Mode analysis and Q-factor enhancement due to mode coupling in rectangular resonators

Modes in rectangular resonators are analyzed and classified according to symmetry properties, and quality factor (Q-factor) enhancement due to mode coupling is observed. In the analysis, mode numbers p and q are used to denote the number of wave nodes in the direction of two orthogonal sides. The even and odd mode numbers correspond to symmetric and antisymmetric field distribution relative to the midlines of sides, respectively. Thus, the modes in a rectangle resonator can be divided into four classes according to the parity of p and q. Mode coupling between modes of different classes is forbidden; however, anti-crossing mode coupling between the modes in the same class exists and results in new modes due to the combination of the coupled modes. One of the combined modes has very low power loss and high Q-factor based on far-field emission of the analytical field distribution, which agrees well with the numerical results of the finite-difference time-domain (FDTD) simulation. Both the analytical and FDTD results show that the Q-factors of the high Q-factor combined modes are over one order larger than those of the original modes. Furthermore, the general condition required to achieve high-Q modes in the rectangular resonator is given based on the analytical solution.

Influence of mode symmetry on quality factors of degenerate states in microlasers with an equilateral triangle resonator

Modes in equilateral triangle resonator (ETR) are analyzed and classified according to the irreducible representations of the point group C-3v., Both the analytical method based on the far field emission and the numerical method by FDTD technique are used to calculate the quality factors (Q-factors) of the doubly degenerate states in ETR. Results obtained from the two methods are in reasonable agreement. Considering the different symmetry properties of the doubly degenerate eigenstates, we also discuss the ETR joined with an output waveguide at one of the vertices by FDTD technique and the Pade approximation. The variation of Q-factors versus width of output waveguide is analyzed. The numerical results show that doubly degenerate eigenstates of TM0.36 and TM0.38 whose wavelengths are around 1.5 mu m in the resonator with side-length of 5 mu m have the Q-factors larger than 1000 when the width of the output waveguide is smaller than 0.4 mu m. When the width of the output waveguide is set to 0.3 mu m, the symmetrical states that are more efficiently coupled to output waveguide have Q-factors about 8000, which are over 3 times larger than those of asymmetric state.

Mode Characteristics for Square Resonators With a Metal Confinement Layer

Microsquare resonators laterally confined by SiO2/Au/air multilayer structure are investigated by light ray method with reflection phase-shift of the multiple layers and two-dimensional (2-D) finite-difference time-domain (FDTD) technique. The reflectivity and phase shift of the mode light ray on the sides of the square resonator with the semiconductor/SiO2/Au/air multilayer structure are calculated for TE and TM modes by transfer matrix method. Based on the reflection phase shift and the reflectivity, the mode wavelength and factor are calculated by the resonant condition and the mirror loss, which are in agreement well with that obtained by the FDTD simulation. We find that the mode factor increases greatly with the increase of the SiO2 layer thickness, especially as d < 0.3 mu m. For the square resonator with side length 2 mu m and refractive index 3.2, anticrossing mode couplings are found for confined TE modes at wavelength about 1.6 mu m at d = 0.11 mu m, and confined TM modes at d = 0.71 mu m, respectively.

Mode coupling and vertical radiation loss for whispering-gallery modes in 3-D microcavities

The characteristics of whispering-gallery modes (WGMs) in 3-D cylindrical, square, and triangular microcavities with vertical optical confinement of semiconductors are numerically investigated by the finite-difference time-domain (FDTD) technique. For a microcylinder with a vertical refractive index 3.17/3.4/3.17 and a center layer thickness 0.2 mu m, Q-factors of transverse electric (TE) WGMs around wavelength 1550 nm are smaller than 10(3), as the radius R < 4 mu m and reach the orders of 10(4) and 10(6) as R = 5 and 6 mu m, respectively. However, the Q-factor of transverse magnetic (TM) WGMs at wavelength 1.659 mu m reaches 7.5 x 10(5) as R = 1 mu m. The mode coupling between the WGMs and vertical radiation modes in the cladding layer results in vertical radiation loss for the WGMs. In the microcylinder, the mode wavelength of TM WGM is larger than the cutoff wavelength of the vertical radiation mode with the same mode numbers, so TM WGMs cannot couple with the vertical radiation mode and have high Q-factor. In contrast, TE WGMs can couple with the corresponding vertical radiation mode in the 3-D microcylinder as R < 5 mu m. However, the mode wavelength of the TE WGM approaches (is larger than) the cutoff wavelength of the corresponding radiation modes at R = 5 mu m (6 mu m), so TE WGMs have high Q-factors in such microcylinders too. The results show that a critical lateral size is required for obtaining high, Q-factor TE WGMs in the 3-D microcylinder. For 3-D square and triangular microcavities, we also find that the Q-factor of TM WGM is larger than that of TE WGM.

Investigation of mode coupling in a microdisk resonator for realizing directional emission

Mode coupling between the whispering-gallery modes (WGMs) is numerically investigated for a two-dimensional microdisk resonator with an output waveguide. The equilateral-polygonal shaped mode patterns can be constructed by mode coupling in the microdisk, and the coupled modes can still keep high quality factors (Q factors). For a microdisk with a diameter of 4.5 mu m and a refractive index of 3.2 connected to a 0.6-mu m-wide output waveguide, the coupled mode at the wavelength of 1490 nm has a Q factor in the order of 10(4), which is ten times larger than those of the uncoupled WGMs, and the output efficiency defined as the ratio of the energy flux confined in the output waveguide to the total radiation energy flux is about 0.65. The mode coupling can be used to realize high efficiency directional-emission microdisk lasers. (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.

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.

Investigation of mode characteristics for a square cavity with a pedestal by a three-dimensional finite-difference time-domain technique

Mode characteristics of a strongly confined square cavity suspended in air via a pedestal on the substrate are investigated by a three-dimensional finite-difference time-domain technique. The mode wavelengths and mode quality factors (Q factors) are calculated as the functions of the size of the pedestal and the slope angle 0 of the sidewalls of the square slab, respectively For the square slab with side length of 2 mu m, thickness of 0.2 mu m, and refractive index of 3.4, on a square pedestal with refractive index of 3.17, the Q factor of the whispering-gallery (WG)-like mode transverse-electric TE(3.5)o first increases with the side length b of the square pedestal and then quickly decreases as b > 0.4 mu m, but the Q factor of the WG-like mode TE(4.6)o drops down quickly as b > 0.2 mu m, owing to their different symmetries. The results indicate that the pedestal can also result in mode selection in the WG-like modes. In addition, the numerical results show that the Q factors decrease 50% as the slope angle of the sidewalls varies from 90 degrees to 80 degrees. The mode characteristics of WG-like modes in the square cavity with a rectangular pedestal are also discussed. The results show that the nonsquare pedestal largely degrades the WG-like modes. (c) 2006 Optical Society of America

Analysis of mode characteristics for deformed square resonators by FDTD technique

The mode frequencies and quality factors (Q-factors) in two-dimensional (2-D) deformed square resonators are analyzed by finite-difference time-domain (FDTD) technique. The results show that the deformed square cavities with circular and cut corners have larger Q-factors than the perfect ones at certain conditions. For a square cavity with side length of 2 mu m and refractive index of 3.2, the mode Q-factor can increase 13 times as the perfect corners are replaced by a quarter of circle with radius of 0.3 pm. Furthermore the blue shift with the increasing deformations is found as a result of the reduction in effective resonator area. In square cavities with periodic roughness at sidewalls which maintains the symmetry of the square, the Q-factors of the whisperin gallery (WG)-like modes are still one order of magnitude larger that those of non-WG-like modes. However, the Q-tactors of these two types of modes are of the same order in the square cavity with random roughness. We also find that the rectangular and rhombic deformation largely reduce the Q-factors with the increasing offset and cause the splitting of the doubly degenerate modes due to the breaking of certain symmetry properties.

High Q-factor TM modes in three-dimensional semiconductor microresonators

We have investigated the mode characteristics for three-dimensional (3D) semiconductor microresonators by finite-difference time-domain (FDTD) technique. The results show that the quality-factors (Q-factors) of TM-like modes are much larger than those of TE-like modes as the vertical waveguidng formed by semiconductor materials.

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.

Trace and rare elements and factors at DSDP Hole 71-511

The distribution of paragenetic assemblages of trace and rare elements, as revealed by factor analysis (R-mode, Q-mode), the ratios of elements to Zr and the interpretation of these data in the context of the known mineralogy, lithology, and geology of the region, provide the bases for the outline of the geochemical history of sedimentation in the study area that forms the subject of this chapter. Two stages may be discerned. 1. Late-Middle Jurassic-Early Cretaceous (160-106? Ma). The sediments that accumulated in relatively shallow water (shelf) were predominantly clay, with dispersed sapropelic organic matter, plant fragments, pyrite, admixtures of acid-medium volcanic glass, and epigenetic crystals of gypsum. The bottom water layers of the basin are notably stagnant. The sediments are characterized by higher amounts of V, Zn, Cu, Cr, Rb, and Be associated with organic matter. Lower Cretaceous sediments, separated from those of the Upper Jurassic by a hiatus, accumulated in a deepened and enlarging basin. These Lower Cretaceous deposits are chemically similar to those of the Upper Jurassic, but contain diagenetic concentrations of Zn, Ni, and La. 2. Early-middle Albian (Unit 5)-middle Maestrichtian (1067-66.6Ma). The prevailing regime was that of an open ocean basin that tended to expand and deepen. During the second half of the early-middle Albian, the biogenic components Ba, Sr, and CaCO3 accumulated. By the end of this interval, Ti/Zr values had increased. In conjunction data on mineral composition, they testify to an outburst of basaltoid volcanism related to tectonic activity before an erosional hiatus (late Albian-Cenomanian). At the end of the Cenomanian-Turonian, residual deposits of predominantly clay sediments with relatively high amounts of Ti and Zr and associated rare alkalis (Li, Rb) accumulated. Clay sediments deposited during the Coniacian-Santonian were characterized by higher concentrations of Ti, Zr, Li, and Rb, by diagenetic carbonate phases of Ni, Zn, and La, and by sulphides and Fe-oxides with an admixture of Ni and Co. The latter half of the interval saw the deposition of fine basaltoid volcanoclastic material, diagenetically altered by zeolitization and carbonatization and enriched with Se, Pb, Ti, Sr, Ba, Y, and Yb. Sediments with a similar chemistry accumulated in the Campanian-middle Maestrichtian. Strong current activity preceding a global hiatus at the Mesozoic/Cenozoic boundary is reflected in both lower sedimentation rates and the presence of higher residual concentrations of Ti, Zr, Ba, Sr, and other elements studied in this chapter.

Quantum and non-Markovian effects in the electron transfer reaction dynamics in the Marcus inverted region

Electron transfer reactions in large molecules may often be coupled to both the polar solvent modes and the intramolecular vibrational modes of the molecule. This can give rise to a complex dynamics which may in some systems, like betaine, be controlled more by vibrational rather than by solvent effects. Additionally, a significant contribution from an ultrafast relaxation component in the solvation dynamics may enhance the complexity. To explain the wide range of behavior that has been observed experimentally, Barbara et al. recently proposed that a model of an electron transfer reaction should minimally consist of a low-frequency classical solvent mode (X), a low-frequency vibrational mode (Q), and a high-frequency quantum mode (q) (J. Phys. Chem. 1991, 96, 3728). In the present work, a theoretical study of this model is described. This study generalizes earlier work by including the biphasic solvent response and the dynamics of the low-frequency vibrational mode in the presence of a delocalized, extended reaction zone. A novel Green's function technique has been developed which allowed us to study the non-Markovian dynamics on a multidimensional surface. The contributions from the high-frequency vibrational mode and the ultrafast component in the non-Markovian solvent dynamics are found to be primarily responsible for the dramatic increase in charge transfer rate over the prediction of the classical theories that neglect both these factors. These, along with a large coupling between the reactant and the product states, may combine to render the electron transfer rate both very large and constant over a wide range of solvent relaxation rates. A study on the free energy gap dependence of the electron transfer rate reveals that the rates are sensitive to changes in the quantum frequency particularly when the free energy gap is very large.

Influence factors on wear resistance of two alumina matrix composites

We measured the wear resistances of alumina, alumina/silicon carbide composite and alumina/mullite composite by abrasive wear. And we studied the influence of fracture mode and worn surface pullout on wear resistance. The results are as follows: the main wear mechanisms of alumina and alumina/silicon carbide were fracture wear and plastic wear respectively, and for alumina/mullite composite, fracture wear and plastic wear mechanisms worked together. The wear resistance of the alumina/silicon carbide composite and the alumina/mullite composite was better by a factor of 1 similar to 3 than that of the monolithic alumina. There were two main reasons for the better wear resistance, i.e., the improved mechanical properties and the more smooth worn surfaces. However, The primary reason was the reduction of area fraction of pullout on the worn surfaces induced by fracture mode transition. (C) 2007 Published by Elsevier B.V.

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.