Reduced divergence angle of photonic crystal vertical-cavity surface-emitting laser

The reduced divergence angle of the photonic crystal vertical-cavity surface-emitting laser (PC-VCSEL) was investigated in both theory and experiment. The photonic crystal waveguide possessed the weakly guiding waveguide characteristic, which accounted for the reduction of the divergence angle. The three-dimensional finite-difference time-domain method was used to simulate the designed PC-VCSEL, and a calculated divergence angle of 5.2 degrees was obtained. The measured divergence angles of our fabricated PC-VCSEL were between 5.1 degrees and 5.5 degrees over the entire drive current range, consistent with the numerical results. This is the lowest divergence angle of the fabricated PC-VCSEL ever reported.

Resonant Enhanced Wave Filter and Waveguide via Surface Plasmons

The authors present an analysis of plasmonic wave filter and curved waveguide, simulated using a 2-D finite-difference time-domain technique. With different dielectric materials or surface structures located on the interface of the metal/dielectric, the resonant enhanced wave filter can divide light waves of different wavelengths and guide them with low losses. And the straight or curved waveguide can confine and guide light waves in a subwavelength scale. Within the 20 mu m simulation region, it is found that the intensity of the guided light at the interface is roughly four times the peak intensity of the incident light.

Analysis of mode characteristics for equilateral-polygonal resonators with a center hole

Mode characteristics for equilateral triangles, squares, and hexagonal resonators with a center hole are numerically simulated by the finite-different time domain (FDTD) technique. The center hole does not break the symmetry behavior of the original resonators and can result in modification of the mode field patterns and mode Q factors. In an equilateral triangle resonator the center hole can suppress the symmetry state of degenerate states with the merit of single mode operation. In a square resonator, the Q factor can be enhanced for some modes with a suitable size of the hole. For a hexagonal resonator with a side length of 1 mu m and a refractive index of 3.2, the mode Q factors first gradually decrease with the increase of the hole diameter for modes at a wavelength of about 1500 nm, then the modes transform to that of a microdisk with a jump of the mode wavelength as the hole diameter approaches 0.7 mu m. Finally, the mode Q factors greatly enhance as the hole diameter reaches about 1 mu m. The results indicate that the center hole can greatly modify mode characteristics, especially that of the mode Q factor. (C) 2009 Optical Society of America

Mode Analysis for Equilateral-Triangle-Resonator Microlasers with Metal Confinement Layers

Mode characteristics are analyzed for electrically injected equilateral-triangle-resonator (ETR) semiconductor microlasers, which are laterally confined by insulating barrier SiO2 and electrode metals Ti-Au. For the ETR without metal layers, the totally confined mode field patterns are derived based on the reflection phase shifts, and the Q-factors are calculated from the far-field emission of the analytical near field distribution, which are agreement very well with the numerical results of the finite-difference time-domain (FDTD) simulation. The polarization dependence reflections for light rays incident on semiconductor-SiO2 -Ti-Au multi-layer structures are accounted in considering the confinement of TE and TM modes in the ETR with the metal layers. The reflectivity will greatly reduce with a Ti layer between SiO2 and Au for light rays with incident angle less than 30 especially for the TE mode, even the thickness of the Ti layer is only 10 nm. If the ETR is laterally confined by SiO2-Au layers without the Ti layer, the Fabry-Perot type modes with an incident angle of zero on one side of the ETR can also have high Q-factor. The FDTD simulation for the ETR confined by metal layers verifies the above analysis based on multi-layer reflections. The output spectra with mode intervals of whispering-gallery modes and Fabry-Perot type modes are observed from different ETR lasers with side length of 10 m, respectively.

Analysis of mode characteristics for equilateral triangle semiconductor microlasers with imperfect boundaries

The influence of imperfect boundaries on the mode quality factor is investigated for equilateral-triangle-resonator (ETR) semiconductor microlasers by the finite difference time domain technique and the Pade approximation with Baker's algorithm. For 2-D ETR with a refractive index of 3.2 and side length of 5 mum, the confined modes can still have a quality factor of about 1000 as small triangles with side length of 1 mum are cut from the vertices of the ETR. For a deformed 5 mum ETR with round vertices and curve sides, the simulated mode quality factors are comparable to the measured results.

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.

Dynamics of spin-dependent tunneling through a semiconductor double-barrier structure

The dynamics of spin-dependent tunneling through a nonmagnetic semiconductor double-barrier structure is studied including the k(3) Dresselhaus spin orbit coupling is solved by the time-dependent Schrodinger equation with a developed method for the finite-difference relaxation. The resonant peak and quasibound level lifetime are determined by the in-plane wave vector and the applied electric field. The buildup time and decay lifetime of resonant probability amplitude are different for the spin-down and spin-up electrons due to the Dresselhaus spin-orbit coupling. Further investigation shows that the steady spin-polarization in both the well and collector regions has been obtained in the time domain. (C) 2007 American Institute of Physics.

Design, fabrication, and characterization of an ultracompact low-loss photonic crystal corner mirror

An ultracompact, low-loss, and broad-band corner mirror, based on photonic crystals, is investigated in this paper. Based on the theoretical analysis of the loss mechanism, the boundary layers of the photonic crystal region are revised to improve the extra losses, and the transmission characteristics are evaluated by using the 3-D finite-difference time-domain method. The device with optimized structure was fabricated on silicon-on-insulator substrate by using electron-beam lithography and inductively coupled plasma etching. The measured extra losses are about 1.1 +/- 0.4 dB per corner mirror for transverse-electronic polarization for the scanning wavelength range of 1510-1630 nm. Dimensions of the achieved PC corner mirror are less than ;7 x 7 mu m(2), which are only about one tenth of conventional wave-guide corner mirrors.

Symmetry analysis and numerical simulation of mode characteristics for equilateral-polygonal optical microresonators

Mode characteristics for two-dimensional equilateral-polygonal microresonators are investigated based on symmetry analysis and finite-difference time-domain numerical simulation. The symmetries of the resonators can be described by the point group C-Nv, accordingly, the confined modes in these resonators can be classified into irreducible representations of the point group C-Nv. Compared with circular resonators, the modes in equilateral-polygonal resonators have different characteristics due to the break of symmetries, such as the split of double-degenerate modes, high field intensity in the center region, and anomalous traveling-wave modes, which should be considered in the designs of the polygonal resonator microlasers or optical add-drop filters.