Vol. 102
Latest Volume
All Volumes
PIER 180 [2024] PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2010-02-11
Parameterization of the Tilted Gaussian Beam Waveobjects
By
Progress In Electromagnetics Research, Vol. 102, 65-80, 2010
Abstract
Novel time-harmonic beam fields have been recently obtained by utilizing a non-orthogonal coordinate system which is a priori matched to the field's planar linearly-phased Gaussian aperture distribution. These waveobjects were termed tilted Gaussian beams. The present investigation is concerned with parameterization of these time-harmonic tilted Gaussian beams and of the wave phenomena associated with them. Specific types of tilted Gaussian beams that are characterized by their aperture complex curvature matrices, are parameterized in term of beam-widths, waist-locations, collimation-lengths, radii of curvature, and other features. Emphasis is placed on the difference in the parameterization between the conventional (orthogonal coordinates) beams and the tilted ones.
Citation
Yakir Hadad, and Timor Melamed, "Parameterization of the Tilted Gaussian Beam Waveobjects," Progress In Electromagnetics Research, Vol. 102, 65-80, 2010.
doi:10.2528/PIER09120405
References

1. Cerveny, V., M. M. Popov, and I. Psencik, "Computation of wave fields in inhomogeneous media --- Gaussian beam approach," Geophys. J. Roy. Asro. Soc., Vol. 70, 109-128, 1982.

2. Heyman, E., "Pulsed beam propagation in an inhomogeneous medium," IEEE Trans. Antennas and Propagat., Vol. 42, 311-319, 1994.
doi:10.1109/8.280715

3. Melamed, T., "Phase-space Green's functions for modeling time-harmonic scattering from smooth inhomogeneous objects," J. Math. Phys., Vol. 46, 2232-2246, 2004.
doi:10.1063/1.1737812

4. Shin, S. Y. and L. B. Felsen, "Gaussian beams in anisotropic media," Applied Phys., Vol. 5, 239-250, 1974.
doi:10.1007/BF00928135

5. Simon, R., "Anisotropic Gaussian beams," Opt. Commun., Vol. 46, 265-269, 1983.
doi:10.1016/0030-4018(83)90002-0

6. Simon, R., N. Mukunda, and , "Shape-invariant anisotropic Gaussian Schell-model beams: A complete characterization," J. Opt. Soc. Am. A, Vol. 15, 1361-1370, 1998.
doi:10.1364/JOSAA.15.001361

7. Poli, E., G. V. Pereverzev, and A. G. Peeters, "Paraxial Gaussian wave beam propagation in an anisotropic inhomogeneous plasma," Physics of Plasmas, Vol. 6, 5-11, Jan.~1999.
doi:10.1063/1.873254

8. Perez, L. I. and M. T. Garea, "Propagation of 2D and 3D Gaussian beams in an anisotropic uniaxial medium: Vectorial and scalar treatment," Optik, Vol. 111, 297-306, 2000.

9. Tinkelman, I. and T. Melamed, "Gaussian beam propagation in generic anisotropic wavenumber profiles," Optics Letters, Vol. 28, 1081-1083, 2003.
doi:10.1364/OL.28.001081

10. Tinkelman, I. and T. Melamed, "Local spectrum analysis of field propagation in anisotropic media, Part I --- Time-harmonic fields," J. Opt. Soc. Am. A, Vol. 22, 1200-1207, 2005.
doi:10.1364/JOSAA.22.001200

11. Tinkelman, I. and T. Melamed, "Local spectrum analysis of field propagation in anisotropic media, Part II --- Time-dependent fields," J. Opt. Soc. Am. A, Vol. 22, 1208-1215, 2005.
doi:10.1364/JOSAA.22.001208

12. Khatkevich, A. G., "Propagation of pulses and wave packets in dispersive gyrotropic crystals," J. Appl. Spectrosc., Vol. 46, 203-207, 1987.
doi:10.1007/BF00665565

13. Melamed, T. and L. B. Felsen, "Pulsed beam propagation in lossless dispersive media, Part I: Theory," J. Opt. Soc. Am. A, Vol. 15, 1268-1276, 1998.
doi:10.1364/JOSAA.15.001268

14. Melamed, T. and L. B. Felsen, "Pulsed beam propagation in lossless dispersive media, Part II: A numerical example," J. Opt. Soc. Am. A, Vol. 15, 1277-1284, 1998.
doi:10.1364/JOSAA.15.001277

15. Melamed, T. and L. B. Felsen, "Pulsed beam propagation in dispersive media via pulsed plane wave spectral decomposition," IEEE Trans. Antennas and Propagat., Vol. 48, 901-908, 2000.
doi:10.1109/8.865222

16. Kiselev, A. P., "Localized light waves: Paraxial and exact solutions of the wave equation (a review)," Opt. Spectrosc., Vol. 102, 603-622, 2007.
doi:10.1134/S0030400X07040200

17. Maciel, J. J. and L. B. Felsen, "Systematic study of fields due to extended apertures by Gaussian beam discretization," IEEE Trans. Antennas and Propagat., Vol. 37, 884-892, 1989.
doi:10.1109/8.29383

18. Steinberg, B. Z., E. Heyman, and L. B. Felsen, "Phase space beam summation for time-harmonic radiation from large apertures," J. Opt. Soc. Am. A, Vol. 8, 41-59, 1991.
doi:10.1364/JOSAA.8.000041

19. Shlivinski, A., E. Heyman, A. Boag, and C. Letrou, "A phase-space beam summation formulation for ultra wideband radiation," IEEE Trans. Antennas and Propagat., Vol. 52, 2042-2056, 2004.
doi:10.1109/TAP.2004.832513

20. Shlivinski, A., E. Heyman, and A. Boag, "A pulsed beam summation formulation for short pulse radiation based on windowed radon transform (WRT) frames ," IEEE Trans. Antennas and Propagat., Vol. 53, 3030-3048, 2005.
doi:10.1109/TAP.2005.854550

21. Steinberg, B. Z., E. Heyman, and L. B. Felsen, "Phase space beam summation for time dependent radiation from large apertures: Continuous parametrization," J. Opt. Soc. Am. A, Vol. 8, 943-958, 1991.
doi:10.1364/JOSAA.8.000943

22. Melamed, T., "Phase-space beam summation: A local spectrum analysis for time-dependent radiation," Journal of Electromagnetic Waves and Applications, Vol. 11, No. 6, 739-773, 1997.
doi:10.1163/156939397X00945

23. Melamed, T., "Exact beam decomposition of time-harmonic electromagnetic waves," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 8-9, 975-986, 2009.

24. Hadad, Y. and T. Melamed, "Non-orthogonal domain parabolic equation and its Gaussian beam solutions," IEEE Trans. Antennas and Propagat., Vol. 58, accepted for publication, 2010.

25. Hoppe, D. J. and Y. Rahmat-Sami, "Gaussian beam reflection at a dielectric-chiral interface," Journal of Electromagnetic Waves and Applications, Vol. 6, No. 1-4, 603-624, 1992.

26. Ianconescu, R. and E. Heyman, "Pulsed beam diffraction by a perfectly conducting wedge. Exact solution," IEEE Trans. Antennas and Propagat., Vol. 42, 1377-1385, 1994.
doi:10.1109/8.320743

27. Heyman, E. and R. Ianconescu, "Pulsed beam diffraction by a perfectly conducting wedge. Local scattering models," IEEE Trans. Antennas and Propagat., Vol. 43, 519-528, 1995.
doi:10.1109/8.384197

28. Pascal, O., F. Lemaitre, and G. Soum, "Paraxial approximation effect on a dielectric interface analysis," Ann. Telecommun., Vol. 51, 206-218, 1996.

29. Pascal, O., F. Lemaitre, and G. Soum, "Dielectric lens analysis using vectorial multimodal Gaussian beam expansion," Ann. Telecommun., Vol. 52, 519-528, 1997.

30. Dou, W. B. and E. K. N. Yung, "Diffraction of an electromagnetic beam by planar structures," Journal of Electromagnetic Waves and Applications, Vol. 15, No. 11, 1539-1549, 2001.
doi:10.1163/156939301X00094

31. Sakurai, H. and S. Kozaki, "Scattering of a Gaussian beam by a radially inhomogeneous dielectric sphere," Journal of Electromagnetic Waves and Applications, Vol. 15, No. 12, 1673-1693, 2001.
doi:10.1163/156939301X00193

32. Anastassiu, H. T. and P. H. Pathak, "Closed form solution for three-dimensional reflection of an arbitrary Gaussian beam by a smooth surface," Radio Science, Vol. 37, 1-8, 2002.

33. Katsav, M. and E. Heyman, "A beam summation representation for 3-D radiation from a line source distribution," IEEE Trans. Antennas and Propagat., Vol. 56, 602-605, 2008.
doi:10.1109/TAP.2007.913173

34. Katsav, M. and E. Heyman, "Gaussian beams summation representation of half plane diffraction: A full 3-D formulation," IEEE Trans. Antennas and Propagat., Vol. 57, 1081-1094, 2009.
doi:10.1109/TAP.2009.2013436

35. Norris, A. N., "Complex point-source representation of real sources and the Gaussian beam summation method," J. Opt. Soc. A, Vol. 3, 205-210, 1986.

36. Heyman, E. and L. B. Felsen, "Gaussian beam and pulsed beam dynamics: Complex-source and complex spectrum formulations within and beyond paraxial asymptotics," J. Opt. Soc. Am. A, Vol. 18, 1588-1611, 2001.
doi:10.1364/JOSAA.18.001588

37. Heyman, E. and T. Melamed, "Certain considerations in aperture synthesis of ultrawideband/short-pulse radiation," IEEE Trans. Antennas and Propagat., Vol. 42, 518-525, 1994.
doi:10.1109/8.286220

38. Heyman, E. and T. Melamed, "Space-time representation of ultra wideband signals," Advances in Imaging and Electron Physics, Vol. 103, 1-63, Elsevier, 1998.

39. Kravtsov, Y. A. and Y. L. Orlov, Geometrical Optics of Inhomogeneous Media, Springer-Verlag, 1991.