Click icons to see AVI movie:Photonic bandgaps occur in the spectrum of light waves due to Bragg resonance between incident light and the fiber grating (periodic modulation of the refractive index). The small-intensity light with frequencies inside the photonic bandgap is strongly reflected. Illuminated with larger intensities, the light gets transmitted through the gratings due to nonlinearity. The average Kerr nonlinearity leads to optical bistability and, ultimately, to switching pulsations between lower-transmisive and higher-transmissive stationary states. The switchings occur as regular and, sometimes, irregular oscillations, arising at the left end of the grating, where the light is illuminated, and traveling to the right end of the gratings.
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Pulsations of the forward wave
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Pulsations of the backward wave
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Pulsations of light in the optical grating display a series of localized pulses traveling across the periodic structure with constant speed. These localised pulses are called gap solitons, or, equivalently, Bragg solitons. Bragg solitons are supported by the Bragg resonance between light and periodic structure, when the uniform stationary transmission is modulationally unstable. Bragg solitons have frequencies which fit inside the photonic bandgap, i.e. the solitons are nonlinear objects that realize a balance between Kerr nonlinearity and the bandgap dispersion. Bragg solitons may not exist in resonance with light waves, when their frequencies lie outside the photonic bandgap. Bragg solitons may travel with all velocities from zero to the speed of light in the bare fiber.
Bragg solitons were first experimentally reported in 1996-1998 at Bell Laboratories and at Southampton University in England. The nonlinear optical pulses can be used for all-optical switches, soliton lasers, pulse compressors, optical buffers, and storing devices. The main advantage of Bragg solitons in periodic nonlinear optical structures is that the input pulse is stationary transmitted from input to the output, preserving its shape and amplitude.
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Transmission of a single pulse
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When the Kerr nonlinearity is compensated by periodic modulation of the nonlinear refractive index across different optical layers, the regime of optical bistability changes into the regime of uniform stability and all-optical limiting. Simulateneously, the gap soliton ceases to exist in uniformly stable photonic gratings. When Bragg solitons are not supported by the nonlinear periodic structure, input signals are strongly distorted due to transmission. The pulse amplitude decays, the pulse shape splits into double-pulse structure and, ultimately, into multi-pulse small-amplitude noice of mixed light waves.
Mathematical analysis of existence, stability and transmission of optical pulses (Bragg solitons) can be performed on the basis of coupled-mode equations. Details can be found in our recent papers:
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Vibrations and Oscillatory Instabilities of Gap Solitons, Phys. Rev. Lett. 80, 5117-5120 (1998) |
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Stable all-optical limiting in nonlinear periodic structures. III: Non-solitonic pulse propagation J. Opt. Soc. Am. B, 20 695-705 (2003) |
New directions in simulations of Bragg solitons arise in studies of out-of-phase nonlinearity-compensated photonic gratings that allow local optical bistability and global all-optical limiting. Continuous waves are modulationally unstable and Bragg solitons may exist in such systems. However, blow-up develops in a finite time and leads ultimately to the break-up of the coupled-mode approximation. Analysis and modeling of Bragg solitons in such out-of-phase gratings are yet to be performed...
