## Tilted Gaussian beam propagation in inhomogeneous media

JOSA A, Vol. 27, Issue 8, pp. 1840-1850 (2010)

http://dx.doi.org/10.1364/JOSAA.27.001840

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### Abstract

The present work is concerned with applying a ray-centered non-orthogonal coordinate system which is *a priori* matched to linearly-phased localized aperture field distributions. The resulting beam-waveobjects serve as the building blocks for beam-type spectral expansions of aperture fields in 2D inhomogeneous media that are characterized by a generic wave-velocity profile. By applying a rigorous paraxial-asymptotic analysis, a novel parabolic wave equation is obtained and termed “Non-orthogonal domain parabolic equation”—NoDope. Tilted Gaussian beams, which are exact solutions to this equation, match Gaussian aperture distributions over a plane that is tilted with respect to the beam-axes initial directions. A numerical example, which demonstrates the enhanced accuracy of the tilted Gaussian beams over the conventional ones, is presented as well.

© 2010 Optical Society of America

**OCIS Codes**

(070.2580) Fourier optics and signal processing : Paraxial wave optics

(080.2720) Geometric optics : Mathematical methods (general)

(350.5500) Other areas of optics : Propagation

**ToC Category:**

Fourier Optics and Signal Processing

**History**

Original Manuscript: April 26, 2010

Revised Manuscript: June 11, 2010

Manuscript Accepted: June 16, 2010

Published: July 22, 2010

**Citation**

Yakir Hadad and Timor Melamed, "Tilted Gaussian beam propagation in inhomogeneous media," J. Opt. Soc. Am. A **27**, 1840-1850 (2010)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-8-1840

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### References

- V. Cerveny, M. M. Popov, and I. Pŝencik, “Computation of wave fields in inhomogeneous media—Gaussian beam approach,” Geophys. J. R. Astron. Soc. 70, 109–128 (1982). [CrossRef]
- E. Heyman, “Pulsed beam propagation in an inhomogeneous medium,” IEEE Trans. Antennas Propag. 42, 311–319 (1994). [CrossRef]
- T. Melamed, “Phase-space Green’s functions for modeling time-harmonic scattering from smooth inhomogeneous objects,” J. Math. Phys. 46, 2232–2246 (2004). [CrossRef]
- S. Y. Shin and L. B. Felsen, “Gaussian beams in anisotropic media,” Appl. Phys. 5, 239–250 (1974). [CrossRef]
- R. Simon and N. Mukunda, “Shape-invariant anisotropic Gaussian Schell-model beams: a complete characterization,” J. Opt. Soc. Am. A 15, 1361–70 (1998). [CrossRef]
- E. Poli, G. V. Pereverzev, and A. G. Peeters, “Paraxial Gaussian wave beam propagation in an anisotropic inhomogeneous plasma,” Phys. Plasmas 6, 5–11 (1999). [CrossRef]
- L. I. Perez and M. T. Garea, “Propagation of 2D and 3D Gaussian beams in an anisotropic uniaxial medium: vectorial and scalar treatment,” Optik 111, 297–306 (2000).
- I. Tinkelman and T. Melamed, “Gaussian beam propagation in generic anisotropic wavenumber profiles,” Opt. Lett. 28, 1081–1083 (2003). [CrossRef] [PubMed]
- I. Tinkelman and T. Melamed, “Local spectrum analysis of field propagation in anisotropic media. I. Time-harmonic fields,” J. Opt. Soc. Am. A 22, 1200–1207 (2005). [CrossRef]
- I. Tinkelman and T. Melamed, “Local spectrum analysis of field propagation in anisotropic media. II. Time-dependent fields,” J. Opt. Soc. Am. A 22, 1208–1215 (2005). [CrossRef]
- A. G. Khatkevich, “Propagation of pulses and wave packets in dispersive gyrotropic crystals,” J. Appl. Spectrosc. 46, 203–207 (1987). [CrossRef]
- T. Melamed and L. B. Felsen, “Pulsed beam propagation in lossless dispersive media. I. Theory,” J. Opt. Soc. Am. A 15, 1268–1276 (1998). [CrossRef]
- T. Melamed and L. B. Felsen, “Pulsed beam propagation in lossless dispersive media. II. A numerical example,” J. Opt. Soc. Am. A 15, 1277–1284 (1998). [CrossRef]
- T. Melamed and L. B. Felsen, “Pulsed beam propagation in dispersive media via pulsed plane wave spectral decomposition,” IEEE Trans. Antennas Propag. 48, 901–908 (2000). [CrossRef]
- A. P. Kiselev, “Localized light waves: paraxial and exact solutions of the wave equation (a review),” Opt. Spectrosc. 102, 603–622 (2007). [CrossRef]
- A. Shlivinski, E. Heyman, A. Boag, and C. Letrou, “A phase-space beam summation formulation for ultra wideband radiation,” IEEE Trans. Antennas Propag. 52, 2042–2056 (2004). [CrossRef]
- A. Shlivinski, E. Heyman, and A. Boag, “A pulsed beam summation formulation for short pulse radiation based on windowed radon transform (WRT) frames,” IEEE Trans. Antennas Propag. 53, 3030–3048 (2005). [CrossRef]
- T. Melamed, “Exact beam decomposition of time-harmonic electromagnetic waves,” J. Electromagn. Waves Appl. 23, 975–986 (2009).
- B. Z. Steinberg, E. Heyman, and L. B. Felsen, “Phase space beam summation for time-harmonic radiation from large apertures,” J. Opt. Soc. Am. A 8, 41–59 (1991). [CrossRef]
- B. Z. Steinberg, E. Heyman, and L. B. Felsen, “Phase space beam summation for time dependent radiation from large apertures: Continuous parametrization,” J. Opt. Soc. Am. A 8, 943–958 (1991). [CrossRef]
- T. Melamed, “Phase-space beam summation: A local spectrum analysis for time-dependent radiation,” J. Electromagn. Waves Appl. 11, 739–773 (1997). [CrossRef]
- M. A. Leontovich and V. A. Fock, “Solution of the problem of EM wave propagation along the earth surface by the parabolic equation method,” J. Phys. 10, 13 (1946).
- G. D. Malyuzhinets, “Progress in understanding diffraction phenomena (in Russian),” Sov. Phys. Usp. 69, 321–334 (1959).
- A. V. Popov, “Numerical solution of the wedge diffraction problem by the transversal diffusion method (in Russian),” Sov. Phys. Acoust. 15, 226–233 (1969).
- S. N. Vlasov and V. I. Talanov, “The parabolic equation in the theory of wave propagation,” Radiophys. Quantum Electron. 38, 1–12 (1995). [CrossRef]
- M. Levys, Parabolic Equation Methods for Electromagnetic Wave Propagation (The Institution of Electrical Engineers, 2000). [CrossRef]
- C. Chapman, Fundamentals of Seismic Wave Propagation (Cambridge Univ. Press, 2004). [CrossRef]
- J. A. Arnaud and H. Kogelnik, “Gaussian light beams with general astigmatism,” Appl. Opt. 8, 1687–1693 (1969). [CrossRef] [PubMed]
- G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7, 684–685 (1971). [CrossRef]
- S. D. Patil, S. T. Navare, M. V. Takale, and M. B. Dongare, “Self-focusing of cosh-Gaussian laser beams in a parabolic medium with linear absorption,” Opt. Lasers Eng. 47, 604–606 (2009). [CrossRef]
- Y. Hadad and T. Melamed, “Non-orthogonal domain parabolic equation and its Gaussian beam solutions,” IEEE Trans. Antennas Propag. 58, 1164–1172 (2010). [CrossRef]
- Y. Hadad and T. Melamed, “Parameterization of the tilted Gaussian beam waveobjects,” PIER 102, 65–80 (2010). [CrossRef]
- V. M. Babič and V. S. Buldyrev, Short-Wavelength Diffraction Theory: Asymptotic Methods (Springer-Verlag, 1991).
- E. Heyman and T. Melamed, “Certain considerations in aperture synthesis of ultrawideband/short-pulse radiation,” IEEE Trans. Antennas Propag. 42, 518–525 (1994). [CrossRef]
- E. Heyman and T. Melamed, “Space-time representation of ultra wideband signals,” in Advances in Imaging and Electron Physics, Vol. 103 (Elsevier, 1998), pp.1–63. [CrossRef]
- A. Shlivinski, E. Heyman, and A. Boag, “A phase-space beam summation formulation for ultrawide-band radiation—Part II: A multiband scheme,” IEEE Trans. Antennas Propag. 53, 948–957 (2005). [CrossRef]
- A. P. Wills, Vector Analysis with an Introduction to Tensor Analysis (Dover, 1958).
- W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE, 1995).
- E. Heyman and L. B. Felsen, “Real and complex spectra—a generalization of WKBJ seismograms,” Geophys. J. R. Astron. Soc. 91, 1087–1126 (1987). [CrossRef]

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