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Gallium arsenide optical resonators have been identified as platforms for light-matter interactions ranging from optomechanics to quantum electrodynamics involving nonlinear optics. Here, we present a 5-mm-diameter whispering gallery mode resonator made of undoped gallium arsenide. The fabrication was done using single-point diamond turning followed by polishing with diamond solutions of varying grain size. The resulting resonator was optically characterized to have a quality factor of more than a million.

As the field of terahertz (THz) photonics advances, we present a monolithic gallium arsenide (GaAs) disk-shaped whispering gallery mode resonator that has potential as a component in THz nonlinear optics. GaAs is a material with significant optical nonlinearity which can be enhanced when the crystal is shaped into a microdisk resonator. A 4-mm-disk-resonator was fabricated using single-point diamond turning and was characterised to obtain a quality (Q) factor of 2.2k at ~150 GHz and 1.4k at ~300 GHz. We also demonstrated the blue-shifting of up to ~0.3 GHz of the THz modes using a block of metal. This post-fabrication degree of freedom could be useful for phase-matching requirements for nonlinear optical processes, such as detection based on optical up-conversion of THz radiation. Such a compact, tunable and efficient device could be integrated into nonlinear photonic platforms for THz generation, manipulation and detection., Comment: 8 pages, 5 figures

We showcase an erbium-doped whispering-gallery-mode resonator with optical modes that display intrinsic quality factors better than $10^8$ (linewidths less than 2 MHz), and coupling strengths to collective erbium transitions of up to 2$\pi\times$1.2 GHz - enough to reach the ensemble strong coupling regime. Our optical cavity sits inside a microwave resonator, allowing us to probe the spin transition which is tuned by an external magnetic field. We show a modified optically detected magnetic resonance measurement that measures population transfer by a change in coupling strength rather than absorption coefficient. This modification was enabled by the strong coupling to our modes, and allows us to optically probe the spin transition detuned by more than the inhomogeneous linewidth. We contrast this measurement with electron paramagnetic resonance to experimentally show that our optical modes are confined in a region of large microwave magnetic field and we explore how such a geometry could be used for coherent microwave-optical transduction., Comment: 8 pages, 6 figures

In this work, we analyze the first whispering gallery mode resonator (WGMR) made from monocrystalline yttrium lithium fluoride (YLF). The disc-shaped resonator is fabricated using single-point diamond turning and exhibits a high intrinsic quality factor ($Q$) on the order of $10^9$. Moreover, we employ a novel method based on microscopic imaging of Newton's rings through the back of a trapezoidal prism. This method can be used to evanescently couple light in to a WGMR and monitor the separation between the cavity and the coupling prism. Accurately calibrating the distance between a coupling prism and a WGMR is desirable as it can be used to improve experimental control and conditions, i.e., accurate coupler gap calibration can aid in tuning into desired coupling regimes and can be used to avoid potential damage caused by collisions between the coupling prism and the WGMR. Here, we use two different trapezoidal prisms together with the high-$Q$ YLF WGMR to demonstrate and discuss this method., Comment: Main text (5 pages, 3 figures) Supplemental document (2 pages, 2 figures)

The nonlinear scattering of a linear optical wave from a conservative soliton has been widely studied in optical fibers as a mechanism for nonlinear frequency conversion. Here we extend this analysis to consider the scattering of an externally injected probe wave from a dissipative Kerr cavity soliton circulating in a Kerr microresonator. We demonstrate, both theoretically and experimentally, that this nonlinear interaction can be harnessed for useful expansion of the soliton frequency comb via the formation of a secondary idler comb. We explore the physics of the process, showing that the phase detuning of the injected probe from a cavity resonance plays a key role in setting the central frequency of the idler comb, thus providing a convenient parameter through which to control the spectral envelope of that comb. Our results elucidate the dynamics that govern the interactions between dissipative Kerr cavity solitons and externally injected probe waves, and could prove useful in the design of future Kerr frequency comb systems by enabling the possibility to provide high-power comb lines in a specified spectral region simply through the injection of a suitably chosen probe., Comment: 7 pages, 5 figures

Titanium doped sapphire (Ti:sapphire) is a laser gain material with broad gain bandwidth benefiting from the material stability of sapphire. These favorable characteristics of Ti:sapphire have given rise to femtosecond lasers and optical frequency combs. Shaping a single Ti:sapphire crystal into a millimeter sized high quality whispering gallery mode resonator ($Q\sim10^8$) reduces the lasing threshold to 14.2 mW and increases the laser slope efficiency to 34%. The observed lasing can be both multi-mode and single-mode. This is the first demonstration of a Ti:sapphire whispering-gallery laser. Furthermore, a novel method of evaluating the gain in Ti:sapphire in the near infrared region is demonstrated by introducing a probe laser with a central wavelength of 795 nm. This method results in decreasing linewidth of the modes excited with the probe laser, consequently increasing their $Q$. These findings open avenues for the usage of whispering gallery mode resonators as cavities for the implementation of compact Ti:sapphire lasers. Moreover, Ti:sapphire can also be utilized as an amplifier inside its gain bandwidth by implementing a pump-probe configuration., Comment: Main text (13 pages, 7 figures) Supplemental document (11 pages, 9 figures)

Small perturbations in the dielectric environment around a high quality whispering gallery mode resonator usually lead to a frequency shift of the resonator modes directly proportional to the polarizability of the perturbation. Here, we report experimental observations of strong frequency shifts that can be opposite and even exceed the contribution of the perturbations' polarizability. The mode frequencies of a lithium niobate whispering gallery mode resonator are shifted using substrates of refractive indices ranging from 1.50 to 4.22. Both blue- and red-shifts are observed, as well as an increase in mode linewidth, when substrates are moved into the evanescent field of the whispering gallery mode. We compare the experimental results to a theoretical model by Foreman et al. and provide an additional intuitive explanation based on the Goos-H\"anchen shift for the optical domain., Comment: 7 pages, 4 figures

The quantum bits (qubits) on which superconducting quantum computers are based have energy scales corresponding to photons with GHz frequencies. The energy of photons in the gigahertz domain is too low to allow transmission through the noisy room-temperature environment, where the signal would be lost in thermal noise. Optical photons, on the other hand, have much higher energies, and signals can be detected using highly efficient single-photon detectors. Transduction from microwave to optical frequencies is therefore a potential enabling technology for quantum devices. However, in such a device the optical pump can be a source of thermal noise and thus degrade the fidelity; the similarity of input microwave state to the output optical state. In order to investigate the magnitude of this effect we model the sub-Kelvin thermal behavior of an electro-optic transducer based on a lithium niobate whispering gallery mode resonator. We find that there is an optimum power level for a continuous pump, whilst pulsed operation of the pump increases the fidelity of the conversion., Comment: 12 pages, 4 figures

Fiber optic communication is the backbone of our modern information society, offering high bandwidth, low loss, weight, size and cost, as well as an immunity to electromagnetic interference. Microwave photonics lends these advantages to electronic sensing and communication systems, but - unlike the field of nonlinear optics - electro-optic devices so far require classical modulation fields whose variance is dominated by electronic or thermal noise rather than quantum fluctuations. Here we present a cavity electro-optic transceiver operating in a millikelvin environment with a mode occupancy as low as 0.025 $\pm$ 0.005 noise photons. Our system is based on a lithium niobate whispering gallery mode resonator, resonantly coupled to a superconducting microwave cavity via the Pockels effect. For the highest continuous wave pump power of 1.48 mW we demonstrate bidirectional single-sideband conversion of X band microwave to C band telecom light with a total (internal) efficiency of 0.03 % (0.7 %) and an added output conversion noise of 5.5 photons. The high bandwidth of 10.7 MHz combined with the observed very slow heating rate of 1.1 noise photons s$^{-1}$ puts quantum limited pulsed microwave-optics conversion within reach. The presented device is versatile and compatible with superconducting qubits, which might open the way for fast and deterministic entanglement distribution between microwave and optical fields, for optically mediated remote entanglement of superconducting qubits, and for new multiplexed cryogenic circuit control and readout strategies., Comment: 16 pages, 11 figures

We report on the experimental observation of internally-pumped parametric oscillation in a high-Q lithium niobate microresonator under conditions of natural phase-matching. Specifically, launching near-infrared pump light around 1060 nm into a $z$-cut congruent lithium niobate microresonator, we observe the generation of optical sidebands around the input pump under conditions where second-harmonic generation is close to natural phase-matching. We find that a wide range of different sideband frequency shifts can be generated by varying the experimental parameters. Under particular conditions, we observe the cascaded generation of several equally-spaced sidebands around the pump -- the first steps of optical frequency comb generation via cavity-enhanced second-harmonic generation., Comment: 5 pages, 5 figures; a wider range of indicative results added to Fig. 3 and text changed accordingly in version 2

Photon pairs and heralded single photons, obtained from cavity-assisted parametric down-conversion (PDC), play an important role in quantum communications and technology. This motivated a thorough study of the spectral and temporal properties of parametric light, both above the Optical Parametric Oscillator (OPO) threshold, where the semiclassical approach is justified, and deeply below it, where the linear cavity approximation is applicable. The pursuit of a higher two-photon emission rate leads into an interesting intermediate regime where the OPO still operates considerably below the threshold but the nonlinear cavity phenomena cannot be neglected anymore. Here, we investigate this intermediate regime and show that the spectral and temporal properties of the photon pairs, as well as their emission rate, may significantly differ from the widely accepted linear model. The observed phenomena include frequency pulling and broadening in the temporal correlation for the down-converted optical fields. These factors need to be taken into account when devising practical applications of the high-rate cavity-assisted SPDC sources.

Triplet down conversion, the process of converting one high-energy photon into three low-energy photons, may soon be experimentally feasible due to advances in optical resonator technology. We use quantum phase-space techniques to analyse the process of degenerate intracavity triplet down conversion by solving stochastic differential equations within the truncated positive-P representation. The time evolution of both intracavity mode populations are simulated, and the resulting steady-states are examined as a function of the pump intensity. Quantum effects are most pronounced in the region immediately above the semi-classical pumping threshold, where our numerical results differ significantly from semi-classical predictions. Regimes of measurable squeezing and bipartite entanglement are identified from steady-state spectra of the cavity output fields. We validate the truncated positive-P description against Monte Carlo wave function simulations, finding good agreement for low mode populations., Comment: 9 pages, 9 figures

Quantum information technology based on solid state qubits has created much interest in converting quantum states from the microwave to the optical domain. Optical photons, unlike microwave photons, can be transmitted by fiber, making them suitable for long distance quantum communication. Moreover, the optical domain offers access to a large set of very well developed quantum optical tools, such as highly efficient single-photon detectors and long-lived quantum memories. For a high fidelity microwave to optical transducer, efficient conversion at single photon level and low added noise is needed. Currently, the most promising approaches to build such systems are based on second order nonlinear phenomena such as optomechanical and electro-optic interactions. Alternative approaches, although not yet as efficient, include magneto-optical coupling and schemes based on isolated quantum systems like atoms, ions or quantum dots. In this Progress Report, we provide the necessary theoretical foundations for the most important microwave-to-optical conversion experiments, describe their implementations and discuss current limitations and future prospects., Comment: 17 Pages, 8 Figures

Squeezed vacuum states enable optical measurements below the quantum limit and hence are a valuable resource for applications in quantum metrology and also quantum communication. However, most available sources require high pump powers in the milliwatt range and large setups, which hinders real world applications. Furthermore, degenerate operation of such systems presents a challenge. Here, we use a compact crystalline whispering gallery mode resonator made of lithium niobate as a degenerate parametric oscillator. We demonstrate about 1.4 dB noise reduction below the shot noise level for only 300 $\mu\text{W}$ of pump power in degenerate single mode operation. Furthermore, we report a record pump threshold as low as 1.35 $\mu\text{W}$. Our results show that the whispering gallery based approach presents a promising platform for a compact and efficient source for nonclassical light., Comment: $\copyright$ 2019 Optical Society of America. Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained. All other rights are reserved

Parametric nonlinear optical processes allow for the generation of new wavelengths of coherent electromagnetic radiation. Their ability to create radiation that is widely tunable in wavelength is particularly appealing, with applications ranging from spectroscopy to quantum information processing. Unfortunately, existing tunable parametric sources are marred by deficiencies that obstruct their widespread adoption. Here we show that ultrahigh-Q crystalline microresonators made of magnesium fluoride can overcome these limitations, enabling compact and power-efficient devices capable of generating clean and widely-tunable sidebands. We consider several different resonators with carefully engineered dispersion profiles, achieving hundreds of nanometers of sideband tunability in each device when driven with a standard low-power laser at 1550 nm. In addition to direct observations of discrete tunability over an entire optical octave from 1083 nm to 2670 nm, we record signatures of mid-infrared sidebands at almost 4000 nm. The simplicity of the devices considered -- compounded by their remarkable tunability -- paves the way for low-cost, widely-tunable sources of electromagnetic radiation., Comment: 10 pages, 4 figures, submitted 1st of November 2018

The vast majority of resonant systems show a red-shift for the resonance frequency when a perturbation, e.g. losses, are introduced to the system. In contrast, here we report for the first time the experimental demonstration of both red- and anomalous blue-shifting of whispering-gallery modes (WGMs) using dielectric and metallic substrates. The maximum blue-shift is more than three times as large as the expected red-shift, proving that the anomalous blue-shift is more than a peculiar curiosity. The experiments are performed in the terahertz (THz) frequency range with coherent continuous-wave spectroscopy. The results establish dielectric and metallic tuning as a novel, and viable approach to tune high quality (high-Q) WGMs, and provide valuable insights into the anomalous blue-shift of WGM cavity systems. The tuning capabilities for these compact monolithic resonators is of significant interest for fundamental science and technological applications alike.

High speed optical telecommunication is enabled by wavelength division multiplexing, whereby hundreds of individually stabilized lasers encode the information within a single mode optical fiber. In the seek for larger bandwidth the optical power sent into the fiber is limited by optical non-linearities within the fiber and energy consumption of the light sources starts to become a significant cost factor. Optical frequency combs have been suggested to remedy this problem by generating multiple laser lines within a monolithic device, their current stability and coherence lets them operate only in small parameter ranges. Here we show that a broadband frequency comb realized through the electro-optic effect within a high quality whispering gallery mode resonator can operate at low microwave and optical powers. Contrary to the usual third order Kerr non-linear optical frequency combs we rely on the second order non-linear effect which is much more efficient. Our result uses a fixed microwave signal which is mixed with an optical pump signal to generate a coherent frequency comb with a precisely determined carrier separation. The resonant enhancement enables us to operate with microwave powers three order magnitude smaller than in commercially available devices. We can expect the implementation into the next generation long distance telecommunication which relies on coherent emission and detection schemes to allow for operation with higher optical powers and at reduced cost.

Recent experiments have demonstrated the generation of widely-spaced parametric sidebands that can evolve into "clustered" optical frequency combs in Kerr microresonators. Here we describe the physics that underpins the formation of such clustered comb states. In particular, we show that the phase-matching required for the initial sideband generation is such that (at least) one of the sidebands experiences anomalous dispersion, enabling that sideband to drive frequency comb formation via degenerate and non-degenerate four-wave mixing. We validate our proposal through a combination of experimental observations made in a magnesium-fluoride microresonator and corresponding numerical simulations. We also investigate the coherence properties of the resulting clustered frequency combs. Our findings provide valuable insights on the generation and dynamics of widely-spaced parametric sidebands and clustered frequency combs in Kerr microresonators., Comment: 5 pages, 4 figures

We demonstrate second harmonic generation (SHG) in an $x$-cut congruent lithium niobate (LN) whispering gallery mode resonator. We first show theoretically that independent control of the coupling of the pump and signal modes is optimal for high conversion rates. A scheme based on our earlier work in Ref. [1] is then implemented experimentally to verify this. Thereby we are able to improve on the efficiency of SHG by more than an order of magnitude by selectively out-coupling using a LN prism, utilizing the birefringence of it and the resonator in kind. We report 5.28%/mW efficiency for SHG from 1555.4 nm to 777.7 nm., Comment: 6 pages, 4 figures

Whispering gallery mode (WGM) resonators are an important building block for linear, nonlinear and quantum optical experiments. In such experiments, independent control of coupling rates to different modes can lead to improved conversion efficiencies and greater flexibility in generation of non-classical states based on parametric down conversion. In this work, we introduce a scheme which enables selective out-coupling of WGMs belonging to a specific polarization family, while the orthogonally polarized modes remain largely unperturbed. Our technique utilizes material birefringence in both the resonator and coupler such that a negative (positive) birefringence allows selective coupling to TE (TM) polarized WGMs. We formulate a new coupling condition suitable for describing the case where the refractive indices of the resonator and the coupler are almost the same, from which we derive the criterion for polarization-selective coupling. We experimentally demonstrate our proposed method using a lithium niobate disk resonator coupled to a lithium niobate prism, where we show a 22dB suppression of coupling to TM modes relative to TE modes.

Optical whispering gallery mode (WGM) resonators are a powerful and versatile tool used in many branches of science. Fine tuning of the central frequency and line width of individual resonances is however desirable in a number of applications including frequency conversion, optical communications and efficient light-matter coupling. To this end we present a detailed theoretical analysis of dielectric tuning of WGMs supported in axisymmetric resonators. Using the Bethe-Schwinger equation and adopting an angular spectrum field representation we study the resonance shift and mode broadening of high $Q$ WGMs when a planar dielectric substrate is brought close to the resonator. Particular focus is given to use of a uniaxial substrate with an arbitrarily aligned optic axis. Competing red and blue resonance shifts ($\sim 30$ MHz), deriving from generation of a near field material polarisation and back action from the radiation continuum respectively, are found. Anomalous resonance shifts can hence be observed depending on the substrate material, whereas mode broadening on the order of $\sim 50$ MHz can also be simply realised. Furthermore, polarisation selective coupling with extinction ratios of $> 10^4$ can be achieved when the resonator and substrate are of the same composition and their optic axes are chosen correctly. Double refraction and properties of out-coupled beams are also discussed.

Optical Whispering Gallery Modes (WGMs) derive their name from a famous acoustic phenomenon of guiding a wave by a curved boundary observed nearly a century ago. This phenomenon has a rather general nature, equally applicable to sound and all other waves. It enables resonators of unique properties attractive both in science and engineering. Very high quality factors of optical WGM resonators persisting in a wide wavelength range spanning from radio frequencies to ultraviolet light, their small mode volume, and tunable in- and out- coupling make them exceptionally efficient for nonlinear optical applications. Nonlinear optics facilitates interaction of photons with each other and with other physical systems, and is of prime importance in quantum optics. In this paper we review numerous applications of WGM resonators in nonlinear and quantum optics. We outline the current areas of interest, summarize progress, highlight difficulties, and discuss possible future development trends in these areas., Comment: This is a review paper with 615 references, submitted to J. Opt

Linking classical microwave electrical circuits to the optical telecommunication band is at the core of modern communication. Future quantum information networks will require coherent microwave-to-optical conversion to link electronic quantum processors and memories via low-loss optical telecommunication networks. Efficient conversion can be achieved with electro-optical modulators operating at the single microwave photon level. In the standard electro-optic modulation scheme this is impossible because both, up- and downconverted, sidebands are necessarily present. Here we demonstrate true single sideband up- or downconversion in a triply resonant whispering gallery mode resonator by explicitly addressing modes with asymmetric free spectral range. Compared to previous experiments, we show a three orders of magnitude improvement of the electro-optical conversion efficiency reaching 0.1% photon number conversion for a 10GHz microwave tone at 0.42mW of optical pump power. The presented scheme is fully compatible with existing superconducting 3D circuit quantum electrodynamics technology and can be used for non-classical state conversion and communication. Our conversion bandwidth is larger than 1MHz and not fundamentally limited., Comment: 8 pages, 5 figures; comments welcome!

Quantum repeaters rely on an interfacing of flying qubits with quantum memories. The most common implementations include a narrowband single photon matched in bandwidth and central frequency to an atomic system. Previously, we demonstrated the compatibility of our versatile source of heralded single photons, which is based on parametric down-conversion in a triply-resonant whispering-gallery mode resonator, with alkaline transitions [Schunk et al., Optica 2, 773 (2015)]. In this paper, we analyze our source in terms of phase matching, available wavelength-tuning mechanisms, and applications to narrow-band atomic systems. We resonantly address the D1 transitions of cesium and rubidium with this optical parametric oscillator pumped above its oscillation threshold. Below threshold, the efficient coupling of single photons to atomic transitions heralded by single telecom-band photons is demonstrated. Finally, we present an accurate analytical description of our observations. Providing the demonstrated flexibility in connecting various atomic transitions with telecom wavelengths, we show a promising approach to realize an essential building block for quantum repeaters., Comment: 18 pages, 14 figures

Quantum information technology strongly relies on coupling of optical photons with narrowband quantum systems, such as quantum dots, color centers, and atomic systems. This coupling requires matching the optical wavelength and bandwidth to the desired system, which presents a considerable problem for most available sources of quantum light. Here we demonstrate coupling of alkali dipole transitions with a tunable source of photon pairs. Our source is based on spontaneous parametric down-conversion in a triply-resonant whispering-gallery mode resonator. For this, we have developed novel wavelength tuning mechanisms, which allow for a coarse tuning to either cesium or rubidium wavelength with subsequent continuous fine-tuning to the desired transition. As a demonstration of the functionality of the source, we performed a heralded single photon measurement of the atomic decay. We present a major advance in controlling the spontaneous down-conversion process, which makes our bright source of single photons now compatible with a plethora of narrow-band resonant systems., Comment: 8 pages, 5 figures

We demonstrate a method to perform spectroscopy of near-infrared single photons without the need of dispersive elements. This method is based on a photon energy resolving transition edge sensor and is applied for the characterization of widely wavelength tunable narrow-band single photons emitted from a crystalline whispering gallery mode resonator. We measure the emission wavelength of the generated signal and idler photons with an uncertainty of up to 2 nm., Comment: 4 pages, 4 figures

We present our experiments on refractometric sensing with ultrahigh-Q, crystalline, birefringent magnesium fluoride (MgF$_2$) whispering gallery mode resonators. The difference to fused silica which is most commonly used for sensing experiments is the small refractive index of MgF$_2$ which is very close to that of water. Compared to fused silica this leads to more than 50% longer evanescent fields and a 4.25 times larger sensitivity. Moreover the birefringence amplifies the sensitivity difference between TM and TE type modes which will enhance sensing experiments based on difference frequency measurements. We estimate the performance of our resonators and compare them with fused silica theoretically and present experimental data showing the interferometrically measured evanescent decay and the sensitivity of mm-sized MgF$_2$ whispering gallery mode resonators immersed in water. They show reasonable agreement with the developed theory. Furthermore, we observe stable Q factors in water well above $1 \times 10^8$., Comment: 10 pages, 4 figures

Identifying the mode numbers in whispering-gallery mode resonators (WGMRs) is important for tailoring them to experimental needs. Here we report on a novel experimental mode analysis technique based on the combination of frequency analysis and far-field imaging for high mode numbers of large WGMRs. The radial mode numbers q and the angular mode numbers p=$\ell$-m are identified and labeled via far-field imaging. The polar mode numbers $\ell$ are determined unambiguously by fitting the frequency differences between individual whispering gallery modes (WGMs). This allows for the accurate determination of the geometry and the refractive index at different temperatures of the WGMR. For future applications in classical and quantum optics, this mode analysis enables one to control the narrow-band phase-matching conditions in nonlinear processes such as second-harmonic generation or parametric down-conversion., Comment: 12 pages, 6 figures

We report a highly efficient source of narrow-band photon pairs based on parametric down-conversion in a crystalline whispering gallery mode resonator. Remarkably, each photon of a pair is strictly emitted into a single spatial and temporal mode, as witnessed by Glaubers autocorrelation function. We explore the phase-matching conditions in spherical geometries, and determine the requirements of the single-mode operation. Understanding these conditions has allowed us to experimentally demonstrate a single-mode pair-detection rate of $0.97 \cdot 10^6$ pairs/s per mW pump power per 20 MHz bandwidth without the need of additional filter cavities., Comment: 7 pages, 6 figures

The usual configuration of uniaxial whispering gallery mode resonators is a disk shaped geometry where the optic axis points along the symmetry axis, a so called z-cut resonator. Recently x-cut resonators, where the optic axis lies in the equatorial plane, became of interest as they enable extremely broadband second harmonic generation. In this paper we report on the properties of a more generalized system, the so called angle-cut resonator, where the optic axis exhibits an arbitrary angle against the symmetry axis. We show experimentally that the modal structure and quality factors are similar to common resonators but that the polarization properties differ quite significantly: due to the asymmetry the polarization depends on the equatorial position and is, in general, elliptical.

We present an optical mode solver for a whispering gallery resonator coupled to an adjacent arbitrary shaped nano-particle that breaks the axial symmetry of the resonator. Such a hybrid resonator-nanoparticle is similar to what was recently used for bio-detection and for field enhancement. We demonstrate our solver by parametrically studying a toroid-nanoplasmonic device and get the optimal nano-plasmonic size for maximal enhancement. We investigate cases near a plasmonic resonance as well as far from a plasmonic resonance. Unlike common plasmons that typically benefit from working near their resonance, here working far from plasmonic resonance provides comparable performance. This is because the plasmonic resonance enhancement is accompanied by cavity quality degradation through plasmonic absorption., Comment: Supplementary COMSOL script, see http://www.quantumchaos.de/Media/comsol2013/Supplement_Script_for_Fig.3_Comsol_4.3a.mph

In the Terahertz (THz) domain, we investigate both numerically and experimentally the directional emission of whispering gallery mode resonators that are perturbed by a small scatterer in the vicinity of the resonators rim. We determine quality factor degradation, the modal structure and the emission direction for various geometries. We find that scatterers do allow for directional emission without destroying the resonator's quality factor. This finding allows for new geometries and outcoupling scenarios for active whispering gallery mode structures such as quantum cascade lasers and passive resonators such as evanescent sensors. The experimental results agree well with finite difference time domain simulations.

A numerically efficient Fredholm formulation of the billiard problem is presented. The standard solution in the framework of the boundary integral method in terms of a search for roots of a secular determinant is reviewed first. We next reformulate the singularity condition in terms of a flow in the space of an auxiliary one-parameter family of eigenproblems and argue that the eigenvalues and eigenfunctions are analytic functions within a certain domain. Based on this analytic behavior we present a numerical algorithm to compute a range of billiard eigenvalues and associated eigenvectors by only two diagonalizations., Comment: 15 pages, 10 figures; included systematic study of accuracy with 2 new figures, movie to Fig. 4, http://www.quantumchaos.de/Media/0703030media.avi

Dielectric microcavities based on cylindrical and deformed cylindrical shapes have been employed as resonators for microlasers. Such systems support spiral resonances with finite momentum along the cylinder axis. For such modes the boundary conditions do not separate and simple TM and TE polarization states do not exist. We formulate a theory for the dispersion relations and polarization properties of such resonances for an infinite dielectric rod of arbitrary cross-section and then solve for these quantities for the case of a circular cross-section (cylinder). Useful analytic formulas are obtained using the eikonal (Einstein-Brillouin-Keller) method which are shown to be excellent approximations to the exact results from the wave equation. The major finding is that the polarization of the radiation emitted into the far-field is linear up to a polarization critical angle (PCA) at which it changes to elliptical. The PCA always lies between the Brewster and total-internal-reflection angles for the dielectric, as is shown by an analysis based on the Jones matrices of the spiraling rays., Comment: submitted to JOSA B

Dielectric optical micro-resonators and micro-lasers represent a realization of a wave-chaotic system, where the lack of symmetry in the resonator shape leads to non-integrable ray dynamics. Modes of such resonators display a rich spatial structure, and cannot be classified through mode indices which would require additional constants of motion in the ray dynamics. Understanding and controlling the emission properties of such resonators requires the investigation of the correspondence between classical phase space structures of the ray motion inside the resonator and resonant solutions of the wave equations. We first discuss the breakdown of the conventional eikonal approximation in the short wavelength limit, and motivate the use of phase-space ray tracing and phase space distributions. Next, we introduce an efficient numerical method to calculate the quasi-bound modes of dielectric resonators, which requires only two diagonalizations per N states, where N is approximately equal to the number of half-wavelengths along the perimeter. The relationship between classical phase space structures and modes is displayed via the Husimi projection technique. Observables related to the emission pattern of the resonator are calculated with high efficiency., Comment: 33 pages, 16 figures, RevTeX 4

Recent experiments on similarly shaped polymer micro-cavity lasers show a dramatic difference in the far-field emission patterns. We show for different deformations of the ellipse, quadrupole and hexadecapole that the large differences in the far-field emission patterns is explained by the differing ray dynamics corresponding to each shape. Analyzing the differences in the appropriate phase space for ray motion, it is shown that the differing geometries of the unstable manifolds of periodic orbits are the decisive factors in determining the far-field pattern. Surprisingly, we find that strongly chaotic ray dynamics is compatible with highly directional emission in the far-field., Comment: 14 pages, 16 figures (eps), RevTeX 4, submitted to JOSA B