volume | PIER Journals

Abstract

An analysis of quasi-optical unstable Bessel-Gauss resonator (QOUBGR) at millimeter wavelengths is presented in this paper. The QOUBGR, formed by a conical mirror and a convex mirror, is designed on the basic of quasi-optical theory and techniques. For the purpose of precisely analyzing the designed QOUBGR, a new algorithm known as iterative dyadic Green's functions (IDGF) is proposed, which originates from famous Fox-Li algorithm. The IDGF algorithm can calculate not only two-dimension (2-D) but also three-dimension (3-D) resonating modes in the cavity. Simulation results demonstrate that the designed QOUBGR can steadily support both zero-order and high-order resonant modes that are approximations to Bessel-Gauss beams. These beams will find their promising applications in the MM- and/or quasi-optical imaging and measurement systems.

1. 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 Google Scholar

2. 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 Google Scholar

3. Gori, F., G. Guattari, and C. Padovani, "Bessel-Gauss beams," Opt. Commun., Vol. 64, No. 6, 491-495, 1987.
doi:10.1016/0030-4018(87)90276-8 Google Scholar

4. Mahon, R. J., W. Lanigan, J. A. Murphy, et al. "Novel techniques for millimeter wave imaging systems operating at 100 GHz," Proc. SPIE Int. Soc. Opt. Eng., Vol. 5789, 93-100, 2005. Google Scholar

5. Lu, J., T. K. Song, R. R. Kinnick, et al. "In vitro and in vivo real-time imaging with ultrasonic limited diffraction beams," IEEE Trans. Med. Imag., Vol. 12, No. 12, 819-829, 1993.
doi:10.1109/42.251134 Google Scholar

6. Hegner, M., "Optics: The light fantastic," Nature, Vol. 419, 125-127, 2002.
doi:10.1038/419125a Google Scholar

7. Garces-Chavez, V., D. Mcgloin, and E. H. Melvill, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature, Vol. 419, 145-147, 2002.
doi:10.1038/nature01007 Google Scholar

8. Hughes, S. and J. M. Burzler, "Theory of Z-scan measurements using Gaussian-Bessel beams," Physical Review A, Vol. 56, No. 2, R1103-R1106, 1997.
doi:10.1103/PhysRevA.56.R1103 Google Scholar

9. Cox, A. J. and D. C. Dibble, "Nondiffracting beam from a spatially filtered Fabry-Perot resonator," J. Opt. Soc. Am. A, Vol. 9, No. 2, 282-286, 1992.
doi:10.1364/JOSAA.9.000282 Google Scholar

10. Monk, S., J. Arlt, D. A. Robertson, et al. "The generation of Bessel beams at millimetre-wave frequencies by use of an axicon," Opt. Commun., Vol. 170, 213-215, 1999.
doi:10.1016/S0030-4018(99)00463-0 Google Scholar

11. Meltaus, J., J. Salo, E. Noponen, et al. "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech., Vol. 51, No. 4, 1274-1279, 2003.
doi:10.1109/TMTT.2003.809679 Google Scholar

12. Muys, P. and E. Vandamme, "Direct generation of Bessel beams," Appl. Opt., Vol. 41, 6375-6379, 2002.
doi:10.1364/AO.41.006375 Google Scholar

13. Hernandez-Aranda, R. I., S. Chavez-Cerda, and J. C. Gutierrez-Vega, "Theory of the unstable Bessel resonator," J. Opt. Soc. Am. A, Vol. 22, 1909-1917, 2005.
doi:10.1364/JOSAA.22.001909 Google Scholar

14. Wu, F. T., Y. B. Chen, and D. D. Guo, "Nanosecond pulsed Bessel-Gauss beam generated directly from a Nd: YAG axicon-based resonator," Appl. Opt., Vol. 46, No. 22, 4943-4947, 2007.
doi:10.1364/AO.46.004943 Google Scholar

15. Khilo, A. N., E. G. Katranji, and A. A. Ryzhevich, "Axicon-based Bessel resonator: Analytical description and experiment," J. Opt. Soc. Am. A, Vol. 18, No. 8, 1986-1992, 2001.
doi:10.1364/JOSAA.18.001986 Google Scholar

16. Rogel-Salazar, J., G. H. C. New, and S. Chávez-Cerda, "Bessel-Gauss beam optical resonator," Opt. Commun., Vol. 190, 117-122, 2001.
doi:10.1016/S0030-4018(01)01075-6 Google Scholar

17. Tsangaris, C. L., G. H. C. New, and J. Rogel-Salazar, "Unstable Bessel beam resonator," Opt. Commun., Vol. 223, 233-238, 2003.
doi:10.1016/S0030-4018(03)01681-X Google Scholar

18. Ling, D. X. and J. C. Li, "Analysis of eigenfields in the axicon-based Bessel-Gauss resonator by the transfer-matrix method," J. Opt. Soc. Am. A, Vol. 23, No. 4, 912-918, 2006.
doi:10.1364/JOSAA.23.000912 Google Scholar

19. Yu, Y.-Z. and W.-B. Dou, "Quasi-optical Bessel resonator," Progress In Electromagnetics Research, Vol. 93, 205-219, 2009.
doi:10.2528/PIER09042902 Google Scholar

20. Yu, Y.-Z. and W.-B. Dou, "Investigation of quasi-optical Bessel-Gauss resonator at mm- and submm-wavelengths," Progress In Electromagnetics Research, Vol. 138, 453-466, 2013.
doi:10.2528/PIER13022007 Google Scholar

21. Meng, H. F., B. Xiang, J. L. Zhang, W. B. Dou, and Y. Z. Yu, "The generation of bessel beam and its application in millimeter wave imaging," Journal of Infrared, Millimeter, and Terahertz Waves, Vol. 35, No. 2, 208-217, 2014.
doi:10.1007/s10762-013-0037-9 Google Scholar

22. Bagini, V., F. Frezza, M. Santarsiero, G. Schettini, and G. Schirripa Spagnolo, "Generalized Bessel-Gauss beams," Journal of Modern Optics, Vol. 43, No. 6, 1155-1166, 1996. Google Scholar

23. Fox, A. G. and T. Li, "Resonant modes in a maser interferometer," Bell Syst. Tech. J., Vol. 40, 453-488, 1961.
doi:10.1002/j.1538-7305.1961.tb01625.x Google Scholar

24. Hsu, W. and R. Barakat, "Stratton-Chu vectorial diffraction of electromagnetic fields by apertures with application to small-Fresnel-number systems," J. Opt. Soc. Am. A, Vol. 11, No. 2, 623-629, 1994.
doi:10.1364/JOSAA.11.000623 Google Scholar

25. Eroglu, A. and J. K. Lee, "Simplified formulation of dyadic Green’s functions and their duality relations for general anisotropic media," Progress In Electromagnetics Research, Vol. 77, 391-408, 2007.
doi:10.2528/PIER07082401 Google Scholar

26. Gao, G., C. Torres-Verdin, and T. M. Habashy, "Analytical techniques to evaluate the integrals of 3D and 2D spatial dyadic Green’s functions," Progress In Electromagnetics Research, Vol. 52, 47-80, 2005.
doi:10.2528/PIER04070201 Google Scholar

27. Li, L.-W., N.-H. Lim, W.-Y. Yin, and J.-A. Kong, "Eigenfunctional expansion of dyadic Green’s functions in gyrotropic media using cylindrical vector wave functions," Progress In Electromagnetics Research, Vol. 43, 101-121, 2003.
doi:10.2528/PIER03020201 Google Scholar

28. Hanson, G. W., A. I. Nosich, and E. M. Kartchevski, "Green’s function expansions in dyadic root functions for shielded layered waveguides," Progress In Electromagnetics Research, Vol. 39, 61-91, 2003.
doi:10.2528/PIER02082205 Google Scholar

29. Li, L. W., S. B. Yeap, M. S. Leong, T. S. Yeo, and P. S. Kooi, "Dyadic Green’s functions in multilayered stratified gyroelectric chiral media," Progress In Electromagnetics Research, Vol. 35, 53-81, 2002.
doi:10.2528/PIER01042401 Google Scholar

30. Tan, E. L. and S. Y. Tan, "On the eigenfunction expansions of the dyadic Green’s functions for bianisotropic media," Progress In Electromagnetics Research, Vol. 20, 227-247, 1998.
doi:10.2528/PIER98022500 Google Scholar

31. Gao, Z. H., "Wave pattern property of self-reproductive mode in laser resonator," Guangzi Xuebao/Acta Photonica Sinica, Vol. 29, No. 8, 726-729, 2000. Google Scholar

Dr. Yan-Zhong Yu

Dr. Hongfu Meng

Dr. Wen-Bin Dou