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 the molecular geometry and tuning the inter-cavity coupling distances. Potential applications of the spectrally engineered coupled-resonator structures to low-threshold microdisk lasers, optical biosensors, and random powder lasers are discussed.
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 …
Recently, it has been shown that spiral-shaped microdisk cavities support highly nonorthogonal pairs of copropagating modes with a preferred sense of rotation (spatial chirality) [Wiersig et al., Phys. Rev. A 78, 053809 (2008)]. Here, we provide numerical evidence which indicates that such pairs are a common feature of deformed microdisk cavities which lack mirror symmetries. In particular, we demonstrate that discontinuities of the cavity boundary such as the notch in the spiral cavity are not needed. We find a quantitative relation between the nonorthogonality and the chirality of the modes …
Low threshold lasers realized within compact, high quality optical cavities enable a variety of nanophotonics applications. Gallium nitride (GaN) materials containing indium gallium nitride (InGaN) quantum dots and quantum wells offer an outstanding platform to study light matter interactions and realize practical devices such as efficient light emitting diodes and nanolasers. Despite progress in the growth and characterization of InGaN quantum dots, their advantages as the gain medium in low threshold lasers have not been clearly demonstrated. This work seeks to better understand the reasons …
We report on the radiative interaction of two single quantum dots (QDs) each in a separate InP/GaInP-based microdisk cavity via resonant whispering gallery modes. The investigations are based on ab initio coupled disk modes. We apply optical spectroscopy involving a $4f$-setup, as well as mode-selective real space imaging and photoluminescence mapping to discern single QDs coupled to a resonant microdisk mode. Excitation of one disk of the double cavity structure and detecting photoluminescene from the other yields proof of single photon emission of a QD excited by incoherent energy transfer f…
In single microdisks, embedded active emitters intrinsically affect the cavity mode of microdisks, which results in a trivial symmetric backscattering and a low controllability. Here we propose a macroscopical control of the backscattering direction by optimizing the cavity size. The signature of positive and negative backscattering directions in each single microdisk is confirmed with two strongly coupled microdisks. Furthermore, the diabolical points are achieved at the resonance of two microdisks, which agrees well with the theoretical calculations considering backscattering directions. The…
GeSn alloys are nowadays considered as the most promising materials to build Group IV laser sources on silicon (Si) in a full complementary metal oxide semiconductor-compatible approach. Recent GeSn laser developments rely on increasing the band structure directness, by increasing the Sn content in thick GeSn layers grown on germanium (Ge) virtual substrates (VS) on Si. These lasers nonetheless suffer from a lack of defect management and from high threshold densities. In this work we examine the lasing characteristics of GeSn alloys with Sn contents ranging from 7 \% to 10.5 \%. The GeSn layer…
Effective, permanent tuning of the whispering gallery modes (WGMs) of p-i-n doped GaN microdisk cavity with embedded InGaN quantum dots over one free spectral range is successfully demonstrated by irradiating the microdisks with a ultraviolet laser (380nm) in DI water. For incident laser powers between 150 and 960 nW, the tuning rate varies linearly. Etching of the top surface of the cavity is proposed as the driving force for the observed shift in WGMs, and is supported by experiments. The tuning for GaN/InGaN microdisk cavities is an important step for deterministically realizing novel nanop…
We investigate two coupled microdisks with non-identical radii focusing on the parametric evolution of energy levels and the unidirectional far-field emission. We show that the evolution of energy levels is characterized by the avoided crossing intrinsically associated with the exceptional point or the non-Hermitian degeneracy. These spectral properties explain highly asymmetric near-field intensity pattern of the resonance mode. The observed unidirectional far-field emission is shown to be understood by considering the forbidden inter-disk coupling in the ray picture induced by the frustrated…
Erbium-doped lithium niobate high-Q microdisk cavities were fabricated in batches by UV exposure, inductively coupled plasma reactive ion etching and chemo-mechanical polishing. The stimulated emission at 1531.6 nm was observed under the pump of a narrow-band laser working at 974 nm in erbium-doped lithium niobate microdisk cavity with threshold down to 400 μW and a conversion efficiency of 3.1{\times}10^{-4} %, laying the foundation for the LNOI integrated light source research.
GeSn alloys are promising candidates for complementary metal-oxide-semiconductor (CMOS)-compatible, tunable lasers. Relaxation of residual compressive strain in epitaxial GeSn has recently shown promise in improving the lasing performance. However, the suspended device configuration that has thus far been introduced to relax the strain is destined to limit heat dissipation, thus hindering the device performance. Herein, we demonstrate that strain-free GeSn microdisk laser devices fully released on Si outperform the canonical suspended devices. This approach allows to simultaneously relax the l…
The 4-bar crystal symmetry in materials such as GaAs can enable quasi-phasematching for efficient frequency conversion without poling, twinning or other engineered domain inversions. 4-bar symmetry means that a 90 degree rotation is equivalent to a crystallographic inversion. Therefore, propagation geometries where light circulates about the 4-bar axis produce effective domain inversions, useful for quasi-phasematching. Microdisk optical cavities also offer resonance field-enhancement and excellent spatial overlap, resulting in highly efficient frequency conversion in micrometer-scale volumes.…
We demonstrate gallium phosphide (GaP) microdisk optical cavities with intrinsic quality factors $ > 2.8\times10^{5}$ and mode volumes $< 10 (λ/n)^3$, and study their nonlinear and optomechanical properties. For optical intensities up to $8.0\times10^4$ intracavity photons, we observe optical loss in the microcavity to decrease with increasing intensity, indicating that saturable absorption sites are present in the GaP material, and that two-photon absorption is not significant. We observe optomechanical coupling between optical modes of the microdisk around 1.5 $μ$m and several mechanical res…
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…
Resonances in optical cavities have been used to manipulate light propagation, enhance light-matter interaction, modulate quantum states, and so on. However, in traditional cavities, the permittivity contrast in and out the cavity is not so high. Recently, zero-index materials (ZIMs) with unique properties and specific applications have attracted great interest. By putting optical cavity into ZIMs, the extreme circumstance with infinite permittivity contrast can be obtained. Here, we theoretically study Mie resonances of dielectric cavities embedded in ZIMs with $\varepsilon \approx 0$, or $μ\…
The life times of optical modes in whispering-gallery cavities crucially depend on the underlying classical ray dynamics and may be spoiled by the presence of classical nonlinear resonances due to resonance--assisted tunneling. Here we present an intuitive semiclassical picture which allows for an accurate prediction of decay rates of optical modes in systems with a mixed phase space. We also extend the perturbative description from near-integrable systems to systems with a mixed phase space and find equally good agreement. Both approaches are based on the approximation of the actual ray dynam…
We report on controllable cavity modes through controlling the backscattering by two identical scatterers. Periodic changes of the backscattering coupling between two degenerate cavity modes are observed with the angle between two scatterers and elucidated by a theoretical model using two-mode approximation and numerical simulations. The periodically appearing single-peak cavity modes indicate mode degeneracy at diabolical points. Then interactions between single quantum dots and cavity modes are investigated. Enhanced emission of a quantum dot with a six-fold intensity increase is obtained in…
An important building block for on-chip photonic applications is a scaled emitter. Whispering gallery mode cavities based on III-Vs on Si allow for small device footprints and lasing with low thresholds. However, multimodal emission and wavelength stability over a wider range of temperature can be challenging. Here, we explore the use of Au nanorods on InP whispering gallery mode lasers on Si for single mode emission. We show that by proper choice of the antenna size and positioning, we can suppress the side-modes of a cavity and achieve single mode emission over a wide excitation range. We es…
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.
Controlling gain and loss of coupled optical cavities can induce non-Hermitian degeneracies of eigenstates, called exceptional points (EPs). Various unconventional phenomena around EPs have been reported, and expected to incorporate extra functionalities into photonic devices. The eigenmode exactly under the EP degeneracy is also predicted to exhibit enhanced radiation. However, such responses have yet to be observed in on-chip lasers, because of both the limited controllability of their gain and loss and the lifting of degeneracy by pump-induced cavity detuning. Here, we report the first non-…
We study the frequency splitting of the polarization eigenmodes of the fundamental transverse mode in CO2 laser-machined, high-finesse optical Fabry-Perot cavities and investigate the influence of the geometry of the cavity mirrors. Their highly reflective surfaces are typically not rotationally symmetric but have slightly different radii of curvature along two principal axes. We observe that the eccentricity of such elliptical mirrors lifts the degeneracy of the polarization eigenmodes. The impact of the eccentricity increases for smaller radii of curvature. A model derived from corrections t…
The H1 photonic crystal cavity supports two degenerate dipole modes of orthogonal linear polarization which could give rise to circularly polarized fields when driven with a $π$/$2$ phase difference. However, fabrication errors tend to break the symmetry of the cavity which lifts the degeneracy of the modes, rendering the cavity unsuitable for supporting circular polarization. We demonstrate numerically, a scheme that induces chirality in the cavity modes, thereby achieving a cavity that supports intrinsic circular polarization. By selectively modifying two air holes around the cavity, the dip…
The differential response of chiral molecules to incident left- and right- handed circularly polarized light is used for sensing the handedness of molecules. Currently, significant effort is directed towards enhancing weak differential signals from the molecules, with the goal of extending the capabilities of chiral spectrometers to lower molecular concentrations or small analyte volumes. Previously, optical cavities for enhancing vibrational circular dichroism have been introduced. Their enhancements are mediated by helicity-preserving cavity modes which maintain the handedness of light due t…
We present a method to analyze the suitability of particular photonic cavity designs for information exchange between arbitrary superposition states of a quantum emitter and the near-field photonic cavity mode. As an illustrative example, we consider whether quantum dot emitters embedded in "L3" and "H1" photonic crystal cavities are able to transfer a spin superposition state to a confined photonic superposition state for use in quantum information transfer. Using an established dyadic Green's function (DGF) analysis, we describe methods to calculate coupling to arbitrary quantum emitter posi…
In this paper, we report the model and the experimental demonstration of a new optical resonator formed by inserting a Fiber Bragg Grating (FBG) in a closed fiber loop. The spectral characteristics of the ring depend on the reflectivity of the FBG. When the FBG reflectivity tends to zero, the overall resonant system exhibits the usual degenerate mode conditions. On the other hand, when the reflection coefficient FBG is not vanishing, the spectral features of the resonator display split resonant modes associated to the degeneracy removal of two counterpropagating modes that resonate within the …
Micro-/nanocavities that combine high quality factor ($Q$) and small mode volume ($V$) have been used to enhance light-matter interactions for cavity quantum electrodynamics (cQED). Whispering gallery mode (WGM) geometries such as microdisks and microrings support high-$Q$ and are design- and fabrication-friendly, but $V$ is often limited to tens of cubic wavelengths to avoid WGM radiation. The stronger modal confinement provided by either one-dimensional or two-dimensional photonic crystal defect geometries can yield sub-cubic-wavelength $V$, yet the requirements on precise design and dimensi…
We demonstrate for the first time the occurrence of a sixth order exceptional point of degeneracy (EPD) in a realistic multimode optical photonic structure by using a modified periodic coupled resonators optical waveguide (CROW), at the optical wavelength ${λ_e} = 1550 nm$. The 6th order EPD is obtained in a CROW without the need of loss or gain and such an EPD corresponds to a very special band edge of the periodic photonic structure where six eigenmode coalesce, so we refer to it as the 6th order degenerate band edge (6DBE). Moreover, we report a new scaling law of the quality factor Q of an…
We numerically implement the concept of thermal radiation pumps in realistic photonic circuits and demonstrate their efficiency to control the radiation current, emitted between two reservoirs with equal temperature. The proposed pumping scheme involves a cyclic adiabatic modulation of two parameters that control the spectral characteristics of the photonic circuit. We show that the resulting pumping cycle exhibits maximum radiation current when a cyclic modulation of the system is properly engineered to be in the proximity of a resonance degeneracy in the parameter space of the photonic circu…
Whispering gallery resonators (WGR's), based on total internal reflection, possess high quality factors in a broad spectral range. Thus, nonlinear optical processes in such cavities are ideally suited for the generation of broadband or tunable electromagnetic radiation. Experimentally and theoretically, we investigate the tunability of optical parametric oscillation in a radially structured WGR made of lithium niobate. With a 1.04 /mum pump wave, the signal and idler waves are tuned from 1.78 to 2.5 \mum - including the point of degeneracy - by varying the temperature between 20 and 62 °C. A w…
Enhancement cavities where a beam of large size (several millimeters) can resonate have several applications, in particular in atomic physics. However, reaching large beam waists in a compact geometry (less than a meter long) typically brings the resonator close to the degeneracy limit. Here we experimentally study a degenerate optical cavity, 44-cm long and consisting of two flat mirrors placed in the focal planes of a lens, in a regime of intermediate finesse ($\sim 150$). We study the impact of the longitudinal misalignement on the optical gain, for different input beam waists up to 5.6~mm,…
Optical cavities can support many transverse and longitudinal modes. A paraxial scalar theory predicts that the resonance frequencies of these modes cluster in different orders. A non-paraxial vector theory predicts that the frequency degeneracy within these clusters is lifted, such that each order acquires a spectral fine structure, comparable to the fine structure observed in atomic spectra. In this paper, we calculate this fine structure for microcavities and show how it originates from various non-paraxial effects and is co-determined by mirror aberrations. The presented theory, which appl…
Exceptional point (EP) degeneracies in coupled cavities with gain and loss provide on-chip photonic devices with unconventional features and performance. However, such systems with realistic structures often miss the exact EPs even in simulation, and the mechanism of this EP disruption has yet to be thoroughly identified. Here, we extend the coupled-mode theory of one-dimensional non-Hermitian resonator arrays to study the effects of the imaginary part of the inter-cavity coupling, which is a second-order term and attributed to material amplification, absorption, and radiation. By taking an ap…
Image-amplifying optical cavities offer an intriguing platform for nonlinear optical processing of two-dimensional signals, with potential applications in optical information processing and optically implemented artificial neural networks. Here, we analyze the performance of a self-imaging degenerate cavity via numerical simulations and show the existence of a cavity size-dependent minimum spread in the transverse mode resonances. This non-degeneracy, in turn, leads to an inherent trade-off between the amplification and the fidelity of the intracavity image as the cavity finesse changes. Our r…
The optical properties of slab waveguides made of indefinite permittivity ($\vep$) materials (IEM) are considered. In this medium the transverse permittivity is negative while the longitudinal permittivity is positive. At any given frequency the waveguide supports an infinite number of transverse magnetic (TM) eigenmodes. For a slab waveguide with a fixed thickness, at most only one TM mode is forward-wave. The rest of them are backward waves which can have very large phase index. At a critical thickness, the waveguide supports degenerate forward- and backward-wave modes with zero group veloci…
