Method of adiabatic modes in studying problems of smoothly irregular open waveguide structures

Sevastianov, Leonid A.; Egorov, A. A.; Sevastianov, Anton

doi:10.1134/s1063778813010134

Cited by 16 publications

(7 citation statements)

References 43 publications

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“…Waveguides with different thicknesses (25,75, and 125 μm) were studied in experiments, but the main part of the results is given only for NLC waveguides with h = 25 and 75 μm. Distance between copper electrodes was 0.2 cm.…”

Section: Results Of the Study Of Nlc Structuresmentioning

confidence: 99%

Properties of nematic LC planar and smoothly-irregular waveguide structures: research in the experiment and using computer modeling

et al. 2019

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Nematic liquid crystal planar and smoothly-irregular waveguide structures were studied experimentally and by the computer modeling. Two types of optical smoothly-irregular waveguide structures promising for application in telecommunications and control systems are studied by numerical simulation: liquid crystal waveguides and thin film solid generalized waveguide Luneburg lens. Study of the behavior of these waveguide structures where liquid crystal layer can be used to control the properties of the entire device, of course, promising, especially since such devices are also able to perform various sensory functions when changing some external parameters, accompanied by a change in a number of their properties. It can be of interest to researchers not only in the field of the integrated optics but also in some others areas: nano-photonics, optofluidics, telecommunications, and control systems. The dependences of the attenuation coefficient (optical losses) of waveguide modes and the effective sizes (correlation radii) of quasi-stationary irregularities of the liquid-crystal layers on the linear laser radiation polarization and on the presence of pulse-periodic electric field were experimentally observed. An estimate was made of the correlation radii of liquid-crystal waveguide quasi-stationary irregularities. The obtained results are undoubtedly important for further research of waveguide liquid crystal layers, both from the theoretical point of view, and practical – in the organization and carrying out new experimental researches, for example, when developing promising integrated-optical LC sensors.

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Section: Results Of the Study Of Nlc Structuresmentioning

confidence: 99%

Properties of nematic LC planar and smoothly-irregular waveguide structures: research in the experiment and using computer modeling

et al. 2019

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“…This algorithm was implemented in the computer algebra system Maple [4,5,9,10]. In the algorithm there is a function of the accuracy problem of calculations.…”

Section: Solution Algorithmmentioning

confidence: 99%

“…Applying the separation of variables method, we obtain the equation for the transverse and longitudinal parts [4][5][6][7][8][9]   2 2 2 2 0 0…”

Section: Introductionmentioning

confidence: 99%

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

2018

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Abstract. 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.

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“…The solution of the first equation of system (10) is found using the generalized Kantorovich method [11], [12], which is analogous to the method of separation of variables proposed in [13]. We find the solutions to an auxiliary problem analogous to a problem of finding eigenvalues and eigenfunctions that depend on a parameter.…”

Section: Setting Of the Physical Problemmentioning

confidence: 99%

Single-mode propagation of adiabatic guided modes in smoothly irregular integral optical waveguides

Sevastianov

2020

Discrete and Continuous Models

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This paper investigates the waveguide propagation of polarized electromagnetic radiation in a thin-film integral optical waveguide. To describe this propagation, the adiabatic approximation of solutions of Maxwells equations is used. The construction of a reduced model for adiabatic waveguide modes that retains all the properties of the corresponding approximate solutions of the Maxwell system of equations was carried out by the author in a previous publication in DCM ACS, 2020, No 3. In this work, for a special case when the geometry of the waveguide and the electromagnetic field are invariant in the transverse direction. In this case, there are separate nontrivial TEand TM-polarized solutions of this reduced model. The paper describes the parametrically dependent on longitudinal coordinates solutions of problems for eigenvalues and eigenfunctions - adiabatic waveguide TE and TM polarizations. In this work, we present a statement of the problem of finding solutions to the model of adiabatic waveguide modes that describe the stationary propagation of electromagnetic radiation. The paper presents solutions for the single-mode propagation of TE and TM polarized adiabatic waveguide waves.

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Method of adiabatic modes in studying problems of smoothly irregular open waveguide structures

Cited by 16 publications

References 43 publications

Properties of nematic LC planar and smoothly-irregular waveguide structures: research in the experiment and using computer modeling

Properties of nematic LC planar and smoothly-irregular waveguide structures: research in the experiment and using computer modeling

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

Single-mode propagation of adiabatic guided modes in smoothly irregular integral optical waveguides

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