Use of decomposition of the wave equations and pseudo-differential operators for the description of nonparaxial beams and broadband wave packets

• Published in: Radiophysics and quantum electronics Vol. 49; no. 4; pp. 288 - 301
• Main Authors: Vlasov, S. N., Koposova, E. V., Talanov, V. I.
• Format: Journal Article
• Language: English
• Published: New York Springer Nature B.V 01-04-2006
• Subjects: Approximation; Beams (radiation); Broadband; Decomposition; Mathematical analysis; Operators; Plane waves; Wave equations; Wave packets
• ISSN: 0033-8443; 1573-9120
• DOI: 10.1007/s11141-006-0062-9

We discuss the common approach for deriving the equations for the description of wave beams and wave packets in a wide range of angles and frequencies by decomposition of the initial equations into coupled equations of normal waves with the use of pseudo-differential operators. Estimates of accuracy of the one-wave approximation as a function of accuracy of approximation for the propagation-constant operator are given. We propose to use the method of moments for the description of pulses with a wide spectrum. The transition from the obtained to known equations is described. As an example of using the obtained equations, we analyze the self-focusing and modulation instabilities of plane waves in quartz in the range of transition from the normal to anomalous dispersion of the group velocity.[PUBLICATION ABSTRACT]