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2008-11-29
Vector Analyses of Nondiffracting Bessel Beams
By
Progress In Electromagnetics Research Letters, Vol. 5, 57-71, 2008
Abstract
An increasing attention has been concentrated on nondiffracting Bessel beams, due to their novel properties and prospective applications. In order to study their properties entirely, including the transverse modes, the polarization states and the flow of energy, vector analyses should be done. In this paper, based on auxiliary functions of Hertzian vector potential, nondiffracting Bessel beams are analyzed. The useful results are obtained and presented in this paper.
Citation
Yan-Zhong Yu Wen-Bin Dou , "Vector Analyses of Nondiffracting Bessel Beams," Progress In Electromagnetics Research Letters, Vol. 5, 57-71, 2008.
doi:10.2528/PIERL08110906
http://www.jpier.org/PIERL/pier.php?paper=08110906
References

1. Brittingham, J. N., "Focus wave modes in homogeneous Maxwell's equations — TE mode," J. Appl. Phys., Vol. 54, No. 3, 1179-1189, 1983.
doi:10.1063/1.332196

2. Ziolkowski, R. W., "Exact solutions of the wave equation with complex source locations," J. Math. Phys., Vol. 26, No. 4, 861-863, 1985.
doi:10.1063/1.526579

3. Ziolkowski, R. W., D. K. Lewis, and B. D. Cook, "Evidence of localized wave transmission," Phys. Rev. Lett., Vol. 62, No. 2, 147-150, 1989.
doi:10.1103/PhysRevLett.62.147

4. Shaarawi, A. M., I. M. Besieris, and R. W. Ziolkowski, "Localized energy pulse trains launched from an open, semi-infinite, circular waveguide," J. Appl. Phys., Vol. 65, No. 2, 805-813, 1989.
doi:10.1063/1.343070

5. Durnin, J., "Exact solutions for nondiffracting beams. I. The scalar theory," J. Opt. Soc. Am. A, Vol. 4, No. 4, 651-654, 1987.
doi:10.1364/JOSAA.4.000651

6. Durnin, J., J. J. Miceli, Jr., and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett., Vol. 58, No. 15, 1499-1501, 1987.
doi:10.1103/PhysRevLett.58.1499

7. Arlt, J. and K. Dholakia, "Generation of high-order Bessel beams by use of an axicon," Opt. Commun., Vol. 177, 297-301, 2000.
doi:10.1016/S0030-4018(00)00572-1

8. Volke-Sepulveda, K., V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B: Quantum Semiclass. Opt., Vol. 4, S82–S89, 2002.

9. Lu, J.-Y. and J. F. Greenleaf, "Nondiffracting X waves — Exact solutions to free-space scalar wave equation and their finite aperture realizations," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., Vol. 39, No. 1, 19-31, 1992.
doi:10.1109/58.166806

10. Lu, J.-Y. and J. F. Greenleaf, "Experimental verification of nondiffracting X waves," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., Vol. 39, No. 5, 441-446, 1992.
doi:10.1109/58.143178

11. Lu, J.-Y., "Bowtie limited diffraction beams for low-sidelobe and large depth of field imaging," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., Vol. 42, No. 6, 1050-1063, 1995.
doi:10.1109/58.476549

12. Lu, J.-Y., "Producing bowtie limited diffraction beams with synthetic array experiment," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., Vol. 43, No. 5, 893-900, 1996.
doi:10.1109/58.535492

13. Dartora, C. A. and H. E. Hernandez-Figueroa, "Properties of a localized Mathieu pulse," J. Opt. Soc. Am. A, Vol. 21, No. 4, 662-667, 2004.
doi:10.1364/JOSAA.21.000662

14. Davila-Rodriguez, J. and J. C. Gutierrez-Vega, "Helical Mathieu and parabolic localized pulses," J. Opt. Soc. Am. A, Vol. 24, No. 11, 3449-3455, 2007.
doi:10.1364/JOSAA.24.003449

15. Mishra, S. R., "A vector wave analysis of a Bessel beam," Opt. Commun., Vol. 85, 159-161, 1991.
doi:10.1016/0030-4018(91)90386-R

16. Bouchal, Z. and M. Olivik, "Non-diffractive vector Bessel beams," J. Mod. Opt., Vol. 42, No. 8, 1555-1566, 1995.
doi:10.1080/09500349514551361

17. Greene, P. L. and D. G. Hall, "Properties and diffraction of vector Bessel-Gauss beams," J. Opt. Soc. Am. A, Vol. 15, No. 12, 3020-3027, 1998.
doi:10.1364/JOSAA.15.003020

18. Girgel, S. S. and S. N. Kurilkina, "Vector properties of Bessel light beams," Proc. SPIE — Int. Soc. Opt. Eng., Vol. 4358, 258-264, 2001.

19. John, L., "Invariants of three types of generalized Bessel beams," J. Opt. A: Pure Appl. Opt., Vol. 6, No. 9, 837-843, 2004.
doi:10.1088/1464-4258/6/9/004

20. Fagerholm, J., et al., "Angularspectrum representation of nondiffracting X waves," Phys. Rev. E, Vol. 54, No. 4, 4347-4352, 1996.
doi:10.1103/PhysRevE.54.4347

21. Volke-Sepulveda, K. and E. Ley-Koo, "General construction and connections of vector propagation invariant optical fields: TE and TM modes and polarization states," J. Opt. A: Pure Appl. Opt., Vol. 8, No. 10, 867-877, 2006.
doi:10.1088/1464-4258/8/10/008

22. Thain, A., J. Fozard, and D. Ellacott, "Different approaches to parabolic-cylinder diffraction," Progress In Electromagnetics Research Symposium, Ext. Pap. Proc., 333-336, 2004.

23. Tadjalli, A. and A. Sebak, "Resonance frequencies and far field patterns of elliptical dielectric resonator antenna: Analytical approach," Progress In Electromagnetics Research, Vol. 64, 81-92, 2006.
doi:10.2528/PIER06060602

24. Menachem, Z. and M. Mond, "Infrared wave propagation in a helical waveguide with inhomogeneous cross section and application," Progress In Electromagnetics Research, Vol. 61, 159-192, 2006.
doi:10.2528/PIER06020205

25. Roumeliotis, J. A. and V. Douvalis, "Electromagnetic scattering from two external spheres one of which has small radius," Journal of Electromagnetic Waves and Applications, Vol. 18, No. 5, 591-614, 2004.
doi:10.1163/156939304774114646

26. Khatir, B. N., M. Al-Kanhal, and A. Sebak, "Electromagnetic wave scattering by elliptic chiral cylinder," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 10, 1377-1390, 2006.
doi:10.1163/156939306779276866

27. Xu, Y. H., K. Li, and L. Liu, "Electromagnetic field of a horizontal electric dipole in the presence of a four-layered region," Progress In Electromagnetics Research, Vol. 81, 371-391, 2008.
doi:10.2528/PIER08012303

28. Arslanagic, S., P. Meincke, E. Jorgensen, and O. Breinbjerg, "An exact line integral representation of the physical optics far field from plane pec scatterers illuminated by hertzian dipoles," Journal of Electromagnetic Waves and Applications, Vol. 17, No. 1, 51-69, 2003.
doi:10.1163/156939303766975344

29. Yla-Oijala, P., M. Taskinen, and J. Sarvas, "Multilayered media Green's functions for MPIE with general electric and magnetic sources by the Hertz potential approach," Journal of Electromagnetic Waves and Applications, Vol. 15, No. 7, 913-914, 2001.
doi:10.1163/156939301X00869

30. Lindell, I. V. and G. Dassios, "The Helmholtz theorem and scalar potential expansion," Journal of Electromagnetic Waves and Applications, Vol. 15, No. 19, 1281-1295, 2001.
doi:10.1163/156939301X01174

31. Yu, Y. Z. and W. B. Dou, "Generation of Bessel beams at mm- and submm-wave bands using binary optical elements," 2008 Global Symposium on Millimeter Waves, 115-118, 2008.
doi:10.1109/GSMM.2008.4534573

32. Yu, Y. Z. and W. B. Dou, "Generation of Bessel beams at mm- and sub mm-wavelengths by binary optical elements," Int. J. Infrared Milli. Waves, Vol. 29, No. 7, 693-703, 2008.
doi:10.1007/s10762-008-9365-6

33. Dou, W. B. and Y. Z. Yu, "Non-diffracting Bessel beams at millimeter and sub-millimeter waves," 2008 China-Japan Joint Microwave Conference, 307-309, 2008.

34. Yu, Y. Z. and W. B. Dou, "Generation of mm- and sub mm-wave Bessel beams using DOE's designed by BOR-FDTD method and MGA," Int. J. Infrared Milli. Waves, (published on line).

35. Yu, Y. Z. and W. B. Dou, "Properties of approximate Bessel beams at millimeter wavelengths generated by fractal conical lens," Progress In Electromagnetics Research, Vol. 87, 105-115, 2008.
doi:10.2528/PIER08070503