On the accuracy of the WKB approximation in optical dielectric waveguides

Hartog, Arthur H.; Adams, Matthew

doi:10.1007/bf00619733

Cited by 34 publications

(7 citation statements)

References 25 publications

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“…for the elements defined by Equations (14) to (19). Since we are primarily interested in y(x) = u 1 (x), the top row of Equation (21) shows the final desired solution for System Two:…”

Section: Of 24mentioning

confidence: 99%

Feedback Diagram Application for the Generation and Solution of Linear Differential Equations Solvable by Quadrature

Pascone

Callahan

2020

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A novel method for generating and providing quadrature solutions to families of linear, second-order, ordinary differential equations is presented in this paper. It is based upon a comparison of control system feedback diagrams—one representing the system and equation under study and a second equalized to it and providing solutions. The resulting Riccati equation connection between them is utilized to generate and solve groups of equations parameterized by arbitrary functions and constants. This method also leads to a formal solution mechanism for all second-order linear differential equations involving an infinite series of integrals of each equation’s Schwarzian derivative. The practicality of this mechanism is strongly dependent on the series rates of and allowed regions for convergence. The feedback diagram method developed is shown to be equivalent to a comparable method based on the differential equation’s normal form and another relying upon the grouping of terms for a reduction of the equation order, but augmenting their results. Applications are also made to the Helmholtz equation.

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“…for the elements defined by Equations (14) to (19). Since we are primarily interested in y(x) = u 1 (x), the top row of Equation (21) shows the final desired solution for System Two:…”

Section: Of 24mentioning

confidence: 99%

Feedback Diagram Application for the Generation and Solution of Linear Differential Equations Solvable by Quadrature

Pascone

Callahan

2020

Axioms

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“…Thought the method here described can be applied to different functions for the optic index n, however in this work the analysis will be limited to the parabolic profile for n ( r), that is n(r)=n 124] , [2] with 1 -0 and m 1 , where m is associated with the mth mode number. The general equation [ 1 ] is now written as d2'P(r) 1 d+'(r) [3] dr r dr with the usual boundary condition P ( r =a ) = 0 . Here we have to obtain a power series expansions along the center of the waveguide ( r = 0 ) and an asymptotic expansion on the other limit r = a.…”

Section: Theorymentioning

confidence: 99%

<title>Generalized guided-wave mode calculations in graded-index fibers</title>

2004

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In this paper a novel approximated method is introduce to calculate guided-wave modes in graded-index fibers. Useful solutions have been obtained on the whole range of r for the corresponding scalar wave equation, using two-point quasirational approximations. This approach is better than the WKB approximation which is good only for the ray optic pictures and when the phase changes at the caustic are ignored. Here an adequate change of variables have been found that allows determine power series and asymptotic expansions suitable for application of the two-point quasi-rational approximant method. The results presented here agree very well with the numerical solutions.

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“…Leaky channels have been previously studied for a variety of applications, such as the minimization of instabilities (e.g., forward Raman scattering). 13 The approach used in our study draws on the source dependent expansion (SDE) formalism, [14][15][16][17] which has been shown to effectively model the evolution of Laguerre-Gaussian (LG) modes, as well as the Wentzel-Kramers-Brillouin (WKB) approximation 18,19 to evaluate mode leakage in the channel.…”

Section: Introductionmentioning

confidence: 99%

Filtering higher-order laser modes using leaky plasma channels

et al. 2018

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Plasma structures based on leaky channels are proposed to filter higher-order laser mode content. The evolution and propagation of non-Gaussian laser pulses in leaky channels are studied, and it is shown that, for appropriate laser-plasma parameters, the higher-order laser mode content of the pulse may be removed while the fundamental mode remains well-guided. The behavior of multimode laser pulses is described analytically and numerically using envelope equations, including the derivation of the leakage coefficients, and compared to particle-in-cell simulations. Laser pulse propagation, with reduced higher-order mode content, improves guiding in parabolic plasma channels, enabling extended interaction lengths for laser-plasma accelerator applications.

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On the accuracy of the WKB approximation in optical dielectric waveguides

Cited by 34 publications

References 25 publications

Feedback Diagram Application for the Generation and Solution of Linear Differential Equations Solvable by Quadrature

Feedback Diagram Application for the Generation and Solution of Linear Differential Equations Solvable by Quadrature

<title>Generalized guided-wave mode calculations in graded-index fibers</title>

Filtering higher-order laser modes using leaky plasma channels

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