Theory of Irregular Waveguides with Slowly Changing Parameters

Katsenelenbaum, B. Z.

doi:10.21236/ada083533

Cited by 35 publications

(60 citation statements)

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“…This result can be considered as a justification of the well known in the physical literature the cross-section method for waveguides with slowly varying parameters (see for instance [8,32,33]). …”

Section: Introductionmentioning

confidence: 64%

Invertibility of Helmholtz operators for nonhomogeneous medias

Rabinovich

Cerdan

2009

Math Methods in App Sciences

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The paper is devoted to the investigation of the Helmholtz operators describing the propagation of acoustic waves in non‐homogeneous space. We consider the operator A with a wave number k such that where k0 is a positive function, k± are complex constants with ℑ︁(k)>0. The Helmholtz operator A with such wave number describes the propagation of acoustic waves in the waveguides being no homogeneous layer between two absorbing half‐space. We prove that the operator A has an inverse operator A‐1 bounded in the Hilbert space L2(ℝn). Our proof is based on the limit operators method.We also consider the construction of the inverse operator for the Helmholtz operator Aε with the density ρ = ρ(xn) depending on xn only and wave number k0 = k0(εx′, xn) depending on a small parameter ε>0 which characterizes the slowness of variation of the wave number in the horizontal direction. Copyright © 2009 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 64%

Invertibility of Helmholtz operators for nonhomogeneous medias

Rabinovich

Cerdan

2009

Math Methods in App Sciences

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“…A similar situation holds for the circle η(ϕ), whose center is located in the vicinity of l cs ; however, the CS begins for lesser values of r imp . Each CS phenomenon is accompanied by a sharp decrease in the signal amplitude, what is typical for the CS in a natural waveguide [6,9]. The part played by the segment l cs in the initiation of the CS phenomenon within the limits of the given model can be explained as follows: for the impedances only in the vicinity of this segment, the eigenvalues ν 1 and ν 2 have closely spaced imaginary parts, and consequently, amplitudes of the first and the second modes are nearly equal.…”

Section: To Calculate the Hankel Functions H (J)mentioning

confidence: 93%

“…In the approximation taking no account of the reflection from a discontinuity, its magnitude did not exceed 0.5 even for an abrupt stepwise change of the waveguide height. For the same purpose, the method of cross-sections [9] developed for wave guiding structures with slowly varying parameters over a wavelength has been used in [10]. A two-dimensional model represented a coaxial waveguide with varying in azimuth cross-section and surface impedance Z of one wall.…”

Section: Introductionmentioning

confidence: 99%

The Sycle Slipping Phenomenon and the Degeneration Effect of Guided-Wave Modes

Pazynin¹

2009

PIER M

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Abstract-A model of the ring waveguide of a fixed cross-section and variable distribution of the surface impedance of waveguide's wall has been considered. For a class of circular hodographs of surface impedance the analytical solution of the corresponding boundary-value problem has been obtained. This solution has been used for simulating a 'cycle slipping' phenomenon, known from the observations of VLF signals propagating over long paths in the earth-ionosphere waveguide, with the goal of clarifying the cause for its initiation. Numerical experiments have shown that this phenomenon, in the context of the model in question, is a consequence of the interconversion of two dominant waveguide modes in circumstances where their propagation constants are close.

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“…Monograph [23] is one of the fundamental works of this direction. Effects of wave interaction in irregular waveguides are exact described by the coupled mode theory.…”

Section: Brief Overview Of Methods For Simulation Of Pulse Propagatiomentioning

confidence: 99%

Modeling and Simulation of Piecewise Regular Multimode Fiber Links Operating in a Few-Mode Regime

Bourdine

2013

Advances in Optical Technologies

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This work presents an alternative model of multimode fiber links with conventional silica weakly-guiding graded-index irregular multimode fibers under a few-mode optical signal propagation generated by laser source. The proposed model is based on the piecewise regular representation. It takes into account launch conditions, differential mode delay, both lower-and higherorder mode chromatic dispersion, differential mode attenuation, and mode mixing and power diffusion occurring due to real fiber irregularity and micro-and macrobends. We present some results of introduced model approbation with following pulse propagation simulations. A close matching with measured pulse responses at the output of test fibers is noticed.

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Theory of Irregular Waveguides with Slowly Changing Parameters

Cited by 35 publications

References 1 publication

Invertibility of Helmholtz operators for nonhomogeneous medias

Invertibility of Helmholtz operators for nonhomogeneous medias

The Sycle Slipping Phenomenon and the Degeneration Effect of Guided-Wave Modes

Modeling and Simulation of Piecewise Regular Multimode Fiber Links Operating in a Few-Mode Regime

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