Modes in square resonators

Modes in square resonators are analyzed and classified according to the irreducible representations of the point group C-4v. If the mode numbers p and q that denote the number of wave nodes in the directions of two orthogonal square sides are unequal and have the same even-odd characteristics, the corresponding double modes are accidentally degenerate and can be combined into two new distributions with definite parities relative to the square diagonal mirror planes. The distributions with odd parities belong to the whispering-gallery-like modes in square resonators. The mode frequencies and quality factors are also calculated by the finite-difference time-domain technique and Pade approximation method. The numerically calculated mode frequencies agree with the theoretical ones very well and the whispering-gallery-like modes have quality factors much higher than other modes, including their accidentally degenerate counterparts in square resonators.

Experimental observation of resonant modes in GaInAsP microsquare resonators

GaInAsP-InP microsquare resonators with InP pedestals are fabricated by two-step chemical etching, and obvious mode peaks are observed in the photoluminescence spectra of the resonators. The mode Q-factors about 500 are obtained for a microsquare resonator with the side length of 7 mu m. The experimental mode interval is in agreement with that predicted by the light ray method based on the cavity length, instead of that of the whispering-gallery (WG)-like modes, which has mode interval twice of that determined by the cavity length. The finite-difference time-domain simulation shows that a little asymmetry may greatly reduce the difference of the Q-factors between the WG-like modes and the other modes.

Photonic crystal point-shift nanolaser with ultimate small modal volume

A photonic crystal nanolaser consisting of only the shift of two lattice points was fabricated by HJ/Xe inductively coupled plasma etching. The room temperature lasing was observed by photopumping. The three-dimensional finite-difference time-domain calculation showed that the lasing mode has small modal volume close to (lambda/2n)(3).

Two-dimensional photonic band-gap defect modes with deformed lattice

A numerical study of the defect modes in two-dimensional photonic crystals with deformed triangular lattice is presented by using the supercell method and the finite-difference time-domain method. We find the stretch or shrink of the lattice can bring the change not only on the frequencies of the defect modes but also on their magnetic field distributions. We obtain the separation of the doubly degenerate dipole modes with the change of the lattice and find that both the stretch and the shrink of the lattice can make the dipole modes separate large enough to realize the single-mode emission. These results may be advantageous to the manufacture of photonic crystal lasers and provide a new way to realize the single-mode operation in photonic crystal lasers.

Calculation of propagation loss in photonic crystal waveguides by FDTD technique and Pade approximation

The propagation losses in single-line defect waveguides in a two-dimensional (2D) square-lattice photonic crystal (PC) consisted of infinite dielectric rods and a triangular-lattice photonic crystal slab with air holes are studied by finite-difference time-domain (FDTD) technique and a Pade approximation. The decaying constant beta of the fundamental guided mode is calculated from the mode frequency, the quality factor (Q-factor) and the group velocity v(g) as beta = omega/(2Qv(g)). In the 2D square-lattice photonic crystal waveguide (PCW), the decaying rate ranged from 10(3) to 10(-4) cm(-1) can be reliably obtained from 8 x 10(3)-item FDTD output with the FDTD computing time of 0.386 ps. And at most 1 ps is required for the mode with the Q-factor of 4 x 10(11) and the decaying rate of 10(-7) cm(-1). In the triangular-lattice photonic crystal slab, a 10(4)-item FDTD output is required to obtain a reliable spectrum with the Q-factor of 2.5 x 10(8) and the decaying rate of 0.05 cm(-1). (c) 2004 Elsevier B.V. All rights reserved.

Resonant cavity based compact efficient antireflection structures for photonic crystals

We propose an effective admittance ( EA) method to design antireflection structures for two-dimensional photonic crystals (PCs). We demonstrate that a compact and efficient antireflection structure, which is difficult to obtain by the conventional admittance matching method, can be readily designed by the EA method. The antireflection structure consists of an air slot resonant cavity that is constructed only with the materials that constitute the PC. Compared with a bare PC, the reflection from a PC with an antireflection structure is reduced by two orders of magnitude over a wide bandwidth. To confirm the presented EA method, finite-difference time-domain (FDTD) simulations are performed, and the results from the FDTD and the EA method are in good agreement.

Mode coupling between first- and second-order whispering-gallery modes in coupled microdisks

The mode characteristics for two coupled microdisks are investigated by the finite-difference time-domain technique. In the two coupled micodisks, mode coupling between the same order whispering-gallery modes (WGMs) results in coupled WGMs with split mode wavelengths. The numerical results show that the split mode wavelengths of the coupled first- and second-order WGMs can have a crossing point in some cases, which can induce anticrossing mode coupling between them and greatly reduce the mode Q factor of the coupled first-order WGMs. The time variation of mode field pattern shows the transformation between the coupled first- and second-order WGMs. (C) 2007 Optical Society of America

Numerical study of a high-resolution far-field scanning optical microscope via a surface plasmon-modulated light source

In this paper, we analyze light transmission through a single subwavelength slit surrounded by periodic grooves in layered films consisting of An and dielectric material. A subwavelength grating is scanned numerically by the finite difference time domain method in two dimensions. The results show that the transmission field can be confined to a spot with subwavelength width in the far field and can be useful in the application of a high-resolution far-field scanning optical microscope.

A proposal for low cross-talk square-lattice photonic crystal waveguide intersection utilizing the symmetry of waveguide modes

We propose an approach to construct waveguide intersections with broad bandwidth and low cross-talk for square-lattice photonic crystals. by utilizing a vanishing overlap of the propagation modes in the waveguides created by defects which support dipole-like defect modes. The finite-difference time-domain method is used to simulate the waveguide intersection created in the two-dimensional square-lattice photonic crystals. Over a bandwidth of 30 nm with the center wavelength at 1300 nm, transmission efficiency above 90% is obtained with cross-talk below -30 dB. Especially, we demonstrate the transmission of a 500-fs pulse at 1.3 Am through the intersection, and the pulse after transmission shows very little distortion while the cross-talk remains at low level meantime. (c) 2006 Elsevier B.V. All rights reserved.

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.

Design of two-dimensional photonic crystal edge emitting laser for photonic integrated circuits

An edge emitting laser based on two-dimensional photonic crystal slabs is proposed. The device consists of a square lattice microcavity, which is composed of two structures with the same period but different radius of air-holes, and a waveguide. In the cavity, laser resonance in the inner structure benelits from not only the anomalous dispersion characteristic of the first band-edge at the M point in the first Brillouin-zone but also zero photon states in the outer structure. A line defect waveguide is introduced in the outer structure for extracting photons from the inner cavity. Three-dimensional finite-difference time-domain simulations apparently show the in-plane laser output from the waveguide. The microcavity has an effective mode volume of about 3.2(lambda/eta(slab))(3) for oscillation -mode and the quality factor of the device including line defect waveguide is estimated to be as high as 1300.

Light-propagation characteristics of photonic crystal waveguide based on SOI materials at different polarized states

Straight single-line defect optical waveguides in photonic crystal slabs are designed by the plane wave expansion method and fabricated into silicon-on-insulator (SOI) wafer by 248-nm deep UV lithography. We present an efficient way to measure the light transmission spectrum of the photonic crystal waveguide (PhC WG) at given polarization states. By employing the Mueller/Stokes method, we measure and analyse the light propagation properties of the PhC WG at different polarized states. It is shown that experimental results are in agreement with the simulation results of the three-dimensional finite-difference-time-domain method.

Distributed mode coupling in microring channel drop filters

The authors present the observation of wide transmission dips in a microring channel drop filter by two-dimensional finite-difference time-domain simulation. The authors show that distributed mode coupling between the input waveguide and the resonator results in the oscillations of the coupling efficiency and the envelope of transmission spectra with wavelength. The critical coupling as the light just passing through the coupling region is important for optimizing related devices. If the width of the input waveguide is different from that of the ring resonator, the phenomenon can be greatly reduced. (c) 2006 American Institute of Physics.

Dipole mode photonic crystal point defect laser on InGaAsP/InP

In this paper, we focus on the dipole mode of the two-dimensional (2D) photonic crystal (PC) single point defect cavity (SPDC) lasers and we report the fabrication and characterization of 2D PC SPDC lasers with the structure of adjusted innermost air holes. The photonic band and cavity Q factors are simulated by means of plane wave expansion (PWE) and finite-difference time-domain (FDTD), respectively. In order to improve the optical confinement of the SPDC, the diameter of the innermost holes was adjusted. Different lasing performances are observed experimentally. The experimental results agree with the theoretical prediction very well. (c) 2006 Elsevier B.V. All rights reserved.

WG-like modes selectivity in a square cavity with posts

We investigate the characteristics of Whispering-Gallery(WG)-like modes in a square cavity with posts by employing the two-dimentional (2D) finite-difference time-domain (FDTD) technique combined with the effective index method. The results indicate that the posts can result in mode selection in the WG-like modes. The WG-like modes with odd mode numbers are not much sensitive to the sizes of the posts. However, the quality factor (i.e. Q-factor) of the WG-like modes with even mode numbers decreases sharply with the increasing size of the posts. The decreasing Q-factor is attributed to mode leakage and scattering loss due to the presence of the post. The mode selection increases with the mode spacing of square cavity twice in an optimized strucure.