Abstract
In this paper we report a novel transparent boundary (TBC) condition for the 2D parabolic wave equation in which the dielectric constant is linearly dependent on the transversal coordinate. The proposed condition does not involve special functions and can be a basis for an efficient finite difference approximation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Fock, V.A.: Electromagnetic Diffraction and Propagation Problems. Pergamon, Tarrytown (1965)
Tappert, F.D.: The parabolic approximation method. In: Keller, J.B., Papadakis, J.S. (eds.) Wave Propagation and Underwater Acoustics. Lecture Notes in Physics, vol. 70, pp. 224–287 (1977)
Papadakis, J.S.: Exact nonreflecting boundary conditions for parabolic type approximations in underwater acoustics. J. Comput. Acoust. 2, 83–98 (1994)
Attwood, D.: Soft X-rays and Extreme Ultraviolet Radiation. Cambridge University Press, Cambridge (1999)
Baskakov, V.A., Popov, A.V.: Implementation of transparent boundaries for numerical solution of the Schrodinger equation. Wave Motion 14, 123–128 (1991)
Popov, A.V.: Accurate modelling of transparent boundaries in quasi-optics. Radio Sci. 31, 1781–1790 (1996)
Berenger, J.: A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114, 185–200 (1994)
Yevick, D., Friese, T., Schmidt, F.: A comparison of transparent boundary conditions for the Fresnel equation. J. Comput. Phys. 168, 433–444 (2001)
Ehrhardt, M., Mickens, R.E.: Solutions to the discrete Airy equation: application to parabolic equation calculations. J. Comput. Phys. 72, 183–206 (2004)
Acknowledgements
This work was supported in part by the basic research program of Russian Academy of Sciences “Femtosecond optics and new optical materials” (subprogram “New optical materials”), and by the Russian Foundation for Basic Research (RFBR) grant No. 10-02-00991-a.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Feshchenko, R.M., Popov, A.V. (2014). Parabolic Equation and Exact Transparent Boundary Conditions in X-Ray Optics—Application to Waveguides and Whispering Gallery Optics. In: Sebban, S., Gautier, J., Ros, D., Zeitoun, P. (eds) X-Ray Lasers 2012. Springer Proceedings in Physics, vol 147. Springer, Cham. https://doi.org/10.1007/978-3-319-00696-3_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-00696-3_17
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-00695-6
Online ISBN: 978-3-319-00696-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)