and result in two kinds of transmitted waves. Impacted by the evanescent waves, superposition of these transmitted waves brings on complicated near field distributions such as the so-called imaging and its disappearance.

Optical properties of a square-lattice photonic crystal within the partial bandgap

Optical properties of a two-dimensional square-lattice photonic crystal are systematically investigated within the partial bandgap through anisotropic characteristics analysis and numerical simulation of field pattern. Using the plane-wave expansion method and Hellmann-Feynman theorem, the relationships between the incident and refracted angles for both phase and group velocities are calculated to analyze light propagation from air to photonic crystals. Three kinds of flat slab focusing are summarized and demonstrated by numerical simulations using the multiple scattering method. (c) 2007 Optical Society of America

Negative refraction in a honeycomb-lattice photonic crystal

In this paper we theoretically investigate a photonic crystal with dielectric rods in a honeycomb lattice. Two left-handed frequency regions are found in the second and third photonic band by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Subwavelength imaging by the photonic crystal flat lens are systematically studied by numerical simulations using the multiple scattering method. Different from the photonic crystals with noncircular dielectric rods in air, this structure is almost isotropic at the optimal frequency for superlensing. As a comparison, flat slab focusing is also demonstrated at other frequencies in the two left-handed regions. (c) 2006 Elsevier Ltd. All rights reserved.

Design of novel polarization beam splitter in two-dimensional photonic crystal

We present the design and the simulation of an ultracompact high efficiency polarization beam splitter (PBS) based on the properties of the light waves propagating in straight waveguide and composite structure photonic crystal. The splitting properties of the PBS are numerically simulated and analyzed by using the plane wave expansion (PWE) method and finite difference time domain (FDTD) method. The PBS consists of three parts, namely, input waveguide, beam structure and output waveguide. It is shown that a high efficiency and a large separating angle for TE mode and TM mode can be achieved. Owing to these excellent features, including small size and high rate, the PBS makes a promising candidate in the future photonic integrated circuits.

The impact of imperfect symmetry on band edge modes of a two-dimensional photonic crystal with square lattice

A theoretical analysis has been performed by means of the plane-wave expansion method to examine the dispersion properties of photons at high symmetry points of an InP based two-dimensional photonic crystal with square lattice. The Q factors are compared qualitatively. The mechanism of surface-emitting is due to the photon manipulation by periodic dielectric materials in terms of Bragg diffraction. A surface-emitting photonic crystal resonator is designed based on the phenomenon of slow light. Photonic crystal slabs with different unit cells are utilized in the simulation. The results indicate that the change of the air holes can affect the polarization property of the modes. So we can find a way to improve the polarization by reducing the symmetry of the structure.

A ministop band in a single-defect photonic crystal waveguide based on silicon on insulator

This paper reports that a two-dimensional single-defect photonic crystal waveguide in the F-K direction with triangular lattice on a silicon-on-insulator substrate is fabricated by the combination of electron beam lithography and inductively coupled plasma etching. A ministop band (MSB) is observed by the measurement of transmission characteristics. It results from the coupling between the two modes with the same symmetry, which is analysed from the stimulated band diagram by the effective index and the two-dimensional plane wave expansion methods. The parameter working on the MSB is the ratio of the radius of air holes to the lattice constant, r/a. It is obtained that the critical r/a value determining the occurrence or disappearance of MSB is 0.36. When r/a is larger than or equal to 0.36, the MSB occurs. However, when r/a is smaller than 0.36, the MSB disappears.

Photonic band structures of two-dimensional photonic crystals with deformed lattices

Using the plane-wave expansion method, we have calculated and analysed the changes of photonic band structures arising from two kinds of deformed lattices, including the stretching and shrinking of lattices. The square lattice with square air holes and the triangular lattice with circular air holes are both studied. Calculated results show that the change of lattice size in some special ranges can enlarge the band gap, which depends strongly on the filling factor of air holes in photonic crystals; and besides, the asymmetric band edges will appear with the broken symmetry of lattices.

A photonic crystal waveguide with silicon on insulator in the near-infrared band

A two-dimensional (2D) photonic crystal waveguide in the Gamma-K direction with triangular lattice on a silicon-on insulator (SOI) substrate in the near-infrared band is fabricated by the combination of electron beam lithography and inductively coupled plasma etching. Its transmission characteristics are analysed from the stimulated band diagram by the effective index and the 2D plane wave expansion (PWE) methods. In the experiment, the transmission band edge in a longer wavelength of the photonic crystal waveguide is about 1590 nm, which is in good qualitative agreement with the simulated value. However, there is a disagreement between the experimental and the simulated results when the wavelength ranges from 1607 to 1630 nm, which can be considered as due to the unpolarized source used in the transmission measurement.

Optical interleaver based on directional coupler in a 2D photonic crystal slab with triangular lattice of air holes

A small-size optical interleaver based on directional coupler in a 2D photonic crystal slab with triangular lattice of air holes is designed and theoretically simulated using plane wave expansion and finite-difference time-domain method. The interleaver is formed by two parallel and identical photonic crystal slab waveguides which are separated by three rows of air holes. The coupling region is designed below the light line to avoid vertical radiation. The simulated results show that the coupling coefficient is increased and the final length of the interleaver is decreased by enlarging the radius of the middle row of air holes. The transmission properties are analyzed after the interleaver's structure is optimized, and around 100 GHz channel spacing can be got when the length of the interleaver is chosen as 40.5 mu m. (c) 2006 Elsevier B.V. All rights reserved.

Structure dependence of mode edges in photonic crystal waveguide with silicon on insulator

The mode edges of photonic crystal waveguide with triangular lattice based on a silicon-on-insulator slab are investigated by combination of the effective index method and two-dimensional plane wave expansion method. The variations of waveguide-mode edges with structure parameters of photonic crystal are deduced. When the ratio of the radius of air holes to the lattice constrant, r/Lambda, is fixed and the lattice constant of photonic crystal, Lambda, increases, the waveguide-mode edges shift to longer wavelengths. When Lambda is fixed and r/Lambda increases, the waveguide-mode edges shift to shorter wavelengths. Additionally, when r/Lambda and Lambda are both fixed, the radius of the two-row air holes adjacent to the waveguide increases, the waveguide-mode edges shift to shorter wavelengths.

A two-dimensional photonic crystal slab mirror with silicon on insulator for wavelength 1.3 mu m

A concrete two-dimensional photonic crystal slab with triangular lattice used as a mirror for the light at wavelength 1.3 mu m with a silicon-on-insulator (Sol) substrate is designed by the three-dimensional plane wave expansion method. For TE-like modes, the bandgap in the F-K direction is from 1087nm to 1559nm. The central wavelength in the bandgap is about 1.3 mu m, hence the incident light at wavelength 1.3 mu m will be strongly reflected. Experimentally, such a photonic crystal slab is fabricated on an SOI substrate by the combination of EBL and ICP etching. The measurement of its transmission characteristics shows the bandgap edge in a longer wavelength is about 1540mn. The little discrepancy between the experimental data and the theoretical values is mainly due to the size discrepancy of the fabricated air holes.