Comparison of Q-factors between TE and TM modes in 3-D microsquares by FDTD simulation

Mode characteristics of three-dimensional (3-D) microsquare resonators are investigated by finite-difference time-domain (FDTD) simulation for the transverse electric (TE)-like and the transverse magnetic (TM)-like modes. For a pillar microsquare with a side length of 2 pin in air, we have Q-factors about 5 X. 103 for TM-like modes at the wavelength of 1550 run, which are one order larger than those of TE-like modes, as vertical refractive index distribution is 3.17/3.4/3.17 and the cororresponding center layer thickness is 0.2 mu m. The mode field patterns show that TM-like modes have much weaker vertical radiation coupling loss than TE-like modes. TM-like modes can have high Q-factors in a microsquare with weak vertical field confinement.

Integration of a photonic crystal polarization beam splitter and waveguide bend

In this work, we present the design of an integrated photonic-crystal polarization beam splitter (PC-PBS) and a low-loss photonic-crystal 60 waveguide bend. Firstly, the modal properties of the PC-PBS and the mechanism of the low-loss waveguide bend are investigated by the two-dimensional finite-difference time-domain (FDTD) method, and then the integration of the two devices is studied. It shows that, although the individual devices perform well separately, the performance of the integrated circuit is poor due to the multi-mode property of the PC-PBS. By introducing deformed airhole structures, a single-mode PC-PBS is proposed, which significantly enhance the performance of the circuit with the extinction ratios remaining above 20dB for both transverse-electric (TE) and transverse-magnetic (TM) polarizations. Both the specific result and the general idea of integration design are promising in the photonic crystal integrated circuits in the future. (C) 2009 Optical Society of America

Mode quality factor based on far-field emission for square resonators

The quality factors of modes in square resonators are calculated based on the far-field emission of the analytical field distribution. The obtained quality factors are in reasonable agreement with those calculated by the finite-difference time-domain (FDTD) technique and Pade approximation method. The emission power in the square diagonal directions for whispering-gallery-like modes in square resonators is zero due to the interference cancellation caused by the odd field distributions relative to the diagonal mirror planes, so they have larger quality factors than the modes with even field distribution.

Comparison of free spectral range and quality factor for two-dimensional square and circular microcavities

Free spectral range of whispering-gallery (WG)-like modes in a two-dimensional (2D) square microcavity is found to be twice that in a 2D circular microcavity. The quality factor of the WG-like mode with the low mode number in a 2D square microcavity, calculated by the finite-difference time-domain (FDTD) technique and the Pade approximation method, is found to exceed that of the WG mode in 2D circular microcavity with the same cavity dimension and close mode wavelength.

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.