high-Q Whispering Gallery Mode Research Articles

Designing arbitrary-shaped whispering-gallery cavities based on transformation optics.

A novel approach to designing anisotropic whispering gallery modes in gradient index cavities has been reported recently. These cavities, called transformation cavities, can support high-Q whispering gallery modes with directional emission. However, it is usually difficult to find the desired conformal mapping, and it may contain unwanted singularities inside. We show that arbitrary-shaped transformation cavities can be designed by virtue of a quasi-conformal mapping method without confronting such problems. Even though the quasi-conformal mapping method is exploited, we verify that the resulting mappings in our case are strictly conformal. As a demonstration, Q-factor, near field intensity, far field pattern, and phase space description of resonant modes formed in so-designed quadrupole-shaped transformation cavities are presented.

Whispering-gallery mode hexagonal micro-/nanocavity lasers [Invited

Whispering-gallery-mode (WGM) hexagonal optical micro-/nanocavities can be utilized as high-quality (Q) resonators for realizing compact-size low-threshold lasers. In this paper, the progress in WGM hexagonal micro-/nanocavity lasers is reviewed comprehensively. High-Q WGMs in hexagonal cavities are divided into two kinds of resonances propagating along hexagonal and triangular periodic orbits, with distinct mode characteristics according to theoretical analyses and numerical simulations; however, WGMs in a wavelength-scale nanocavity cannot be well described by the ray model. Hexagonal micro-/nanocavity lasers can be constructed by both bottom-up and top-down processes, leading to a diversity of these lasers. The ZnO- or nitride-based semiconductor material generally has a wurtzite crystal structure and typically presents a natural hexagonal cross section. Bottom-up growth guarantees smooth surface faceting and hence reduces the scattering loss effectively. Laser emissions have been successfully demonstrated in hexagonal micro-/nanocavities synthesized with various materials and structures. Furthermore, slight deformation can be easily introduced and precisely controlled in top-down fabrication, which allows lasing-mode manipulation. WGM lasing with excellent single-transverse-mode property was realized in waveguide-coupled ideal and deformed hexagonal microcavity lasers.

Anomalous blue-shift of terahertz whispering-gallery modes via dielectric and metallic tuning.

The vast majority of resonant systems show a red-shift for the resonance frequency when a perturbation, e.g.,losses, is introduced to the system. In contrast, here we report for the first time, to the best of our knowledge, 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 frequency range with coherent continuous-wave spectroscopy. The results establish dielectric and metallic tuning as a novel and viable approach to tune high-quality WGMs and provide valuable insights into the anomalous blue-shift of WGM cavity systems. The tuning capabilities for these compact monolithic resonators are of significant interest for fundamental science and technological applications alike.

Long Period Grating-Based Fiber Coupling to WGM Microresonators.

A comprehensive model for designing robust all-in-fiber microresonator-based optical sensing setups is illustrated. The investigated all-in-fiber setups allow light to selectively excite high-Q whispering gallery modes (WGMs) into optical microresonators, thanks to a pair of identical long period gratings (LPGs) written in the same optical fiber. Microspheres and microbubbles are used as microresonators and evanescently side-coupled to a thick fiber taper, with a waist diameter of about 18 µm, in between the two LPGs. The model is validated by comparing the simulated results with the experimental data. A good agreement between the simulated and experimental results is obtained. The model is general and by exploiting the refractive index and/or absorption characteristics at suitable wavelengths, the sensing of several substances or pollutants can be predicted.

Eigen-frequencies of whispering gallery modes of disk dielectric resonators: a dimensional quantization method

A method for calculation of the resonant frequencies as well as free spectral range was developed for the high-Q whispering gallery mode disk dielectric resonators. The method is based on application of the size quantization to the dispersion equation derived for an infinite dielectric cylinder. The size quantization is caused by the requirement of the phase balance for standing waves in the resonator.

Nonlinear photonics with high-Q whispering-gallery-mode resonators

High- and ultrahigh-Q whispering-gallery mode resonators have the capability to trap photons by total internal reflection for a duration ranging from nanoseconds to milliseconds. These exceptionally long photon lifetimes enhance the light–matter interactions at all scales, namely at the electronic, molecular, and lattice levels. As a consequence, nonlinear photon scattering can be triggered with very low threshold powers, down to a few microwatts. The possibility to efficiently harness photon–photon interactions with a system optimizing size, weight, power, and cost constraints has created a new, quickly thriving research area in photonics science and technology. This topic is inherently cross-disciplinary, as it stands at the intersection of nonlinear and quantum optics, crystallography, optoelectronics, and microwave photonics. From a fundamental perspective, high-Q whispering-gallery mode resonators have emerged as an ideal platform to investigate light–matter interactions in nonlinear bulk materials. From an applied viewpoint, technological applications include time-metrology, aerospace engineering, coherent optical fiber communications, or nonclassical light generation, among others. The aim of this paper is to provide an overview of the most recent advances in this area, which is increasingly gaining importance in contemporary photonics.

Self-injection locking of a laser diode to a high-Q WGM microresonator

We present the analysis of the self-injection locking of a single-frequency laser diode to a high-Q whispering gallery mode (WGM) microresonator with Rayleigh backscattering. Simple analytical formulas for the width of the locking band and resulting laser linewidth are derived.

Counting statistics of chaotic resonances at optical frequencies: Theory and experiments.

A deformed dielectric microcavity is used as an experimental platform for the analysis of the statistics of chaotic resonances, in the perspective of testing fractal Weyl laws at optical frequencies. In order to surmount the difficulties that arise from reading strongly overlapping spectra, we exploit the mixed nature of the phase space at hand, and only count the high-Q whispering-gallery modes (WGMs) directly. That enables us to draw statistical information on the more lossy chaotic resonances, coupled to the high-Q regular modes via dynamical tunneling. Three different models [classical, Random-Matrix-Theory (RMT) based, semiclassical] to interpret the experimental data are discussed. On the basis of least-squares analysis, theoretical estimates of Ehrenfest time, and independent measurements, we find that a semiclassically modified RMT-based expression best describes the experiment in all its realizations, particularly when the resonator is coupled to visible light, while RMT alone still works quite well in the infrared. In this work we reexamine and substantially extend the results of a short paper published earlier [L. Wang et al., Phys. Rev. E 93, 040201(R) (2016)2470-004510.1103/PhysRevE.93.040201].

Fabrication of Lasing Whispering Gallery Mode Microresonators by Controllable Injection Method

Dye-doped polymer microdroplet resonators were fabricated by injecting dye solutions into a low refractive index UV curable polymer. The self-assembled microdroplets had the various sizes ranging from 5 to 200 μm. Pumped by a pulse laser, whispering-gallery-mode (WGM) lasing emission from the microresonators was achieved. Experimental results show that the microresonators had the advantages of high-Q factors, low lasing thresholds, and good long-term stabilities. The injection method can provide a promising approach for fabricating the high-Q WGM microresonators, which had some potential applications in the fields of tunable microlasers and on-chip biosensing system.

Highly Efficient Integrated Generator of Tripartite Entanglement from χ (2) Whispering Gallery Microresonator

Whispering gallery microresonator (WGM) filled with nonlinear material has proven to be valuable for enhancing nonlinear optical effects. Here we explore the production of the pump-signal-idler tripartite entanglement based on the integrated high-Q whispering gallery mode cavities filled with lithium niobate. Our theoretical analysis about the entanglement condition when the van Loock and Furusawa criteria are violated paves the way for future investigation of integrated entanglement based on nonlinear high-Q microresonator. In addition, we present parameters used in our designed generator and our theoretical model is highly expansible to further exploration of entanglement over general χ (2) whispering gallery microresonator.

Refractometry-based air pressure sensing using glass microspheres as high-Q whispering-gallery mode microresonators

In this work a refractometric air pressure sensing platform based on spherical whispering-gallery mode microresonators is presented and analyzed. The sensitivity of this sensing approach is characterized by measuring the whispering-gallery mode spectral shifts caused by a change of air refractive index produced by dynamic sinusoidal pressure variations that lie between extremes of ±1.8kPa. A theoretical frame of work is developed to characterize the refractometric air pressure sensing platform by using the Ciddor equation for the refractive index of air, and a comparison is made against experimental results for the purpose of performance evaluation.

On-chip asymmetric microcavity optomechanics.

High quality factor (Q) optical resonators have enabled rapid growth in the field of cavity-enhanced, radiation pressure-induced optomechanics. However, because research has focused on axisymmetric devices, the observed regenerative excited mechanical modes are similar. In the present work, a strategy for fabricating high-Q whispering gallery mode microcavities with varying degrees of asymmetry is developed and demonstrated. Due to the combination of high optical Q and asymmetric device design, two previously unobserved modes, the asymmetric cantilever and asymmetric crown mode, are demonstrated with sub-mW thresholds for onset of oscillations. The experimental results are in good agreement with computational modeling predictions.

Free-space coupling efficiency in a high-Q deformed optical microcavity.

The free-space coupling technique provides a promising means to excite high-Q whispering gallery modes in deformed microcavities, but the precise quantification of the coupling efficiency remains challenging because of the non-Lorentzian spectral lineshape in the transmission and the partial collection in emission. Here, we experimentally identify the free-space coupling efficiency by measuring the threshold of stimulated Raman scattering in a slightly deformed microcavity. The measured efficiency is up to 30%. Furthermore, the dependence of the coupling efficiency on the incident angle is obtained by focusing the laser beam on the microcavity periphery, which is consistent with the prediction of the mode field distribution. Finally, it is experimentally demonstrated that free-space coupling efficiencies remain high even when the focusing beam has been translated several micrometers, both horizontally and vertically.

Light confinement in a low-refraction-index microcavity bonded on a silicon substrate

The trapping of photons in low-refraction-index materials is thought to be prohibited in conventional photonic structures that employ total internal reflection. Specifically, the whispering gallery mode (WGM) microcavity, which is an important optical component, has to rely on a high contrast of the refraction index with the surrounding environment to manifest excellent light confinement. Here, we propose and demonstrate experimentally an optical microcavity structure consisting of a low-refraction-index silica microtoroid directly bonded on a high-refraction-index silicon substrate. The resonant structure supports high-Q fundamental WGMs in both visible and communication bands, while higher-order modes are suppressed significantly due to the strong leakage into the silicon substrate at long wavelengths. The highest measured quality factor exceeds ten million and low-threshold microcavity Raman lasing is also realized.

A batteryless temperature sensor based on high temperature sensitive material

The major challenge in wireless sensor networks is the reduction of energy consumption. Passive wireless sensor network is an attractive solution for measuring physical parameters in harsh environment for large range of applications requiring sensing devices with low cost of fabrication, small size and long term measurement stability. Batteryless temperature sensing techniques are an active research field. The approach developed in our work holds a promising future for temperature sensor applications in order to successfully reduce the energy consumption. The temperature sensor presented in this paper is based on the electromagnetic transduction principle using the integration of the high temperature sensitive material into a passive structure. Variation in temperature makes the dielectric constant of this material changing, and such modification induces variation in the resonant frequencies of high-Q whispering-gallery modes (WGM) in the millimeter-wave frequency range. Following the results achieved, the proposed device shows a linear response to the increasing temperature and these variations can be remotely detected from a radar interrogation.

Low-threshold stimulated Brillouin scattering in high-Q whispering gallery mode tellurite microspheres

We demonstrate the first observation of stimulated Brillouin scattering (SBS) in a high-Q whispering gallery mode tellurite microsphere. Tellurite glass with composition of 70TeO₂-20ZnO-5Na₂O-5La₂O₃ (molar ratio) was prepared in-house using a melt-quenching technique. Moreover, tellurite microspheres with Q in excess of 13 millions at 1550 nm were fabricated by melting tellurite microwires using a CO₂ laser. By pumping the tellurite microspheres with a tunable single frequency laser, SBS is further realized with a threshold as low as 0.58 mW. At last, the beat notes between the pump and the Stokes signals were measured, which indicated the Brillouin frequency shift is at the 8.2 GHz band for our tellurite glass. Our results could propel significant applications utilizing SBS by employing tellurite microspheres.

High-Q whispering gallery modes in a polymer microresonator with broad strain tuning

We have reported the high- Q whispering gallery modes (WGMs) in a polydimethylsiloxane (PDMS) optical microresonators with broad tuning range. The PDMS microresonators are fabricated at the center of two collimating fiber tips, which can be controlled by the piezoelectric stage. Through stretching the fiber stem, the tuning range of WGMs are demonstrated more than 50 nm. Further investigations demonstrated that the WGM shift has a high force sensitivity (~ 19.7 pm/μN) of the gravitation when the microcavity is stretched by a weight. The theoretical analysis reveals that the high force sensitivity of polymer microresonator can be used for the weak force or height measurement.

Optical manipulation in optofluidic microbubble resonators

An optical manipulation system based on optofluidic microbubble resonators (MBR) is proposed. As the high-Q whispering gallery modes (WGMs) are excited in an MBR, the buildup of the field intensity inside the resonator is large enough to trap nanoscale particles. The optical gradient forces generated by the WGMs with different radial orders are investigated numerically. The negative effect of the resonance detuning induced by the particles is taken into account to investigate the optical gradient forces exerting on the particles. By the stability analysis, the WGMs with high radial orders show a better trapping stability under Brownian motion since most of the optical fields reside within the water core.

Stand-off biodetection with free-space coupled asymmetric microsphere cavities.

Asymmetric microsphere resonant cavities (ARCs) allow for free-space coupling to high quality (Q) whispering gallery modes (WGMs) while exhibiting highly directional light emission, enabling WGM resonance measurements in the far-field. These remarkable characteristics make “stand-off” biodetection in which no coupling device is required in near-field contact with the resonator possible. Here we show asymmetric microsphere resonators fabricated from optical fibers which support dynamical tunneling to excite high-Q WGMs, and demonstrate free-space coupling to modes in an aqueous environment. We characterize the directional emission by fluorescence imaging, demonstrate coupled mode effects due to free space coupling by dynamical tunneling, and detect adsorption kinetics of a protein in aqueous solution. Based on our approach, new, more robust WGM biodetection schemes involving microfluidics and in-vivo measurements can be designed.

Analysis of third-order nonlinearity effects in very high-Q WGM resonator cavity ringdown spectroscopy

The time domain coupled-mode theory (CMT) is applied to the analysis of the dynamic of third-order optical nonlinear effects in high-finesse whispering-gallery-mode (WGM) resonators. We show that this model is well adapted to the analysis of cavity-ringdown spectroscopy signal under modal-coupling due to Rayleigh backscattering in linear and nonlinear regimes. The experiments are carried out in silica WGM microspheres. Considering thermal and Kerr effects, CMT simulations are in good agreement, with experimental results for input power up to about 1 mW. For well-known optical materials such as silica, this experimental data analysis method can be used to measure the quality factor, the coupling regime, and the mode volume of high-finesse WGM. Furthermore, this technique could be developed to infer linear and nonlinear properties of high-finesse coated WGM microspheres.