Circular Dielectric Waveguide Research Articles

Interaction of a dielectric waveguide mode with a resonant scatterer: Scattering properties, propelling force, and torque

A system of a resonant scatterer described as a two-level atom coupled to a circular dielectric waveguide is studied. The system is characterized by the scattering properties of a guided mode (guided transmission and reflection, bulk radiation) and optomechanical properties (propelling force and torque on the scatterer). The results are based on a self-consistent solution of the scattering problem using the Green's functions and cover the cases of scatterers inside and outside waveguides. It is shown that while a scatterer with a fixed dipole orientation gives rise to scattering spectra described by Lorentzian line shapes, an isotropic scatterer can produce non-Lorentzian line shapes. The parameters defining the line shape are analyzed. The complicated line shapes are likely to arise in the coherent characterization of an emerging class of photonic devices based on photon emitters coupled to well-confined modes of dielectric waveguides. It is obtained that the propelling force and axial torque on the scatterer at resonance can be directly expressed in terms of the spontaneous emission coupling factor $(\ensuremath{\beta})$ of the system. The balances of the linear and angular momentum in the system are discussed. Numerical results are presented for strongly confined guided modes which allow efficient mode scattering and conversion of the linear and angular mode momentum to the force and torque, respectively.

Mode properties of elliptical dielectric waveguide with nested eccentric hollow cylinder coated with graphene

An elliptical dielectric nanowire waveguide with a nested eccentric hollow cylinder is designed, the inner surface and the outer surface of the waveguide are both coated with graphene. The transmission characteristics of the three lowest order modes supported by the waveguide, i.e. the field distribution, the real part of the effective refractive index, the propagation length, and the quality factor, are obtained by multipole method. The results show that the three lowest order modes of the waveguide can be synthesized by the lowest order modes supported by a single cylinder and an elliptic cylinder coated with graphene. With the increase of the radius of the embedded cylinder, the three evaluation indexes of the waveguide increase slightly. The change of the semi major axis of the ellipse will slightly increase the real part of the effective refractive index, propagation length and quality factor of Mode 0 and Mode 1, while Mode2 will slightly decrease. When <inline-formula><tex-math id="M1">\begin{document}$a = {{b}} = 170\;{\rm{nm}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20212321_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20212321_M1.png"/></alternatives></inline-formula>, the performance of the circular nested circular waveguide becomes slightly worse than that of the structure in this paper. With the decrease of the semi minor axis of the ellipse, the real part of the effective refractive index, propagation length and quality factor for each of the three modes increase to a certain extent, and have the greatest impact on Mode 1. When <inline-formula><tex-math id="M2">\begin{document}${{b}} = {{a}} = 190\;{\rm{nm}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20212321_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20212321_M2.png"/></alternatives></inline-formula>, the transmission performance of the circular nested circular waveguide is not so good as that of the structure in this paper. When the distance between the inner rod and the outer rod on the right side increases, the real part of the effective refractive index for each of the three modes decreases, the propagation length and quality factor of Mode 0 and Mode1 gradually decrease, while the propagation length of Mode 2 increases slightly, and the quality factor is basically unchanged. On the contrary, the mode transmission performance can be significantly improved by increasing the working wavelength and Fermi energy and reducing the dielectric constant of elliptical dielectric nanowires. Compared with the circular dielectric nanowire waveguide nested with an eccentric hollow cylinder coated with graphene, the waveguide designed in this paper can be found to have a good transmission performance. These results are verified by the finite element method. This waveguide can provide a theoretical basis for the design, fabrication and application of nested waveguides of the same type.

Фурье-анализ мод микроструктурных оптических волокон

An vectorial mode solver for microstructured optical fibers based on the representation of the longitudinal components of the mode fields at the interfaces of media in the fiber cross section by Fourier series in angular variables is formulated. The coefficients of the series are found from a homogeneous algebraic system solved by the reduction method. The matrix elements of the system are determined on the basis of the Green's theorem, which is considered in the internal and external regions of the fiber cross section and the inclusions that form the microstructure. The elements are represented by regular integrals, i.e. difficulties associated with the singularities of the Green's functions are absent. The applicability of the approach is limited only by the requirement that the contours of the inclusions and the outer boundary of the fiber are described by single-valued functions of the angular variables. In the special case of a circular dielectric waveguide, the method gives an exact analytical solution of the waveguide problem. Estimates are obtained for the internal convergence of the method in computing the modes of a dielectric elliptical waveguide and microstructural fibers with elliptical inclusions. It is established that the attenuation coefficients of the modes caused by radiation leakage from the fiber core are significantly affected by both the internal microstructure and the outer fiber boundary.

Fourier analysis of modes of microstructured optical fibers

An vectorial mode solver for microstructured optical fibers based on the representation of the longitudinal components of the mode fields at the interfaces of media in the fiber cross section by Fourier series in angular variables is formulated. The coefficients of the series are found from a homogeneous algebraic system solved by the reduction method. The matrix elements of the system are determined on the basis of the Green's theorem, which is considered in the internal and external regions of the fiber cross section and the inclusions that form the microstructure. The elements are represented by regular integrals, i.e. difficulties associated with the singularities of the Green's functions are absent. The applicability of the approach is limited only by the requirement that the contours of the inclusions and the outer boundary of the fiber are described by single-valued functions of the angular variables. In the special case of a circular dielectric waveguide, the method gives an exact analytical solution of the waveguide problem. Estimates are obtained for the internal convergence of the method in computing the modes of a dielectric elliptical waveguide and microstructural fibers with elliptical inclusions. It is established that the attenuation coefficients of the modes caused by radiation leakage from the fiber core are significantly affected by both the internal microstructure and the outer fiber boundary. Keywords: microstructured fiber, Green's theorem, Fourier series, internal convergence, leaky modes.

Topological sensing with photonic arrays of resonant circular waveguides

We propose that a photonic array of resonant circular dielectric waveguides with subwavelength grating can be designed as a robust and sensitive topological chemical sensor. The device can detect trace amounts of a given chemical species through photonic edge modes that are impervious to most sources of disorder. We perform a simulation in the mid-infrared that accounts for the absorption loss introduced by chemical molecules in contact with a strongly coupled photonic lattice of resonators. Due to the topological nature of the device, its chemical sensitivity scales linearly with the system size and can reach parts-per-billion range at the millimeter scale. Our findings suggest that topological chemical sensors could empower the development of novel on-chip integrated photonic sensing technologies.

Control of tightly focused laser beams in the THz range

AbstractThe possibility for control of tightly focused laser beams excited by the resonator modes of a THz laser based on a hollow circular dielectric waveguide is studied theoretically and experimentally. The wavelength of the radiation under study is 0.4326 mm corresponding to the generation line of the optically pumped HCOOH‐molecule THz laser. The focusing system is implemented by a short‐focus lens covered by absorbing masks in the central region. The focal area parameters were controlled by changing the size of the masks. The electric field components of the laser modes are calculated using the Rayleigh‐Sommerfeld integral transformations under non‐paraxial approximation. The use of absorbing masks made it possible to reduce the beam diameter in the focal region and increase the depth of focus of the linearly polarized EH11‐mode and azimuthally polarized TE01‐mode as well. In this case, despite of the presence of an absorbing mask, the distribution of the total field intensity of the TE01‐mode retained its annular shape, and the field maximum of the EH11‐mode is observed at center of the focal spot. The results of this work can be implemented in medical diagnostics, high‐speed communications, and environmental monitoring.

Dispersion Analysis of Twist-Symmetric Dielectric Waveguides

We propose a circular twist-symmetric dielectric waveguide that is polarization-selective. In the practical implementation of optical fibers, a selective circular polarization is more convenient than its linearly polarized counterpart where previous knowledge of the emitted polarization from the transmitter is unknown. The analysis of the waveguide was conducted with three methods: an eigenmode approach, simulation of a truncated structure, and the so-called multimodal transfer-matrix method (MMTMM). The presented simulations demonstrate that the operational band can be manipulated by tuning the parameters of the structure. Furthermore, the MMTMM allows for a direct and accurate calculation of the attenuation constant of the rejected circular polarization.

Signal distortions in circular dielectric waveguides at mm-wave frequencies

AbstractDespite the great progress in data transmission systems using dielectric waveguides (DWGs) in the millimeter-wave (mm-wave) frequency band (30–300 GHz), the signal distortions caused by DWGs have not yet been fully understood. However, such investigations would help to optimize DWGs as a transmission channel in order to further increase data rate and transmission distance of such systems without the need for more complex transceivers. Therefore, this paper presents a detailed study of the expected signal distortions caused by frequency-dependent attenuation and frequency-dependent group delay of circular DWGs at mm-wave frequencies. Based on a low-complexity digital transmission system, the effects of DWGs on the signal-to-noise ratio and the intersymbol interference at the receiver are evaluated. The figures and equations given in this paper allow the reader to easily calculate the channel properties and signal distortions for a wide range of circular DWGs without the need of finite element method solver or other time-consuming numerical simulations. Finally, design recommendations are given to minimize signal distortions for transmitting signals along DWGs.

Diffraction properties of azimuthally symmetric gratings in a hollow circular dielectric waveguide

Diffraction gratings can be used in cavities of terahertz lasers for generating wave beams with special polarization. Adequate using of such gratings needs preliminary theoretical investigation of their diffraction properties. To solve the problem a specially adopted numerical method should be used because the structures under study frequently have many elements (many periods) and well-known theoretical approaches or commercial solvers cannot cope with such task. In this paper, a Finite Difference in Time Method for Body of Revolution (BOR FDTD) is applied to the problem. Updating formulae for electromagnetic field and some calculation features of the method are presented. Different types of diffraction gratings that homogeneously and inhomogeneously change their properties with the radial coordinate are studied. Some physical peculiarities of diffraction modes of a hollow dielectric waveguide with different polarization are revealed and discussed.

Robust design of a broadband dual-polarized transition from PCB to circular dielectric waveguide for mm-wave applications

A growing interest in dielectric waveguides (DWGs) as an alternative to commonly used waveguides (like coaxial or twisted-pair cables) for high data rate interconnects could be observed in the last few years. Especially in the mm-wave frequency range (30–300 GHz) applications with these waveguides benefit from low losses and low dispersion. Moreover, using both polarizations of the fundamental mode in such waveguides could theoretically double the data rate without the need of higher bandwidth or additional fibers. The connection between DWGs and commonly available transceiver chips requires broadband transitions from planar waveguides like microstrip lines to DWGs. In this paper, an overview of the current developments of such transitions is given and a novel low-complexity design is presented that reduces the space consumption by 35% related to recently published works. This allows an easy integration into a printed circuit board layout or a chip package. Furthermore, an extensive sensitivity analysis is presented to prove the robustness toward manufacturing tolerances. The transition is realized at W-band frequencies (75–110 GHz) and achieves a relative 10 dB-bandwidth of more than 25% with a minimum insertion loss of 1.2 dB. It is shown that these properties even hold for manufacturing tolerances of nowadays manufacturing processes.

Numerical Method for Electromagnetic Wave Propagation Problem in a Cylindrical Anisotropic Waveguide with Longitudinal Magnetization

The propagation of monochromatic electromagnetic waves in metal circular cylindrical dielectric waveguide with longitudinal magnetization filled with anisotropic inhomogeneous waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. Numerical results are obtained using a modification of the projecting methods. The comparison with known exact solutions (for particular values of parameters) are made.

Improvement of Broadband Characterization of Dielectric Waveguide at the $Ka$ -Band by Using TRL Calibration Method

When evaluating a dielectric waveguide, it is necessary to convert it into a metallic coaxial line or a metallic waveguide in order to connect it to a measurement port of a vector network analyzer (VNA). Mismatches in connections of different types of cables lead to an error in measurements, which have been a serious problem in the characterization of dielectric waveguides. To this end, we propose the use of two-line standards and a reflect standard made of dielectric waveguides as thru-reflect-line (TRL) calibration devices in order to ensure the accuracy of measurement of the propagation characteristics of dielectric waveguides. By using the developed TRL calibration devices, the calibration planes in VNA measurements are extended to the cross sections of the dielectric waveguide, which makes it possible to perform accurate measurements of the dielectric waveguide without the influence of mismatches between different types of cables. To demonstrate the usefulness of the proposed approach, we performed numerical calculations to investigate the robustness of the proposed method against dimensional variations in the calibration devices. Furthermore, we experimentally verified the method by applying it to measurements on circular dielectric waveguides made of polytetrafluoroethylene in the 28-GHz band, which has been planned to be implemented in the next-generation wireless communications.

Formation of the Source Function Generating a Specified Radiation Field

The spectrum of symmetric modes forming a specified distribution of the radiation field is calculated using solution to the self-consistent problem of radiation from the end of a circular dielectric waveguide. The self-consistent problem is reduced to solution of a system of integral equations. In the case of the synthesis of the source function in the space of eigenfunctions of the boundary value problem for a circular dielectric waveguide, these equations are the Fredholm integral equations of the first kind.

On the existence of non-polarized azimuthal-symmetric electromagnetic waves in circular dielectric waveguide filled with nonlinear isotropic homogeneous medium

The propagation of monochromatic nonlinear symmetric hybrid waves in a cylindrical nonlinear dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. The problem is reduced to the new type of nonlinear eigenvalue problem. The analytical method of solving this problem is presented. New propagation regime is found.

NUMERICAL METHOD FOR ELECTROMAGNETIC WAVE PROPAGATION PROBLEM IN A CYLINDRICAL INHOMOGENEOUS METAL DIELECTRIC WAVEGUIDING STRUCTURES

The propagation of monochromatic electromagnetic waves in metal circular cylindrical dielectric waveguides filled with inhomogeneous medium is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. Numerical results are found with a projection method. The comparison with known exact solutions (for particular values of parameters) is made.

Plots of modal field distribution in circular dielectric waveguide

ABSTRACTA method to plot the modal field distributions in the circular dielectric waveguides is discussed in this article. By tracing the directions of fields, closed contours of the fields can be formed in dielectric waveguides. This method is a simple and general approach to plot and visualize the field distributions of the waveguides if the solutions of fields can be found. © 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:2599–2601, 2015

Guided Electromagnetic Waves Propagating in a Two-Layer Cylindrical Dielectric Waveguide with Inhomogeneous Nonlinear Permittivity

The paper focuses on the problem of monochromatic electromagnetic TM wave propagation in a two-layer circular cylindrical dielectric waveguide. The space outside the waveguide is filled with isotropic medium having constant permittivity. The inner core of the waveguide is filled with isotropic medium having constant permittivity; the cladding of the core is filled with isotropic inhomogeneous nonlinear permittivity (the nonlinear term is expressed by Kerr law). Existence of guided modes which depend harmonically onz(the waveguide axis coincides withz-axis) is proved and their localization is found. Numerical results including different type of nonlinearities are presented. A comparison with the linear case is given. The existence of a new propagation regime is predicted.

Nonlinear Double-Layer Bragg Waveguide: Analytical and Numerical Approaches to Investigate Waveguiding Problem

The paper is concerned with propagation of surface TE waves in a circular nonhomogeneous two-layered dielectric waveguide filled with nonlinear medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green function. The existence of propagating TE waves for chosen nonlinearity (the Kerr law) is proved using the contraction mapping method. Conditions under which k waves can propagate are obtained, and intervals of localization of the corresponding propagation constants are found. For numerical solution of the problem, a method based on solving an auxiliary Cauchy problem (the shooting method) is proposed. In numerical experiment, two types of nonlinearities are considered and compared: the Kerr nonlinearity and nonlinearity with saturation. New propagation regime is found.

Nonlinear transmission eigenvalue problem describing TE wave propagation in two-layered cylindrical dielectric waveguides

The paper is concerned with propagation of surface TE waves in a circular nonhomogeneous two-layered dielectric waveguide filled with a Kerr nonlinear medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of a Green's function. The existence of propagating TE waves is proved using the contraction mapping method. For the numerical solution of the problem, two methods are proposed: an iterative algorithm (whose convergence is proved) and a method based on solving an auxiliary Cauchy problem (the shooting method). The existence of roots of the dispersion equation (propagation constants of the waveguide) is proved. Conditions under which k waves can propagate are obtained, and regions of localization of the corresponding propagation constants are found.

Propagation of TM modes in a circular dielectric waveguide filled with a medium with Kerr nonlinearity

Eigenmodes propagating in a cylindrical dielectric waveguide of circular cross section filled with a nonlinear medium whose nonlinearity is described by the Kerr law are analyzed. The nonlinear eigenvalue boundary problem for the nonlinear Helmholtz equation is considered. An iterative numerical method for obtaining the approximate solutions is developed. Numerical results are presented.