## Generalized eikonal approximation. 2. Propagation of stationary electromagnetic waves in linear and nonlinear media

JOSA A, Vol. 15, Issue 10, pp. 2725-2729 (1998)

http://dx.doi.org/10.1364/JOSAA.15.002725

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### Abstract

A recent study [J. Opt. Soc. Am. A **15**, 2720 (1998)] showed that the eikonal equation can be generalized to include higher-order terms that can describe the dispersion of a pulse in a linear medium. In this companion paper, the formalism of this generalized eikonal approximation is investigated for stationary waves in both linear and nonlinear media. A local refractive index can be defined that includes higher-order terms in the form of the second derivatives of the amplitude of the wave. It is shown that wave phenomena such as diffraction, self-focusing, and self-trapping of a finite beam in linear and nonlinear media can be derived naturally as a result of the differences in the local refractive indices that arise from the spatial variation of the wave amplitude and the nonlinearity of the medium. This formalism can be readily extended to the study of other complex electromagnetic wave-propagation phenomena in both linear and nonlinear media.

© 1998 Optical Society of America

**OCIS Codes**

(080.2720) Geometric optics : Mathematical methods (general)

(190.0190) Nonlinear optics : Nonlinear optics

(260.1960) Physical optics : Diffraction theory

(260.2030) Physical optics : Dispersion

(260.2110) Physical optics : Electromagnetic optics

(350.5500) Other areas of optics : Propagation

**Citation**

S. C. Yap, B. C. Quek, and K. S. Low, "Generalized eikonal approximation. 2. Propagation of stationary electromagnetic waves in linear and nonlinear media," J. Opt. Soc. Am. A **15**, 2725-2729 (1998)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-10-2725

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### References

- B. C. Quek, B. R. Wong, and K. S. Low, “Generalized eikonal approximation. 1. Propagation of an electromagnetic pulse in a linear dispersive medium,” J. Opt. Soc. Am. A 15, 2720–2724 (1998).
- H. Guo and X. Deng, “Differential geometrical methods in the study of optical transmission (scalar theory). I. Static transmission case,” J. Opt. Soc. Am. A 12, 600–606 (1995).
- H. Guo and X. Deng, “Differential geometrical methods in the study of optical transmission (scalar theory). II. Time-dependent transmission theory,” J. Opt. Soc. Am. A 12, 607–610 (1995).
- J. Durnin, “Exact solution for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
- R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
- M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1965).
- A. Yariv, Optical Electronics (Saunders, Philadelphia, Pa., 1991).
- P. L. Kelly, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005–1008 (1965).
- H. A. Haus, “Higher order trapped light beam solutions,” Appl. Phys. Lett. 8, 128–129 (1966).
- D. Pohl, “Vectorial theory of self-trapped light beams,” Opt. Commun. 2, 305–308 (1970).
- V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972).
- S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, “Self-focusing and self-trapping of intense light beams in a nonlinear medium,” Sov. Phys. JETP 23, 1025–1033 (1966).

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