Arbitrary Cavities Research Articles

Extensible multi-wavelength interrogation method for arbitrary cavities in low-fineness multi-cavity Fabry-Pérot interferometric sensors.

To the best of our knowledge, a novel extensible multi-wavelength (EMW) method to interrogate arbitrary cavities in low-fineness fiber-optic multi-cavity Fabry-Pérot interferometric (LFMFPI) sensors is proposed and experimentally demonstrated. Based on the derived model of the LFMFPI sensor with any amount of cascaded cavities, theoretically, variation in each cavity of a LFMFPI sensor can be extracted simultaneously once the necessary parameters are acquired in advance. The feasibility of this method is successfully demonstrated in simulations and experiments utilizing LFMFPI sensors. In experiments with the LFMFPI sensor, optical path differences (OPD) of 78 nm and 2.95 µm introduced by temperature variation in two cavities, and the OPD induced by vibration with the amplitude from 5.891 nm to 38.116 nm were extracted, respectively. The EMW method is potential in multi-parameter sensing for pressure, vibration, and temperature.

Statistical Computation for Multipactors in Arbitrary Microwave Devices

Multipactors are avalanches of secondary electrons occurred in high-power vacuum microwave devices. Accurate prediction of their occurrences is challenging, especially for devices with complex geometric cavities under complex excitations. In this article, a generalized statistical theory is derived for predicting multipactors occurred in arbitrary metallic cavities under arbitrary excitations. Its computation burden is independent on the number of electrons, enabling investigations for dynamic evolutions of multipactors even in the presence of huge amount of avalanching electrons. Exampled with coaxial, rectangular, and ridged rectangular waveguides and excited with sinusoidal, multicarrier, and wideband radar signals, dynamic electron populations and breakdown levels were computed. While the obtained results agree well with previously reported experiments and particle-in-cell simulations, these results also explain three special phenomena occurred during multipactors, verifying the validity and accuracy of the proposed solution.

Scattering resonances in unbounded transmission problems with sign-changing coefficient

Abstract It is well known that classical optical cavities can exhibit localized phenomena associated with scattering resonances, leading to numerical instabilities in approximating the solution. This result can be established via the ‘quasimodes to resonances’ argument from the black box scattering framework. Those localized phenomena concentrate at the inner boundary of the cavity and are called whispering gallery modes. In this paper we investigate scattering resonances for unbounded transmission problems with sign-changing coefficient (corresponding to optical cavities with negative optical properties, e.g. made of metamaterials). Due to the change of sign of optical properties, previous results cannot be applied directly, and interface phenomena at the metamaterial-dielectric interface (such as the so-called surface plasmons) emerge. We establish the existence of scattering resonances for arbitrary two-dimensional smooth metamaterial cavities. The proof relies on an asymptotic characterization of the resonances, and shows that problems with sign-changing coefficient naturally fit the black box scattering framework. Our asymptotic analysis reveals that, depending on the metamaterial’s properties, scattering resonances situated close to the real axis are associated with surface plasmons. Examples for several metamaterial cavities are provided.

Analytical theory of frequency-modulated combs: generalized mean-field theory, complex cavities, and harmonic states.

Frequency-modulated (FM) combs with a linearly-chirped frequency and nearly constant intensity occur naturally in certain laser systems; they can be most succinctly described by a nonlinear Schrödinger equation with a phase potential. In this work, we perform a comprehensive analytical study of FM combs in order to calculate their salient properties. We develop a general procedure that allows mean-field theories to be constructed for arbitrary sets of master equations, and as an example consider the case of reflective defects. We derive an expression for the FM chirp of arbitrary Fabry-Perot cavities-important for most realistic lasers-and use perturbation theory to show how they are affected by finite gain bandwidth and linewidth enhancment in fast gain media. Lastly, we show that an eigenvalue formulation of the laser's dynamics can be useful for characterizing all of the stable states of the laser: the fundamental comb, the continuous-wave solution, and the harmonic states.

Complex TE-modes in Slotted Waveguides of Arbitrary Cross Section

Implementation of the rigorous Analytical Regularization Method is presented for plane wave scattering by arbitrary two-dimensional cavities with longitudinal slit. The general solution of the Neumann boundary value problem for Helmholtz equation is obtained in a form of two coupled infinite systems of linear algebraic equations of the second kind. Compactness of the matrix operator provides efficient numerical solution of the joint system by truncation method. Fast convergence of the truncated system of linear algebraic equations makes this method an effective instrument for accurate analysis of spectral and diffraction problems. Considering the homogeneous version of equations and finding the complex roots of their determinants, we calculate the complex eigenvalues of complex oscillations. Employing spline interpolation and mollifier function the problem geometry is generalized.

A novel semi-analytical methodology for predicting sound absorption of anechoic coatings with arbitrary rotary cavities dependent on temperature and frequency

In response to the shortcomings of existing studies on the sound-absorbing characteristics of an anechoic coating, which most ignore the frequency factor and are expensive for temperature-tunable hydroacoustic experiments, a novel semi-analytical methodology that considers both frequency and temperature is proposed in this paper. Based on the dynamic mechanical thermal analysis technique and time–temperature superposition principle, the temperature and frequency spectra of two rubber materials are tested and expanded in turn. Meanwhile, a complete acoustic prediction model is developed employing the non-uniform waveguide theory for an overburden containing arbitrary rotary cavities. Furthermore, taking a lining embedded with ramped cavities as the research structure, the theoretical model is firstly validated by an absorptive measurement conducted with the hydroacoustic impedance tube test-system, and then the acoustic influences of the material properties and geometric parameters of each sublayer, as well as the temperature factor, are investigated in-depth to reveal the multiple energy dissipation mechanisms. These results show that the present semi-analytical method can accurately and effectively predict the dynamic sound absorptions of a covering in the wide temperature-frequency range of Tg ~ Tg + 50 ℃ and 10 Hz ~ 106 Hz.

Equivalent inclusion method for arbitrary cavities or cracks in an elastic infinite/semi-infinite space

Shallow tunnels free of or subjected to the surface effects excavated in an elastic rock mass are usually simplified as an elastic infinite or semi-infinite plane problem with cavities in mechanics, respectively. In this paper, the equivalent inclusion method (EIM), a classic solution due to Eshelby usually used for predicting the elastic field caused by inhomogeneities embedded in a heterogeneous material, is extended to predict the elastic field induced by an arbitrarily shaped cavity. Similar to that of the inhomogeneity problems, the implementation of the EIM for the cavity problem is conducted by treating a cavity whose elastic modulus is zero as an inclusion having identical material properties to the matrix but containing eigenstrains. Based on an elementary solution for the eigenstress arising from the eigenstrains representing the cavity of an arbitrary shape can be calculated with the help of numerical discretization and superposition of contributions from each discretized element. A circular or rectangular cavity can be reduced to a crack when the distance between their upper and lower surfaces approaches an infinitesimal but not a zero value, hence the elastic field caused by cracks can be also resolved with the proposed solution method. The results obtained with the proposed method and the finite element method (FEM) for both the cavity and the crack are in good agreements. Parametric analyses on the effects of depth, length of the crack and the interactions among multiple cavities and cracks on the elastic field demonstrates the EIM as a good potential application in some significant applications in fracture behaviors for the excavated material.

Complex eigenvalues of slotted arbitrary cylindrical cavities: Sound-soft elliptic cavity with variably placed longitudinal slit.

A generalization of the rigorous method of regularization is implemented to calculate the complex eigenvalues for a two dimensional arbitrarily shaped acoustically soft cavity with a longitudinal slit. The problem is reduced to the finding of non-trivial solutions of the coupled homogeneous well-conditioned Fredholm second kind infinite systems of linear algebraic equations that are solved numerically by the truncation method. The guaranteed fast convergence of the solution of the truncated system to the exact solution allows one to achieve any pre-determined accuracy by proper choice of truncation number. Formally, the complex eigenvalues coincide with the complex roots of the characteristic equation of the truncated infinite system. All calculations are performed with an accuracy of six significant decimal digits. The algorithm is free from limitations on the slit width, frequency band, and slit location along the bounding contour of a cavity. As an example, the spectrum of the complex eigenvalues for open elliptic cavity with moveable longitudinal slit is accurately investigated for various ellipse eccentricities, including the case of degenerated elliptic cavity-circular cavity. The slit width varies from zero value (closed cavity) to open semi-elliptic cavity.

Electromagnetic plane wave scattering by arbitrary two-dimensional cavities: Rigorous approach

Scattering of an E-polarised plane wave from an arbitrary two-dimensional cavity is examined. The cavity may be represented as an infinitesimally thin open contour with sharp edges or more realistically, as an open (slotted) arbitrary profiled cylinder with finite thickness walls and smoothly rounded edges. The studies of the reflectivity of open 2-D cavities are based on a rigorous Method of Regularisation applicable in a wide frequency range from Rayleigh scattering (passing through the interval of resonance scattering) to high-frequency scattering, where the wavelength is much less than the characteristic size of a cavity. Implementation produces the infinite system of the linear algebraic equations of the second kind. Boundedness and compactness of the system operator allows the use of truncation methods for numerical analysis, where the predetermined accuracy of computations is guaranteed by proper choice of truncation number. Backscattering of some general cavities with infinitesimally thin walls is examined over a wide frequency range. Special focus is on resonance scattering by cavities possessing a spectrum of high Q-factor oscillations. The developed algorithm is directly applicable to examine scattering of plane acoustic waves by arbitrary acoustically soft two-dimensional cavities.

Programming Nanophotonic Materials with DNA

DNA is a unique nanoscale material that enables the design and synthesis of nanoscale structures of prescribed shape and functionality via programmable self-assembly. Angstrom-level control over the location and orientation of programmed Watson-Crick basepairs offers the ability to scaffold and spatially organize optically active materials to yield novel optical and photonic properties. Here, we present two distinct strategies for designing and synthesizing DNA-based photonic materials, and emphasize the roles of computational modeling in this process. First, we use computational modeling to design mechanically stiff nanoscale DNA “molds” that have user-specified three-dimensional cavity with a nucleating gold seed, which grows in solution to fill and replicate the cavity. We demonstrate the capability of producing nanoparticles of various shapes and materials that exhibit plasmonic properties that are consistent with electromagnetism simulations. In silico design of stiff molds of nearly arbitrary geometric cavities with resulting optical properties that are prescribed a priori enable a property-by-design framework for producing inorganic particles with prescribed functional properties. Second, we use DNA to program the scaffolding of chromophores into complex three-dimensional assemblies, enabling controlled energy transfer at the nanoscale. This strategy is inspired by nature, where cells use organized assemblies of chromophores to capture photons and funnel the resulting excitons toward the reaction center where they are converted to chemical energy. In particular, the close-packing of chromophores results in the emergence of quantum coherence that can strongly affect exciton transport across the structure. Using Forster energy transfer modeling, as well as a hybrid molecular dynamics and quantum mechanical approach, we demonstrate how emergent excitonic and light-harvesting properties of diverse DNA-dye assemblies can be elucidated.

Measurement of Microvibration by Using Dual-Cavity Fiber Fabry-Perot Interferometer for Structural Health Monitoring

Extensive researches have recently been performed to study structural integrity using structural vibration data measured by in-structure sensors. A fiber optic sensor is one of candidates for the in-structure sensors because it is low in cost, light in weight, small in size, resistant to EM interference, long in service life, and so forth. Especially, an interferometric fiber optic sensor is very useful to measure vibrations with high resolution and accuracy. In this paper, a dual-cavity fiber Fabry-Perot interferometer was proposed with a phase-compensating algorithm for measuring micro-vibration. The interferometer has structurally two arbitrary cavities; therefore the initial phase difference between two sinusoidal signals induced from the interferometer was also arbitrary. In order to do signal processing including an arc-tangent method, a random value of the initial phase difference is automatically adjusted to the exact 90 degrees in the phase-compensating algorithm part. For the verification of the performance of the interferometer, a simple vibration-test was performed to measure micro-vibration caused by piezoelectric transducer (PZT). As an experimental result, the interferometer attached on the PZT successfully measured the 50 Hz-vibration of which the absolute displacement oscillated between −424 nm and +424 nm.

A 2.5D boundary element formulation for modeling damped waves in arbitrary cross-section waveguides and cavities

A regularized 2.5D boundary element method (BEM) is proposed to predict the dispersion properties of damped stress guided waves in waveguides and cavities of arbitrary cross-section. The wave attenuation, induced by material damping, is introduced using linear viscoelastic constitutive relations and described in a spatial manner by the imaginary component of the axial wavenumber. The discretized dispersive wave equation results in a nonlinear eigenvalue problem, which is solved obtaining complex axial wavenumbers for a fixed frequency using a contour integral algorithm. Due to the singular characteristics and the multivalued feature of the wave equation, the requirement of holomorphicity inside the contour region over the complex wavenumber plane is fulfilled by the introduction of the Sommerfeld branch cuts and by the choice of the permissible Riemann sheets. A post processing analysis is developed for the extraction of the energy velocity of propagative guided waves. The reliability of the method is demonstrated by comparing the results obtained for a rail and a bar with square cross-section with those obtained from a 2.5D Finite Element formulation also known in literature as Semi Analytical Finite Element (SAFE) method. Next, to show the potential of the proposed numerical framework, dispersion properties are predicted for surface waves propagating along cylindrical cavities of arbitrary cross-section. It is demonstrated that the attenuation of surface waves approaches asymptotically the attenuation of Rayleigh waves.

General Linewidth Formula for Steady-State Multimode Lasing in Arbitrary Cavities

A formula for the laser linewidth of arbitrary cavities in the multimode nonlinear regime is derived from a scattering analysis of the solutions to semiclassical laser theory. The theory generalizes previous treatments of the effects of gain and openness described by the Petermann factor. The linewidth is expressed using quantities based on the nonlinear scattering matrix, which can be computed from steady-state ab initio laser theory; unlike previous treatments, no passive cavity or phenomenological parameters are involved. We find that low cavity quality factor, combined with significant dielectric dispersion, can cause substantial deviations from the Shawlow-Townes-Petermann theory.

A Gurson-type criterion for porous ductile solids containing arbitrary ellipsoidal voids—II: Determination of yield criterion parameters

The aim of this paper is to fully determine the parameters of the approximate homogenized yield criterion for porous ductile solids containing arbitrary ellipsoidal cavities proposed in Part I. This is done through improvements of the limit-analysis of some representative hollow cell presented there. The improvements are of two kinds. For hydrostatic loadings, the limit-analysis is refined by performing micromechanical finite element computations in a number of significant cases, so as to replace Leblond and Gologanu (2008)'s trial velocity field representing the expansion of the void by the exact, numerically determined one. For deviatoric loadings, limit-analysis is dropped and direct use is made of some general rigorous results for nonlinear composites derived by Ponte-Castaneda (1991), Willis (1991) and Michel and Suquet (1992) using the earlier work of Willis (1977) and the concept of “linear comparison material”. This hybrid approach is thought to lead to the best possible expressions of the yield criterion parameters. The criterion proposed reduces to (variants of) classical approximate criteria proposed by Gurson (1977) and Gologanu et al. (1993, 1994, 1997) in the specific cases of spherical or spheroidal, prolate or oblate cavities. An overview of the validation of this criterion through micromechanical finite element computations is finally presented.

Efficient Computation of Longitudinal Lasing Modes in Arbitrary Active Cavities: The Bidirectional Time Evolution Method

In this paper, we develop the Bidirectional Time Evolution Method (BTEM) as an efficient technique to determine the frequencies of the longitudinal lasing modes in arbitrary 1-D active cavities. The BTEM is based on a mathematical property of linear Maxwell equations for active media at real frequencies: the backward Fourier transform of their frequency-domain solution provides nonphysical <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">time-reversed</i> fields when the threshold condition is fulfilled (i.e., the round-trip gains overcome the round-trip losses). Although such time-reversed fields are not physically feasible, they can be easily computed and their spectrum provides all the (real) frequencies at which the threshold condition is fulfilled. On the other hand, the phase condition is given by the peaks of the cavity transmittance modulus. Numerical examples of Fabry-Perot, distributed Bragg reflector, DFB, random, and metamaterial active cavities illustrate the capabilities of our method.

Analytical study and numerical experiments of true and spurious eigensolutions of free vibration of circular plates using real-part BIEM

Following the success of the CHEEF method [Chen IL, Chen JT, Kuo SR, Liang MT. A new method for true and spurious eigensolutions of arbitrary cavities using the combined Helmholtz exterior integral equation formulation method. J Acoust Soc Am 2001; 109(3):982–98] and the real-part BEM [Kuo SR, Chen JT, Huang CX. Analytical study and numerical experiments for true and spurious eigensolutions of a circular cavity using the real-part dual BEM. Int J Numer Methods Eng 2000; 48:1401–22] for solving the membrane eigenproblem, we extend to the plate problem in this paper. The boundary integral equation method (BIEM) using only the real-part kernel instead of the complex-valued kernel is employed to solve the plate eigenproblem for saving half effort in computation. The spurious eigenvalue that resulted due to insufficient constraint is examined. To deal with this problem, a combined Helmholtz exterior integral equation formulation method (CHEEF) is employed to provide sufficient constraints to filter out spurious eigenvalues. The constraint equations of the transverse displacement, normal derivative and tangent derivative for the exterior collocating points are derived. If these constraint equations are properly chosen, one collocating point was sufficient to filter out all the spurious eigenvalues easily and efficiently, even for the repeated spurious eigenvalues. Finally, numerical experiments are performed to verify the analytical results.

Higher order hierarchical curved hexahedral vector finite elements for electromagnetic modeling

A novel higher order finite-element technique based on generalized curvilinear hexahedra with hierarchical curl-conforming polynomial vector basis functions is proposed for microwave modeling. The finite elements are implemented for geometrical orders from 1 to 4 and field-approximation orders from 1 to 10 in the same Galerkin-type finite-element method and applied to eigenvalue analysis of arbitrary electromagnetic cavities. Individual curved hexahedra in the model can be as large as approximately 2/spl lambda//spl times/2/spl lambda//spl times/2/spl lambda/, which is 20 times the traditional low-order modeling discretization limit of /spl lambda//10 in each dimension. The examples show excellent flexibility and efficiency of the higher order (more precisely, low-to-high order) method at modeling of both field variation and geometrical curvature, and its excellent properties in the context of p-refinement of solutions, for models with both flat and curved surfaces. The reduction in the number of unknowns is by an order of magnitude when compared to low-order solutions.

A new method for true and spurious eigensolutions of arbitrary cavities using the combined Helmholtz exterior integral equation formulation method.

Integral equation methods have been widely used to solve interior eigenproblems and exterior acoustic problems (radiation and scattering). It was recently found that the real-part boundary element method (BEM) for the interior problem results in spurious eigensolutions if the singular (UT) or the hypersingular (LM) equation is used alone. The real-part BEM results in spurious solutions for interior problems in a similar way that the singular integral equation (UT method) results in fictitious solutions for the exterior problem. To solve this problem, a Combined Helmholtz Exterior integral Equation Formulation method (CHEEF) is proposed. Based on the CHEEF method, the spurious solutions can be filtered out if additional constraints from the exterior points are chosen carefully. Finally, two examples for the eigensolutions of circular and rectangular cavities are considered. The optimum numbers and proper positions for selecting the points in the exterior domain are analytically studied. Also, numerical experiments were designed to verify the analytical results. It is worth pointing out that the nodal line of radiation mode of a circle can be rotated due to symmetry, while the nodal line of the rectangular is on a fixed position.

Self-homodyne tomography of a laser diode

Considerable interest is growing around self-homodyne techniques. Such techniques allow one to avoid non-unitary detection efficiencies due to inefficient mode matching of the local oscillator. Galatola et al (1991 Opt. Commun. 85 95) proposed one possible scheme of self-homodyne detection of a field with a strong coherent component involving the use of a Fabry-Perot cavity with a perfectly reflecting mirror. We extend the theory to arbitrary cavities, and we observe a remarkable agreement between the theory and the observed data. Using the same setup we performed a tomographic measure of the Wigner function of the field emitted by a laser diode.

Quantum theory of microcavity-modified fluorescence decay rate under a strong coupling condition

In this article, we propose a simple approach to deal with the fluorescence of a quasi-three-level system in $\ensuremath{\Lambda}$ configuration in which one of the ``levels'' is actually a band with possibly a large width. By solving this quasi-three-level molecule model, we obtain an analytical expression for the microcavity-modified fluorescence decay rate suitable for arbitrary cavities with any geometrical shape under a strong coupling condition. Applying the general result to a microsphere, we express explicitly the fluorescence decay rate's dependence on the cavity radius, emission linewidth, and the quantities characterizing the involved cavity modes, and find it in remarkable agreement with the recent fluorescence experiment by Barnes et al. [Phys. Rev. Lett. 76, 3931 (1996)]. In addition we briefly discuss the suitability of the approach for other microcavity-modified optical processes such as lasing and Raman scattering.