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.
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 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.…
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\…
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 …
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 analyze the optical resonances of a dielectric sphere whose surface has been slightly deformed in an arbitrary way. Setting up a perturbation series up to second order, we derive both the frequency shifts and modified linewidths. Our theory is applicable, for example, to freely levitated liquid drops or solid spheres, which are deformed by thermal surface vibrations, centrifugal forces or arbitrary surface waves. A dielectric sphere is effectively an open system whose description requires the introduction of non-Hermitian operators characterized by complex eigenvalues and not normalizable e…
Light injected into a spherical dielectric body may be confined very efficiently via the mechanism of total internal reflection. The frequencies that are most confined are called resonances. If the shape of the body deviates from the perfect spherical form the resonances change accordingly. In this thesis, a perturbation theory for the optical resonances of such a deformed sphere is developed. The optical resonances of such an open system are characterized by complex eigenvalues, where the real part relates to the frequency of the resonant light and the imaginary part to the energy leakage out…
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…
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…
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…
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.
Hybrid photonic-plasmonic cavities have emerged as a new platform to increase light-matter interaction capable to enhance the Purcell factor in a singular way not attainable with either photonic or plasmonic cavities separately. In the hybrid cavities proposed so far, mainly consisting of metallic bow-tie antennas, the plasmonic gap sizes defined by lithography in a repeatable way are limited to minimum values \approx 10 nm. Nanoparticle-on-a-mirror (NPoM) cavities are far superior to achieve the smallest possible mode volumes, as gaps smaller than 1 nm can be created. Here, we design a hybrid…
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…
Short pitch deformed helix ferroelectric liquid crystals have numerous applications as active materials in displays, optical telemetry and biomedical devices. In this paper, we derive convenient analytical formulas to calculate the effective dielectric tensor of these materials beyond the space average approximation. By comparison with exact numerical calculations, we show that our formulas are remarkably accurate in predicting optical properties in virtually all practical situations, including the important case of large tilt angles, where the space average approximation breaks down. We also …
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…
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 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…
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…
Spherical and cylindrical dielectric cavities support high Q whispering gallery modes due to total internal reflection of the trapped light. When such a cavity is deformed smoothly the ray dynamics of these modes becomes chaotic in a manner determined by the KAM theory of classical hamiltonian dynamics. The universal properties of the ray dynamics predicted by KAM theory allow a general understanding of the whispering gallery modes of such asymmetric resonant cavities (ARCs). This theory combined with simulations of the non-linear map describing the ray motion provides the basis for a ray-opti…
We report a circuit cavity optomechanical system in which a nanomechanical resonator is adiabatically embedded inside an optical ring resonator with ultralow transition loss. The nanomechanical device forms part of the top layer of a horizontal silicon slot ring resonator, which enables dispersive coupling to the dielectric substrate via a tapered nanogap. Our measurements show nearly uncompromised optical quality factors (Q) after the release of the mechanical beam.
The construction of perturbation series for slightly deformed dielectric circular cavity is discussed in details. The obtained formulae are checked on the example of cut disks. A good agreement is found with direct numerical simulations and far-field experiments.
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…
The paper is devoted to optimization of resonances in a 1-D open optical cavity. The cavity's structure is represented by its dielectric permittivity function e(s). It is assumed that e(s) takes values in the range 1 <= e_1 <= e(s) <= e_2. The problem is to design, for a given (real) frequency, a cavity having a resonance with the minimal possible decay rate. Restricting ourselves to resonances of a given frequency, we define cavities and resonant modes with locally extremal decay rate, and then study their properties. We show that such locally extremal cavities are 1-D photonic crystals consi…
An invisible cavity is an open resonant device that confines a localized field without producing any scattering outside of the device volume. By exploiting the scatter-less property of such device, it is possible to nest two invisible cavities, as the outer cavity would simply not notice the presence of the inner one, regardless of their relative position. As a result, the position of the inner cavity becomes a means to easily control the field localized inside the cavity and its quality factor. In this paper, we discuss the properties of nested invisible cavities as a simple method to achieve…
We demonstrate that multiple topological transitions can occur, with high-sensitivity, by continuous change of the geometry of a simple 2D dielectric-frame photonic crystal consisting of circular air-holes. By changing the radii of the holes and/or the distance between them, multiple transitions between normal and topological photonic band gaps (PBGs) can appear. The time-reversal symmetric topological PBGs resemble the quantum spin-Hall insulator of electrons and have two counter-propagating edge states. We search for optimal topological transitions, i.e., sharp transitions sensitive to the g…
By modifying the density of optical states at the location of an emitter, weak cavity-emitter coupling can enable a host of potential applications in quantum optics, from the development of low- threshold lasers to brighter single-photon sources for quantum cryptography. Although some of the first demonstrations of spontaneous emission modification occurred in metallic structures, it was only after the recent demonstration of cavity quantum electrodynamics effects in dielectric optical cavities that metal-based optical cavities were considered for quantum optics applications. Advantages of met…
We describe a general recipe for designing high-quality factor (Q) photonic crystal cavities with small mode volumes. We first derive a simple expression for out-of-plane losses in terms of the k-space distribution of the cavity mode. Using this, we select a field that will result in a high Q. We then derive an analytical relation between the cavity field and the dielectric constant along a high symmetry direction, and use it to confine our desired mode. By employing this inverse problem approach, we are able to design photonic crystal cavities with Q > 4*10^6 and mode volumes V ~ (λ/n)^3. Our…
Thermal effects are already important in currently operating interferometric gravitational wave detectors. Planned upgrades of these detectors involve increasing optical power to combat quantum shot noise. We consider the ramifications of this increased power for one particular class of laser beams--wide, flat-topped, mesa beams. In particular we model a single mesa beam Fabry-Perot cavity having thermoelastically deformed mirrors. We calculate the intensity profile of the fundamental cavity eigenmode in the presence of thermal perturbations, and the associated changes in thermal noise. We als…
A numerical model based on the finite-difference time-domain (FDTD) method is developed to simulate thermal noise in open cavities owing to output coupling. The absorbing boundary of the FDTD grid is treated as a blackbody, whose thermal radiation penetrates the cavity in the grid. The calculated amount of thermal noise in a one-dimensional dielectric cavity recovers the standard result of the quantum Langevin equation in the Markovian regime. Our FDTD simulation also demonstrates that in the non-Markovian regime the buildup of the intracavity noise field depends on the ratio of the cavity pho…
Defect cavities in 3D photonic crystal can trap and store light in the smallest volumes allowable in dielectric materials, enhancing non-linearities and cavity QED effects. Here, we study inverse rod-connected diamond (RCD) crystals containing point defect cavities using plane-wave expansion and finite-difference time domain methods. By optimizing the dimensions of the crystal, wide photonic band gaps are obtained. Mid-bandgap resonances can then be engineered by introducing point defects in the crystal. We investigate a variety of single spherical defects at different locations in the unit ce…
We demonstrate a fiber-integrated Fabry-Pérot cavity formed by attaching a pair of dielectric metasurfaces to the ends of a hollow-core photonic-crystal fiber segment. The metasurfaces consist of perforated membranes designed as photonic-crystal slabs that act as planar mirrors but can potentially allow injection of gases through their holes into the hollow core of the fiber. We have so far observed cavities with finesse of ~11 and Q factors of ~$4.5 \times 10^5$, but much higher values should be achievable with improved fabrication procedures. We expect this device to enable development of ne…
We introduce a second quantization scheme based on quasinormal modes, which are the dissipative modes of leaky optical cavities and plasmonic resonators with complex eigenfrequencies. The theory enables the construction of multi-plasmon/photon Fock states for arbitrary three-dimensional dissipative resonators and gives a solid understanding to the limits of phenomenological dissipative Jaynes-Cummings models. In the general case, we show how different quasinormal modes interfere through an off-diagonal mode coupling and demonstrate how these results affect cavity-modified spontaneous emission.…
