Abstract
The passage of an optical pulse through a resonant grating is considered. The conditions under which the resonant grating differentiates the envelope of the incident pulse are determined. It is shown that the necessary condition for computing the k-order derivative is the presence of k resonances in the transmission spectrum of the grating in the vicinity of the central frequency of the incident pulse. A method is described for constructing the stacked structure for computing the kth derivative on the basis of repetition of the structure for computing the first derivative. The results of numerical simulation of diffraction of the pulse from the analyzed structure for computing the first, second, and third derivative are presented.
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References
M. Kulishov and J. Azaña, Opt. Express 15, 6152 (2007).
R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, Opt. Express 14, 10699 (2006).
M. Kulishov and J. Azaña, Opt. Lett. 30, 2700 (2005).
R. Slavík, Y. Park, M. Kulishov, and J. Azaña, Opt. Lett. 34, 3116 (2009).
L. M. Rivas, S. Boudreau, Y. Park, R. Slavík, S. LaRochelle, A. Carballar, and J. Azaña, J. Opt. Lett. 34, 1792 (2009).
N. K. Berger, B. Levit, B. Fischer, M. Kulishov, D. V. Plant, and J. Azaña, Opt. Express 15, 371 (2007).
M. Li, D. Janner, J. Yao, and V. Pruneri, Opt. Express 17, 19798 (2009).
M. A. Preciado and M. A. Muriel, Opt. Lett. 33, 2458 (2008).
H. Li, T. Kumagai, K. Ogusu, and Y. Sheng, J. Opt. Soc. Am. B 21, 1929 (2004).
R. Feced, M. N. Zervas, and M. A. Muriel, IEEE J. Quantum Electron. 35, 1105 (1999).
S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, Phys. Rev. B: Condens. Matter 66, 045102 (2002).
N. A. Gippius, S. G. Tikhodeev, and T. Ishihara, Phys. Rev. B: Condens. Matter 72, 045138 (2005).
D. A. Bykov, L. L. Doskolovich, V. A. Soifer, and N. L. Kazanskiy, JETP 111(6), 967 (2010).
M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, Phys. Rev. B: Condens. Matter 67, 085415 (2003).
N. A. Gippius, T. Weiss, S. G. Tikhodeev, and H. Giessen, Opt. Express 18, 7569 (2010).
M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light (Pergamon, London, 1959; Nauka, Moscow, 1973).
V. Lomakin and E. Michielssen, IEEE Trans. Antennas Propag. 54, 970 (2006).
R. Magnusson, D. Shin, and Z. S. Liu, Opt. Lett. 23, 612 (1998).
T. Tamir and S. Zhang, J. Opt. Soc. Am. A 14, 1607 (1997).
T. Sun, J. Ma, J. Wang, Y. Jin, H. He, J. Shao, and Z. Fan, J. Opt. A: Pure Appl. Opt. 10, 125003 (2008).
J.-F. Bonnans, J.-C. Gilbert, C. Lemaréchal, and C. A. Sagastizábal, Numerical Optimization, Theoretical and Numerical Aspects (Springer, New York, 2003).
M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, J. Opt. Soc. Am. A 12, 1068 (1995).
M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, J. Opt. Soc. Am. A 12, 1077 (1995).
L. Li, J. Opt. Soc. Am. A 13, 1870 (1996).
W. Nakagawa, R.-C. Tyan, P.-C. Sun, F. Xu, and Y. Fainman, J. Opt. Soc. Am. A 18, 1072 (2001).
N. V. Smirnov and I. V. Dunin-Barkovskii, Course of the Probability Theory and Mathematical Statistics for Engineering Applications (Nauka, Moscow, 1965) [in Russian].
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Original Russian Text © D.A. Bykov, L.L. Doskolovich, V.A. Soifer, 2012, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2012, Vol. 141, No. 5, pp. 832–839.
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Bykov, D.A., Doskolovich, L.L. & Soifer, V.A. On the ability of resonant diffraction gratings to differentiate a pulsed optical signal. J. Exp. Theor. Phys. 114, 724–730 (2012). https://doi.org/10.1134/S1063776112030028
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DOI: https://doi.org/10.1134/S1063776112030028