Integration of optical pulses by resonant diffraction gratings

Abstract

Optical components for integration [1][2][3][4] and dif ferentiation [5][6][7] of optical pulses are of great interest for numerous applications including optical ultrafast information processing, optical computing, optical image recognition and coding, and formation of pulses of a specified time profile [5]. Integration (dif ferentiation) of an optical pulse is understood as inte gration (differentiation) of its envelope. At present, pulse integration and differentiation is accomplished with the use of various versions of Bragg gratings [1][2][3][4][5]. The longitudinal size of Bragg gratings for integra tion of picosecond pulses ranges from millimeters to centimeters.In our previous works [6,7], we showed that reso nance diffraction gratings provide differentiation of optical pulses. The differentiation occurs near the res onance frequencies, associated with the excitation of quasiguided eigenmodes of the grating. In this work, we demonstrate for the first time the capability of a resonant diffraction grating to integrate optical pulses. For applications, it is important that the resonant dif fraction gratings have a much smaller longitudinal size (from fractions of a micron to several microns) com pared to Bragg structures.Let us consider an optical pulse with central fre quency ω 0 and envelope P inc (t) propagating along the Oz axis. The pulse field has the form (1)is the x or y component of the electric field depending on the polarization, k(ω) = ω/c is the wavenumber, v g = c/ is the group velocity, ε is the dielectric constant of the medium, and G(ω) is the spectrum of the pulse envelope.Let the pulse be normally incident on the diffrac tion grating (Fig. 1). The envelope of the transmitted pulse in the zeroth diffraction order takes the form (2) where T(ω) is the complex transmittance (the com plex amplitude of the transmitted zeroth diffraction order) as a function of the frequency. According to Eq. (2), the transformation of the envelope of the inci ε εThe possibility of integrating optical pulses by resonant diffraction gratings has been considered. It has been shown that a diffraction grating provides integration of the pulse envelope in the vicinity of quasiguided mode resonances. The integration is performed with an exponential weight function, whose decay rate is deter mined by the quality factor of the resonance. Metallic diffraction gratings for integration of picosecond pulses have been computed. The calculation of the grating eigenmodes with the use of the scattering matrix method has shown that the integration is performed in the vicinity of the resonances corresponding to the excitation of surface plasmon polaritons at the grating boundary. According to the results of numerical simulation, the integration quality is quite high. Fig. 1. Geometry of the diffraction grating. The parame ters of the grating at ε sub = 1 are period d = 1540 nm, height h = 90 nm, and slit width a = 185 nm. The param eters of the grating at ε sub = 2.09 are d = 1070 nm, h = 110 nm, and a = 20 nm. gr tr

For the Anniversary of Professor L.L. Doskolovich

“…Ongoing studies are in line with technologies of silicon nanophotonics, aimed at creating a new generation of computer systems in which the light pulses will be used as information carriers instead of electrical signals. Doskolovich`s works theoretically prove the possibility of analog optical information processing and optical computing on the basis of resonant diffraction structures: diffraction gratings, Bragg multilayer structures, microresonators [57][58][59][60][61][62][63][64][65][66][67][68][69][70][71]. In the mentioned works, it is shown that these planar diffraction structures enable performing basic operations of spatio-temporal filtering, including spatial and temporal differentiation and integration of optical signals.…”

Optical Computing: Status and Perspectives

“…Soifer et al achieved several significant discoveries in this field. The pro-cesses of differentiation (integration) of the pulse envelope may be successfully conducted by employing a resonant diffraction grating, as described in studies [174][175][176][177][178][179]. High-order derivatives may be calculated quickly using a set of multiple stacked diffraction gratings [178].…”

Enhanced third-harmonic generation in photonic crystals at band-gap pumping

“…A photonic crystal has a structure characterized by a spatially periodic distribution of the medium's optical properties. The spatial periodicity leads to band structure of photon dispersion [1][2][3][4][5][6][7][8], due to which the photon behavior in photonic crystals differs significantly from that in homogeneous media. The latter makes these materials potentially useful for broad range of applications, in particular, for optical waveguiding [5,6,9,10], nonlinear generation in photoniccrystalline waveguides [11,12] and fibers [13][14][15][16], novel devices based on tunable properties of the light [17][18][19][20], supercontinuum generation [21], and highly-efficient nonlinear light conversion [22][23][24][25][26][27][28][29][30][31][32][33][34].…”