We show how a nonlinear system that supports solitons can be driven to generate exact (regular) Cantor set fractals. As an example, we use numerical simulations to demonstrate the formation of Cantor set fractals by temporal optical solitons. This fractal formation occurs in a cascade of nonlinear optical fibers through the dynamical evolution from a single input soliton.

We experimentally demonstrate a new scheme for generating amplitude-squeezed solitons in an asymmetric fiber Sagnac loop. We measure by direct detection what is to our knowledge a record reduction of 5.7 6 0.1 dB (73%) and, with corrections for linear losses, 6.2 6 0.1 dB (76%) in the photon-number f luctuations below the shot-noise level. The same scheme is also shown to generate significant classical noise reduction and is limited by Raman effects in fiber. © 1998 Optical Society of America OCIS codes: 270.6570, 270.5530, 270.1670. Generation of amplitude-squeezed states by use of Kerr nonlinearity in optical fibers was recently demonstrated in a novel scheme pioneered by Friberg et al., who used soliton propagation followed by spectral f iltering. 1By launching a solitonlike pulse with energy slightly greater than the fundamental soliton energy ͑N . 1͒ into a fiber of length equivalent to several soliton periods followed by a spectral f ilter, it is possible to observe a reduction in photon-number f luctuations by direct detection. In subsequent experiments a reduction of as much as 3.8 dB was directly detected with femtosecond pulses. 2,3The f iltering action also introduces additional zero-point f luctuations into the system, limiting the highest achievable squeezing to approximately 8 dB below the shot-noise level for ideal fibers and bandpass filters. 4 Recently it was proposed that amplitude-squeezed pulses can be produced by interference between counterpropagating fields in an asymmetric fiber Sagnac loop. 5For the case of soliton squeezing the idea that interfering a high-energy ͑N . 1͒ soliton pulse with a weaker pulse or a dispersive wave can produce squeezing is also consistent with soliton perturbation treatment 6 as well as the general quantum theory of soliton propagation. 7,8 The geometry proposed in Ref. 5 is well suited for testing this idea in practice and was recently explored experimentally by Schmitt et al. 9Different geometries for achieving amplitude squeezing, such as polarization interferometry, were also demonstrated recently. 10In this Letter we experimentally demonstrate the asymmetric f iber Sagnac approach and report what is to our knowledge a record 5.7 6 0.1 dB (73%) directly detected photon-number squeezing below the shot-noise level. With correction for linear system losses, the actual amplitude squeezing is 6.2 6 0.1 dB (76%). We have also measured a significant reduction in the classical noise inherent in the optical signal.The experimental setup is shown in Fig. 1. A Spectra-Physics Opal optical parametric oscillator is used as a source of 182-fs (FWHM) sech-shaped optical pulses at a repetition rate of 82 MHz and centered at 1550 nm. The corresponding dispersion length ͑b 00 219 ps 2 ͞km͒ in the standard polarizationmaintaining (PM) fiber, Fujikura SM15-P-8 with an 8-mm core diameter, that was used in the experiments is ϳ54 cm, and the soliton period is 86 cm. The average power required for production of a fundamental ͑N 1͒ soliton, as determined by measurement of the ...

In the experiment the efficiency of the 50 GeV proton beam extraction from accelerator by means of a bent crystal as a function of crystal orientation was measured. This allowed one to make a comparative analysis of efficiencies of high-energy protons deflection by different crystal atomic planes with different values of the electrostatic field. The results of simulation of high-energy protons deflection by means of crystal atomic planes and crystal atomic strings are also presented in the article. In the case of planar channeling the simulation shows a good agreement with experimental data. In the case of proton motion in the regime of stochastic scattering by bent atomic strings the simulation shows that angles of particle deflection are much greater than the critical channeling angle.

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The possibilities of the extraction and collimation of a circulating beam by a new method due to the reflection of particles in crystals with axial orientation were experimentally investigated in the Fall-2010 run at the U_70 synchrotron. Such crystals have positive features, because the axial potential is five times larger than the planar potential. It has been shown that the collimation efficiency can reach 90% due to axial effects in the crystal. Losses of the circulating beam on a collimator have been reduced by several times; this makes it possible to suppress the muon jet near the steel collimator of the circulating beam.