Use of decomposition of the wave equations and pseudo-differential operators for the description of nonparaxial beams and broadband wave packets
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...
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| Published in: | Radiophysics and quantum electronics Vol. 49; no. 4; pp. 288 - 301 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Springer Nature B.V
01-04-2006
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| Abstract | 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] |
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| AbstractList | 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. 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] |
| Author | Vlasov, S. N. Koposova, E. V. Talanov, V. I. |
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| Cites_doi | 10.1103/PhysRevLett.24.1217 10.1364/OL.20.001598 10.1103/PhysRevLett.87.203901 10.1103/PhysRevLett.24.584 10.1103/PhysRevE.71.016601 10.1007/BF01041026 10.1103/PhysRevLett.24.592 10.1109/JQE.1987.1073392 10.1103/PhysRevE.70.036607 10.1103/PhysRevLett.78.3282 |
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| DOI | 10.1007/s11141-006-0062-9 |
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| References | R. R. Alfano (62_CR17) 1970; 24 M. E. Taylor (62_CR22) 1981 S. A. Kozlov (62_CR10) 1999; 7 R. R. Alfano (62_CR16) 1970; 24 R. R. Alfano (62_CR18) 1970; 24 G. P. Agraval (62_CR6) 1995 62_CR14 62_CR13 62_CR12 N. G. Bondarenko (62_CR19) 1970; 12 62_CR5 62_CR2 E. M. Gromov (62_CR9) 1996; 110 62_CR3 N. G. Bondarenko (62_CR20) 1987; 33 A. G. Litvak (62_CR7) 1967; 10 (62_CR21) 1989 S. N. Vlasov (62_CR1) 1995; 38 S. Chi (62_CR15) 1995; 20 Th. Brabec (62_CR11) 1997; 78 H. C. Yuen (62_CR4) 1982 Y. Codama (62_CR8) 1987; 23 |
| References_xml | – volume: 38 start-page: 1 issue: s.1–2 year: 1995 ident: 62_CR1 publication-title: Radiophys. Quantum Electron. contributor: fullname: S. N. Vlasov – volume: 24 start-page: 1219 issue: 22 year: 1970 ident: 62_CR18 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.24.1217 contributor: fullname: R. R. Alfano – volume-title: The Supercontinuum Laser Source year: 1989 ident: 62_CR21 – volume: 20 start-page: 1598 issue: 15 year: 1995 ident: 62_CR15 publication-title: Opt. Lett. doi: 10.1364/OL.20.001598 contributor: fullname: S. Chi – volume: 7 start-page: 19 issue: 1 year: 1999 ident: 62_CR10 publication-title: Phys. Vibration contributor: fullname: S. A. Kozlov – ident: 62_CR5 – ident: 62_CR12 doi: 10.1103/PhysRevLett.87.203901 – volume-title: Pseudo-differential Operators, Princeton Mathematical Series year: 1981 ident: 62_CR22 contributor: fullname: M. E. Taylor – volume: 24 start-page: 584 issue: 11 year: 1970 ident: 62_CR16 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.24.584 contributor: fullname: R. R. Alfano – ident: 62_CR14 doi: 10.1103/PhysRevE.71.016601 – ident: 62_CR2 – ident: 62_CR3 – volume: 110 start-page: 137 issue: 1 year: 1996 ident: 62_CR9 publication-title: Zh. Éksp. Teor. Fiz. contributor: fullname: E. M. Gromov – volume: 10 start-page: 296 issue: 4 year: 1967 ident: 62_CR7 publication-title: Radiophys. Quantum Electron. doi: 10.1007/BF01041026 contributor: fullname: A. G. Litvak – volume: 12 start-page: 125 issue: 3 year: 1970 ident: 62_CR19 publication-title: Pis’ma Zh. Éksp. Teor. Fiz. contributor: fullname: N. G. Bondarenko – volume-title: Nonlinear Fiber Optics year: 1995 ident: 62_CR6 contributor: fullname: G. P. Agraval – volume: 24 start-page: 592 issue: 11 year: 1970 ident: 62_CR17 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.24.592 contributor: fullname: R. R. Alfano – volume: 23 start-page: 510 issue: 5 year: 1987 ident: 62_CR8 publication-title: IEEE J. Quantum Electron. doi: 10.1109/JQE.1987.1073392 contributor: fullname: Y. Codama – volume-title: Nonlinearity Dynamics of Deep-Water Gravity Waves year: 1982 ident: 62_CR4 contributor: fullname: H. C. Yuen – volume: 33 start-page: 89 year: 1987 ident: 62_CR20 publication-title: Kvant. Élektron. contributor: fullname: N. G. Bondarenko – ident: 62_CR13 doi: 10.1103/PhysRevE.70.036607 – volume: 78 start-page: 3282 issue: 17 year: 1997 ident: 62_CR11 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.78.3282 contributor: fullname: Th. Brabec |
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| SubjectTerms | Approximation Beams (radiation) Broadband Decomposition Mathematical analysis Operators Plane waves Wave equations Wave packets |
| Title | Use of decomposition of the wave equations and pseudo-differential operators for the description of nonparaxial beams and broadband wave packets |
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