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.

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

Investigation of mode characteristics for microdisk resonators by S-matrix and three-dimensional finite-difference time-domain technique

The mode characteristics of a three-dimensional (3D) microdisk with a vertical refractive index distribution of n(2)/3.4/n(2) are investigated by the S-matrix method and 3D finite-difference time-domain (FDTD) technique. For the microdisk with a thickness of 0.2 mu m. and a radius of 1 mu m, the mode wavelengths and quality factors for the HE7,1 mode obtained by 3D FDTD simulation and the S-matrix method are in good agreement as n(2) increases from 1.0 to 2.6. But the Q factor obtained by the 3D FDTD rapidly decreases from 1.12 X 10(4) to 379 as n2 increases from 2.65 to 2.8 owing to the vertical radiation losses, which cannot be predicted by the proposed S-matrix method. The comparisons also show that quality factors obtained from the analytical solution of two-dimensional microdisks under the effective index approximation are five to seven times smaller than those of the 3D FDTD as n(2) = 1 and R = 1 mu m. (c) 2006 Optical Society of America.

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.

Mode-coupling analysis of three-dimensional microdisk resonators by the finite-difference time-domain technique

Quality factor enhancement due to mode coupling is observed in a three-dimensional microdisk resonator. The microdisk, which is vertically sandwiched between air and a substrate, with a radius of 1 mu m, a thickness of 0.2 mu m, and a refractive index of 3.4, is considered in a finite-difference time-domain (FDTD) numerical simulation. The mode quality factor of the fundamental mode HE71 decreases with an increase of the refractive index of the substrate, n(sub), from 2.0 to 3.17. However, the mode quality factor of the first-order mode HE72 reaches a peak value at n(sub) = 2.7 because of the mode coupling between the fundamental and the first-order modes. The variation of mode field distributions due to the mode coupling is also observed. This mechanism may be used to realize high-quality-factor modes in microdisks with high-refractive-index substrates. (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.

Lasing of CdSSe quantum dots in glass spherical microcavity

Glass spherical microcavities containing CdSSe semiconductor quantum dots (QDs) of a few microns in diameter are fabricated using a physical method. When a single glass microspherical cavity is excited by a laser beam at room temperature, very strong and sharp whispering gallery modes are shown on the background of PL spectra of CdSSe QDs, which confirms that coupling between the optical emission of embedded QDs and spherical cavity modes is realized. For a glass microsphere only 4.6 mum in diameter, it was found that the energy separation is nearly up to 26 nm both for TE and TM modes. With the increasing excitation intensity, the excitation intensity dependence of the emission intensity is not linear in the double-logarithmic scale. Above the threshold value, the linewidths of resonance modes become narrower. The lasing behavior is achieved at relatively low excitation intensity at room temperature. High optical stability and low threshold value make this optical system promising in visible microlaser applications. (C) 2002 Elsevier Science B.V. All rights reserved.

Lasing of CdSexS1-x quantum dots in a glass spherical microcavity

A glass spherical microcavity only a few microns in diameter embedded with CdSexS1-x quantum dots (QDs) was fabricated using a physical method; it exhibited good optical stability under continuous-wave laser excitation with high power. We investigated the excitation power dependences of the emission intensity and the linewidth of both transverse electric and transverse magnetic resonance peaks of whispering gallery modes. Stimulated emission behaviour of multi-frequency modes is observed at room temperature. The low threshold value and large mode separation makes QD-containing microspheres promising for visible microlaser applications.

Photoluminescence behavior of quantum dots in spherical glass microcavity

Micrometer-sized spherical glass microspheres were fabricated. CdSeS semiconductor nanometer clusters were incorporated into spherical microcavities. When a single microsphere was excited by a laser beam, the whispering gallery mode resonance of the photoluminescence of CdSeS quantum dots in the spherical microcavities was realized by the multiple total internal reflections at the spherical interface. The coupling of restricted electronic and photonic states was realized.

Photoluminescence study of CdSexS1-x quantum dots in a glass spherical microcavity

The photoluminescence (PL) of CdSexS1-x semiconductor quantum dots (QDs) in a glass spherical microcavity is investigated. The CdSexS1-x semiconductor clusters embedded in a glass matrix are fabricated by using the heat treatment method. Periodical structures consisting of sharp spectral lines are observed in the PL spectra of CdSexS1-x QDs, which can be well explained by the coupling with the whispering gallery modes of the spherical microcavity based on Mie scattering theory.

Quantum dots in glass spherical microcavity

Glass spherical microcavities containing CdSexS1-x semiconductor quantum dots (QDs) are fabricated. The coupling between the optical emission of embedded CdSexS1-x QDs and spherical cavity modes is realized. When the luminescence of QDs is excited by a laser beam, the strong whispering gallery mode resonance with high Q factors is achieved in the photoluminescence spectra. (C) 2001 American Institute of Physics.

Characteristics of triangle and square InP/InGaAsP microlasers

Directional emission triangle and square InGaAsP/InP lasers have been fabricated by standard photolithography, inductively coupled plasma etching technique combined with wet chemical etching process. In this article, the characteristics of the microcavity lasers are presented. For an equilateral triangle microcavity laser with the side length of 30 mu m, we got the laser spectra fitted very well with the mode wavelength formulate LIP to the 8(th) transverse mode at room temperature. But the laser spectra are usually more complex than the formulae for the lasers, especially for the lasers with a smaller side length. For a square microcavity laser with side length of 20 mu m, we observed the mode competition between the Fabry-Perot (FP) modes and Whispering-Gallery (WG) modes at 200K. The output spectra below the threshold have the mode interval of FP modes with a large mode interval, and the laser spectra agree very well with the WG modes, which have mode interval less than the FP modes. The output spectra are dominated by the FP modes below the threshold, because the FP modes have a higher output coupling efficiency than the WG modes.