Eigenmodes Of Waveguide Research Articles

Optical-force laws for guided light in linear media

The mechanical response of transparent materials to optical forces is a topic that concerns a wide range of fields, from the manipulation of biological material by optical tweezers to the design of nano-optomechanical systems (NOMS). However, the fundamental aspects of such forces have always been surrounded by controversies, and several different formulations have been proposed. In this work, we focus on the specific case of light propagating as a superposition of guided modes in lossless dielectric waveguides as a physical example upon which to build a general stress tensor. We use this formalism to calculate optical forces for straight and curved waveguide sections and all possible excitation configurations for a given set of coupled eigenmodes, and then compare the results for each of the known proposed optical force laws as well as a novel one derived from this general stress tensor. We show that proper use of the divergence theorem is crucial to account for all force terms, many of which vanish if the procedure most commonly used is applied for situations other than eigenmodes in straight waveguides. A better understanding of how different stress tensors predict very different forces for certain waveguide geometries opens a pathway for new experimental tests of each formulation.

Mathematical Modeling of Impedance Waveguide Systems

A method for constructing eigenmodes of an infinite waveguide of a constant rectangular cross section with low losses in the walls, which are described by the Shchukin—Leontovich boundary conditions, is discussed. The dispersion characteristics of these waveguides are constructed.

Synchrotron Radiation from a Charge on Eigenmodes of a Dielectric Cylinder

The electromagnetic radiation on the eigenmodes of a dielectric waveguide is investigated for the charge rotating around a dielectric cylinder. A formula for radiation intensity at a given harmonic is obtained. The corresponding fields exponentially decay at distances from the surface of the cylinder larger than the radiation wavelength. A comparison is made for the intensities of the parts of the radiations propagating inside and outside the cylinder, as well as with the intensity of the radiation at large distances from the cylinder.

Separation of Rectangularly Symmetric Modes of Light With Fan-Out Elements

We present a method to efficiently separate the rectangularly symmetric modes of light with two phase-only holograms. The holograms, known as fan-out elements, can split the input modes into multiple copies. A subsequent lens focuses these modes to different lateral positions. We use two spatial light modulators to create the desired optical elements. The separation of rectangularly symmetric modes, such as eigenmodes in rectangular waveguides and Hermite-Gaussian modes, is experimentally demonstrated.

INTERNAL PARTIAL CONDUCTANCES OF A LONGITUDINAL SLOT WITH PARTIAL DIELECTRIC FILLING

Among the ways of enhancement of functional capabilities of antenna-feeder devices on the basis of slot coupling elements one is partial filling of the slot cavity by a dielectric medium. Solution of the scattering problem with the use of the continuity condition for the tangential component of the magnetic field on the slot surfaces is reduced to a set of linear algebraic equations of the Galerkin method whose matrix elements represent partial conductions of the slot. In the present paper, analytical expressions have first been derived for partial internal conductions of a longitudinal slot with a layered dielectric filling cut in the wider wall of a rectangular waveguide. The LEq0 eigenmodes of a rectangular waveguide partially filled with a dielectric material are used in the capacity of the basis functions in the Galerkin procedure. Frequency dependences of the intrinsic and transfer conductances of the slot are analyzed. It is shown that by changing the dielectric layer parameters in the slot it is possible to control the active and reactive components of the intrinsic conductivity of the slot which effect can be used for controlling the characteristics of slotted waveguide antenna arrays.

The Method of Calculation of Open and Closed Waveguides, Which Is Based on the Modified Method of Discrete Sources

The problem of calculation of eigenmode characteristics is considered for 3D open dielectric waveguides and waveguides with the anisotropic impedance boundary condition. An efficient algorithm is proposed for finding eigenmodes of waveguides having different cross-sections. It is based on the solution of the auxiliary problem of diffraction of the field of a filamentous source located inside the waveguide. The method is tested using weakly directing dielectric waveguides having circular and elliptical sections and a waveguide with the two-sheeted section. The results of calculation of dielectric waveguides obtained with the help of the proposed method, the method of finite elements, and the method of the integral equation over the waveguide section are compared. The circular and elliptical waveguides and the waveguide having a two-sheeted section with an anisotropic impedance are also investigated. The calculation results are compared with the results obtained with the use of the method of separation of variables and the Galerkin method.

Symbolic-Numeric Computation of the Eigenvalues and Eigenfunctions of the Leaky Modes in a Regular Homogeneous Open Waveguide

In this paper the algorithm of finding eigenvalues and eigenfunctions for the leaky modes in a three-layer planar dielectric waveguide is considered. The problem on the eigenmodes of open three-layer waveguides is formulated as the Sturm-Liouville problem with the corresponding boundary and asymptotic conditions. In the case of guided and radiation modes of open waveguides, the Sturm-Liouville problem is formulated for self-adjoint second-order operators on the axis and the corresponding eigenvalues are real quantities for dielectric media. The search for eigenvalues and eigenfunctions corresponding to the leaky modes involves a number of difficulties: the boundary conditions for the leaky modes are not self-adjoint, so that the eigenvalues can turn out to be complex quantities. The problem of finding eigenvalues and eigenfunctions will be associated with finding the complex roots of the nonlinear dispersion equation. In the present paper, an original scheme based on the method of finding the minimum of a function of several variables is used to find the eigenvalues. The paper describes the algorithm for searching for eigenvalues, the algorithm uses both symbolic transformations and numerical calculations. On the basis of the developed algorithm, the dispersion relation for the weakly flowing mode of a three-layer open waveguide was calculated in the Maple computer algebra system.

Radiation of surface waves from a charge rotating around a dielectric cylinder

The radiation of electromagnetic surface waves is investigated for a charged particle rotating around a dielectric cylinder immersed into a homogeneous medium. Formulae are provided for the corresponding electric and magnetic fields and for the radiation intensity. It is shown that the surface waves are radiated on the eigenmodes of the cylindrical waveguide.

Electrodynamical Model of Composite Cylindrical Structure with Laminated Dielectric

The article is devoted to the problem of the natural electromagnetic modes, the regions of their existence and the relationship with all possible types of resonances in the waveguide junction of a cylindrical and radial waveguides with a layered (laminated) filling of the radial waveguide with dielectric material. An electrodynamic model is created on the basis of a rigorous method of modal matching technique, with the separation of the common waveguide coupling region and the representation of the field in it in the form of a superposition of the fields of the partial waveguide eigenmodes. The structure under investigation can be used to measure the electrical parameters of dielectric samples of a cylindrical cross-section. It is shown that the measurements will have a local character, since the spectral characteristics of the junctions are determined mainly by the size of the central coupling region of the waveguides and by the electrical parameters of the dielectric that is in the junction. The problem of edge effects for samples of finite length (partial filling of a radial waveguide with dielectric) is investigated. Taking into account the edge effect enables reducing the error in measuring the permittivity for samples of arbitrary sizes in the investigated structure.

Acoustic Waveguide Eigenmode Solver Based on a Staggered-Grid Finite-Difference Method

A numerical method of solving for the elastic wave eigenmodes in acoustic waveguides of arbitrary cross-section is presented. Operating under the assumptions of linear, isotropic materials, it utilizes a finite-difference method on a staggered grid to solve for the acoustic eigenmodes (field and frequency) of the vector-field elastic wave equation with a given propagation constant. Free, fixed, symmetry, and anti-symmetry boundary conditions are implemented, enabling efficient simulation of acoustic structures with geometrical symmetries and terminations. Perfectly matched layers are also implemented, allowing for the simulation of radiative (leaky) modes. The method is analogous to that in eigenmode solvers ubiquitously employed in electromagnetics to find waveguide modes, and enables design of acoustic waveguides as well as seamless integration with electromagnetic solvers for optomechanical device design. The accuracy of the solver is demonstrated by calculating eigenfrequencies and mode shapes for common acoustic modes across four orders of magnitude in frequency in several simple geometries and comparing the results to analytical solutions where available or to numerical solvers based on more computationally expensive methods. The solver is utilized to demonstrate a novel type of leaky-guided acoustic wave that couples simultaneously to two independent radiation channels (directions) with different polarizations – a ‘bi-leaky’ mode.

Long-range propagation of plasmon and phonon polaritons in hyperbolic-metamaterial waveguides

We study photonic multilayer waveguides that include layers of materials and metamaterials with a hyperbolic dispersion (HMM). We consider the long-range propagation of plasmon and phonon polaritons at the dielectric–HMM interface in different waveguide geometries (single boundary or different layers of symmetric cladding). In contrast to the traditional analysis of geometrical parameters, we make an emphasis on the optical properties of constituent materials: solving dispersion equations, we analyze how dielectric and HMM permittivities affect propagation length and mode size of waveguide eigenmodes. We derive figures of merit that should be used for each waveguide in a broad range of permittivity values as well as compare them with plasmonic waveguides. We show that the conventional plasmonic quality factor, which is the ratio of real to imaginary parts of permittivity, is not applicable to the case of waveguides with complex structure. Both telecommunication wavelengths and mid-infrared spectral ranges are of interest considering recent advances in van der Waals materials, such as hexagonal boron nitride. We evaluate the performance of the waveguides with hexagonal boron nitride in the range where it possesses hyperbolic dispersion (wavelength 6.3–7.3 μm), and we show that these waveguides with natural hyperbolic properties have higher propagation lengths than metal-based HMM waveguides.

Complex coupled mode theory electromagnetic mode solver

We present a method for computing waveguide eigenmodes based on complex coupled mode theory (CCMT). This approach generalizes Fourier transform methods by allowing an arbitrary but convenient basis set to be used for the expansion. In the presented approach, one is free to choose an arbitrary basis representation; for example, we show the use of electromagnetic modes of a cylindrical metal waveguide. CCMT-computed modes are compared with modes computed using analytic expressions and results obtained using a finite difference solver. In cases where the basis set is small, the method can efficiently re-compute modes after structural refinements are made, and can efficiently compute dispersion. The parallel nature of the algorithm makes it well suited to a graphics processing unit implementation, as demonstrated here.

Short and broadband silicon asymmetric Y-junction two-mode (de)multiplexer using fast quasiadiabatic dynamics.

A short and broadband silicon asymmetric Y-junction two-mode (de)multiplexer is proposed and simulated. An adiabaticity parameter suitable for high index-contrast silicon waveguides is defined. The fast quasiadiabatic dynamics protocol is used to homogeneously distribute adiabaticity over the device length. This protocol limits the power coupled into the unwanted waveguide eigenmode under a fixed value along the propagation. A 16 μm long mode (de)multiplexer with crosstalk < -34 dB is obtained. Simulations show that the optical bandwidth is as large as 300 nm (1400 nm ~ 1700 nm). The design is also fabrication tolerant.

Energy flux in 2‐D MHD waveguide in the outer magnetosphere

AbstractThe problems of large‐scale wave propagation and amplification in the outer magnetosphere are considered. Kelvin‐Helmholtz (KH) instability growth rate of the magnetospheric waveguide eigenmodes is investigated as a function of a coordinate along the magnetopause. The problem of solar wind MHD wave penetration into the waveguide is investigated for a broad range near Pc3 and Pc5 geomagnetic pulsation frequencies and realistic models of the magnetospheric waveguide. The expression for the waveguide eigenmode energy flux is obtained. This expression includes the effects of external wave penetration and mode amplification due to the KH instability, as well as losses due to dissipation in the vicinity of the Alfven resonance which are incorporated into the growth rate coefficient together with the instability.

Metamaterials based on wedge-shaped electrodynamic structures

The paper studies a possibility of simulation of artificial composite media with negative values of the real part of the equivalent dielectric (magnetic) permittivity, by the use of segments of hollow composite waveguides with cylindrical guided waves in evanescent mode. Reactive evanescent fields of wedge-shaped waveguide eigenmodes are formed in the evanescent region before the critical section of the waveguide which separates the quasistatic field region from the distributing field of the evanescent waveguide mode. The possibility of simulation is determined by the equivalence of dispersion equation of the eigenmode propagation constant and the dispersion equation for the electric (magnetic) permittivity of plasma-like medium if cut-off frequency and electric (magnetic) plasma frequency of the medium are equal.

Theoretical and numerical modeling of linear and nonlinear propagation in graphene waveguides

A formulation for the theoretical and numerical modeling of electromagnetic wave propagation in graphene-comprising waveguides is presented, targeting applications in the linear and nonlinear regime. Waveguide eigenmodes are rigorously calculated using the finite-element method (FEM) in the linear regime and are subsequently used to extract nonlinear properties in terms of the nonlinear Schrodinger equation framework. Graphene sheets are naturally represented as sheet/2D media and are seamlessly implemented with interface conditions in the FEM, thus greatly enhancing the computational efficiency. This formulation is used to analyze the nonlinear performance of several graphene-comprising waveguide configurations in the optical band, including silicon-based photonic waveguides, metal-based plasmonic waveguides and glass microfibers. Optimal design choices are identified for each configuration and subtle aspects of the FEM-based modeling, especially important for plasmonic waveguides, are highlighted.

Waveguide Mode Splitter Based on Multi-mode Dielectric-Loaded Surface Plasmon Polariton Waveguide**Supported by the National Basic Research Program of China under Grant Nos 2011CBA00200 and 2011CB921200, the Strategic Priority Research Program (B) of the Chinese Academy of Sciences under Grant No XDB01030200, the National Natural Science Foundation of China under Grant No 11374289, the Fundamental Research Funds for the Central Universities

In photonic integrated circuits, information is usually encoded in the optical path. In this work, based on the multi-mode dielectric-loaded surface plasmon polariton waveguide, we numerically design a directional coupler, which can divide the different waveguide eigenmodes into different optical paths. The results show a possibility to encode information onto different waveguide modes. We also experimentally demonstrate that the splitting ratio of this directional coupler structure can be tuned without changing its size.

Azimuthal inhomogeneity in the MHD waveguide in the outer magnetosphere

AbstractGeomagnetic field and plasma inhomogeneities in the outer equatorial part of the magnetosphere create a channel with low Alfvén speeds which spans from the nose to the far flanks of the magnetosphere, in both the morning and the evening sectors. This channel plays the role of a waveguide for fast magnetosonic waves. The waveguide eigenmodes and corresponding Alfvén resonance (field line resonance) regions are directly related to geomagnetic pulsations Pc3 and Pc5. U‐shaped model of the waveguide allows for full analytical investigation of waveguide eigenmodes. Quantities such as mode wave numbers, group velocities, and their energy density distribution are found as functions of coordinate along the waveguide. The linkage of the waveguide magnetosonic oscillation energy to the Alfvén waves in the vicinity of the field line resonance deeper inside the magnetosphere is investigated, and corresponding energy leakage coefficient is found. Thus, the influence of longitudinal (i.e., azimuthal) waveguide inhomogeneity on wave propagation is analytically investigated. Obtained results can be used for interpretation of the observed wave power distribution in the frequency bands of geomagnetic pulsations Pc3 and Pc5, as well as for explanation of their spectral properties in the outer magnetosphere.

Repulsion of dispersion curves of quasidipole modes of anisotropic waveguides studied by finite element method.

In this letter repulsion of phase-velocity dispersion curves of quasidipole eigenmodes of waveguides with non-circular cross section in non-axisymmetric anisotropic medium is studied by the semi-analytical finite element technique. Borehole waveguide is used as an example. The modeling helps in clarifying the nature of this phenomenon, which is accompanied by the rotation of the orientation of two quasidipole modes with frequency and by the exchange of their behavior at near-crossover point. The dispersion curves cross only in the presence of exact symmetry. Such a scenario is the alternative to the stress-induced anisotropy crossing of dispersion curves.

Silicon hybrid (de)multiplexer enabling simultaneous mode and wavelength-division multiplexing.

On-chip simultaneous mode and wavelength division-multiplexing (MWDM) is proposed using a tapered directional coupler and multimode interference (MMI) waveguide. A simulation is performed on the two different MWDM architectures, in which, two waveguide eigenmodes and two wavelength channels (1310/1550nm) are multiplexed. One of the proposed devices is compact (6μm x 100μm) and exhibits insertion loss as low as 1.2dB with a cross-talk of (-18dB).