Whispering-gallery Resonators Research Articles

Magnetic and Electric Solid-State Plasmon Spherical Resonators

Electrodynamic study of solid-state plasmon spherical resonators applicable in the range from microwave to optical frequencies is undertaken. Influence of dimensions and electromagnetic properties of media on the resonance frequency and Q-factor of these resonators is analyzed. It is shown that transcendental equations resulting from electrodynamic analysis of plasmon resonators can be also applied to the analysis of whispering gallery resonators if the resonator’s medium is isotropic, although this is a completely different kind of a resonator. Special attention is focused on the Q-factor analysis and theoretical and practical Q-factor limits for the magnetic plasmon and the electric plasmon resonators. In the addition, the impact of the finite size of a resonator on the resonance frequency and Q-factor is considered. Computations of the resonance frequency and Q-factor of magnetic plasmon resonators are supported by experiments performed at microwave frequencies.

Bound states in the continuum in whispering gallery resonators

We report the formation of bound states in the continuum in a whispering gallery resonator coupled to a one-dimensional waveguide. We find that an incident photon wave packet is partially stored in the bound state in the continuum due to a roughness-induced symmetry breaking. We discuss quantum interference effects such as Fano in the transmission spectra and the photonic density of states. The conditions under which the bound state can be accessed through single-photon transport processes are investigated.

Ultranarrow Second-Harmonic Resonances in Hybrid Plasmon-Fiber Cavities.

We demonstrate second-harmonic generation with ultranarrow resonances in hybrid plasmon-fiber cavities, formed by depositing single-crystalline gold nanorods onto the surface of tapered microfibers with diameters in the range of 1.7-1.8 μm. The localized surface plasmon mode of the single gold nanorod efficiently couples with a whispering gallery mode of the fiber, resulting in a very narrow hybrid plasmon-fiber resonance with a high quality factor Q of up to 250. When illuminated with a tunable 100 fs laser, a sharp SHG peak narrower than half of the spectral width of the impinging laser emerges, superimposed on a broad multiphoton photoluminescence background. The enhancement of the SHG peak of the hybrid system is typically 1000-fold when compared to that of a single gold nanorod alone. Tuning the laser over the hybrid resonance enables second-harmonic spectroscopy and yields an ultranarrow line width as small as 6.4 nm. We determine the second-harmonic signal to rise with the square of the laser power, while the multiphoton photoluminescence background rises with powers between 4 and 6, indicating a very efficient higher-order process. A coupled anharmonic oscillator model is able to describe the linear as well as second-harmonic resonances very well. Our work will open the door to the simultaneous utilization of narrow whispering gallery resonances together with high plasmonic near-field enhancement and should allow for nonlinear sensing and extremely efficient nonlinear light generation from ultrasmall volumes.

Quasi-phase-matched nonlinear optical frequency conversion in on-chip whispering galleries

Chip-integrated whispering-gallery resonators (WGRs) enable compact and wavelength-agile nonlinear optical frequency synthesizers. So far, the most flexible phase-matching technique, i.e., quasi-phase matching, has not been applied in this configuration. The reason is the lack of suitable thin films with alternating crystal structure on a low-refractive-index substrate. Here, we demonstrate an innovative method of realizing thin film substrates suitable for quasi-phase matching by field-assisted domain engineering of lithium niobate, and subsequent direct bonding and polishing. We are able to fabricate high-Q on-chip WGRs with these substrates by using standard semiconductor manufacturing techniques. The Q-factors of the resonators are up to one million, which allows us to demonstrate quasi-phase-matched second-harmonic generation in on-chip WGRs for the first time, to the best of our knowledge. The normalized conversion efficiency is 9×10−4 mW−1. This method can also be transferred to other material systems.

Nanoparticle sensing beyond evanescent field interaction with a quasi-droplet microcavity

Sensing with whispering gallery resonators (WGRs) is largely limited by the weak perturbation of the whispering gallery mode (WGM) via the evanescent field. A new sensing regime using quasi-droplet WGMs allows WGRs to move beyond the limitation of the evanescent field and push the detection sensitivity to new heights. We present experimental results on the detection of 100 nm and 500 nm polystyrene particles in aqueous solution using thin-walled, hollow WGRs supporting quasi-droplet modes. The detection sensitivity in terms of mode shift and broadening is measured, with mode shifts of 400 MHz observed for 100 nm particles. In terms of the number of linewidths, this is 276 times larger than similar experiments with microsphere WGRs, thus showing a significant increase in detection sensitivity beyond the capability of standard evanescent field sensing with WGRs.

Continuous-wave whispering-gallery optical parametric oscillator based on CdSiP2.

Continuous-wave (cw) optical parametric oscillators (OPOs) are ideally suited for applications, for example high-resolution spectroscopy, that need coherent sources combining narrow-linewidth emission with good wavelength tunability. Here, we demonstrate for the first time cw OPOs based on a millimeter-sized whispering gallery resonator (WGR) made of cadmium silicon phosphide (CdSiP2). By employing a compact laser diode at 1.57-μm wavelength for pumping, a cw OPO with wavelength tunability from 2.3 μm to 5.1 μm is realized based on such a resonator. The oscillation thresholds are in the milliwatt range. The maximum total power conversion efficiency reaches more than 15%. The intrinsic quality factor at 1.57 μm is determined to be 3.5 × 106. This work suggests that CdSiP2 is a very promising alternative for constructing mid-infrared parametric devices.

Single-photon routing with whispering-gallery resonators

Quantum routing of single photons in a system with two waveguides coupled to two whispering-gallery resonators (WGRs) are investigated theoretically. Using a real-space full quantum theory, photonic scattering amplitudes along four ports of the waveguide network are analytically obtained. It is shown that, by adjusting the geometric and physical parameters of the two-WGR configuration, the quantum routing properties of single photons along the present waveguide network can be controlled effectively. The routing capability from input waveguide to another one can significantly exceed 0.5 near the resonance point of scattering spectra, which can be achieved with only one resonator. By properly designing the distance between two WGRs and the waveguide-WGR coupling strengths, the transfer rate between the waveguides can also reach certain sufficiently high values even in the non-resonance regime. Moreover, Fano-like resonances in the scattering spectra are designable. The proposed system may provide a potential application in controlling single-photon quantum routing.

Cascaded second-order optical nonlinearities in on-chip micro rings.

We demonstrate cascaded Stimulated Raman Scattering (SRS), Second-Harmonic Generation (SHG), and Sum-Frequency Generation (SFG) in integrated on-chip whispering-gallery resonators (WGRs). These lithium niobate-based WGRs are fabricated using highly-parallel semiconductor manufacturing techniques coupled with specialized polishing as a post-processing step and thus represent a novel means for batch fabrication of this family of non-linear devices. We achieved record high Q-factors for on-chip lithium niobate WGRs reaching up to 3 × 106. Furthermore, we present a flexible but stable coupling scheme, which gives us the opportunity to optimize the coupling regarding the non-linear optical processes we observe.

LED-pumped whispering-gallery laser

A low-cost light-emitting diode (LED) is sufficient to pump a quasi-continuous-wave bidirectional high-Q whispering-gallery resonator laser made of Nd:YVO4. This is remarkable because of the very limited spatial and spectral coherence of an LED. The LED, delivering up to 3.5 W, centered around 810 nm, is turned on in intervals of 100 μs duration, and for these periods a laser output exceeding 0.8 mW has been verified. Furthermore, 0.1-s-long laser pulses are demonstrated. To the best of our knowledge, this is the first demonstration of an LED-pumped high-Q whispering-gallery laser. The concept can be extended easily to other laser active materials. A prospect is also to pump several of such lasers with a single LED.

Geometric tuning: spectroscopy using whispering-gallery resonator frequency-synthesizers

Continuous fine-tuning of nonlinear processes in whispering-gallery resonators is still in its infancy. We demonstrate an innovative, fast, and compact tuning-method by enlarging a ring-like whispering-gallery resonator made out of lithium niobate with the help of a piezo actuator disk embedded inside the resonator. The radial expansion of the actuator forces the resonator to change its size and shape. This process is much faster than thermal tuning and has the additional benefit of a smaller dispersion. Using just this method to tune the resonator, a second-harmonic process pumped at around 1 μm wavelength can be tuned mode-hop-free over a range of 28 GHz, and an optical parametric oscillator pumped at the same wavelength achieved 4.5 GHz continuous tuning. In addition to presenting and demonstrating this novel concept, the influence of the elasto-optic effect and the refractive-index dispersion are discussed, and an analytic model to predict the wavelength dependent tuning efficiency is presented.

Off-resonant Raman quantum memory in impurity crystals: signal-to-noise ratio analysis

The possibility of implementing an off-resonant Raman scheme of optical quantum memory on the basis of an ensemble of three-level atoms is investigated under the condition of equal polarisations of resonant transitions forming the Λ-scheme. The developed model is used to analyse the signal-to-noise ratio at the output of an optical quantum memory device in 143Nd3+ : Y 7LiF4. It is shown that this ratio can significantly exceed unity for single-photon input pulses. The required values of the parameters can be obtained by using an impurity crystal in the form of a whispering-gallery mode ring resonator.

Self-frequency doubling in a laser-active whispering-gallery resonator.

Lasing and self-frequency doubling are achieved in a millimeter-sized laser-active whispering-gallery resonator made of neodymium-doped lithium niobate. A low-cost 808-nm laser diode without external frequency stabilization is sufficient to pump the neodymium ions. Laser oscillation around 1.08μm drives a frequency-doubling process within the same cavity providing green light. The electrical-optical efficiency of the system reaches up to 2×10-4. To the best of our knowledge, this is the first demonstration of combining lasing and χ(2) frequency conversion in a single high-Q whispering-gallery resonator. This approach is general and can be applied to other materials and other nonlinear optical processes.

Continuous-wave optical parametric oscillation tunable up to 8 μm wavelength

We demonstrate the first cw OPO emitting mid-infrared light at wavelengths up to 8 μm. This device is based on a 3.5-mm-diameter whispering gallery resonator made of silver gallium selenide (AgGaSe2) pumped by a compact distributed feedback laser diode emitting light at 1.57 μm wavelength. Phase-matching is achieved for a c-cut resonator disk pumped with extraordinarily polarized light at this wavelength. The oscillation thresholds are in the mW region, while the output power ranges from 10 to 800 μW. Wavelength tuning is achieved via changing the radial mode number of the pump wave and by changing the resonator temperature. Simulations predict that whispering gallery OPOs based on AgGaSe2 with diameters around 2 mm can generate idler waves exceeding 10 μm wavelength.

Continuous-wave optical parametric oscillation tunable up to an 8 μm wavelength

High-resolution spectroscopy of molecular gases requires sources of mid-infrared laser light combining narrow linewidths and wavelength tunability. Continuous-wave optical parametric oscillators (cw OPOs) fulfill these demands; however, their mid-infrared tuning range has been limited to wavelengths below 5.5 μm so far. Here, we demonstrate the first cw OPO emitting mid-infrared light at wavelengths up to 8 μm. This device is based on a 3.5-mm-diameter whispering gallery resonator made of silver gallium selenide (AgGaSe2) pumped by a compact distributed feedback laser diode emitting at the 1.57 μm wavelength. The oscillation thresholds are in the mW region, while the output powers range from 10 to 800 μW. By changing the radial mode number of the pump wave, wavelengths of up to 8 μm are achieved. Temperature variation enables 100-nm-wide wavelength tuning. The measured tuning branches are in good accordance with the simulations. Furthermore, the latter show that whispering-gallery OPOs based on AgGaSe2 with diameters around 2 mm can generate idler waves exceeding the 10 μm wavelength.

Tunable erbium-doped microbubble laser fabricated by sol-gel coating.

In this work, we show that the application of a sol-gel coating renders a microbubble whispering gallery resonator into an active device. During the fabrication of the resonator, a thin layer of erbium-doped sol-gel is applied to a tapered microcapillary, then a microbubble with a wall thickness of 1.3 μm is formed with the rare earth ions diffused into its wall. The doped microbubble is pumped at 980 nm and lases in the emission band of the Er3+ ions at 1535 nm. The laser wavelength can be shifted by aerostatic pressure tuning of the whispering gallery modes of the microbubble. Up to 240 pm tuning is observed with 2 bar of applied pressure. We also show that the doped microbubble could be used as a compact, tunable laser source.

Impact of the photorefractive and pyroelectric-electro-optic effect in lithium niobate on whispering-gallery modes.

Whispering-gallery resonators made of undoped and MgO-doped congruently grown lithium niobate are used to study electro-optic refractive index changes. Hereby, we focus on the volume photovoltaic and the pyroelectric effect, both providing an electric field driving the electro-optic effect. Our findings indicate that the light-induced photorefractive effect, combining the photovoltaic and electro-optic effect, is present only in the non-MgO-doped lithium niobate for exposure with light having wavelengths of up to 850 nm. This leads to strong resonance frequency shifts of the whispering-gallery modes. No photorefractive effect was observed in the MgO-doped material. One has to be aware that surface charges induced by the pyroelectric effect result in a similar phenomenon and are present in both materials.

Triple-Resonant Brillouin Light Scattering in Magneto-Optical Cavities.

An enhancement in Brillouin light scattering of optical photons with magnons is demonstrated in magneto-optical whispering gallery mode resonators tuned to a triple-resonance point. This occurs when both the input and output optical modes are resonant with those of the whispering gallery resonator, with a separation given by the ferromagnetic resonance frequency. The identification and excitation of specific optical modes allows us to gain a clear understanding of the mode-matching conditions. A selection rule due to wave vector matching leads to an intrinsic single-sideband excitation. Strong suppression of one sideband is essential for one-to-one frequency mapping in coherent optical-to-microwave conversion.

Whispering gallery resonators with broken axial symmetry: Theory and experiment.

Axial symmetry is the cornerstone for theory and applications of high-Q optical whispering gallery resonators (WGRs). Nevertheless, research on birefringent crystalline material persistently pushes towards breaking this symmetry. We show theoretically and experimentally that the effect of broken axial symmetry, caused by optical anisotropy, is modest for the resonant frequencies and Q-factors of the WGR modes. Thus, the most important equatorial whispering gallery modes can be quantitatively described and experimentally identified. At the same time, the effect of broken axial symmetry on the light field distribution of the whispering gallery modes is typically very strong. This qualitatively modifies the phase-matching for the χ(2) nonlinear processes and enables broad-band second harmonic generation and optical parametric oscillation. The effect of weak geometric ellipticity in nominally symmetric WGRs is also considered. Altogether our findings pave the way for an extensive use of numerous birefringent (uniaxial and biaxial) crystals with broad transparency window and large χ(2) coefficients in nonlinear optics with WGRs.

Strong forward-backward asymmetry of stimulated Raman scattering in lithium-niobate-based whispering gallery resonators.

We show experimentally and prove theoretically that the pump-power thresholds of stimulated Raman scattering (SRS) in lithium-niobate-based whispering gallery resonators (WGRs) are strongly different for the signal waves propagating in the backward and forward directions with respect to the pump wave. This feature is due to a strong polaritonic effect. It leads to a cascade of alternating forward-backward Raman lines with increasing pump power. The measured polarization and spectral properties of SRS are in good agreement with theory. Similar properties have to be inherent in other WGRs made of polar crystals.

Single envelope equation modeling of multi-octave comb arrays in microresonators with quadratic and cubic nonlinearities

We numerically study, by means of the single envelope equation, the generation of optical frequency combs ranging from the visible to the mid-infrared spectral regions in resonators with quadratic and cubic nonlinearities. Phase-matched quadratic wave-mixing processes among the comb lines can be activated by low-power continuous wave pumping in the near infrared of a radially poled lithium niobate whispering gallery resonator (WGR). We examine both separate and co-existing intra-cavity doubly resonant second-harmonic generation and parametric oscillation processes, and find that modulation instabilities may lead to the formation of coupled comb arrays extending over multiple octaves. In the temporal domain, the frequency combs may correspond to pulse trains, or isolated pulses.