The mathematical theory of laser beam-splitting gratings

Progress in Optics

Volumn 54, Issue C, 2010, Pages 319-386

  Romero, Louis A ^a   Dickey, Fred M ^b  

^a SANDIA NATIONAL LABORATORIES   (United States)

^b FMD Consulting   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78049383445     PISSN: 00796638     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0079-6638(10)05411-9     Document Type: Chapter

References (46)

1. Apostol, T. M. (1974). Mathematical analysis. Addison Wesley.
2. Baker, C. (2002). Absolutism and the scientific revolution-1600-1720. Greenwood Press.
3. Barton, I. M., Blair, P., & Taghizadeh, M. R. (1997). Diffractive phase elements for pattern formation: Phase-encoding geometry considerations. Applied Optics, 36(35), 9132-9137.
4. Blair, P., Lüpken, H., Taghizadeh, M. R., &Wyrowski, F. (1997). Multilevel phase-only array generators with a trapezoidal phase topology. Applied Optics, 36(20), 4713-4721.
5. Boivin, L. P. (1998). Multiple imaging using various types of simple phase gratings. Spie Milestone Series MS, 146, 3-13.
6. Borghi, R., Cincotti, G., & Santarsiero, M. (2000). Diffractive variable beam splitter: Optimal design. Journal of the Optical Society of America A, 17(1), 63-67.
7. Born, M., & Wolf, E. (1999). Principles of optics. Cambridge: Cambridge University Press.
8. Bryngdahl, O., & Wyrowski, F. (1993). Digital holography-computer-generated holograms. Progress in Optics, 31, 1-1.
9. Courant, R. (1947). Differential and integral calculus. Interscience.
10. Daly, D., Hodson, S. M., & Hutley, M. C. (1991). Fan-out gratings with a continuous profile. Optics Communications, 82(3-4).
11. Dammann, G. H., & Gortler, K. (1971). High efficiency in-line multiple imaging by means of multiple phase holograms. Optics Communications, 3(5), 312-315.
12. Dammann, H., & Klotz, (1977). Coherent optical generation and inspection of twodimensional periodic structures. Optica Acta, 24(4), 505-515.
13. Doskolovich, L. L., Soifer, V. A., Alessandretti, G., Perlo, P., & Repetto, P. (1994). Analytical initial approximation for multiorder binary grating design. Pure and Applied Optics: Journal of the European Optical Society Part A, 3, 921-930.
14. Feldman, M. R., & Guest, C. C. (1989). Iterative encoding of high-efficiency holograms for generation of spot arrays. Optics Letters, 14(10), 479-481.
15. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman lectures on physics. Vol. 1. Addison-Wesley.
16. Goodman, J. W. (1968). Introduction to Fourier optics. New York: McGraw Hill.
17. Gori, F. (1997). Diffractive optics: An introduction. In S. Martellucci, & A. N. Chester (Eds.), Diffractive optics and optical microsystems. New York: Plenum.
18. Gori, F., Santarsiero, M., Vicalvi, S., Borghi, R., Cincotti, G., Di Fabrizio, E., & Gentili, M. (1998). Analytical derivation of the optimum triplicator. Optics Communications, 157(1-6), 13-16.
19. Halliday, D., & Resnick, R. (1978). Physics: Parts I and II. Wiley.
20. Hatakoshi, G., & Nakamura, M. (1993). Grating lenses for optical branching. Applied Optics, 32, 3661-3667.
21. Herzig, H. P., Prongué, D., & Dändliker, R. (1990). Design and fabrication of highly efficient fan-out elements. Japanese Journal of Applied Physics, 29(7).
22. Hutley, M. C. (1982). Diffraction gratings. New York: Academic Press.
23. Killat, U., Rabe, G., & Rave, W. (1982). Binary phase gratings for star couplers with high splitting ratio. Fiber and Integrated Optics, 4(2), 159-167.
24. Krackhardt, U., Mait, J. N., & Streibl, N. (1992). Upper bound on the diffraction efficiency of phase-only fanout elements. Applied Optics, 31(1), 27-37.
25. Krackhardt, U.,&Streibl, N. (1989). Design of dammann-gratings for array generation. Optics Communications, 74(1-2), 31-36.
26. Mait, J. N. (1989). Design of Dammann gratings for two-dimensional, nonseparable, noncentrosymmetric responses. Optics Letters, 14(4), 196-198.
27. Mait, J. N. (1990). Design of binary-phase and multiphase Fourier gratings for array generation. Journal of the Optical Society of America A, 7(8), 1514.
28. Mait, J. N. (1997). Fourier array generators. In H. P. Herzig (Ed.), Micro-optics-elements, systems and applications. Taylor and Francis.
29. Miller, J. M., Taghizadeh, M. R., Turunen, J., & Ross, N. (1993). Multilevel-grating array generators: Fabrication error analysis and experiments. Applied Optics, 32(14), 2519-2525.
30. Morrison, R. L. (1992). Symmetries that simplify the design of spot array phase gratings. Journal of the Optical Society of America A, 9(3), 464-471.
31. O'Connor, J. J., & Robinson, E. F. James Gregory, (2008). http://www-history.mcs.standrews.ac.uk/Biographies/Gregory.html.
32. Palmer, C., & Loewen, E. (2002). Diffraction Grating Handbook. Newport Corp, Rochester NY.
33. Prongué, D., Herzig, H. P., Dändliker, R., & Gale, M. T. (1992). Optimized kinoform structures for highly efficient fan-out elements. Applied Optics, 31(26), 5706-5711.
34. Ripoll, O., Kettunen, V., & Herzig, H. P. (2004). Review of iterative Fourier-transform algorithms for beam shaping applications. Optical Engineering, 43, 2549.
35. Romero, L. A., & Dickey, F. M. (2007a). A theory for optimal beam splitting by phase gratings-ii- square and hexagonal gratings. Journal of the Optical Society of America A, 24(8), 2296-2312.
36. Romero, L. A., & Dickey, F. M. (2007b). Theory of optimal beam splitting by phase gratings. I. One-dimensional gratings. Journal of the Optical Society of America A, 24(8), 2280-2295.
37. Tervo, J., & Turunen, J. (2000). Paraxial-domain diffractive elements with one hundred efficiency based on polarization gratings. Optics Letters, 25, 785-786.
38. Turunen, J., Vasara, A., Westerholm, J., Jin, G., & Salin, A. (1988). Optimization and fabrication of grating beamsplitters. Journal of Physics D: Applied Physics, 21, S102-S105.
39. Turunen, J., Vasara, A., Westerholm, J., & Salin, A. (1989). Stripe-geometry two-dimensional Dammann gratings. Optics Communications, 74(3-4), 245-252.
40. Vasara, A., Taghizadeh, M. R., Turunen, J., Westerholm, J., Noponen, E., Ichikawa, H., Miller, J. M., Jaakkola, T., & Kuisma, S. (1992). Binary surface-relief gratings for array illumination in digital optics. Applied Optics, 31, 3320-3336.
41. Walker, S. J., & Jahns, J. (1990). Array generation with multilevel phase gratings. Journal of the Optical Society of America, 7(8), 1509.
42. Wen, F. J., & Chung, P. S. (2008). A new circular Dammann grating using a Hankel transform. Journal of Optics A: Pure and Applied Optics, 10, 075306.
43. Wyrowski, F. (1991). Upper bound of the diffraction efficiency of diffractive phase elements. Optics Letters, 16, 1917.
44. Zhao, S., & Chung, P. S. (2006). Design of a circular Dammann grating. Optics Letters, 31(16), 2387-2389.
45. Zhou, C., Jia, J., & Liu, L. (2003). Circular Dammann grating. Optics Letters, 28(22), 2174-2176.
46. Zhou, C., & Liu, L. (1995). Numerical study of Dammann array illuminators. Applied Optics, 34(26), 5961-5969.