Invited presentations:

Optical transport phenomena in coupled spherical cavities

V. N. Astratov, S. P. Ashili, and S. Yang, University of North Carolina at Charlotte, USA

Due to a unique combination of properties mesoscopic systems of coupled spherical cavities can be used for developing technology of integration of cavities in three spatial dimensions (3D) in chip-scale structures for a variety of optoelectronics applications. These properties include record quality factors of whispering gallery modes (WGMs) in spheres, possibility to achieve supermonodispersive properties of these cavities based on their sorting using spectroscopic methods, and the possibility to control their positions and separations by different methods. In this work using spatially resolved transmission and scattering spectroscopic measurements we demonstrate coupling of plane waves to different types of propagating modes in chains of cavities with various refractive indices. In order to synthesize 3D lattices of cavities we used the technique of self-assembly directed by hydrodynamic flow of suspension of microspheres through a cuvette with submicron holes allowing the liquid to leak out, but stopping the spheres. In such 3D lattices of cavities the coupling efficiencies between close neighbors are randomized due to size variations (~3%) of microspheres. Using local photoexcitation techniques we observed in transmission spectra of such structures spectral signatures of strong coupling between multiple spheres with nearly resonant WGMs. This is confirmed by the results of measurements of thickness dependence of the transmission spectra demonstrating emergence of clusters of 5 mkm spheres with characteristic sizes ~30 mkm which are well connected at the WGM frequencies. These results suggest that the transmission properties can be significantly improved in 3D structures formed by more uniform spheres due to achieving an optical percolation threshold for the WGM transport.

Bound whispering gallery modes in circular arrays of dielectric spherical particles

A. L. Burin, Gail S. Blaustein, Olga M. Samoylova, Tulane University, New Orleans LA, USA

Low-dimensional ordered arrays of dielectric particles can possess bound optical modes having an extremely high quality factor depending on the material used. In this paper we address the following question: can bound modes be formed in dielectric systems where the absorption of light is negligible? Our investigation of circular arrays of spherical particles within the framework of the multisphere Mie scattering theory using the simplest dipolar-like approach shows that high quality modes in an array of 10 or more particles can be attained at least for a refractive index n_r > 2; the most bound modes have nearly transverse polarization perpendicular to the circular plane; and in a particularly interesting case (TiO₂ particles, n_r = 2.7), the quality factor of the most bound mode increases almost by an order of magnitude with the addition of 10 extra particles, while for particles of GaAs the quality factor increases by almost two orders of magnitude. The error of the dipolar approach does not exceed one percent if n_r > 2. Minimum acceptable disordering not affecting the quality factor is also investigated.

Theory and applications of 2D microcavity lasers

T. Harayama, ATR Wave Engineering Laboratories, Japan

Various kinds of devices such as lasers and musical instruments utilize stationary wave oscillations in resonant cavities. In order to maintain the stationary oscillation in these devices, nonlinearity is essential in the mechanism for balancing the pumping of the external energy and the decay of the wave of the quasi-stable resonance in the resonant cavity. Besides, the interaction between nonlinearities and the morphology of the boundary condition imposed on a resonating wave system by the shape of the cavity is also very important for determining the modes of oscillation. We will review the theoretical models of 2D microcavity lasers and discuss their applications such as optical switches and rotation sensors.

Fabrication, characterization, and application of crystalline whispering gallery mode resonators

A. Matsko, Jet Propulsion Laboratory, USA

abstract: to be available soon.

Enhanced frequency shift in optical slow-wave structures

F. Morichetti, C. Ferrari, and A. Melloni, Politecnico di Milano, Italy

Doppler effects in electrooptic media can be exploited to induce a continuous, accurate and fast shift of the carrier frequency of optical signals, without the need for nonlinear materials, additional optical sources or high optical power levels. In this contribution, it is shown that the efficiency of the frequency-shift process can be significantly enhanced by slow-wave propagation in coupled resonator optical structures. By means of time-domain numerical simulations, lumped and traveling wave architectures for slow-wave frequency converters are discussed and compared to the state-of-the-art devices, with the aim of clarifying the role played by optical resonators. Relationships between the maximum frequency shift and the bandwidth of the dynamic slow-wave structure are derived. Stop light effects are also explored, showing that the speed of the frequency-shift process can be arbitrarily slowed down, if the optical pulse is trapped, frequency shifted while inside the structure and finally released.

Theory of the spatial structure of non-linear modes in novel and complex laser cavities

A. D. Stone, L. Ge, and S. Rotter, Yale University, USA
H. E. Tureci, Institute of Quantum Electronics, ETH Zurich, Switzerland

A new formalism for calculating exact steady-state non-linear multi-mode lasing states for complex resonators is developed and applied to dielectric microcavity lasers and to lasers with chaotic or random cavities. The theory solves a long-standing problem in lasing theory: how to describe the multi-mode lasing states of an open cavity including mode competition and spectral hole-burning effects to all orders. Thus the theory can explain the huge increase in output power induced by shape deformation in microcylinder lasers, and may be used to design laser cavities with predictable output power and modal spectra. It also may be used to understand how a random cavity with finesse less than unity can nonetheless produce a narrow line lasing state as observed in nanocluster lasers.
The theory is based on a reformulation of the standard Maxwell-Bloch semiclassical lasing equations for the case of steady state multi-mode operation (multi-periodic solution). Instead of expanding this solution in terms of modes of the passive cavity we derive a set of self-consistent coupled integral equations for the space-dependence of the set of lasing modes. These unknown lasing modes are then expressed in terms of biorthogonal linear modes, which correspond to complex-wavevector solutions inside the cavity and flux-conserving outgoing waves of wavevector outside the cavity. This set is complete and can be used to express any lasing mode. We refer to these biorthogonal states as constant-flux (CF) states. Note that these states are not the resonances of the cavity, which have complex wavevectors outside the cavity and are not an appropriate set for expressing the lasing state. It was shown that when the cavity has high finesse a single CF state represents the lasing mode, but in a low finesse cavity we find that several CF states contribute to the lasing state, particularly far above threshold. An initial application of the method has been completed for a conventional edge-emitting laser cavity with low finesse. Applications to dielectric cylinder lasers and random lasers are in progress .

Contributions announced by:

High-quality-factor WG modes in semiconductor microcavity pillars with circular and elliptical cross section

V. N. Astratov and S. Yang, University of North Carolina at Charlotte, USA
S. Lam, D. Sanvitto, A. Tahraoui, D. M. Whittaker, A. M. Fox, and M. S. Skolnick, University of Sheffield, UK

The authors observed that semiconductor AlAs/GaAs pillar microcavities with well defined "photonic dot" states simultaneously possess whispering gallery modes (WGMs) with very small modal volumes ~0.1 um3 and quality (Q)-factors approaching 20000 for 4-5 um circular pillars.
The WGMs in micropillars are shown to be well confined in a thin central cavity with a disk shape that allows their efficient coupling with near-surface quantum dots. The Q-factors of WGMs in micropillars are found to be in excess of that for .photonic dot. states measured from the same pillars. Such WGM resonances were observed in circular and elliptical micropillars by employing geometry of experiments in which excitation and collection of emission of micropillars is performed at normal to their sidewall surface. The WGM spectra are found to be in a good agreement with the results of 3D numerical modeling performed by finite difference time domain technique. We show that the combination of optical properties of such pillars is unique in terms of possible cavity quantum electrodynamics experiments since it allows selective excitation of various cavity modes coupled to quantum dots with different location inside the cavity.

Optical modes in linear arrays of dielectric spherical particles: a numerical investigation

G. Blaustein and A. Burin, Tulane University, USA

We have investigated bound modes in finite linear chains of dielectric particles of various lengths, interparticle spacing and particle materials. Through a unique application of the multisphere Mie scattering formalism, we developed numerical methods to calculate the eigen-optical modes of the chain where photon emission is forbidden due to the momentum conservation law. These numerical methods incorporate the multisphere scattering formalism as entries in NxN matrices where N represents the number of particles in the chain. Eigenmodes of these matrices correspond to the eigen-optical modes of interest. We identified the eigenmodes with the highest quality factor by the application of a modified version of the Newton-Raphson algorithm. We found that convergence is strong using this algorithm for linear chains of up to 50 particles for materials with a refractive index greater than 2. By comparing the dipolar approach with a more complex approach utilizing a combination of both dipolar and quadrupolar approaches, we demonstrated that the dipolar approach has an accuracy of approximately 99%. We found that the quality factor Q of the mode increases with the cubed value of the number of particles in the chain in agreement with previously developed theory. In addition, we found that the disordering in particle size necessary to reduce the quality factor by a factor of 10 decreases with the number of particles N according to the power law 1/Nb. We will also discuss the effect of an octopolar approach on Q as well as methods for calculating Q for particle chains of materials with refractive indices less than 2.

Two mode interactions in quasi-stadium laser diodes

M. Choi, T. Fukushima, and T. Harayama, ATR Wave Engineering laboratories, Japan

We found alternate oscillations in AlGaAs/GaAs single-quatum-well quasi-stadium laser diodes (QSLD). The alternate oscillations in QSLD can be well explained by the interactions of two different cavity modes due to the geometrical symmetry of QSLD. Unlike the alternate oscillations in semiconductor ring lasers that need the waveguides to extract the light signals, the alternate oscillation signals in QSLD are obtained from the emitting lights spreading over the space since the lasing modes in QSLD arise from two dimensional resonance modes of laser cavity. We also showed the alternate oscillation frequencies are inversely proportional to the amplitudes of two different cavity modes.

Matrix Analysis of Coupled Microring Resonator Polygons

Ioannis Chremmos and Nikolaos Uzunoglu, National Technical University of Athens, Greece

The resonant properties of a photonic molecule, composed by N microring resonators forming a regular polygon, are for the first time determined analytically using the transfer matrix method. It is found that the transfer matrix between rings /n/, /n + 2/, /n + 4/ , ... is independent of the polygon vertex angle, allowing the application of Floquet theorem for periodic propagation in a cylindrically symmetric structure.
Corresponding to even or odd /N/, the molecule possesses /1 + N/2/ or /1 + N/ discrete resonances, which satisfy the dispersion equation of the straight coupled-resonator optical waveguide (CROW) with infinite rings. The field amplitudes in the rings are determined as eigenvectors of the corresponding eigenvalue problem. By incorporating the molecule into a channel dropping filter system, the presence of these resonances in the transmission spectrum is verified.

Propagation of the fundamental whispering gallery mode along a chain of coupled microspheres

L. I. Deych, City University of New York, USA
C. Schmidt, A. Chipouline, T. Pertsch, Friedrich Schiller University, Germany
A. Tünnermann, Fraunhofer Institute for Applied Optics and Precision Engineering, Germany

The aim of this contribution is the development of a theoretical model for the efficient description of light propagation in chains of coupled microresonators.

Among all whispering gallery modes (WGM) with given angular number /m/, which can be excited in a spherical microresonator, a mode whose azimuthal number /m /is equal to /l/ is of greatest interest for applications. This mode is characterized by the smallest mode volume with its electric field concentrated most tightly in the equatorial plane, and is often referred to as fundamental mode. Moreover the coupling between fundamental modes excited in two or more spheres is of primary interest when studying the propagation of light signals in integrated optical networks. However in the simplest case of two or more coupled spheres aligned along a straight line collective modes of the chain are defined in the coordinate system with polar axes directed along this line. The fundamental (/m=l/) mode in this coordinate system is the one, which is perpendicular to the axis of the chain, and has no significant coupling with respective modes in other spheres. The modes, which couple most strongly, are the ones with /m/=1. But they are not the modes whose coupling is of primary interest for our investigation.
It should be realized that the configuration, in which fundamental modes in two or more spheres couple between themselves, is not possible because such field distribution does not correspond to any normal modes of the system of coupled spheres.

The spatial distribution of the field reproducing that of the fundamental mode but being concentrated in the polar plane of the chain can only be obtained as a superposition of normal modes with different azimuthal numbers. In order to find such a superposition one can use transformation properties of vector spherical harmonics upon rotations of the coordinate system. In this work we assume that such superposition is created in one of the spheres of the chain. Subsequently we study its spatial evolution along the chain under steady-state conditions. Using tight-binding equations for the chain of spheres, we find the extent of distortion of the original superposition caused by coupling between modes with different angular numbers in adjacent spheres and its effect on radiative decay of the initial excitation. We also analyze limitations on applications of chains of spheres for waveguides and other photonic devices caused by the discussed effects.

'Single-Mode' Whispering-Gallery Terahertz Quantum-Cascade Lasers with Controlled Degeneracy

G. Fasching, A. Benz, A. M. Andrews, Ch. Deutsch, R. Zobl, W. Schrenk, G. Strasser, K. Unterrainer, Vienna University of Technology, Austria
V. Tamosiunas, Semiconductor Physics Institute &Vilnius Gediminas Technical University, Vilnius, Lithuania

We present whispering-gallery mode terahertz quantum-cascade lasers with either 'single-mode' or 'double-mode' emission depending on the rotational symmetry of such resonators. Strong mode confinement in the growth and in-plane directions are provided by a double-plasmon waveguide and due to the strong impedance mismatch between the gain material and air. These ultra-compact devices exhibit increased temperature performance up to 95 K in continuous-wave mode operation and threshold currents as low as 13.5 mA. We have observed dynamical frequency pulling of the resonator mode on the GHz scale. Thus, we were able to estimate the peak gain of the material to 27 cm/^- /^1 . Finite-difference time-domain calculations were performed to obtain the emission spectra from such microdisk terahertz quantum-cascade lasers.

Radiation-pressure-induced mode splitting in a spherical microcavity with an elastic shell

M. Gerlach, Y. P. Rakovich, and J. F. Donegan, Trinity College Dublin, Ireland

In this work, we present a novel method to reveal the azimuthal whispering gallery modes (WGMs) in a coated spherical microcavity. The microcavity is coated with a nano-meter thick polyelectrolyte shell and one monolayer of CdTe semiconductor quantum dots. The new approach in this experiment is based on the deformation of the spherical shape in a non-contact way using the radiation pressure from a laser beam, which causes the lifting of the degeneracy of the WGMs. The resonance peak linewidth and splitting parameters can be efficiently controlled by the strength of the radiation pressure and the elastic properties of the surface shell. The mode structure found in the experiments is in good agreement with a simple analytical model.

Room-temperature continuous-wave electrically injected InP/GaInAsP equilateral-triangle-resonator lasers

Y.-Z. Huang, Y.-H. Hu, Q. Chen, S.-J. Wang, Y. Du, and Z.-C. Fan, Institute of Semiconductors, China

Directional emission microcavity lasers fabricated by planar technology are required to be light sources in photonic integrated circuits. Equilateral-triangle-resonator (ETR) microlasers can be a simple light source in photonic integrated circuits by directly connecting an output waveguide in one of the vertices of the ETR. In this article, we report fabrication and characteristics of continuous-wave (CW) electrically injected InP/GaInAsP ETR lasers at room temperature. ETR microlasers with the side length of 10 to 30 mkm and an 1 or 2-mkm-width output waveguide are fabricated using standard photolithography, inductively-coupled- plasma etching techniques, and an additional chemically etching process. CW electrically injected InP/GaInAsP ETR lasers are realized at room- temperature with the wavelength of 1550 nm. The maximum output power is 0.067 and 0.17 mW at 290 and 295K for an ETR laser with the side length of 20 um, respectively, which are partly limited by the temperature rising with the increase of the injection current. The corresponding CW threshold currents are 34, 43, and 55 mA at the heat sink temperature of 290, 295, and 298 K, respectively. The results are promising for the development of compact, integrated, and low cost laser sources.

What determines the direction of far-field emission in chaotic microcavities

J.-B. Shim, S.-B. Lee, J. Yang, S. Moon, J.-H. Lee, and K. An, Seoul National University, Korea
H.-W. Lee, Korea Advanced Institute of Science and Technology, Korea

To overcome the disadvantage of the spatially isotropic emission of circular or spherical microcavities the deformed microcavities has been proposed and extensively studied. It is crucial to know how to determine the direction of far-field emission in deformed microcavities. I would like to review the recent advances on this issue focusing on our latest works.

Far-field emission patterns and the emission positions of individual cavity modes in a highly deformed microcavity

S.-B. Lee, J.-B. Shim, J. Yang, S.-K. Moon, J.-H. Lee, and K. An, Seoul National University, Korea, S. W. Kim, Pusan National University, Korea

The characteristics of quasi-bound states of a highly deformed microcavity were investigated in both theory and experiment. Five distinct mode groups were observed in a dielectric microcavity (index of refraction 1.361) with 23% quadrupole deformation. These modes had quality factors different by several orders of magnitude in the range of 104. 106, and consistently they had quite different intracavity mode distributions. However, their far-field emission patterns were found to be almost identical, contrary to common understanding that the emission direction is usually associated with the internal mode distribution. This seeming contradiction, however, can be resolved by close examination of the Husimi plot, the phase-space projection of the mode function, corresponding to a ray-trajectory distribution in the classical limit. Although the Husimi distributions above the critical line, which determine geometric shape of modes, are different, there exist a few tail-like faint structures extending from the region of wave concentration to the region far below the line of critical angle. These structures resemble the unstable manifold of period of four of ray trajectories and thus almost the same for the entire mode groups that we have observed. Although the integrated probability associated with these structures below the line of critical angle is negligibly small compared to that of the total mode distribution, they are the only direct routes to the outside via refractive escape. Both the measured far-field patterns and emission positions support our idea that the output emission is mostly due to the refractive escape at the emission points determined by the unstable manifold of ray trajectory crossing the critical line of total internal reflection.

Effect of openness on resonance patterns in chaotic microcavities

S.-Y. Lee, Seoul National University, Korea

Due to the similarity between ray dynamics in microcavities and particle dynamics in billiards, the ideas developed in quantum chaos field have been successfully applied, e.g., scarring phenomenon, dynamical localization, chaos-assisted tunneling etc. An important difference between them would be the openness of microcavities described by Fresnel equation. It is, therefore, essential to consider the property of openness as well as ray dynamics in understanding intriguing phenomena observed in microcavities. We focus on how the openness affects resonance mode patterns in chaotic microcavities. In some scarred resonances, there is a pattern splitting between waves of different chirality, and the emission pattern of very high Q scarred resonances is uniquely determined by the boundary geometry and refractive index. These can be well explained by the steady probability distribution, a phase space distribution describing both openness and dynamics. The role of openness of chaotic microcavities is more crucial in the quasiscarred resonance which has a scar-like localized pattern without an underlying periodic orbit, because it may not exist in closed billiards. We discuss about the condition for the formation of quasiscarred resonances, and present the property of a quasiscarred resonance in a stadium microcavity.

Mode coupling between coupled first and second order whispering-gallery modes in coupled two microdisks

J.-J. Li, J.-X. Wang, and Y.-Z. Huang, Huaqiao University and Institute of Semiconductors, China

Coupled-microcavities as photonic molecules provide the study of confined photonic modes similar to confined electron states. The improvement of emission performance for photonic integrated circuits and some functionalities are expected in photonic molecule structures using two or more coupled microdisks. In this article, we investigate the mode characteristics for two coupled microdisks by finite-difference time-domain (FDTD) technique. In the two coupled micodisks, mode coupling between the same order whispering-gallery modes (WGMs) results in coupled WGMs with split mode wavelengths. In addition to the well known mode coupling between the same order WGMs, we find that the split mode wavelengths of the coupled first and second order WGMs can have a cross point in some case, which can induce anticrossing mode coupling between the coupled first and second WGMs and greatly reduce the mode Q-factor of the coupled first order WGMs. The time variations of mode field pattern between the coupled first and second order WGMs are observed by the FDTD simulation, although the field pattern becomes that of the second order WGMs in a very short time.

Matrix Analysis of Coupled Microring Resonator Polygons

A.B. Matsko, A.A. Savchenkov, D. Strekalov, V.S. Ilchenko, N. Yu, and L. Maleki, Jet Propulsion Laboratory, California, USA

We review recent progress in fabrication, characterization, and applications of ultra-high-Q crystalline whispering gallery mode (WGM) resonators. We report on the experimental observations of power-dependent, non- exponential decay of light stored inWGMs caused by stimulated Raman scattering in the resonator host material. We show that a proper thermal annealing leads to a significant increase of the quality factors of the resonators. Finally, we demonstrate optical continuous wave parametric oscillations in lithium niobate WGM resonators.

Strong mode selection scheme in a layered cylindrical microcavity laser with a thin dielectric inner coating

H.-J. Moon and D.-Y. Kang, Sejong University, Korea

We investigated strong mode selection scheme in a layered cylindrical microcavity laser with a thin lower refractive dielectric inner coating.
We used a fused silica capillary (outer diameter of 320 micron, inner diameter of 250 micron), filled with dye-doped ethanol, as the cylindrical cavity and coated AF 1600 on the inner wall of the capillary in order to change the reflectivity of light at the inner wall. Because Whispering Gallery Modes perturbed (or split) by inner wall, there exist interferential coupling effect whose modulation depth depends on the reflectivity of inner wall. The strongest mode selection was observed at the reflectivity of about 50%, in which corresponding thickness of AF 1600 was about 0.4 micron. Due to the enhanced interferential coupling effect, the lasing spectrum appeared as few periodic peaks just around the wavelengths corresponding to the constructive interference condition. We compared the lasing spectrum with that from a bare capillary and discussed the role of thin dielectric coating on the strong mode selection.

Beam mode observation in quasi-stadium laser diodes

Y. Nakae, T. Fukushima, T. Sasaki, and T. Harayama, ATR Wave Engineering Laboratories, Japan

Quasi-stadium laser diode, which has two curved end mirrors and two long straight sidewall mirrors exhibit two kinds of beam propagation modes under resonator condition. These modes show different far-field patterns, hence the quasi-stadium laser diodes was expected to apply in beam switching devices. In this work, we fabricated quasi-stadium laser diode by ion-etching technique to InGaAs/GaAs epitaxial wafer. On the top of this cavity, there is one window which can observe for lasing mode pattern inside of cavity. We demonstrated to observed spontaneous emission pattern from upside of cavity by an infrared camera, under the pulse operation. From the result of far-field pattern and I-L characteristic measurement, observed spontaneous emission pattern reflects to mode intensity pattern.

Pre- and post-fabrication tuning of bends in microdisk CROW sections: a numerical study

S. V. Pishko and S. V. Boriskina, V. Karazin, Kharkov National University, Ukraine

We present a comprehensive numerical study of light transport through bends and branches of coupled resonator optical waveguides (CROWs) composed of side-coupled wavelength-size whispering-gallery (WG) mode microdisk resonators. This study aims to reveal the underlying mechanisms of WG-mode coupling in finite-size aperiodic CROW sections.
Understanding of these mechanisms offers ways to reduce CROW bend losses and to design tunable and switchable optical components based on CROWs. We show that by properly choosing the radius of the microdisk positioned at the CROW bend at the pre-fabrication design stage significant reduction of bend losses for any chosen CROW bend angle can be achieved.
Furthermore, we demonstrate a possibility of using thermo-optically or electro-optically tunable microdisks for post-fabrication tuning of CROW bends and for realization of switching in branched CROW sections.

Quantum switching in doped negative-index metamaterials

A. K. Popov, University of Wisconsin-Stevens Point, USA
V . M. Shalaev, Purdue University, USA

Wavelength-selective frequency-tunable narrowband filtering and quantum switching from strong absorption to amplification via transparency is predicted based on quantum interference and extraordinary properties of parametric amplification in doped negative-index metamaterials.
Compensation of losses and generation of counter-propagating entangled right- and left-handed photons controlled by an external laser are investigated in microcavities and in cavity-free regimes.

Symmetric and asymmetric interacting whispering gallery modes in coupled dielectric microdisks

J.-W. Ryu and S. W. Kim, Pusan National University, Korea

We study the characteristics of quasi-eigenmodes in coupled dielectric microdisks. The positions in complex energy plane of the modes and the corresponding mode distribution in real space are strongly affected by the inter-disk distance. As far as two identical microdisks are concerned, it has been shown that the interaction between the modes with odd parity show unexpected behavior for the inter-disk distance less than their wavelengths so as to cause the directional emission. Their directions of emission especially with relatively high-Q value are determined from neither the inter-disk distance nor their wavelengths rather but from the index of refraction of microdisks. Such a directionality can be understood in terms of an effective boundary deformation in ray dynamical analysis.

Early time fields in stratified microdisk resonators with time discontinuity in permittivity

N. K. Sakhnenko, A. G. Nerukh, Kharkov National University of Radio Electronics, Ukraine

In this paper we consider circular cavity consisting of a set of concentric rings with time varying dielectric permittivity. We explore how the transients evolve from the complex interaction of reflections occurring at the multiple dielectric interfaces. A closed form solution is obtained for the electric field component by applying the Laplace transform directly to the wave equation and enforcing the corresponding initial and boundary conditions.

Optical control of ring modes using tandem quasi-stadium laser diodes

T. K. Sasaki, T. Fukushima, Y. Nakae, M. Choi and T. Harayama, ATR Wave Engineering Laboratories, Japan

We present experimental studies on two-dimensional microcavity laser diodes with quasi-stadium shapes. The quasi-stadium laser resonators consist of two curved end mirrors and two long, straight, sidewall mirrors that have a much richer variety of lasing modes than conventional two mirror resonators. In a previous work, two kinds of lasing modes under a confocal resonator condition: beam propagation mode along the cavity axis and bidirectional beam propagation mode along a closed ring trajectory were obtained. Controlling the lasing modes by using external optical injection is an interesting attempt for applying microcavity lasers to an integrated optical circuit. In order to demonstrate controlling directional emissions corresponding to the ring trajectory modes by using external optical injection, we fabricate the AlGaAs/GaAs single-quantum-well tandem quasi-stadium laser diodes consist of the front slave and the rear master laser diodes. The geometry of the laser cavities have been defined by using a lithography system and a reactive-ion-etching technique.

The etched facet with sufficiently smooth curves and verticalness has been formed by the reactive ion etching technique. The optical injection is performed from the master laser to the slave laser. The ring mode switching with the optical injection is evaluated by far-field patterns for the output from the curved end mirror.

Nonlinear effects due to thermo-optical instability in microsphere resonators

C. Schmidt, O. Egorov, A. Chipouline, T. Pertsch, F. Lederer, Friedrich-Schiller-Universität Jena, Germany
A. Tünnermann, Fraunhofer Institute for Applied Optics & Precision Engineering, Germany
L. Deych, City University of New York, USA

Broadening of the resonance coupling peaks and their shifting have been observed in the tests of light coupling into the high-Q microspherical resonators. The both effects have been explained by thermo-optical nonlinearity causing resonance instability.

Tunable high-Q directional random laser from a planar random microcavity

Q. Song, S. Xiao, X. Zhou, L. Liu, L. Xu, Fudan University, China
Y. Wu, Z. Wang, Tongji University, China

Planar photonic crystal microcavity has a conventional cavity structure which is used to enhance photoluminescence. However, the divergence angle of the emitted laser beam from a planar microcavity with a micron-thick defect layer is generally very large because the localization of light in one dimension can not totally suppress the modes in other directions, and the cavity quality factor Q of such devices is low (~100) and determined thoroughly by the reflectivity of the distributed Bragg reflector (DBR). Recently, we proposed a new cavity structure which was a hybrid cavity combining a planar photonic crystal microcavity and a two-dimensional random cavity defect layer. In the new developed microcavity structure, photons inside the hybrid cavity are trapped 3-dimensionally. Therefore, optical modes of the cavity were significantly reduced. Consequently, the laser threshold, divergence angle of emitted laser beam, and the spectral linewidth of the laser emission was substantially reduced by two-fold confinement effects from transverse random cavities and vertical planar microcavity.
In this paper, we demonstrated a wavelength tunable planar random microcavity laser. We used dye doped liquid crystal as the gain layer so that the defect mode position can be easily temperature tuned. We reported a nearly single mode ultra-narrow linewidth laser emission from the optically pumped hybrid cavity structure. The 0.03 nm linewidth (corresponding to Q>20000) is about two orders of magnitude narrower than that from a conventional planar microcavity. Tunable random laser emission was observed when the environment temperature was slightly increased.

Generalized Sagnac effect in rotating optical cavities

S. Sunada, T. Harayama and T. Miyasaka, ATR Wave Engineering Laboratories, Japan

he Sagnac effect is the phase (frequency) difference induced by rotation between counter-propagating waves in ring interferometers (cavities), which is at rest in a rotating frame of reference. The effect has been studied as one of the basic and interesting problems of electromagnetism in accelerated frames, and also, from the viewpoint of applications to optical gyros. Today, the effect has become the basis of the operation of optical gyros, such as fiber-optic gyro or ring laser gyro.

The conventional theory of the Sagnac effect has established on the basis of the following assumptions: (i) The ray-wave correspondence of resonant modes in optical cavities. The theory assumes that there exists a closed (ring) trajectory and the resonant modes localize around the trajectory in ring cavities. (ii) The equivalence of the description for resonance modes by standing waves and propagating waves. The assumption is valid when the cavity-size is much larger than the size of the wavelength of the light. So far, it has been believed that the Sagnac effect can be observed only in ring cavities, based on the assumptions (i) and (ii).

Recently, however, we have established the theory of rotating optical cavities without the assumptions (i) and (ii), based on electromagnetic equations of naturally covariant form. In the present study, by using the theoretical approach, we discuss the effect of rotation in the case which does not satisfy the assumption (i) as well as (ii). We show that, even when the resonant modes of an optical cavity are wave-chaotic, degenerate resonant frequency of those modes split into different frequencies due to the rotation of the cavity. The frequency difference is proportional to the rotation rate, although the splitting resonant modes are still wave-chaotic, which do not have any corresponding counter-propagating waves as well as ray-dynamical counterparts. This result cannot be predicted by the conventional theory of the Sagnac effect.

High quality direct photo-patterned microdisk lasers with organic/inorganic hybrid materials

X. Wu, Q. Song, H. Li, Z. He, Y. Zhang, L. Liu, L. Xu, Fudan University, China

Optical microcavities are widely studied because they have many applications in fundamental physics, nonlinear optics, optical communication, and bio-sensing. At present, microcavity materials can be classified as two families: inorganic and organic materials. Organic microcavities usually have much lower Q value, mostly due to the difficulties in obtaining very smooth cavity boundaries even with proper thermal reflow after complex patterning. Luminescent conducting polymers and dye-doped polymer 2-D microdisk lasers with different shapes were created by microlithography and O2 reactive ion etching steps. So far the achieved Q values from organic microdisk lasers are between several hundred and 10000.

Recently, the sol-gel technology based on the wet processes at low temperature has proven to be one promising approach to produce low-cost organic-inorganic glass integrated optical devices. Photosensitive organic-inorganic hybrid materials can be applied for direct photo-fabrication of optical waveguide devices. Their optical properties such as refractive index can be precisely controlled by selecting the functionality of organic constituents and metal oxide composition. In this work, sol-gel organic-inorganic hybrid microdisk-on-chip technique based on the direct UV patterning and wet etching technique was used to fabricate microdisk lasers on silicon substrate. One-step patterning produces high quality microlaser arrays for experimental study. Moreover, it was found that a thin polymer cladding on the microdisk can obviously improve the cavity boundary smoothness and thus increase the Q value of the cavity to as high as 12000. The organic/inorganic hybrid matrix also enables many other gain materials such as quantum dots and organic semiconductors to be incorporated.

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

Y.-D. Yang, Y.-Z. Huang, and Q. Chen, Institute of Semiconductors, China

The mode characteristics of TE and TM whispering-gallery modes (WGMs) are numerically investigated by 3-D FDTD simulation for 3-D semiconductor cylinder, square, and equilateral triangle microresonators. We find that the Q-factors of TM WGMs are much larger than those of TE WGMs. For microcylinders with vertical semiconductor waveguidings, TM WGMs can have Q-factor over 104 at the radius of the microcylinder of 1 mkm and the vertical refractive index distribution of 3.17/3.4/3.17. The Q-factors of TE WGMs are much smaller than that of TM WGMs in the semicondcutor microcylinders. The variations of mode wavelengths and Q-factors for TE and TM WGMs with the refractive index of the cladding layer clearly show the mode coupling between the TE WGMs and the radiation and guided modes in the microwire of the cladding layer. The reason of the absent of vertical mode-coupling radiation loss for TM WGMs is that the mode wavelengths of TM WGMs are larger than the cut-off wavelengths of the radiated HE and EH modes with the same azimuthal and radial mode numbers in the microwire of the cladding layer (Phys. Rev. A, 75, 013817(2007)). Similar results are obtained for TE and TM WGMs in the 3-D semiconductor square and equilateral triangle microrersonators. Micro-lasers and single photon sources based on TM WGMs can be expected using semiconductor microresonators with high current injection efficiency.

Efficient nonresonant optical pumping of a deformed microcavity based on ray and wave chaos

J. Yang, S.-B. Lee, J.-B. Shim, S. Moon, J.-H. Lee, and K. An, Seoul National University, Korea
S. W. Kim, Pusan National University, Korea

Optical pumping is often used for microcavity lasers for its easy implementation and relatively high efficiency. In circular microcavities, an optical beam or a ray refracted in immediately exits the cavity by subsequent refraction due to the cavity symmetry. However, in deformed microcavities a ray can be injected in and it can circulate near the cavity boundary for many round trips due to the asymmetry imposed by the cavity boundary. We have demonstrated very efficient nonresonant optical pumping of high-Q scar modes in a two-dimensional quadrupole-deformed microlaser. Our microlaser was made of a liquid jet of ethanol doped with Rhodamine 6G dye at a concentration of 10-4 mol/l with an effective radius of 15.m. The threshold pump power for lasing in a particular scar mode was measured for various pumping angles. Up to three-fold reduction in the laser threshold was achieved at a properly chosen pumping angle. The experimental results could be understood in terms of ray and wave chaos; the results were consistent with ray tracing and wave overlap integral calculations. The present nonresonant pumping technique can be applied to microlasers and filters made of asymmetrical resonant cavities.