On the ability of resonant diffraction gratings to differentiate a pulsed optical signal
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MOLECULES, OPTICS
On the Ability of Resonant Diffraction Gratings to Differentiate a Pulsed Optical Signal D. A. Bykov, L. L. Doskolovich, and V. A. Soifer Image Processing Systems Institute, Russian Academy of Sciences, Samara, 443001 Russia Samara State Aerospace University, Samara, 443086 Russia email: [email protected] Received June 27, 2011
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 korder derivative is the presence of k resonances in the transmis sion 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. DOI: 10.1134/S1063776112030028
1. INTRODUCTION Optical elements for differentiating temporal opti cal signals are of considerable interest for a wide range of applications including ultrafast optical information processing, optical calculations, optical recognition and coding, and pulse shaping [1, 2]. For optical differentiation, Bragg structures are widely used. In particular, differentiation of optical pulses using longperiod fiber gratings was consid ered in [2–5]. Here and below, differentiation of an optical pulse has the meaning of differentiation of the pulse envelope. Such structures operate in the trans mission mode, and differentiation is carried out at the resonance frequency of the structure, which cor responds to the effective transformation of the core mode to the cladding mode. In [1, 6], Bragg gratings with defects were used for differentiation in reflec tion. The introduction of a defect ensures the occur rence of an allowed frequency in the bandgap at which differentiation is performed. In [7, 8], the refraction index distribution over the differentiating Bragg grating was calculated using special optimiza tion techniques [9, 10]. In this case, the refraction index distribution is calculated from the condition of the formation of a preset function of the complex transmittance of the structure. A common disadvantage of Bragg’s structures con sidered in [2–8] is their relatively large longitudinal size amounting from fractions of a millimeter to sev eral centimeters. In this study, we analyze differentiation of optical pulses using resonant gratings. Resonant gratings are gratings in which sharp changes in the reflection and
transmission coefficients take place at certain fre quencies. As a rule, resonance changes in the spectra of a periodic structure are associated with excitation of quasiguided eigenmodes in it [11–15]. The applica tion of this type of structures for differentiating optical pulses is
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