Two-dimensional (2-D) boundary integral equation analysis of a notched circular microdisk resonator is presented. Results obtained provide accurate description of optical modes, free from the staircasing and discretization errors of other numerical techniques. Splitting of the double degenerate Whispering-Gallery (WG) modes and directional light output is demonstrated. The effect of the notch depth and width on the resonance wavelengths, Q-factors, and emission patterns is studied. Further improvement of the directionality is demonstrated in an elliptical notched microdisk. Applications of the notched resonators to the design of microdisk lasers, oscillators, and biosensors are discussed.
Lithium Niobate (LN) is an important nonlinear optical material. Here we demonstrate LN microdisk resonators that feature optical quality factor ~ 100,000, realized using robust and scalable fabrication techniques, that operate over a wide wavelength range spanning visible and near infrared. Using our resonators, and leveraging LN's large second order optical nonlinearity, we demonstrate on-chip second harmonic generation with a conversion efficiency of 0.109 W-1.
Ab initio approach is used to describe the time evolution of the amplitudes of whispering gallery modes in a system of coupled microdisk resonators with Kerr nonlinearity. It is shown that this system demonstrates a transition between Josephson-like nonlinear oscillations and self-trapping behavior. Manifestation of this transition in the dynamics of radiative losses is studied.
Microdisks and microstadium resonators were fabricated on erbium doped amorphous hydrogenated silicon (a-Si:H<Er>) layers sandwiched in air and native SiO2 on Si substrates. Annealing condition is optimized to allow large emission at 1550 nm for samples with erbium concentrations as high as 1.02x10^20 atoms/cm3. Near field scanning optical microscopy shows evidences of the simultaneous presence of bow-tie and diamond scars. These modes indicate the high quality of the resonators and the potentiality for achieving amorphous silicon microcavity lasers.
Fast and highly accurate method based on the Muller contour integral equations and a trigonometric-trigonometric Galerkin discretization technique is presented for spectral design and fine-tuning of clusters of whispering-gallery (WG) mode microdisk resonators and photonic crystal (PC) defect cavities. It is shown that degeneracy and near-degeneracy of natural modes as well as modes optical confinement in coupled resonator clusters are significantly influenced by the symmetry of the structure. Photonic molecules with greatly enhanced quality factors are designed by exploiting the symmetry of t…
We demonstrated broadband highly efficient optical nonlinear processes in on-chip integrated lithium niobate (LN) microdisk resonators. The Q factors of the micro-resonators fabricated by femtosecond laser writing and chemo-mechanical polishing are reliably above 10^8, approaching the intrinsic material absorption limit of LN. Broadband nonlinear processes, including optical parametric oscillation (OPO), second harmonic generation (SHG), third harmonic generation, and fourth harmonic generation, were observed with ultrahigh efficiencies in the same LN microdisk without introducing domain inver…
A system for studying microcavity resonators at cryogenic temperatures (~10 K) through evanescent coupling via optical fiber taper waveguides is reported, and efficient fiber coupling to AlGaAs microdisk cavities with embedded quantum dots is demonstrated. As an immediate application of this tool, we study high-resolution tuning of microdisk cavities through nitrogen gas adsorption, as first discussed by Mosor, et al. By proper regulation of the nitrogen gas flow and delivery of the gas to the sample surface, continuous tuning can be achieved with modest gas flows, and overall wavelength shift…
We report on visible light emission from Si-nanocrystal based optically active microdisk resonators. The room temperature photoluminescence (PL) from single microdisks shows the characteristic modal structure of whispering-gallery modes. The emission is both TE and TM-polarized in 300 nm thick microdisks, while thinner ones (135 nm) support only TE-like modes. Thinner disks have the advantage to filter out higher order radial mode families, allowing for measuring only the most intense first order modal structure. We reveal subnanometer linewidths and corresponding quality factors as high as 28…
We present a new design of dielectric microcavities supporting modes with large quality factors and highly directional light emission. The key idea is to place a point scatterer inside a dielectric circular microdisk. We show that, depending on the position and strength of the scatterer, this leads to strongly directional modes in various frequency regions while preserving the high Q-factors reminiscent of the whispering gallery modes of the microdisk without scatterer. The design is very appealing due to its simplicity, promising a cleaner experimental realisation than previously studied micr…
We report on fabrication of on-chip calcium fluoride (CaF2) microdisk resonators using water-assisted femtosecond laser micromachining. Focused ion beam (FIB) milling is used to create ultra-smooth sidewalls. The quality (Q)-factors of the fabricated microresonators are measured to be 4.2x10^4 at wavelengths near 1550 nm. The Q factor is mainly limited by the scattering from the bottom surface of the disk whose roughness remains high due to the femtosecond laser micromachining process. This technique facilitates formation of on-chip microresonators on various kinds of bulk crystalline material…
We study the optomechanical design introduced by M. Li et al. [Phys. Rev. Lett. {\bf 103}, 223901 (2009)], which is very effective for investigation of the effects of reactive coupling. We show the normal mode splitting which is due solely to reactive coupling rather than due to dispersive coupling. We suggest feeding the waveguide with a pump field along with a probe field and scanning the output probe for evidence of reactive-coupling-induced normal mode splitting.
We have demonstrated a new photonic structure to achieve strong optical coupling between nanoparticle and photonic molecule by utilizing a notched micro ring resonators. By creating a notch in the ring resonator and putting a nanoparticle inside the notch, large spectral shifts and splittings at nm scale can be achieved, compared to only pm scale observed by fiber tip evanescently coupled to the surface of microsphere, thereby significantly lowered the quality factor requirement for single nanoparticle detection. The ability for sorting the type of nanoparticles due to very different mode shif…
In this paper we report on the measurement and modelling of enhanced optical refractometric sensors based on whispering-gallery-modes. The devices under test are optical microresonators made of silicon nitride on silicon oxide. In our approach, these microresonators are vertically coupled to a buried waveguide with the aim of creating integrated and cost-effective devices. The optimization analysis is a delicate balance of resonance quality factor and evanescent field overlap with the sorrounding environment to analyze. By numerical simulations we show that the microdisk thickness is critical …
An erbium doped micro-laser is demonstrated utilizing $\mathrm{SiO_{2}}$ microdisk resonators on a silicon chip. Passive microdisk resonators exhibit whispering gallery type (WGM) modes with intrinsic optical quality factors of up to $6\times{10^{7}}$ and were doped with trivalent erbium ions (peak concentration $\mathrm{\sim3.8\times{10^{20}cm^{-3})}}$ using MeV ion implantation. Coupling to the fundamental WGM of the microdisk resonator was achieved by using a tapered optical fiber. Upon pumping of the $^{4}% I_{15/2}\longrightarrow$ $^{4}I_{13/2}$ erbium transition at 1450 nm, a gradual tra…
Wavelength-sized microdisk resonators were fabricated on a single crystalline 4H-silicon-carbide-oninsulator platform (4H-SiCOI). By carrying out microphotoluminescence measurements at room temperature, we show that the microdisk resonators support whispering-gallery modes (WGMs) with quality factors up to $5.25 \times 10^3$ and mode volumes down to $2.69 \times(λ/n)^3$ at the visible and near-infrared wavelengths. Moreover, the demonstrated wavelength-sized microdisk resonators exhibit WGMs whose resonant wavelengths compatible with the zero-phonon lines of spin defects in 4H-SiCOI, making th…
We demonstrate optomechanically-mediated electromagnetically-induced transparency and wavelength conversion in silicon nitride (Si3N4) microdisk resonators. Fabricated devices support whispering gallery optical modes with a quality factor (Q) of 10^6, and radial breathing mechanical modes with a Q=10^4 and a resonance frequency of 625 MHz, so that the system is in the resolved sideband regime. Placing a strong optical control field on the red (blue) detuned sideband of the optical mode produces coherent interference with a resonant probe beam, inducing a transparency (absorption) window for th…
We analyze normal mode splitting in a pair of vertically coupled microdisk resonators. A full vectorial finite element model is used to find the eigen frequencies of the symmetric and antisymmetric composite modes as a function of coupling distance. We find that the coupled microdisks can compete with the best Fabry-Perot resonators in displacement sensing. We also show how we configured FreeFem++ for the sphere eigenvalue problem.
We propose and optimize a vertically-loaded diamond microdisk resonator (VLDMoRt) coupled to a nitrogen-vacancy (NV) center in diamond for efficient collection of zero-phonon-line emission into low numerical aperture ($\text{NA}$) free-space modes. The VLDMoRt achieves a Purcell enhancement of 172 with $39\%$ of the emitted light collected within a $\text{NA}$ of 0.6, leading to a total external spin-photon collection efficiency of 0.33. As the design is compatible with established nanofabrication techniques and couples to low-NA modes accessible by cryogenic free-space optical systems, it is …
Fiber taper waveguides are used to improve the efficiency of room temperature photoluminescence measurements of AlGaAs microdisk resonant cavities with embedded self-assembled InAs quantum dots. As a near-field collection optic, the fiber taper improves the collection efficiency from microdisk lasers by a factor of ~ 15-100 times in comparison to conventional normal incidence free-space collection techniques. In addition, the fiber taper can serve as a efficient means for pumping these devices, and initial measurements employing fiber pumping and collection are presented. Implications of this …
Optical microresonators with low quality factor ($Q$) can be efficiently excited by and scatter freely propagating optical waves, but those with high $Q$ typically cannot. Here, we present a universal model for resonators interacting with freely propagating waves and show that the stored energy of a resonator excited by a plane wave is proportional to the product of its $Q$ and directivity. Guided by this result, we devise a microdisk with periodic protrusions in its circumference that couples efficiently to normally incident plane waves. We experimentally demonstrate several microdisk designs…
Optical characterization of AlGaAs microdisk resonant cavities with a quantum dot active region is presented. Direct passive measurement of the optical loss within AlGaAs microdisk resonant structures embedded with InAs/InGaAs dots-in-a-well (DWELL) is performed using an optical-fiber-based probing technique at a wavelength (lambda~1400 nm) that is red-detuned from the dot emission wavelength (lambda~1200 nm). Measurements in the 1400 nm wavelength band on microdisks of diameter D = 4.5 microns show that these structures support modes with cold-cavity quality factors as high as 360,000. DWELL-…
Single-walled carbon nanotubes have advantages as a nanoscale light source compatible with silicon photonics because they show room-temperature luminescence at telecom-wavelengths and can be directly synthesized on silicon substrates. Here we demonstrate integration of individual light-emitting carbon nanotubes with silicon microdisk resonators. Photons emitted from nanotubes are efficiently coupled to whispering gallery modes, circulating within the disks and lighting up their perimeters. Furthermore, we control such emission by tuning the excitation wavelength in and out of resonance with hi…
We report disk-shaped silicon optomechanical resonators with frequency up to 1.75 GHz in the ultrahigh frequency band. Optical transduction of the thermal motion of the disks' in-plane vibrational modes yields a displacement sensitivity of 4.1 \times 10^(-17) m/Hz^(1/2). Due to the reduced clamping loss, these disk resonators possess high mechanical quality factors (Q), with the highest value of 4370 for the 1.47 GHz mode measured in ambient air. Numerical simulation on the modal frequency and mechanical Q for disks of varying undercut shows modal coupling and suggests a realistic pedestal siz…
We demonstrate a high frequency phase-sensitive heterodyne vibrometer, operating up to 10 GHz. Using this heterodyne vibrometer, the amplitude and phase fields of the fundamental thickness mode, the radial fundamental and the 2nd-order modes of an AlN optomechanical microdisk resonator are mapped with a displacement sensitivity of around 0.36 picometer at 1 Hz resolution bandwidth. The simultaneous amplitude and phase measurement allows precise mode identification and characterization. The recorded modal frequencies and proles are consistent with numerical simulations. This vibrometer will be …
Sensitive transduction of the motion of a microscale cantilever is central to many applications in mass, force, magnetic resonance, and displacement sensing. Reducing cantilever size to nanoscale dimensions can improve the bandwidth and sensitivity of techniques like atomic force microscopy, but current optical transduction methods suffer when the cantilever is small compared to the achievable spot size. Here, we demonstrate sensitive optical transduction in a monolithic cavity-optomechanical system in which a sub-picogram silicon cantilever with a sharp probe tip is separated from a microdisk…
We demonstrate aqueous refractive index sensing with 15 to 30 μm diameter silicon nitride microdisk resonators to detect small concentrations of Li salt. A dimpled-tapered fiber is used to couple 780 nm visible light to the microdisks, in order to perform spectroscopy their optical resonances. The dimpled fiber probe allows testing of multiple devices on a chip in a single experiment. This sensing system is versatile and easy to use, while remaining competitive with other refractometric sensors. For example, from a 20 μm diameter device we measure a sensitivity of 200 $\pm$ 30 nm/RIU with a lo…
Miniature semiconductor lasers have attracted a large amount of interest owing to their potential as highly integrated components in photonic circuits or in sensors. Particularly, microdisk lasers exploiting whispering gallery modes have been regarded as an important candidate because of their relatively small footprint and low threshold. However, it has been challenging for microdisk to operate under single mode operation and to lase in a preselected mode. We report subwavelength microdisk resonators suspended in air with connecting bridges and propose a simple method using the number and sym…
High refractive index contrast optical microdisk resonators fabricated from silicon-on-insulator wafers are studied using an external silica fiber taper waveguide as a wafer-scale optical probe. Measurements performed in the 1500 nm wavelength band show that these silicon microdisks can support whispering-gallery modes with quality factors as high as 5.2 x 10^5, limited by Rayleigh scattering from fabrication induced surface roughness. Microdisks with radii as small as 2.5 microns are studied, with measured quality factors as high as 4.7 x 10^5 for an optical mode volume of 5.3 cubic wavelengt…
Whispering gallery mode microdisk cavities fabricated by direct laser writing are studied using dark-field imaging and spectroscopy in the visible spectral range. {Dark-field imaging allows us to directly visualize the spatial intensity distribution of whispering gallery modes. We extract their azimuthal and radial mode indices from dark-field images, and find the axial mode number from the dispersion relation. The scattering spectrum obtained in the confocal arrangement provides information on the density of optical states in the resonator. The proposed technique is a simple non-invasive way …
We demonstrate an on-chip Yb3+-doped lithium niobate (LN) microdisk laser. The intrinsic quality factors of the fabricated Yb3+-doped LN microdisk resonator are measured up to 3.79x10^5 at 976 nm wavelength and 1.1x10^6 at 1514 nm wavelength. The multi-mode laser emissions are obtained in a band from 1020 nm to 1070 nm pumped by 984 nm laser and with the low threshold of 103 μW, resulting in a slope efficiency of 0.53% at room temperature. Furthermore, the second-harmonic frequency of pump light and the sum-frequency of the pump light and laser emissions are both generated in the on-chip Yb3+-…
Waveguides composed of electromagnetically-coupled optical microcavities (coupled resonator optical waveguides or CROWs) can be used for light guiding, slowing and storage. In this paper, we present a two-dimensional analysis of finite-size straight and curved CROW sections based on a rigorous Muller boundary integral equations method. We study mechanisms of the coupling of whispering gallery (WG) modes and guiding light around bends in CROWs composed of both identical and size-mismatched microdisk resonators. Our accurate analysis reveals differences in WG modes coupling in the vicinity of be…
We report on fabrication of crystalline lithium niobate microresonators with quality factors above 10^7 as measured around 770 nm wavelength. Our technique relies on femtosecond laser micromachining for patterning a mask coated on the lithium niobate on insulate (LNOI) into a microdisk, followed by a chemo-mechanical polishing process for transferring the disk-shaped pattern to the LNOI. Nonlinear processes including second harmonic generation and Raman scattering have been demonstrated in the fabricated microdisk.
We study the dispersion relations in slow-light waveguide structures consisting of coupled microdisk resonators. A group theoretical analysis of the symmetry properties of the propagating modes reveals an interesting phenomenon: The degeneracy of the CW and CCW rotating modes is removed, giving rise to two distinct transmission bands. This effect induces symmetry-based dispersion which may limit usable bandwidth of such structures. The properties of this band splitting and its impact on CROW performance for optical communications are studied in detail.
We present the design, fabrication and characterization of cubic (3C) silicon carbide microdisk resonators with high quality factor modes at visible and near infrared wavelengths (600 - 950 nm). Whispering gallery modes with quality factors as high as 2,300 and corresponding mode volumes V ~ 2 (λ/n)^3 are measured using laser scanning confocal microscopy at room temperature. We obtain excellent correspondence between transverse-magnetic (TM) and transverse-electric (TE) polarized resonances simulated using Finite Difference Time Domain (FDTD) method and those observed in experiment. These stru…
We demonstrate integrating a high quality factor lithium niobate microdisk resonator with a free-standing membrane waveguide. Our technique is based on femtosecond laser direct writing which produces the pre-structure, followed by focused ion beam milling which reduces the surface roughness of sidewall of the fabricated structure to nanometer scale. Efficient light coupling between the integrated waveguide and microdisk was achieved, and the quality factor of the microresonator was measured as high as 1.67*10^5.
We report on a combined theoretical and experimental study of the optical coupling between a microdisk resonator and a waveguide laying on different planes. While the lateral coupling between a planar resonator and a waveguide is characterized by a unique distance at which the resonant waveguide transmission vanishes because of destructive interference, the vertical coupling geometry exhibits an oscillatory behavior in the coupling amplitude as a function of the vertical gap. This effect manifests experimentally as oscillations in both the waveguide transmission and the mode quality factor. An…
We present theoretical results of a low-loss all-optical switch based on electromagnetically induced transparency and the classical Zeno effect in a microdisk resonator. We show that a control beam can modify the atomic absorption of the evanescent field which suppresses the cavity field buildup and alters the path of a weak signal beam. We predict more than 35 dB of switching contrast with less than 0.1 dB loss using just 2 micro-Watts of control-beam power for signal beams with less than single photon intensities inside the cavity.
Achieving single-mode operation and highly directional (preferably unidirectional) in-plane light output from whispering-gallery (WG) mode semiconductor microdisk resonators without seriously degrading the mode Q-factor challenges designers of low-threshold microlasers. To address this problem, basic design rules to tune the spectral and emission characteristics of micro-scale optical cavity structures with nanoscale features by tailoring their geometry are formulated and discussed in this paper. The validity and usefulness of these rules is demonstrated by reviewing a number of previously stu…
We investigate the range of validity of the recently developed steady-state ab-initio laser theory (SALT). While very efficient in describing various microlasers, SALT is conventionally believed not to be applicable to lasers featuring fully or nearly degenerate pairs of resonator modes above the lasing threshold. Here we demonstrate how SALT can indeed be extended to describe such cases as well, with the effect that we significantly broaden the theory's scope. In particular, we show how to use SALT in conjunction with a linear stability analysis to obtain stable single-mode lasing solutions t…
Photonic-based low-phase-noise microwave generation with real-time frequency tuning is crucial for a broad spectrum of subjects, including next-generation wireless communications, radar, metrology, and modern instrumentation. Here, for the first time to the best of our knowledge, narrow-bandwidth dual-wavelength microlasers are generated from nearly degenerate polygon modes in a high-Q active lithium niobate microdisk. The high-Q polygon modes formation with independently controllable resonant wavelengths and free spectral ranges is enabled by the weak perturbation of the whispering gallery mi…
Low-loss nanophotonic resonators have been widely used in fundamental science and applications thanks to their ability to concentrate optical energy. Key for resonator engineering, the total intrinsic loss is easily determined by spectroscopy, however, quantitatively separating absorption and radiative losses is challenging. While the concentrated heat generated by absorption within the small mode volume results in generally unwanted thermo-optical effects, they can provide a way for quantifying absorption. Here, we propose and experimentally demonstrate a technique for separating the loss mec…
We first present a quasinormal mode (QNM) theory for coupled loss-gain resonators working near an exceptional point. Assuming linear media, which can be fully quantified using the complex pole properties of the QNMs, we show how the QNMs yield a quantitatively good model to a full dipole spontaneous emission response in Maxwell's equations at various spatial positions and frequencies (linear response). We also develop a highly accurate and intuitive QNM coupled-mode theory, which can be used to rigorously model such systems using only the QNMs of the bare resonators, where the hybrid QNMs of t…
We present a quantized quasinormal approach to rigorously describe coupled lossy resonators, and quantify the quantum coupling parameters as a function of distance between the resonators. We also make a direct connection between classical and quantum quasinormal modes parameters and theories, offering new and unique insights into coupled open cavity resonators. We present detailed calculations for coupled microdisk resonators and show striking interference effects that depend on the phase of the quasinormal modes, an effect that is also significant for high quality factor modes. Our results de…
Low-contrast all-optical Zeno switching has been demonstrated in a silicon nitride microdisk resonator coupled to a hot atomic vapor. The device is based on the suppression of the field build-up within a microcavity due to non-degenerate two-photon absorption. This experiment used one beam in a resonator and one in free-space due to limitations related to device physics. These results suggest that a similar scheme with both beams resonant in the cavity would correspond to input power levels near 20 nW.
Chip-based cavity optomechanical systems are being considered for applications in sensing, metrology, and quantum information science. Critical to their development is an understanding of how the optical and mechanical modes interact, quantified by the coupling rate $g_{0}$. Here, we develop GaAs optomechanical resonators and investigate the moving dielectric boundary and photoelastic contributions to $g_{0}$. First, we consider coupling between the fundamental radial breathing mechanical mode and a 1550 nm band optical whispering gallery mode in microdisks. For decreasing disk radius from $R=…
In the presence of arbitrary three-dimensional linear media with material loss and amplification, we present an electromagnetic field quantization scheme for quasinormal modes (QNMs), extending previous work for lossy media [Franke et al., Phys. Rev. Lett. 122, 213901 (2019)]. Applying a symmetrization transformation, we show two fundamentally different ways for constructing a QNM photon Fock space, including (i) where there is a separate operator basis for both gain and loss, and (ii) where the loss and gain degrees of freedom are combined into a single basis. These QNM operator bases are sub…
