high-Q Whispering Gallery Mode Research Articles

Picotesla-sensitivity microcavity optomechanical magnetometry.

Cavity optomechanical systems have enabled precision sensing of magnetic fields, by leveraging the optical resonance-enhanced readout and mechanical resonance-enhanced response. Previous studies have successfully achieved mass-produced and reproducible microcavity optomechanical magnetometry (MCOM) by incorporating Terfenol-D thin films into high-quality (Q) factor whispering gallery mode (WGM) microcavities. However, the sensitivity was limited to 585 pT Hz-1/2, over 20 times inferior to those using Terfenol-D particles. In this work, we propose and demonstrate a high-sensitivity and mass-produced MCOM approach by sputtering a FeGaB thin film onto a high-Q SiO2 WGM microdisk. Theoretical studies are conducted to explore the magnetic actuation constant and noise-limited sensitivity by varying the parameters of the FeGaB film and SiO2 microdisk. Multiple magnetometers with different radii are fabricated and characterized. By utilizing a microdisk with a radius of 355 μm and a thickness of 1 μm, along with a FeGaB film with a radius of 330 μm and a thickness of 1.3 μm, we have achieved a remarkable peak sensitivity of 1.68 pT Hz-1/2 at 9.52 MHz. This represents a significant improvement of over two orders of magnitude compared with previous studies employing sputtered Terfenol-D film. Notably, the magnetometer operates without a bias magnetic field, thanks to the remarkable soft magnetic properties of the FeGaB film. Furthermore, as a proof of concept, we have demonstrated the real-time measurement of a pulsed magnetic field simulating the corona current in a high-voltage transmission line using our developed magnetometer. These high-sensitivity magnetometers hold great potential for various applications, such as magnetic induction tomography and corona current monitoring.

Fabrication of ultra-high-Q Ta2O5 microdisks by photolithography-assisted chemo-mechanical etching

Tantalum pentoxide (Ta2O5) is widely recognized as a promising material platform for photonic integration. This is primarily attributed to its exceptional properties including large bandgap of 3.8 eV, broad transparency window ranging from 300 nm to 8000 nm, high nonlinear refractive index of ∼7.2 × 10−19 m2/W, low optical loss, moderate refractive index of 2.05, low intrinsic material stress, compatibility with CMOS technology, and high solubility for rare-earth ions. However, dry etching of Ta2O5 is challenging and typically results in sidewall roughness with substantial scattering losses. Here, we report on fabrication of a high-Q whispering gallery mode (WGM) microdisk with a diameter of 120 µm and a loaded Q factor of 1.92 × 106 by femtosecond laser photolithography assisted chemo-mechanical etching (PLACE) on amorphous Ta2O5 film. Thanks to the suppression of sidewall scattering, the loaded Q factor is two orders of magnitude higher than the best reported value in dispersion engineered Ta2O5 microresonators.

High-Q WGM microcavity-based optofluidic sensor technologies for biological analysis.

High-quality-factor (Q) optical microcavities have attracted extensive interest due to their unique ability to confine light for resonant circulation at the micrometer scale. Particular attention has been paid to optical whispering-gallery mode (WGM) microcavities to harness their strong light-matter interactions for biological applications. Remarkably, the combination of high-Q optical WGM microcavities with microfluidic technologies can achieve a synergistic effect in the development of high-sensitivity optofluidic sensors for many emerging biological analysis applications, such as the detection of proteins, nucleic acids, viruses, and exosomes. They can also be utilized to investigate the behavior of living cells in human organisms, which may provide new technical solutions for studies in cell biology and biophysics. In this paper, we briefly review recent progress in high-Q microcavity-based optofluidic sensor technologies and their applications in biological analysis.

Red narrow-linewidth lasing and frequency comb from gain-switched self-injection-locked Fabry–Pérot laser diode

Narrow-linewidth lasers are in extensive demand for numerous cutting-edge applications. Such lasers operating at the visible range are of particular interest. Self-injection locking of a laser diode frequency to a high-Q whispering gallery mode is an effective and universal way to achieve superior laser performance. We demonstrate ultranarrow lasing with less than 10 Hz instantaneous linewidth for 20 mus averaging time at 638 nm using a Fabry–Pérot laser diode locked to a crystalline MgF_2 microresonator. The linewidth measured with a beta-separation line technique that characterizes 10 ms stability is as low as 1.4 kHz. Output power exceeds 80 mW. Demonstrated results are among the best for visible-range lasers in terms of linewidth combined with solid output power. We additionally report the first demonstration of a gain-switched regime for such stabilized Fabry–Pérot laser diode showing a high-contrast visible frequency comb generation. Tunable linespacing from 10 MHz to 3.8 GHz is observed. We demonstrated that the beatnote between the lines has sub-Hz linewidth and experiences spectral purification in the self-injection locking regime. This result might be of special importance for spectroscopy in the visible range.

Fabrication and optical characterization of GaN micro-disk cavities undercut by laser-assisted photo-electrochemical etching

GaN micro-disk cavities undercut by laser-assisted photo-electrochemical (PEC) etching are fabricated and optically characterized. The laser source used in the PEC etching is tuned to be absorbed by the InGaN/GaN superlattice beneath the GaN disk to selectively etch the superlattice. Whispering gallery modes (WGMs) in fabricated GaN micro-disk cavities are evaluated by micro-photoluminescence spectroscopy of light emission from the embedded InGaN quantum wells. Quality factors estimated for the WGMs reach approximately 6700 at blue-violet wavelengths. Detailed analysis suggests that the high-Q WGMs are the fundamental WGMs. These results indicate the high applicability of laser-assisted PEC etching to the fabrication of air-clad GaN micro-cavities.

Single Whispering-Gallery-Mode Resonator With Microfluidic Chip as a Basis for Multifrequency Microwave Permittivity Measurement of Liquids

The accurate measurement of complex liquid permittivity in a frequency range provides important information on liquid properties in comparison to single frequency permittivity investigations. The multifrequency microwave characterization technique based on a single quartz whispering-gallery-mode (WGM) resonator with a microfluidic chip are proposed, developed, and demonstrated. This technique allows the complex permittivity of small volumes of liquid to be measured at six resonant frequencies in the 30-40 GHz frequency range. The calibration is performed by simulating the measurement cell and by plotting the calibration nomogram charts for all six investigated frequencies. The novel approach is applied in studies of the complex permittivity of the L-lysine in water solutions. The results open up possibilities to investigate the complex permittivity of biological liquids at several frequencies and to further develop the microwave dielectrometry of small liquid volumes in a certain frequency range using the quasi-optical nature of a single high-Q WGM resonator.

Ultrahigh electric and magnetic near field enhancement based on high-Q whispering gallery modes in subwavelength all-dielectric resonators

Here, we show that whispering gallery modes of subwavelength dielectric resonators can exhibit ultrahigh electric and magnetic field enhancements due to their high-quality factors. The resonators are dielectric disks. The field enhancements are dependent on the height of the disk, the refractive index n and the azimuthal mode index, and they can reach ∼102 inside a subwavelength disk of n = 3.5. For a disk dimer of n = 3.5, the electric field enhancement reaches ∼103 in the small gap. The Purcell factor of an electric and magnetic dipole emitter in the dimer can reach ∼105 and ∼104, respectively.

A robust scheme for unidirectional emission from a hybrid whispering gallery cavity system based on transformation optics.

Using the transformation cavity, a gradient index cavity designed by transformation optics, we propose a hybrid resonator system to extract unidirectional narrow-beam emission from high-Q whispering gallery modes by embedding a transformation cavity inside a deformed uniform index cavity that exhibits unidirectional narrow-beam emission. For effective mode coupling between the transformation cavity and enclosing cavity, the embedded transformation cavity is designed to have bidirectional evanescent emission, which enables most of the emission from the transformation cavity to be laterally incident on the rim of the enclosing deformed cavity. Consequently, ultrahigh-Q resonances of this system can provide a sharp free-space light output, which is difficult to achieve by embedding a homogeneous disk cavity instead of the transformation cavity.

Stochastic Analysis of Miniature Optoelectronic Oscillators Based on Whispering-Gallery Mode Electrooptical Modulators

We propose a theoretical analysis of the stochastic dynamics of miniature optoelectronic oscillators (OEOs) based on whispering-gallery mode resonators. The core element in this microwave photonic oscillator is a high-Q whispering-gallery mode resonator with quadratic nonlinearity, which simultaneously performs electrooptical modulation, frequency filtering and energy storage. This multi-task resonator allows the oscillator to feature improved size, weight and power metrics. In this article, we analyze how the various sources of optical and electrical noise in the oscillator are converted to output microwave signal fluctuations. We use an approach based on stochastic differential equations to characterize the dynamics of the microwave signal as a function of radiofrequency gain and laser pump power. This stochastic analysis also allows us to understand how key parameters of the resonator such as its intrinsic and extrinsic Q-factors influence the system's dynamics below and above threshold. The time-domain numerical simulations for miniature OEO stochastic dynamics provides an excellent agreement with the analytical predictions.

Mode Splitting of High-Q Whispering-Gallery Modes in a Microring Resonator Coated With a Fluorescent High-Refractive-Index Film

A microring resonator coated with a fluorescent high-refractive-index film provides a structure that supports whispering-gallery modes (WGMs) via the contrast in the refractive index. In the past, number, size, and refractive index of nanoparticles were analyzed by the degree of resonant mode splitting in the cavity. Compared with the small mode shift, this splitting is easier to detect and has strong anti-interference ability. However, there are several mechanisms for the mode splitting due to the different sizes of nanoparticles. The magnitudes of different mode splittings are quite different, which easily leads to confusion in spectral analysis. In this work, the mechanisms of resonant mode splitting are studied by the FDTD method combined with light field distributions and spectra. Field distributions of the symmetric mode and the asymmetric mode relative to the position of the nanoparticle for the fundamental order and second radial order were simulated. We first distinguished the splitting of the fundamental mode (~0.010 THz) due to the backscattering of the particles from the separation between the fundamental mode and the high-order mode (~1 THz) for the same particle (~100 nm). In addition, fundamental mode splitting was used to estimate the size and number of particles, and these sizes were consistent with those in the design. This work demonstrates the potential application of microring cavities based on WGMs in single particle detection.

Birefringent whispering gallery cavities designed by linear transformation optics.

It was reported that whispering gallery cavities designed by conformal transformation optics can support high-Q resonant modes with emission directionality. Intrinsically, these cavities have gradient index profiles implementing conformal mappings in physical space. In this paper, using the linear coordinate transformation, we propose another design scheme of whispering gallery cavities with (piecewise-) homogeneous, anisotropic index profile. We numerically show that so-designed cavities are also able to support high-Q whispering gallery modes with directional far-field emission patterns. We verify such characteristics by using a phase space representation (called the Poincaré Husimi function) of the intracavity wave function.

A Current Sensor Based on Capillary Microresonator Filled With Terfenol-D Nanoparticles

Electric current sensors are widely utilized in high-frequency power and electronic circuits which spread over numerous industries. Here, a current sensor based on the high-Q whispering gallery mode optical capillary microresonator filled with Terfenol-D nanoparticles is experimentally demonstrated. The device shows a peak AC current sensitivity of 5.285 μA Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1/2</sup> with a corresponding high accuracy of 0.0009%. It possesses a wide detection frequency bandwidth of approximately 12 MHz and exhibits good linearity, enabling for partial discharge signals detection.

Integrated end-to-end instrumentation for the study of whispering gallery modes in dynamic liquid micro-cavities coupled to sub-micron tapered fibers

An integrated table-top facility with the end-to-end instrumentation for the study of high-Q Whispering Gallery Modes in solid and liquid micro-cavities is described, with emphasis on the in situ fabrication of reliable tapered fibers of sub-micron waist sizes for coupling light into time-dependent liquid micro-cavities. The experimental parameters have been chosen to get nearly adiabatic tapers, with their waist size consistent with the theoretical model. The oscillations in the transmitted power during fiber tapering are monitored to check the coupling of higher order modes and identify the point when the fiber is suitable for pure single mode coupling. The fabricated tapered fibers have greater than 85% transmission on the average and very good polarization fidelity. The tapered fibers have been used for efficiently exciting and detecting WGMs of Q∼107 in silica microspheres and of Q up to 7×107 in microdrops of silicone oils. The set-up is suitable for conversion to a transportable system, for sensing applications involving WGMs in liquid microdrops.

Microresonator and Laser Parameter Definition via Self-Injection Locking

Self-injection locking to a high-quality-factor microresonator is a key component of various up-to-date photonic applications, including compact narrow-linewidth lasers and microcomb sources. For optimal construction of such devices it is necessary to know the parameters of the locking mode, which is a challenging task. We developed and verified experimentally an original technique based on the fundamentals of the self-injection locking effect, which allows determining the key parameters of the mode of the microresonator (quality factor, vertical index) as well as laser diode parameters. We demonstrated that this method can be used in the spectral ranges where conventional methods are not applicable, for example, in the mid-IR. We stabilized a 2.64 $\mu$m laser diode by a high-Q whispering gallery mode microresonator made of crystalline silicon. Using the elaborated technique, the quality factor of the microresonator was determined to be $5\cdot10^8$.

Circular Dielectric Rod With Conformal Strip of Graphene as Tunable Terahertz Antenna: Interplay of Inverse Electromagnetic Jet, Whispering Gallery and Plasmon Effects

In this article, we consider the radiation characteristics of a THz antenna made of a circular dielectric rod decorated with conformal graphene strip and illuminated by the field of a line magnetic current. The strip has arbitrary angular size and location and its surface impedance is characterized with Kubo theory. Our mathematically accurate analysis uses a dedicated hypersingular integral equation for the current induced on the strip. Discretization of this equation is carried out by the Nystrom-type method, which has a guaranteed convergence. We study the dependences of the powers radiated and absorbed in this configuration and also the directivity of antenna emission, in wide frequency range from 0 to 10 THz. They show very interesting interplay between the broadband inverse photonic-jet effect of lens-like dielectric rod and two types of resonances: on the moderate-Q plasmon modes of graphene strip and on the extremely high-Q whispering-gallery modes of the circular rod.

Resonator-assisted single-molecule quantum state detection

We propose a state-sensitive scheme to optically detect a single molecule without a closed transition, through strong coupling to a high-Q whispering-gallery mode high-Q resonator. A background-free signal can be obtained by detecting a molecule-induced transparency in a photon bus waveguide that is critically coupled to the resonator, with a suppressed depumping rate to other molecular states by the cooperativity parameter $C$. We numerically calculate the dynamics of the molecule-resonator coupled system using Lindblad master equations, and develop analytical solutions through the evolution of quasi-steady states in the weak-driving regime. Using Rb$_2$ triplet ground state molecules as an example, we show that high fidelity state readout can be achieved using realistic resonator parameters. We further discuss the case of multiple molecules collectively coupled to a resonator, demonstrating near-unity detection fidelity and negligible population loss.

Tunable laser emissions in freestanding high-Q polymethylmethacrylate microbubbles

A freestanding dye-doped polymethylmethacrylate microbubble laser based on high-Q whispering gallery mode (WGM) is demonstrated. Low threshold tunable laser emissions are observed in microbubbles with different sizes fabricated by a volumetric pipette. The whispering gallery mode laser emissions in the 944 nm diameter microbubble have a low laser threshold of about 15 μJ pulse−1 and a 0.083 nm free spectral range. The smooth wall of the microbubble ensures a high quality factor of approximately 24 120. In addition, 590 nm–610 nm laser emission is achieved by the reabsorption effect of the dye. This work provides an efficient way to implement a freestanding,easily doped and low cost tunable WGM micro-laser.

Ultrasensitive optofluidic enzyme-linked immunosorbent assay by on-chip integrated polymer whispering-gallery-mode microlaser sensors.

Optical whispering-gallery-mode (WGM) microcavities offer great promise in ultrasensitive biosensors because of their unique ability to enable resonant recirculation of light to achieve strong light-matter interactions in microscale volumes. However, it remains a challenge to develop cost-effective, high-performance WGM microcavity-based biosensing devices for practical disease diagnosis applications. In this paper, we present an optofluidic chip that is integrated with directly-printed, high-quality-factor (Q) polymer WGM microlaser sensors for ultrasensitive enzyme-linked immunosorbent assay (ELISA). Optical 3D μ-printing technology based on maskless ultraviolet lithography is developed to rapidly fabricate high-Q suspended-disk WGM microcavities. After deposition with a thin layer of optical gain material, low-threshold WGM microlasers are fabricated and then integrated together with optical fibres upon a microfluidic chip to achieve an optofluidic device. With flexible microfluidic technology, on-chip, integrated, WGM microlasers are further modified in situ with biomolecules on surface for highly selective biomarker detection. It is demonstrated that such an optofluidic biochip can measure horseradish peroxidase (HRP)-streptavidin, which is a widely used catalytic molecule in ELISA, via chromogenic reaction at the concentration level of 0.3 ng mL-1. Moreover, it enables on-chip optofluidic ELISA of the disease biomarker vascular endothelial growth factor (VEGF) at the extremely low concentration level of 17.8 fg mL-1, which is over 2 orders of magnitude better than the ability of current commercial ELISA kits.

Enhance stable coupling region of a high-Q WGM up to micrometer

A configuration to obtain the quasicritical coupling state with an enhanced stable coupling region was proposed and demonstrated experimentally by coupling two perpendicular vector modes in tapered fiber with the whispering gallery mode (WGM) in a microresonator. The observed stable coupling region of the high-Q WGM could be up to 1 μm with reliable polarization stability. This work makes it possible to apply direct laser writing and photolithography to prepare controllable coupling for on-chip ultrahigh-Q WGM microcavities and could also improve the stability of packaged WGM structures, which will be beneficial for WGM-based applications such as narrow-linewidth lasers and configurable microwave photonics.

Regular-Orbit-Engineered Chaotic Photon Transport in Mixed Phase Space.

The dynamical evolution of light in asymmetric microcavities is of primary interest for broadband optical coupling and enhanced light-matter interaction. Here, we propose and demonstrate that the chaos-assisted photon transport can be engineered by regular periodic orbits in the momentum-position phase space of an asymmetric microcavity. Remarkably, light at different initial states experiences different evolution pathways, following either regular-chaotic channels or pure chaotic channels. Experimentally, we develop a nanofiber technique to accurately control the excitation position of light in the phase space. We find that the coupling to high-Q whispering gallery modes depends strongly on excitation in islands or chaotic sea, showing a good agreement with the theoretical prediction. The engineered chaotic photon transport has potential in light manipulation, broadband photonic devices, and phase-space reconstruction.