Modelling adapted to manufacturing aspects of holographic grating structures

O. W. Sandfuchs; C. Schwanke; M. Burkhardt; F. Wyrowski; A. Gatto; R. Brunner

doi:10.2971/jeos.2011.11006

Journal of the European Optical Society - Rapid publications, Vol 6 (2011)

Modelling adapted to manufacturing aspects of holographic grating structures

O. W. Sandfuchs, C. Schwanke, M. Burkhardt, F. Wyrowski, A. Gatto, R. Brunner

Abstract

The diffraction efficiencies of modified sinusoidal and blazed gratings are investigated in the high spatial frequency regime by rigorous numerical methods and are compared to experimentally manufactured gratings. The introduced modifications take actual technological induced variations of the profile geometries, such as specific corner rounding, into account. The high spatial frequency regime (resonance regime) is characterized by a local grating period, g, to wavelength, Î», ratio of 0.7 â‰¤ g/Î» â‰¤ 4 and shows an important relevance for applications in spectroscopy and diffractive imaging. The investigations are carried out for both reflection on metallic surfaces and transmission of dielectric structures over a broad range of grating periods and incidence angles. It was found that near the grating resonance, the more simply producible sine gratings can compete in diffraction efficiency with sawtooth structures. Additionally, for certain application conditions, holographically modified sine structures achieve higher efficiencies than the ideal sine profile. It is also shown that holographical sinusoidal-like profiles measured by AFM can be fitted to a super-Gaussian shape, which is then used to inversely reconstruct the structure profiles from efficiency data.

Full Text: PDF

Citation Details

Cite this article

References

R. Brunner, M. Burkhardt, N. Correns, and K. Rudolf, "Microspectrometer based on holographically recorded diffractive elements using supplementary holograms" Opt. Express 16, 12239-12250 (2008).

M. D. Missig, and G. M. Morris, "Diffractive optics applied to eyepiece design" Appl. Optics 34, 2452-2461 (1995).

W. Knapp, G. Blough, K. Khajurival, R. Michaels, B. Tatian, and B. Volk, "Optical design comparison of 60. eyepieces: one with a diffractive surface and one with aspherics" Appl. Optics 36, 4756-4760 (1997).

R. Brunner, R. Steiner, K. Rudolf, and H.-J. Dobschal, "Diffractiverefractive hybrid microscope objective for 193 nm inspection systems" Proc. SPIE 5177, 9-15 (2003).

R. Brunner, R. Steiner, H.-J. Dobschal, D. Martin, M. Burkhardt, and M. Helgert, "New solutions to realize complex optical systems by a combination of diffractive and refractive optical components" Proc. SPIE 5183, 47-55 (2003).

R. Brunner, M. Burkhardt, A. Pesch, O. Sandfuchs, M. Ferstl, S. C. Hohng, and J. O. White, "Diffraction based solid immersion lens" J. Opt. Soc. Am. A 21, 1186-1191 (2004).

O. Sandfuchs, R. Brunner, D. Pätz, S. Sinzinger, and J. Ruoff, "Rigorous analysis of shadowing effects in blazed transmission gratings" Opt. Lett. 31, 3638-3640 (2006).

O. Sandfuchs, A. Pesch, and R. Brunner, "Rigorous modeling of dielectric and metallic blaze gratings in the intermediate structure regime" Proc. SPIE 6675, 667501-1-667501-8 (2007).

A. Rathsfeld, G. Schmidt, and B. H. Kleemann, "On a fast integral equation method for diffraction gratings" Commun. Comput. Phys. 1, 984-1009 (2006).

J. Nelder, and R. Mead, "A simplex method for function minimization." Comput. J. 7, 308-313 (1965).

M. Burkhardt, and R. Brunner, "Functional integrated optical elements for beam shaping with coherence scrambling property, realized by interference lithography" Appl. Optics 46, 7061-7067 (2007).

E. G. Loewen, and E. Popov, Diffraction gratings and applications (Marcel Dekker, Inc., New York, 1997).

B. de A. Mello, I. F. Da Costa, C. R. A. Lima, and L. Cescato, "Developed profile of holographically exposed photoresist gratings" Appl. Optics 34, 597-603 (1995).

M. A. Golub, and A. A. Friesem, "Analytic design and solutions for resonance domain diffractive optical elements" J. Opt. Soc. Am. A 24, 687-695 (2007).

O. Sandfuchs, D. Pätz, S. Sinzinger, A. Pesch, and R. Brunner, "Analysis of the influence of the passive facet of blazed transmission gratings in the intermediate diffraction regime" J. Opt. Soc. Am. A 25,1885-1893 (2008).

H. Kogelnik, "Coupled wave theory for thick hologram gratings" Bell Syst. Tech. J. 48, 2909-2947 (1969).

H. J. Gerritsen, D. K. Thornton, and S. R. Bolton, "Application of Kogelnik's two-wave theory to deep, slanted, highly efficient, relief transmission gratings" Appl. Optics 30, 807-814 (1991).