Whispering-gallery-likel modes in square resonators

The mode frequencies and field distributions of whispering-gallery (WG)-like modes of square resonators are obtained analytically, which agree very well with the numerical results calculated by the FDTD technique and Pade approximation method. In the analysis, a perfect electric wall for the transverse magnetic mode or perfect magnetic wall for the transverse electric mode is assumed at the diagonals of the square resonators, which not only provides the transverse mode confinement, but also requires the longitudinal mode number to be an even integer. The WG-like modes of square resonators are nondegenerate modes with high-quality factors, which make them suitable for fabricating single-mode low-threshold semiconductor microcavity lasers.

Investigation of vertical radiation loss for whispering-gallery modes in 3-D microresonators by FDTD simulation

The vertical radiation loss of three-dimensional (3-D) microresonators is investigated by 3-D finite-difference time-domain (FDTD) simulation. The simulation shows that the vertical radiation causes an important loss in the microresonators with weak waveguiding, and result in decrease of the quality factors (Q-factors) of whispering-gallery (WG) modes. Through the simulation, we find that TM-like modes have much weaker vertical radiation loss than TE-like modes. High Q-factor TM-like modes are observed in the 3-D microresonators with weak vertical waveguiding, but the Q-factors of TE-like modes decrease greatly.

Whispering-gallery microcavity semiconductor lasers suitable for photonic integrated circuits and optical interconnects

The characteristics of whispering-gallery-like modes in the equilateral triangle and square microresonators are introduced, including directional emission triangle and square microlasers connected to an output waveguide. We propose a photonic interconnect scheme by connecting two directional emission microlasers with an optical waveguide on silicon integrated circuit chip. The measurement indicates that the triangle microlasers can work as a resonance enhanced photodetector for optical interconnect.

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.

Enhancement of quality factor for TE whispering-gallery modes in microcylinder resonators

The enhancement of quality factor for TE whispering-gallery modes is analyzed for three-dimensional microcylinder resonators based on the destructive interference between vertical leakage modes. In the microcylinder resonator, the TE whispering-gallery modes can couple with vertical propagation modes, which results in vertical radiation loss and low quality factors. However, the vertical loss can be canceled by choosing appropriate thickness of the upper cladding layer or radius of the microcylinder. A mode quality factor increase by three orders of magnitude is predicted by finite-difference time-domain simulation. Furthermore, the condition of vertical leakage cancellation is analyzed.

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.

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

High-Q TM whispering-gallery modes in three-dimensional microcylinders

We present a generation condition for realizing high-Q TM whispering-gallery modes (WGMs) in semiconductor microcylinders. For microcylinders with symmetry or weak asymmetry vertical waveguiding, we show that TM WGMs can have a high Q factor, with the magnitude of 10(4) at the radius of the microcylinder of 1 mu m, by three-dimensional numerical simulation. The Q factor of TE WGMs is much less than that of TM WGMs in the semiconductor microcylinders due to a vertical radiation loss caused by mode coupling with the vertical propagating mode. The results open up a possible application of TM WGMs in semiconductor microcylinders for efficient current injection microlasers and single photon sources.

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.

Strong localization of whispering gallery modes in an optical fiber via asymmetric perturbation of the translation symmetry

Recently introduced Surface Nanoscale Axial Photonics (SNAP) is based on whispering gallery modes circulating around the optical FIber surface and undergoing slow axial propagation. In this paper we develop the theory of propagation of whispering gallery modes in a SNAP microresonator, which is formed by nanoscale asymmetric perturbation of the FIber translation symmetry and called here a nanobump microresonator. The considered modes are localized near a closed stable geodesic situated at the FIber surface. A simple condition for the stability of this geodesic corresponding to the appearance of a high Q-factor nanobump microresonator is found. The results obtained are important for engineering of SNAP devices and structures.

Reflectionless potentials for slow whispering gallery modes in surface nanoscale axial photonic fiber resonators

We consider an optical fiber with a nanoscale variation of the effective fiber radius that supports whispering gallery modes slowly propagating along the fiber, and reveal that the radius variation can be designed to support the reflectionless propagation of these modes. We show that reflectionless modulations can realize control of the transmission amplitude and temporal delay, while enabling close packing due to the absence of cross talk, in contrast to the conventional potentials.

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.

The whispering gallery mode in photonic crystal ring cavity - art. no. 698438

Whispering gallery modes (WGMs) in microcavities possess ultra-high cavity Q factor. Such microcavity are easy to be fabricated, so WGMs have attracted much attention in the area of photonics and integrated photonic circuits. It is well known that the effect of total internal reflection restricts the size of this mirocavity. Such drawback goes against the integration of photon. However, the photonic crystal microcavities (PCMC) make a breakthrough recently. The WGMs in the PCMC are possible to gain both ultra-high Q and ultra-small mode volume. In this paper, the property of the mode in photonic crystal ring cavity is analyzed by FDTD and PWE. By modifying the airholes in the corners of the ring cavity, we can obtain the WGM. Also the Q factor of WGM in photonic crystal ring cavity is calculated. This favors the design of the photonic crystal microcavity components.

Evanescent field sensing: optical nanofibres, whispering-gallery-mode microspherical and microbubble resonators

In this thesis, the evanescent field sensing techniques of tapered optical nanofibres and microspherical resonators are investigated. This includes evanescent field spectroscopy of a silica nanofibre in a rubidium vapour; thermo-optical tuning of Er:Yb co-doped phosphate glass microspheres; optomechanical properties of microspherical pendulums; and the fabrication and characterisation of borosilicate microbubble resonators. Doppler-broadened and sub-Doppler absorption spectroscopic techniques are performed around the D2 transition (780.24 nm) of rubidium using the evanescent field produced at the waist of a tapered nanofibre with input probe powers as low as 55 nW. Doppler-broadened Zeeman shifts and a preliminary dichroic atomic vapour laser lock (DAVLL) line shape are also observed via the nanofibre waist with an applied magnetic field of 60 G. This device has the potential for laser frequency stabilisation while also studying the effects of atom-surface interactions. A non-invasive thermo-optical tuning technique of Er:Yb co-doped microspheres to specific arbitrary wavelengths is demonstrated particularly to 1294 nm and the 5S1/2F=3 to 5P3/2Fʹ=4 laser cooling transition of 85Rb. Reversible tuning ranges of up to 474 GHz and on resonance cavity timescales on the order of 100 s are reported. This procedure has prospective applications for sensing a variety of atomic or molecular species in a cavity quantum electrodynamics (QED) experiments. The mechanical characteristics of a silica microsphere pendulum with a relatively low spring constant of 10-4 Nm-1 are explored. A novel method of frequency sweeping the motion of the pendulum to determine its natural resonance frequencies while overriding its sensitivity to environmental noise is proposed. An estimated force of 0.25 N is required to actuate the pendulum by a displacement of (1-2) μm. It is suggested that this is of sufficient magnitude to be experienced between two evanescently coupled microspheres (photonic molecule) and enable spatial trapping of the micropendulum. Finally, single-input borosilicate microbubble resonators with diameters <100 μm are fabricated using a CO2 laser. Optical whispering gallery mode spectra are observed via evanescent coupling with a tapered fibre. A red-shift of (4-22) GHz of the resonance modes is detected when the hollow cavity was filled with nano-filtered water. A polarisation conversion effect, with an efficiency of 10%, is observed when the diameter of the coupling tapered fibre waist is varied. This effect is also achieved by simply varying the polarisation of the input light in the tapered fibre where the efficiency is optimised to 92%. Thus, the microbubble device acts as a reversible band-pass to band-stop optical filter for cavity-QED, integrated solid-state and semiconductor circuit applications.

Direct Sensing in Liquids Using Whispering-Gallery-Mode Droplet Resonators

Liquid droplets suspended by the tip of a thin wire, a glass capillary, or a needle form high-Q optical resonators, thanks to surface tension. Under gravity equilibrium conditions, the maximum drop diameter is approximately 1.5 mm for paraffin oil (volume ∼ 0.5 μL) using, for instance, a silica fiber with 250 μm thickness. Whispering gallery modes are excited by a free-space near-infrared laser that is frequency locked to the cavity resonance. The droplet cavity serves as a miniature laboratory for sensing of chemical species and particles.