Publication: Near field of stacked diffraction gratings
Full text at PDC
Torcal Milla, Francisco José
Bernabeu Martínez, Eusebio
Advisors (or tutors)
Gustav Fischer Verlag
We obtain a general analytical formulation for determining the near field produced by N diffraction gratings disposed in stack using a scalar approximation. Parameters of the gratings such as type-amplitude/phase-, fill factors, periods and relative positions between gratings along the x and y axes are considered. The obtained formulation is useful for analyzing problems which involve several diffraction gratings, such as optical encoders since it is computationally faster than integral formulations. Finally, analytical results are compared with numerical simulations based on the Rayleigh–Sommerfeld equation.
© 2013 Elsevier GmbH. This work has been partially supported by projects DPI2011-27851 and INNPACTO “FORE”, IPT-020000-2010-9 of the Ministerio de Ciencia e Innovación of Spain.
 C. Palmer, Diffraction Grating Handbook, Richardson Grating Laboratory, Eindhoven University of Technology, Eindhoven, The Netherlands, 2000.  K. Patorski, Moiré Metrology, Pergamon Press, New York, USA, 1998.  E.G. Loewen, E. Popov, Diffraction Gratings and Applications, Marcel Dekker, New York, USA, 1997.  A.W. Lohmann, D.E. Silva, An interferometer based on the Talbot effect, Opt. Commun. 2 (1971) 413–415.  G. Schirripa Spagnolo, D. Ambrosini, D. Paoletti, Displacement measurement using the Talbot effect with a Ronchi grating, J. Opt. A: Pure Appl. Opt. 4 (2002) S376–S380.  W.H.F. Talbot, Facts relating to optical science, Philos. Mag. 9 (1836) 401–407.  D. Crespo, J. Alonso, E. Bernabeu, Reflection optical encoders as three-grating Moiré systems, Appl. Opt. 39 (2000) 3805–3813.  C.F. Kao, M.H. Lu, Optical encoder based on the fractional Talbot effect, Opt. Commun. 250 (2005) 16–23.  C. Champenois, M. Büchner, J. Vigué, Fringe contrast in three grating Mach-Zehnder atomic interferometers, Eur. Phys. J. D 5 (1999) 363–374.  X. Zhang, Y. Huang, X. Ren, H. Huang, Q. Wang, RCE photodetector with cascaded grating structure, Proc. SPIE 7361 (2009), 76311O1–76311O17.  F. Montiel, M. Neviere, Infrared modulation via coupling gratings lying on III-V multiple quantum wells, Opt. Commun. 138 (1997) 172–184.  W. Nakagawa, R.Ch. Tyan, P.Ch. Sun, F. Xu, Y. Fainman, Ultrashort pulse propagation in near field periodic diffractive structures by use of rigorous coupled wave analysis, J. Opt. Soc. Am. A 18 (2001) 1072–1081.  P. Schau, K. Frenner, L. Fu, H. Schweizer, H. Giessen, W. Osten, Design of hightransmission metallic meander stacks with different grating periodicities for subwavelength-imaging applications, Opt. Express 19 (2011) 3627–3636.  G. Michel, K. Dohlen, J. Martignac, J.C. Lecullier, P. Levacher, C. Colin, Interferential scanning grating position sensor operating in space at 4 K, Appl. Opt. 42 (2003) 6305–6313.  L. Liu, Lau effect in a multi-grating system, Opt. Commun. 70 (1989) 267–271.  E. Cagniot, M. Fromager, T. Godin, M. Traiche, N. Passilly, B. Paivanranta, K. Ait- Ameur, Cascades of π phase plates: a transparent diffractive focusing system, J. Opt. Soc. Am. A 27 (2010) 1647–1654.  J.W. Goodman, Introduction to Fourier Optics, Roberts & Company Publishers, Greenwood Village, USA, 2005.  M. Born, E. Wolf, Principles of Optics, Pergamon Press, Oxford, UK, 1991.  E. Keren, O. Kafri, Diffraction effects in Moiré deflectometry, J. Opt. Soc. Am. A 2 (1985) 111–120.  F. Shen, A. Wang, Fast-Fourier-transform based numerical integration method for the Rayleigh–Sommerfeld diffraction formula, Appl. Opt. 45 (2006) 1102–1110.  V. Arrizon, J.G. Ibarra, A.W. Lohmann, Array illuminators with phase gratings in cascade, Opt. Commun. 124 (1996) 229–234.