The resonant optical modes of a high permittivity dielectric prism with an equilateral triangular cross section are discussed. Eigenmode solutions of the scalar Helmholtz equation with Dirichlet boundary conditions, appropriate to a conducting boundary, are applied for this purpose. The particular plane wave components present in these modes are analyzed for their total internal reflection behavior and implied mode confinement when the conducting boundary is replaced by a sharp dielectric mismatch. Improvement in TIR confinement by adjusting the longitudinal wavevector $k_z$ is also discussed. For two-dimensional electromagnetic solutions ($k_z=0$), TE polarization leads to longer lifetime than TM polarization, assuming that escape of evanescent boundary waves at the corners is the primary decay process.
We consider dielectric cavities whose radiation space is restricted by two parallel metallic planes. The TM solutions of the Maxwell equations of the system are equivalent to the solutions of periodical arrays of dielectric cavities. The system readily allows to achieve bound states in the continuum (BICs) of any type including topological BICs as dependent on position and orientation of the cavities relative to the planes. That extremely facilitates experimental studies in comparison to infinite arrays of the cavities. We show the effect of merging of topologically protected BICs that pushes …
In the absence of external excitation, light trapped within a dielectric medium generally decays by leaking out (and also by getting absorbed within the medium). We analyze the leaky modes of a parallel-plate slab, a solid glass sphere, and a solid glass cylinder, by examining those solutions of Maxwell's equations (for dispersive as well as non-dispersive media) which admit of a complex-valued oscillation frequency. Under certain circumstances, these leaky modes constitute a complete set into which an arbitrary distribution of the electromagnetic field residing inside a dielectric body can be…
The stationary states of a microlaser are related to the decaying quasibound states of the corresponding passive cavity. These are interpreted classically as originating from sequential escape attempts of an ensemble of rays obeying a curvature-corrected Fresnel formula. Polarization-dependent predictions of this model, and its limitations for stable orbits in partially chaotic systems are discussed.
The optical resonance problem is similar to but different from time-steady Schrödinger equation. One big challenge is that the eigenfunctions in resonance problem is exponentially growing. We give physical explanation to this boundary condition and introduce perfectly matched layer (PML) method to transform eigenfunctions from exponential-growth to exponential-decay. Based on the complex stretching technique, we construct a non-Hermitian Hamiltonian for the optical resonance problem. We successfully validate the effectiveness of the Hamiltonian by calculate its eigenvalues in the circular cavi…
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\…
Outer resonances are studied as one type of quasinormal modes in two-dimensional dielectric cavities with refractive index $n>1$. The outer resonances can be verified as the resonances which survive only outside the cavity in the small opening limit of the dielectric disk. We have confirmed that the outer resonances universally exist in deformed cavities irrespective of the geometry of cavity and they split into nearly degenerate states in slightly deformed cavity. Also we pointed out that the effective potential analogy is inapplicable to the description of outer resonances. Since most outer …
We present a novel differential refractive index sensor based on arrays of photonic molecules (PM) of dielectric cylinders and two structural defect cavities. The transmission spectrum of the photonic proposed structure as sensor shows a wide photonic stop band with two localized states. One of them, the reference state, is bound to a decagonal ring of cylinders and the other, the sensing state, to the defect cavities of the lattice. It is shown that defect mode is very sensitive to the presence of materials with dielectric permittivity different from that of the surrounding cylinders while th…
The quasi-bound modes localized on stable periodic ray orbits of dielectric micro-cavities are constructed in the short-wavelength limit using the parabolic equation method. These modes are shown to coexist with irregularly spaced "chaotic" modes for the generic case. The wavevector quantization rule for the quasi-bound modes is derived and given a simple physical interpretation in terms of Fresnel reflection; quasi-bound modes are explictly constructed and compared to numerical results. The effect of discrete symmetries of the resonator is analyzed and shown to give rise to quasi-degenerate m…
In this paper, the chaotic ray dynamics inside dielectric cavities is described by the properties of an invariant chaotic saddle. I show that the localization of the far field emission in specific directions is related to the filamentary pattern of the saddle's unstable manifold, along which the energy inside the cavity is distributed. For cavities with mixed phase space, the chaotic saddle is divided in hyperbolic and non-hyperbolic components, related, respectively, to the intermediate exponential (t<t_c) and the asymptotic power-law (t>t_c) decay of the energy inside the cavity. The alignme…
A scalable approach for integrated photonic networks in single-crystal diamond using triangular etching of bulk samples is presented. We describe designs of high quality factor (Q=2.51x10^6) photonic crystal cavities with low mode volume (Vm=1.062x(λ/n)^3), which are connected via waveguides supported by suspension structures with predicted transmission loss of only 0.05 dB. We demonstrate the fabrication of these structures using transferred single-crystal silicon hard masks and angular dry etching, yielding photonic crystal cavities in the visible spectrum with measured quality factors in ex…
We present a versatile numerical algorithm for computing resonances of open dielectric cavities. The emphasis is on the generality of the system's configuration, i.e. the geometry of the (main) cavity (and possible inclusions) and the internal and external dielectric media (homogeneous and inhomogeneous). The method is based on a scattering formalism to obtain the position and width of the (quasi)-eigenmodes. The core of the method lies in the scattering S-matrix and its associated delay Q-matrix which contain all the relevant information of the corresponding scattering experiment. For instanc…
Diamond photonics provides an attractive architecture to explore room temperature cavity quantum electrodynamics and to realize scalable multi-qubit computing. Here we review the present state of diamond photonic technology. The design, fabrication and characterization of a novel triangular cross section nanobeam cavity produced in a single crystal diamond is demonstrated. The present cavity design, based on a triangular cross section allows vertical confinement and better signal collection efficiency than that of slab-based nanocavities, and eliminates the need for a pre-existing membrane. Th…
We conjecture that chaotic resonance modes in scattering systems are a product of a conditionally invariant measure from classical dynamics and universal exponentially distributed fluctuations. The multifractal structure of the first factor depends strongly on the lifetime of the mode and describes the average of modes with similar lifetime. The conjecture is supported for a dielectric cavity with chaotic ray dynamics at small wavelengths, in particular for experimentally relevant modes with longest lifetime. We explain scarring of the vast majority of modes along segments of rays based on mul…
Dielectric resonators are open systems particularly interesting due to their wide range of applications in optics and photonics. In a recent paper [PRE, vol. 78, 056202 (2008)] the trace formula for both the smooth and the oscillating parts of the resonance density was proposed and checked for the circular cavity. The present paper deals with numerous shapes which would be integrable (square, rectangle, and ellipse), pseudo-integrable (pentagon) and chaotic (stadium), if the cavities were closed (billiard case). A good agreement is found between the theoretical predictions, the numerical simul…
A boundary element method based on a Green's function technique is introduced to compute resonances with intermediate lifetimes in quasi-two-dimensional dielectric cavities. It can be applied to single or several optical resonators of arbitrary shape, including corners, for both TM and TE polarization. For cavities with symmetries a symmetry reduction is described. The existence of spurious solutions is discussed. The efficiency of the method is demonstrated by calculating resonances in two coupled hexagonal cavities.
We apply ray-optical methods to dielectric optical microcavities in the shape of triangles made of low refractive index material. We find ray trajectories that maximize the intensity inside the cavity to determine the far-field emission characteristics and to complement the concept of the unstable manifold applicable to chaotic microlasers. As these maximum intensity trajectories need not to be periodic, we suggest that they provide a more general explanation for emission patterns of microlasers than short periodic orbits. Further, the geometrical optics description is extended by the inclusio…
An analysis is provided of the degradation that arises in the quality factor of a whispering gallery mode when a circular or spherical dielectric cavity is deformed. The large quality factors of such resonators are important to their use in applications such as sensors, wavelength filters or lasers. Yet a straightforward analysis of the effect of shape deformation on quality factors cannot given because the underlying complex ray data demanded by a standard eikonal approximation frequently does not exist. In this paper we exploit an approach that has been successfully used elsewhere to describ…
Nanotechnology enables in principle a precise mapping from design to device but relied so far on human intuition and simple optimizations. In nanophotonics, a central question is how to make devices in which the light-matter interaction strength is limited only by materials and nanofabrication. Here, we integrate measured fabrication constraints into topology optimization, aiming for the strongest possible light-matter interaction in a compact silicon membrane, demonstrating an unprecedented photonic nanocavity with a mode volume of $V\sim3\times10^{-4}\,λ^3$, quality factor $Q\sim1100$, and f…
We develop and demonstrate two numerical methods for solving the class of open cavity problems which involve a curved, cylindrically symmetric conducting mirror facing a planar dielectric stack. Such dome-shaped cavities are useful due to their tight focusing of light onto the flat surface. The first method uses the Bessel wave basis. From this method evolves a two-basis method, which ultimately uses a multipole basis. Each method is developed for both the scalar field and the electromagnetic vector field and explicit ``end user'' formulas are given. All of these methods characterize the arbit…
In limaçon-shaped gradient index dielectric cavities designed by conformal transformation optics, the variation of Q-factors and emission directionality of resonant modes was traced in their system parameter space. For these cavities, their boundary shapes and refractive index profiles are determined in each case by a chosen conformal mapping which is taken as a coordinate transformation. Through the numerical exploration, we found that bidirectionality factors of generic high-Q resonant modes are not directly proportional to their Q-factors. The optimal system parameters for the coexistence o…
The majority of sources of coherent optical radiation rely on laser oscillators driven by population inversion. Despite their technological importance in communications, medicine, industry, and other fields, it remains a challenge to access the spectral range of 0.1-10 THz (the "terahertz gap"), a frequency band for applications ranging from spectroscopy to security and high-speed wireless communications. Here, we propose a way to produce coherent radiation spanning the THz gap by efficient second-harmonic generation (SHG) in low-loss dielectric structures, starting from technologically mature…
We perform numerical studies of the effect of sidewall imperfections on the resonant state broadening of the optical microdisk cavities for lasing applications. We demonstrate that even small edge roughness causes a drastic degradation of high-Q whispering gallery (WG) mode resonances reducing their Q-values by many orders of magnitude. At the same time, low-Q WG resonances are rather insensitive to the surface roughness. The results of numerical simulation obtained using the scattering matrix technique, are analyzed and explained in terms of wave reflection at a curved dielectric interface co…
We present a theoretical study of dielectric bowtie cavities and show that they are governed by two essentially different confinement regimes. The first is confinement inside the bulk dielectric and the second is a local lightning-rod regime where the field is locally enhanced at sharp corners and may yield a vanishing mode volume without necessarily enhancing the mode inside the bulk dielectric. We show that while the bulk regime is reminiscent of the confinement in conventional nanocavities, the most commonly used definition of the mode volume gauges in fact the lightning-rod effect when app…
We present an effective model for a subwavelength periodically patterned metallic layer, its cavities being filled with a nonlinear dielectric material, which accounts for both the linear and second order behavior. The effective non linear susceptibility for the homogenized layer is driven by the nonlinearity of the dielectric material and by the geometrical parameters, thus leading to much higher susceptibility than existing materials. This leads to a huge enhancement of non linear processes when used together with resonances. Furthermore, multiple resonances are taking place in the metallic …
In a recent investigation, we studied two-dimensional point-defected photonic bandgap cavities composed of dielectric rods arranged according to various representative periodic and aperiodic lattices, with special emphasis on possible applications to particle acceleration (along the longitudinal axis). In this paper, we present a new study aimed at highlighting the possible advantages of using hybrid structures based on the above dielectric configurations, but featuring metallic rods in the outermost regions, for the design of extremely-high quality factor, bandgap-based, accelerating resonato…
We study a range of radio-frequency ion trap geometries and investigate the effect of integrating dielectric cavity mirrors on their trapping potential. We aim to identify ion trap and cavity configurations that are best suited for achieving small cavity volumes and thus large ion-photon coupling as required for scalable quantum information networks. In particular, we investigate the trapping potential distortions caused by the dielectric material of the cavity mirrors for different mirror orientations with respect to the trapping electrodes, as well as for mirror misalignment. We also analyze…
We have developed a scattering-matrix approach for numerical calculation of resonant states and Q-values of a nonideal optical disk cavity of an arbitrary shape and of an arbitrary varying refraction index. The developed method has been applied to study the effect of surface roughness and inhomogeneity of the refraction index on Q-values of microdisk cavities for lasing applications. We demonstrate that even small surface roughness can lead to a drastic degradation of high-Q cavity modes by many orders of magnitude. The results of numerical simulation are analyzed and explained in terms of wav…
Photonic crystal nanobeam cavities are versatile platforms of interest for optical communications, optomechanics, optofluidics, cavity QED, etc. In a previous work \cite{quan10}, we proposed a deterministic method to achieve ultrahigh \emph{Q} cavities. This follow-up work provides systematic analysis and verifications of the deterministic design recipe and further extends the discussion to air-mode cavities. We demonstrate designs of dielectric-mode and air-mode cavities with $Q>10^9$, as well as cavities with both high-\emph{Q} ($>10^7$) and high on-resonance transmissions ($T>95%$).
Controlling the emission and interaction properties of quantum emitters (QEs) embedded within an optical cavity is a key technique in engineering light-matter interactions at the nanoscale, as well as in the development of quantum information processing. State-of-the-art optical cavities are based on high Q photonics crystals and dielectric resonators. However, wealthier responses might be attainable with cavities carved in more exotic materials. Here, we theoretically investigate the emission and interaction properties of QEs embedded in open epsilon-near-zero (ENZ) cavities. Using analytical…
The interaction of magnetic dipole (MD) emitters and common photonic cavities is usually weak, which is partially due to the low magnetic near field enhancements of the cavities. Here, we show that whispering gallery modes (WGMs) of a subwavelength dielectric cavity can not only greatly boost the emission rate of a MD emitter but also bring efficient couplings between coherent MD emitters. In a WGM cavity, the maximal emission rate (γmax) of a single emitter occurs at an antinode of the field pattern. The emission of the MD emitter can also be greatly affected by another coherent one depending…
We reveal a triangular-lattice planar photonic crystal supports Bloch modes with radially and azimuthally symmetric electric field distributions at the top band-edge of the first photonic band. Bifurcated from the corresponding Bloch modes, two cylindrical vector resonant modes are achieved by simply enlarging the central air-hole of the planar photonic crystal, which have high quality factors around 3,000 and small mode volume. The far-field radiations of the two resonant modes present high-quality cylindrical vector beam profiles. The resonant modes could be optimized by modifying the six ne…
We demonstrate that a triangular cavity can operate as an efficient discriminator for Hermite-Gaussian optical modes. The process is applied to distinct fields produced by a Spatial Light Modulator, decomposing the generated paraxial field onto a basis of modes defined by the resonant modes of the optical cavity. We also present a proposal for the realization of a mode sorter based on a sequence of these cavities, without the need for optical isolation. We discuus its possible applications in sensitive measurements and distribution of information in optical systems. The high purity of the proc…
We demonstrate that a proton irradiation with fluences of $3.6\times10^{10}$/cm$^{2}$ at low energy ($<$ 36 MeV) and $1.46 \times 10^{10}$/cm$^{2}$ at high energy (40 MeV and 90 MeV combined) on the dielectric mirrors of Fabry-Pérot cavities with a finesse of about 700 000 causes less than 5% change in the finesse. Furthermore, no influence on the coupling efficiency to the cavities was observed, the efficiency being approximately 70%. The irradiation was carried out with a spectrum approximating the proton energy spectrum of a highly elliptic Earth orbit with duration of 5 years, proposed for…
Recent progress in nanoscale optical physics is associated with the development of a new branch of nanophotonics exploring strong Mie resonances in dielectric nanoparticles with high refractive index. The high-index resonant dielectric nanostructures form building blocks for novel photonic metadevices with low losses and advanced functionalities. However, unlike extensively studied cavities in photonic crystals, such dielectric resonators demonstrate low quality factors (Q-factors). Here, we uncover a novel mechanism for achieving giant Q-factors of subwavelength nanoscale resonators by realiz…
The way molecules absorb, transfer, and emit light can be dramatically modified by coupling them to optical cavities. The extent of the modification is often defined by the cavity-molecule coupling strength. Evaluating this coupling strength for different types of modes supported by a cavity is crucial in designing cavities for molecule-cavity coupling. Here we probe a unique multimode cavity, a dielectric microsphere, also called a soft-cavity, which supports two distinct types of mode, dark-field scattering (DFS) modes and whispering gallery modes (WGM). Though seemingly similar, these modes…
Crystal-symmetry-protected photonic topological edge states (PTESs) based on air rods in conventional dielectric materials are designed as photonic topological waveguides (PTWs) coupled with side optical cavities. We demonstrate that the cavity coupled with the PTW can change the reflection-free transport of the PTESs, where the cavities with single mode and twofold degenerate modes are taken as examples. The single-mode cavities are able to perfectly reflect the PTESs at their resonant frequencies, forming a dip in the transmission spectra. The dip full width at half depth depends on the coup…
Dielectric spheres of various sizes may sustain electromagnetic whispering-gallery modes resonating at optical frequencies with very narrow linewidths. Arbitrary small deviations from the spherical shape typically shift and broaden such resonances. Our goal is to determine these shifted and broadened resonances. A boundary-condition perturbation theory for the acoustic vibrations of nearly circular membranes was developed by Rayleigh more than a century ago. We extend this theory to describe the electromagnetic excitations of nearly spherical dielectric cavities. This approach permits us to av…
In the absence of external excitation, light trapped within a dielectric medium generally decays by leaking out, and also by getting absorbed within the medium. We analyze the leaky modes of solid dielectric spheres by examining solutions of Maxwell's equations for simple homogeneous, isotropic, linearly dispersive media that admit complex-valued oscillation frequencies. We show that, under appropriate circumstances, these leaky modes constitute a complete set into which an initial electromagnetic field distribution inside a dielectric sphere can be expanded. We provide the outline of a comple…
State-of-the-art optical oscillators employing cryogenic reference cavities are limited in performance by the Brownian thermal noise associated with the mechanical dissipation of the mirror coatings. Recently, crystalline Al$_{1-x}$Ga$_{x}$As/GaAs coatings have emerged as a promising candidate for improved coating thermal noise. We present measurements of the frequency noise of two fully crystalline cryogenic reference cavities with Al$_{0.92}$Ga$_{0.08}$As/GaAs optical coatings. We report on previously unmeasured birefringent noise associated with anti-correlated frequency fluctuations betwee…
Photonic cavities are valued in current research owing to the multitude of linear and nonlinear effects arising from densely confined light. Cavity designs consisting of low loss dielectric materials can achieve significant light confinement, competitive with other schools of cavity design such as plasmonics. However, the basic concepts in all dielectric photonics such as anapole resonances in nanodisks have been primarily studied in high index materials such as WS2 and Si. Without additional measures, low index dielectric nanodisks struggle to achieve similar levels of light confinement. Here…
