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CHAPTER 1 THIS THESIS focuses on the flat focusing mirrors with two different geometric approaches which keep the transversal invariance . Any modulation of a lateral surface of a mirror should be homogeneous so that flat focusing mirrors can keep transversal invariance. Such flat focusing mirror is a near field lensing effect similar to the flat lens. It is different from those far field focusing devices such as conversional curved mirrors and lenses. The different physical focusing mechanisms between far field lens/mirrors and near field lens/mirrors are discussed and compared in the next chapter 2. More details of flat focusing mirrors with two different structures: the Bragg-like multilayer structure and periodic subwavelength gratings are discussed in chapter 3 and chapter 4, respectively. In addition, chapter 3 also demonstrated differently advanced multiplayer structures for a better focusing performance. In chapter 4, in addition to periodic subwavelength gratings, a waveguide-like subwavelength structure consisting of two row gratings are also proposed to observe the near field focusing effect which accompanies with negative Goos-Hänchen effects 31. Finally, the chapter 5 summarizes and concludes our research in the field of flat focusing mirrors with the transversal invariance. Moreover, some proposals for the implementations of the flat focusing mirrors adapting to photonic integrated circuits are discussed with a future outlook. In the appendix, the collections of my scientific publications are listed with the brief highlights. Reference 1. Pitchumani, M., Hockel, H., Mohammed, W. & Johnson, E. G. Additive lithography for fabrication of diffractive optics. Appl. Opt. 41, 6176-6181 (2002). 2. Popovic, Z. D., Sprague, R. A. & Neville Connell, G. A. Technique for monolithic fabrication of microlens arrays. Appl. Opt. 27, 1281-1284 (1988). 3. Sabry, Y. M., Saadany, B., Khalil, D. & Bourouina, T. Silicon micromirrors with three-dimensional curvature enabling lensless efficient coupling of free-space light. Light Sci. Appl. 2, e94 (2013). 4. Fattal, D., Li, J., Peng, Z., Fiorentino, M. & Beausoleil, R. G. Flat dielectric grating reflectors with focusing abilities. Nat. Photonics 4, 466-470 (2010). 5. Aieta, F. et al. Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces. Nano Lett. 12(9), 4932-4936 (2012). 6. Chrostowski, L. Optical gratings: Nano-engineered lenses. Nat. Photonics 4(7), 413-415 (2010). 7. Huang, M. C. Y., Zhou, Y. & Chang-Hasnain, C. J. A surfaceemitting laser incorporating a high-index-contrast subwavelength grating. Nat. Photonics 1, 119-122 (2007). 8. Huang, M. C. Y., Zhou, Y. & Chang-Hasnain, C. J. Single mode high-contrast subwavelength grating vertical cavity surface emitting lasers. Appl. Phys. Lett. 92, 171108 (2008). 9. Xie, R.-J., Hirosaki, N., Mitomo, M., Takahashi, K. & Sakuma, K. Highly efficient white-light-emitting diodes fabricated with short-wavelength yellow oxynitride phosphors. Appl. Phys. Lett. 88, 101104 (2006). 10. Pendry, J. B. Negative refraction makes a perfect lens. Phys.

Rev. Lett. 85, 3966-3969 (2000). 11. Yablonovitch, E. Inhibited spontaneous emission in solid-state physics and electronics. Phys. Rev. Lett. 58(20), 2059-2062 (1987). 12. John, S. Strong localization of photons in certain disordered dielectric superlattices. Phys. Rev. Lett. 58, 2486-2489 (1987). 13. Miyashita, T. Sonic crystals and sonic wave-guides. Meas. Sci. Technol. 16, R47-R63 (2005). 14. Smith, D. R., Pendry, J. B. & Wiltshire, M. C. K. Metamaterials and negative refractive index. Science 305, 788-792 (2004). 15. Ding, Y., Liu, Z., Qiu, C., & Shi, J. Metamaterial with simultaneously negative bulk modulus and mass density. Phys.Rev. Lett. 99, 093904 (2007) 16. Veselago, V. G. The Electrodynamics of substances with simultaneously negative values of ε and μ. Sov. Phys. Usp. 10, 509-514 (1968). 17. Cubukcu, E., Aydin, K., Ozbay, E., Foteinopoulou, S. & Soukoulis, C. M. Electromagnetic waves: Negative refraction by photonic crystals. Nature 423, 604-605 (2003). 18. Yao, J. et al. Optical Negative Refraction in Bulk Metamaterials of Nanowires. Science 321, 930 (2008). 19. Parimi, P. V., Lu, W. T., Vodo, P. & Sridhar, S. Photonic crystals: imaging by flat lens using negative refraction. Nature 426, 404 (2003). 20. Lu, Z. et al. Three-dimensional subwavelength imaging by a photonic-crystal flat lens using negative refraction at microwave frequencies. Phys. Rev. Lett. 95, 153901 (2005). 21. Maigyte, L. et al. Flat lensing in the visible frequency range by woodpile photonic crystals. Opt. Lett. 38, 2376-2378 (2013). 22. Cebrecos, A. et al. Formation of collimated sound beams by three-dimensional sonic crystals. J. Appl. Phys. 111, 104910 (2012). 23. Staliunas, K. & Longhi, S. Subdiffractive solitons of BoseEinstein condensates in time-dependent optical lattices. Phys. Rev. A 78, 033606 (2008). 24. Cheng, Y. C. et al. Beam focusing in reflection from flat chirped mirrors. Phys. Rev. A 87, 045802 (2013). 25. De Silvestri, S., Laporta, P. & Svelto, O. Analysis of quarterwave dielectric-mirror dispersion in femtosecond dye-laser cavities. Opt. Lett. 9(8), 335-337 (1984). 26. Szipocs, R., Ferencz, K., Spielmann, C. & Krausz, F. Chirped multilayer coatings for broadband dispersion control in femtosecond lasers. Opt. Lett. 19(3), 201 (1994). 27. Cheng, Y. C., Redondo, J. & Staliunas, K. Beam focusing in reflections from flat subwavelength diffraction gratings. Phys. Rev. A 89, 33814 (2014). 28. Gomez-Reino, C., Perez, M. V. & Bao, C. in Gradient-Index Optics: Fundamentals and Applications (Springer, Berlin, 2002). 29. Wilkinson, P. B., Fromhold, T. M., Taylor, R. P. & Micolich, A. P. Electromagnetic wave chaos in gradient refractive index optical cavities. Phys. Rev. Lett. 86, 5466-5469 (2001). 30. Smith, D. R., Mock, J. J., Starr, A. F. & Schurig, D. Gradient index metamaterials. Phys. Rev. E 71, 036609 (2005). 31. Cheng, Y.-C. & Staliunas, K. Negative Goos-Hänchen shift in reflection from subwavelength gratings. J. Nanophotonics 8, 084093 (2014).

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