Spatial beam compression of an electromagnetic wave is one of the fundamental techniques employed in microwaves and optics. As there are many ways to achieve this task using the combination of prisms and lenses, recent research suggests the parabolic gradient index photonic crystals (GRIN PC) for the design of spatial beam compressor owing to its functionalities. However, the fabrication of a graded media with the parabolic profile is a difficult challenge in practical realization. To an alternative, present work attempts this problem with respect to the triangular gradient index profile. The performance and aspects of the beam compression are investigated experimentally using the pillar type GRIN PC at the microwave length-scales. The utility of the device for an effective beam injection to the photonic-waveguide component is further demonstrated experimentally.
1. Yablonovitch, E., "Inhibited spontaneous emission in solid state physics and electronics," Phys. Rev. Lett., Vol. 58, No. 20, 2059-2062, 1987. doi:10.1103/PhysRevLett.58.2059
2. Kosaka, H., T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B, Vol. 58, No. 16, R10096, 1998.
3. Kosaka, H., T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett., Vol. 74, No. 9, 1212, 1999.
4. Yogesh, N. and V. Subramanian, "Analysis of self-collimation based cavity resonator formed by photonic crystal," Progress In Electromagnetics Research M, Vol. 12, 115-130, 2010. doi:10.2528/PIERM10012604
5. Luo, C., S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B, Vol. 65, No. 20, 201104(R), 2002.
6. Centeno, E. and D. Cassagne, "Graded photonic crystals," Opt. Lett., Vol. 30, No. 17, 2278-2280, 2005. doi:10.1364/OL.30.002278
7. Kurt, H. and D. S. Citrin, "Graded index photonic crystals," Opt. Exp., Vol. 15, No. 3, 1240-1253, 2007. doi:10.1364/OE.15.001240
8. Lu, M., B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, "Beam aperture modifier and beam deflector using gradient-index photonic crystals," J. Appl. Phys., Vol. 108, No. 10, 103505, 2010, Supplementary material at http://dx.doi.org/10.1063/1.3499630..
9. Ren, K. and X. Ren, "Controlling light transport by using a graded photonic crystal," Appl. Opt., Vol. 50, No. 15, 2152-2157, 2011. doi:10.1364/AO.50.002152
10. Wang, H.-W. and L.-W. Chen, "A cylindrical optical black hole using graded index photonic crystals," J. Appl. Phys., Vol. 109, No. 10, 103104, 2011.
11. Vasi, B. and R. Gaji, "Self-focusing media using graded photonic crystals: Focusing, fourier transforming and imaging, directive emission, and directional cloaking," J. Appl. Phys., Vol. 110, No. 5, 053103, 2011.
12. AbdelMalek, F., W. Belhadj, S. Haxha, and H. Bouchriha, "Realization of a high coupling effciency by employing a concave lens based on two-dimensional photonic crystals with a negative refractive index," J. Lightw. Technol., Vol. 25, No. 10, 3168-3174, 2007. doi:10.1109/JLT.2007.904027
13. Chien, H.-T., C. Lee, H.-K. Chiu, K.-C. Hsu, C.-C. Chen, J. A. Ho, and C. Chou, "The Comparison between the graded photonic crystal coupler and various couplers," J. Lightw. Technol., Vol. 27, No. 14, 2570-2574, 2009. doi:10.1109/JLT.2008.2012271
14. Cakmak, A. O., E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, "High effciency of graded index photonic crystal as an input coupler," J. Appl. Phys., Vol. 105, No. 14, 103708, 2009.
15. Moore, D. T., "Gradient-index optics: A review," Appl. Opt., Vol. 19, No. 7, 1035-1038, 1980. doi:10.1364/AO.19.001035
16. Johnson, S. G. and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a plane wave basis," Opt. Exp., Vol. 8, No. 3, 173-190, 2001, http:/abinitio.mit.edu/mpb.. doi:10.1364/OE.8.000173
17. Sakoda, K., Opitcal Properties of Photonic Crystals, Chapter 2.5, 30-34, Springer, 2005.
19. Roux, F. S. and I. De Leon, "Planar photonic crystal gradient index lens, simulated with a finite difference time domain method," Phys. Rev. B., Vol. 74, No. 11, 113103, 2006.
20., , More information can be found at http://www.cst.com..
21. Taflove, A. and S. C. Hagness, "Computational Electrodynamics the Finite-difference Time-domain Method,", 273-327, Artech House, Boston, 2005.
22. Whiteman, J. R., The Mathematics of Finite Elements and Applications, John Wiley and Sons, Chichester, 1998, http://www.comsol.com..
23. Jarvis, J. B., E. J. Vanzura, and W. A. Kissick, "Improved technique for determining complex permittivity with the transmission/reflection method," IEEE Trans. Microwave Theory Tech., Vol. 38, No. 8, 1096-1103, 1990. doi:10.1109/22.57336
24. Johnson, S. G., S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "Guided modes in photonic crystal slabs," Phys. Rev. B, Vol. 60, No. 8, 5751-5758, 1999. doi:10.1103/PhysRevB.60.5751
25. Yogesh, N. and V. Subramanian, "Directional Cloaking Formed by Photonic Crystal Waveguides," accepted for presentation in International Microwave Symposium 2012, Montreal, Canada, Jun. 16-21, 2012.