## TE and TM beam decomposition of time-harmonic electromagnetic waves |

JOSA A, Vol. 28, Issue 3, pp. 401-409 (2011)

http://dx.doi.org/10.1364/JOSAA.28.000401

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### Abstract

The present contribution is concerned with applying beam-type expansion to planar aperture time-harmonic electromagnetic field distribution in which the propagating elements, the electromagnetic beam-type wave objects, are decomposed into transverse electric (TE) and transverse magnetic (TM) field constituents. This procedure is essential for applying Maxwell’s boundary conditions for solving different scattering problems. The propagating field is described as a discrete superposition of tilted and shifted TE and TM electromagnetic beams over the frame-based spatial–directional expansion lattice. These vector wave objects are evaluated either by applying differential operators to scalar beam propagators, or by using plane-wave spectral representations. Explicit asymptotic expressions for scalar, as well as for electromagnetic, Gaussian beam propagators are presented as well.

© 2011 Optical Society of America

**OCIS Codes**

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

(080.2720) Geometric optics : Mathematical methods (general)

(260.1960) Physical optics : Diffraction theory

(350.5500) Other areas of optics : Propagation

**ToC Category:**

Fourier Optics and Signal Processing

**History**

Original Manuscript: December 20, 2010

Manuscript Accepted: January 18, 2011

Published: February 25, 2011

**Citation**

Timor Melamed, "TE and TM beam decomposition of time-harmonic electromagnetic waves," J. Opt. Soc. Am. A **28**, 401-409 (2011)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-3-401

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### References

- B. Steinberg, E. Heyman, and L. Felsen, “Phase space beam summation for time-harmonic radiation from large apertures,” J. Opt. Soc. Am. A 8, 41–59 (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]
- J. M. Arnold, “Rays, beams and diffraction in a discrete phase space: Wilson bases,” Opt. Express 10, 716–727 (2002). [PubMed]
- 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]
- G. Gordon, E. Heyman, and R. Mazar, “A phase-space Gaussian beam summation representation of rough surface scattering,” J. Acoust. Soc. Am. 117, 1911–1921 (2005). [CrossRef] [PubMed]
- M. Katsav and E. Heyman, “Phase space Gaussian beam summation analysis of half plane diffraction,” IEEE Trans. Antennas Propag. 55, 1535–1545 (2007). [CrossRef]
- T. Melamed, “Phase-space Green’s functions for modeling time-harmonic scattering from smooth inhomogeneous objects,” J. Math. Phys. 45, 2232–2246 (2004). [CrossRef]
- T. Melamed, “Time-domain phase-space Green’s functions for inhomogeneous media,” in Ultrawideband/Short Pulse Electromagnetics 6, E.L.Mokole, M.Kragalott, K.R.Gerlach, M.Kragalott, and K.R.Gerlach, ed. (Springer-Verlag, 2007), pp. 56–63.
- 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 an anisotropic medium. Part 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 an anisotropic medium. Part II. Time-dependent fields,” J. Opt. Soc. Am. A 22, 1208–1215 (2005). [CrossRef]
- T. Melamed and L. Felsen, “Pulsed beam propagation in lossless dispersive media. Part I. Theory,” J. Opt. Soc. Am. A 15, 1268–1276 (1998). [CrossRef]
- T. Melamed and L. Felsen, “Pulsed beam propagation in lossless dispersive media. Part 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]
- V. Ĉerveny, M. M. Popov, and I. Pŝenĉik, “Computation of wave fields in inhomogeneous media—Gaussian beam approach,” Geophys. J. R. Astron. Soc. 70, 109–128 (1982). [CrossRef]
- B. W. A. N. Norris and J. Schrieffer, “Gaussian wave packets in inhomogeneous media with curved interfaces,” Proc. R. Soc. London Ser. A 412, 93–123 (1987). [CrossRef]
- E. Heyman, “Pulsed beam propagation in an inhomogeneous medium,” IEEE Trans. Antennas Propag. 42, 311–319 (1994). [CrossRef]
- R. Collin, “Scattering of an incident Gaussian beam by a perfectly conducting rough surface,” IEEE Trans. Antennas Propag. 42, 70–4 (1994). [CrossRef]
- O. Kilic and R. Lang, “Scattering of a pulsed beam by a random medium over ground,” J. Electromagn. Waves Appl. 15, 481–516(2001). [CrossRef]
- O. Pascal, F. Lemaitre, and G. Soum, “Paraxial approximation effect on a dielectric interface analysis,” Ann. Telecommun. 51, 206–218 (1996).
- H. Anastassiu and P. Pathak, “Closed form solution for three-dimensional reflection of an arbitrary Gaussian beam by a smooth surface,” Radio Sci. 37, 1–8 (2002). [CrossRef]
- J. Hillairet, J. Sokoloff, S. Bolioli, and P. F. Combes, “Analytical physical optics scattering from a PEC finite plate illuminated by a vector Gaussian beam,” in 2007 International Conference on Electromagnetics in Advanced Applications (2007), pp. 170–173.
- F. Bass and L. Resnick, “Wave beam propagation in layered media,” Prog. Electromagn. Res. 38, 111–123 (2002). [CrossRef]
- J. Kong, “Electromagnetic wave interaction with stratified negative isotropic media,” J. Electromagn. Waves Appl. 15, 1319–1320 (2001). [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,” Prog. Electromagn. Res. PIER 102, 65–80 (2010). [CrossRef]
- Y. Hadad and T. Melamed, “Tilted Gaussian beam propagation in inhomogeneous media,” J. Opt. Soc. Am. A 27, 1840–1850(2010). [CrossRef]
- B. Steinberg and E. Heyman, “Phase space beam summation for time dependent radiation from large apertures: discretized parametrization,” J. Opt. Soc. Am. A 8, 959–966 (1991). [CrossRef]
- H.-T. Chou, P. Pathak, and R. Burkholder, “Application of Gaussian-ray basis functions for the rapid analysis of electromagnetic radiation from reflector antennas,” IEE Proc. Microw. Antennas Propag. 150, 177–83 (2003). [CrossRef]
- H.-T. Chou, P. Pathak, and R. Burkholder, “Novel Gaussian beam method for the rapid analysis of large reflector antennas,” IEEE Trans. Antennas Propag. 49, 880–93 (2001). [CrossRef]
- H.-T. Chou and P. Pathak, “Fast Gaussian beam based synthesis of shaped reflector antennas for contoured beam applications,” IEE Proc. Microw. Antennas Propag. 151, 13–20 (2004). [CrossRef]
- T. Melamed, “Exact beam decomposition of time-harmonic electromagnetic waves,” J. Electromagn. Waves Appl. 23, 975–986(2009).
- R. Martínez-Herrero, P. Mejías, S. Bosch, and A. Carnicer, “Vectorial structure of nonparaxial electromagnetic beams,” J. Opt. Soc. Am. A 18, 1678–1680 (2001). [CrossRef]
- H. Guo, J. Chen, and S. Zhuang, “Vector plane wave spectrum of an arbitrary polarized electromagnetic wave,” Opt. Express 14, 2095–2100 (2006). [CrossRef] [PubMed]
- D. Gabor, “A new microscopic principle,” Nature 161, 777(1948). [CrossRef] [PubMed]
- J. Wexler and S. Raz, “Discrete Gabor expansions,” Signal Process. 21, 207–20 (1990). [CrossRef]
- 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 (Elsevier, 1998), pp. 1–63.
- 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. 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]
- L. Felsen and N. Marcuvitz, Radiation and Scattering of Waves, Classic reissue (IEEE, 1994), Chap. 4.2. [CrossRef]

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