Theory of optimal beam splitting by phase gratings. I. One-dimensional gratings.

We give an analytical basis for the theory of optimal beam splitting by one-dimensional gratings. In particular, we use methods from the calculus of variations to derive analytical expressions for the optimal phase function.

[1]  F Wyrowski,et al.  Upper bound of the diffraction efficiency of diffractive phase elements. , 1991, Optics letters.

[2]  W. H. Lee,et al.  High efficiency multiple beam gratings. , 1979, Applied optics.

[3]  Jan Westerholm,et al.  Optimisation and fabrication of grating beamsplitters , 1988 .

[4]  D C O'Shea.  Reduction of the zero-order intensity in binary Dammann gratings. , 1995, Applied optics.

[5]  H. Dammann,et al.  High-efficiency in-line multiple imaging by means of multiple phase holograms , 1971 .

[6]  G. Cincotti,et al.  Diffractive variable beam splitter: optimal design. , 2000, Journal of the Optical Society of America. A, Optics, image science, and vision.

[7]  Louis A Romero,et al.  Theory of optimal beam splitting by phase gratings. II. Square and hexagonal gratings. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[8]  Fred M. Dickey,et al.  Laser Beam Shaping , 2003 .

[9]  U Krackhardt,et al.  Upper bound on the diffraction efficiency of phase-only fanout elements. , 1992, Applied optics.

[10]  Gabriella Cincotti,et al.  Analytical derivation of the optimum triplicator , 1998 .

[11]  M P Dames,et al.  Efficient optical elements to generate intensity weighted spot arrays: design and fabrication. , 1991, Applied optics.

[12]  Joseph N. Mait.  Designs for two-dimensional nonseparable array generators , 1991, Optics & Photonics.

[13]  R Dändliker,et al.  Optimized kinoform structures for highly efficient fan-out elements. , 1992, Applied optics.

[14]  M. E. Prise,et al.  Dammann Gratings For Laser Beam Shaping , 1989 .

[15]  J Turunen,et al.  Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings. , 2000, Optics letters.

[16]  L. Boivin,et al.  Multiple imaging using various types of simple phase gratings. , 1972, Applied optics.

[17]  Erhard Klotz,et al.  Coherent Optical Generation and Inspection of Two-dimensional Periodic Structures , 1977 .