TE Modes In Waveguides Research Articles

Wave-mode dispersions in a relativistic electron beam with ion-channel guiding

An analysis of the eigenmodes of a cylindrical metallic waveguide partially filled with a relativistic electron beam, and guided with an ion channel, is presented. The analysis is performed in the rest frame of the beam with self-fields taken into account. Dispersion relations for five families of electrostatic and EM modes are derived and solved numerically to study the characteristics of azimuthally symmetric TM and TE waveguide modes, betatron modes, and space-charge modes. A strong dependence of the frequencies of these electromagnetic-electrostatic waves on the ratio of the radius of the waveguide to the beam radius is revealed. The physical insight given to the electrostatic modes, at large and small wavelengths, equally applies to the Trivelpiece-Gould modes in an electron beam with axial magnetic field guiding. Interactions between the dispersion curves of different modes are used to find the infinite-space dispersion relation from the finite-radius dispersion relation and to explain the transition from a weak to strong ion channel.

Periodic structures induced by scattered light in a photosensitive film on a dielectric plane-parallel substrate

Periodic structures appearing in a thin AgCl-Ag film on a plane-parallel substrate irradiated with a normally incident, focused, linearly polarized Gaussian laser beam λ=633 nm) with a waist spot size of about 0.01 mm have been studied. The structures are formed in the beam spot and its nearest vicinity (with a radius of up to 0.2 mm) as a result of the interference of the incident beam and the waveguide TE modes excited due to the Rayleigh scattering in the film. In the vicinity of the waist spot, the periodic structures develop under the action of a coherent recurrent scattering from back side of the substrate. In addition, periodic structures of ring symmetry have been revealed far (up to 10 mm) from the irradiated spot. It is demonstrated that these structures are due to the interference of radiation scattered from the film and back side of the substrate and reflected from the two boundaries. Interference models are proposed that provide for a good agreement of the interference period, calculated as a function of the distance from the beam center, with the experimental values.

EVOLUTION EQUATIONS FOR ANALYTICAL STUDY OF DIGITAL SIGNALS IN WAVEGUIDES

excitation and propagation problem of the digital signals in a hollow waveguide is considered by an analytical timedomain method. The waveguide is geometrically regular along Oz axis, and its cross section is a closed singly connected domain. The waveguide surface is a perfect electric conductor. A complete set of TE and TM waveguide modes is obtained in Time Domain (TD) directly. Every modal field is deduced as the sum of its longitudinal and transverse vector components, where each component is the product of two factors. One factor is an element of the waveguide modal basis, which is a vector function of the transverse waveguide coordinates. The other one is a modal amplitude of appropriate field component, which is a scalar function of time t and the axial coordinate z. All the elements of the modal basis are specified via two scalar potentials. They are eigensolutions (normalized in a proper way) of Dirichlet and Neumann boundary eigenvalue problems for the Laplacian. Every element of the modal basis satisfies appropriate boundary conditions over the waveguide surface. The modal amplitudes are solutions of a system of evolution partial differential equations. The problem of Walsh function signals in the waveguide is solved explicitly in compliance with the causality principle and the special theory of relativity.

A few-mode optical fiber retaining optical vortices

The ability of an optical fiber with axial losses to selectively suppress the fundamental HE11 mode, as well as the TE and TM waveguide modes, and, simultaneously, to transmit optical vortices with almost zero energy losses is considered. The attenuation coefficients for the corresponding eigenmodes and vortices are determined. It is shown that such a fiber operates as a mode filter for the feeding beam.

Instability and optical turbulence in the formation of spontaneous gratings in single-mode photosensitive AgCl-Ag films

In experiments on illumination of thin photosensitive AgCl films containing granular Ag by a focused laser beam (λ=633 nm), self-pulsations in the form of optical turbulence were found and studied. In the course of illumination, the turbulence was observed in the pattern of small-angle scattering in the form of “boiling” of light spots separated by dark spacings. The formation of turbulence is associated with spontaneous microgratings, whose origin involves waveguide TE modes scattered in a film, and their competition in the course of illumination, which leads to the growth of one microgratings and the decay of the other.

On probing molecular monolayers: a spectroscopic optical waveguide approach of ultra-sensitivity

A broadband, multichannel, single-mode, planar waveguide based spectrometer was developed for probing molecular monolayers. A protein sub-monolayer (thickness h @ 3 nm, imaginary part of refractive index kl oe 0.01) immobilized on the waveguide surface was characterized by the waveguide attenuated total reflection (ATR) spectrometer. A sensitivity enhancement of 4 orders of magnitude, compared to conventional transmission measurements, has been experimentally achieved in the characterization of ultra-thin films. In addition, polarized spectroscopic measurements at the TE and TM waveguide modes were implemented to determine the average orientation angle of the adsorbed molecules. The work developed here is a new research tool for the investigation of some fundamental aspects of molecular films and a novel platform to develop new technological devices of high sensitivity and selectivity such as biosensors.

Optical and nonlinear optical study of KTa_052Nb_048O_3 epitaxial film

The second-order nonlinear optical coefficients d(33) , d(31) , and d(15) of KTa(0.52) Nb(0.48) O(3) epitaxial thin films grown upon MgO were studied by the standard Maker fringe method of an anisotropic medium. The measured d(33)=-84pm/V is 2.8 times the d(33) of LiNbO(3). The refractive indices n(e) and n(o) at several wavelengths were determined by TE and TM waveguide mode measurements. The data presented here point out the excellent qualities of KTa(1-x) Nb(x)O (3) films for use in integrated optics applications.

Study of nonlinear optical effects in GaN:Mg epitaxial film

The second-order nonlinear optical coefficients d33, d31, and d15 of GaN:Mg epitaxial film were studied by the standard Maker fringe of an anisotropic medium. The measured d33=−(16.5±1.3) pm/V which is 55 times of the d11 of quartz. The measured ratios of d33/d31 and d31/d15 showed that the crystalline film is close to an ideal wurzite structure. The refractive indices and the dispersive curves of ne, n0 were also determined by TM and TE waveguide mode measurements.

Exciton-induced enhancement of optical waveguide confinement in (Zn,Cd)(Se,S) quantum well laser heterostructures

Room-temperature waveguide properties have been studied experimentally in ZnSe-based multiple-quantum-well laser structures. The spectra of waveguide transmission show distinct spectral features associated with heavy- and light-hole quantum well excitons. Refractive index dispersion in the multiple-quantum-well region is derived from interference spectra measured in short waveguide samples. The refractive index increases with approaching the exciton resonances, resulting in perfect confinement and low losses of the fundamental TE waveguide mode in a narrow spectral region below the heavy-hole exciton resonance energy. The spectra of laser generation have been measured under the conditions of optical pumping, showing the position of the lasing line to correlate with the spectral region of the waveguide transparency.

Computation of TM and TE modes in waveguides based on a surface integral formulation

The surface integral formulation is used for the computation of TM and TE modes propagating in dielectric loaded waveguides. This formulation makes use of the surface equivalence principle whereby the field at any point internal or external to the waveguide can be expressed in terms of equivalent surface currents. This procedure reduces the original problem into a set of integro-differential equations which is then reduced to a matrix equation using the method of moments. The solution of this matrix equation provides the propagation characteristics of the waveguide and the equivalent surface currents existing on the waveguide walls. The equivalent surface currents can be used to compute the fields at all points, both inside and outside the waveguide. The surface integral method has been used to compute the propagation characteristics of waves propagating in dielectric loaded waveguides. The computed results agree very well with analytical and published data. A method that can be used to remove spurious modes is illustrated. >

Integrated PLZT thin film waveguide modulators

In this paper we report field-induced spatial variations of outcoupled light in integrated ITO/PLZT/SiO2/Si and ITO/PLZT/SiO2/GaAs waveguiding structures, where the SiO2 layer acts as a buffer layer between the semiconducting substrates and PLZT, facilitating the support of TE and TM waveguide modes. Analysis of the various TE and TM modes is achieved using a prism out-coupling method. An electric field applied transversely to the propagation direction using the transparent ITO electrode induces a change in the effective indices of the waveguide modes which in turn causes an angular variation in the prism out-coupled modes. We have demonstrated an angular shift as large as 0.5° with a calculated field strength of 300 V/mm. The angular variation in the films display a quadratic relation to the applied field. The observed modulation can be explained in terms of a change in the effective index due to electro-optic effects in the PLZT film and/or possibly electrostrictive effects in the film layers.

Technical memorandum: Numerical analysis of the characteristics of TE-modes of waveguides loaded with inhomogeneous dielectrics

The cut-off frequencies of TE-modes of rectangular waveguides loaded with inhomogeneous dielectrics are presented. The eigenequation is useful for any rectangular waveguide filled with dielectrics. As examples, some special dielectric distributions are examined and the results agree with those of previous work very well.

Three-dimensional simulation of the Raman free-electron laser

The nonlinear evolution of the free-electron laser amplifier is investigated numerically in the collective Raman regime for a configuration in which a relativistic electron beam propagates through a loss-free cylindrical waveguide in the presence of a helical wiggler and an axial guide magnetic field. A set of coupled nonlinear differential equations is derived that governs the evolution of the TE waveguide modes, the beam space-charge mode, and the trajectories of an ensemble of electrons. Comparison with experiment shows good agreement for cases in which the intersection between the vacuum waveguide mode and the beam resonance line are near ‘‘grazing’’ (i.e., when the intersections are sufficiently close together to result in one broad gain bandwidth). For interactions in which two distinct gain bands occur, the numerical procedure tends to underestimate the beam–plasma frequency and results in a 15%–20% discrepancy with experiment.

Numerical analysis of silicon–clad planar optical waveguides

AbstractThe results of the numerical calculations related to the propagation characteristics of silicon‐clad planar optical waveguides are presented. The finite‐element method is used for the calculations. First, the propagation characteristics of TE modes in waveguides of silicon layer/dielectric core/homogeneous dielectric substrate are investigated. The results are compared with those of the exact solution to confirm the correctness of the present method. In this case, the phase and attenuation constants both oscillate periodically with the silicon thickness. Then, the TM modes are analyzed and it is indicated that the propagation constants are different from those of the TE modes and that propagation constants do not necessarily oscillate periodically with the silicon thickness. Whether or not the oscillations are present depends on the refractive‐index difference between the dielectric core and the silicon layer. Next, to reduce the propagation losses of the silicon‐clad planar optical waveguides with interesting characteristics, the new structures of silicon layer/inhomogeneous dielectric substrate or silicon layer/dielectric buffer layer/ inhomogeneous dielectric substrate, are proposed. It is shown that the propagation losses of these silicon‐clad planar optical waveguides expressed in decibels, are reduced by one order of magnitude compared with the previous planar waveguides.

Linear and non-linear theory of the Doppler-shifted cyclotron resonance maser based on TE and TM waveguide modes

This paper presents a comprehensive theory of the cyclotron resonance maser (CRM) interaction in a circular waveguide. The kinetic theory is used to derive the dispersion relationships for both TE and TM modes. The TE mode case has been investigated by several authors, but there has been comparatively little work on the TM mode case. However, the TM mode interaction competes effectively with the TE mode interaction at relativistic electron energies. The conditions for maximum temporal and spatial growth rates are shown. The TM mode growth rates are found to vanish when the RF wave group velocity equals the beam axial velocity (‘grazing incidence’). The single particle theory is used to derive a compact set of self-consistent non-linear equations for the TE and TM mode interactions. These equations are particularly appropriate for the cyclotron auto-resonance maser (CARM) regime but applicability extends to other regimes as well. The conditions for optimum efficiency are investigated for oscillator and amp...

Three-dimensional theory of free electron lasers with an axial guide field

The collective interaction in a free electron laser with a combined helical wiggler and uniform axial guide field is presented in the low-gain regime. The wiggler model we employ is fully self-consistent and includes all transverse inhomogeneities. The analysis is performed for a free electron laser (FEL) amplifier in which the radial dependence of the radiation is treated using both the TE and TM waveguide modes. Substantial discrepancies are found to exist between the results for the realizable and ideal wigglers, and a selection rule relating the TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ln</inf> and TM <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ln</inf> modes with resonant amplification at the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</tex> th harmonic of the FEL Doppler upshift.

Observation and Suppression of Radial Beam Blowup in the Maryland ERA

In the Maryland ERA, a rotating electron ring beam is produced by passing a nonrotating hollow beam through a narrow magnetic cusp. As the beam progresses in the acceleration region downstream of the cusp transition, a fast growth in the radial thickness of the beam is observed, resulting in rapid loss of the beam to the conducting boundaries. The effect of different conducting boundary configurations on the radial growth of the beam has been measured using magnetic probes and time-resolved and time-integrated photographs of the beam cross section. Measurements of the microwave radiation produced by the beam as it propagates in the downstream region indicate that a substantial fraction of the total beam power is converted into radiation. This radiation is attributed to the negative mass instability and coupled into the TE and TM waveguide modes of the downstream drift chamber. When the beam is passed through a 6.4mg-cm-2 titanium foil located at the anode plane, microwave radiated power is reduced by a factor of 100 and the radial blowup of the beam is suppressed.

Gigawatt microwave from an intense relativistic electron beam

Microwave generation experiments were carried out on a multimegavolt electron accelerator (3.3 MV, 80 kA). X-band microwave power as high as approximately 1 GW was measured. Results are compared with a non-linear theory of unstable resonant interaction between a TE waveguide mode of the electron drift tube and an electron cyclotron wave on the beam.

Faraday Optical Isolator/Gyrator Design in Planar Dielectric Waveguide Form

The possibilities of using the magnetic Faraday effect to provide a planar dielectric waveguide isolator or circulator are studied. At least two active elements which couple the TE and TM waveguide modes are required. One of these is magnetooptic. Preliminary design data for a dielectric waveguide isolator in which the mode-converting media forms the substrate and top layer of a single waveguide structure are reported. This design should prove more practical than the optical tandem structures proposed previously.

Bulk acoustic wave interaction with guided optical waves

An interaction between longitudinal or shear bulk acoustic waves and guided optical waves has been observed in single-mode and multimode polyurethane and sputtered glass optical waveguides. This interaction produces a number of effects — namely, mode conversion, amplitude modulation, and phase modulation — depending upon whether shear or longitudinal sound is present. Mode conversion between TE and TM waveguide modes occurs with shear sound; longitudinal sound produces amplitude and phase modulation of the guided light. The bulk acoustic wave effect offers promise for producing high-data-rate integrated optical modulators.