Bragg guiding of domainlike nonlinear modes and kink arrays in lower-index core structures

We introduce a novel class of stable nonlinear modes trapped in a lower-index film core sandwiched between two optical lattices, or in the cylindrical core of a radial lattice, imprinted in defocusing media. Such a family of nonlinear modes transforms into defect lattice solitons when the core width is sufficiently small or into an array of kinks when the width is large enough. We find that higher-order modes with multiple zeros inside the guiding core can be stable in one-dimensional settings.     

Subwavelength spatial solitons in inhomogeneous Kerr media

Propagation of a narrow beam in a periodic Kerr medium is analyzed for an arbitrary relation between the beam width, modulation period, and optical wavelength. Maxwell’s equations used to obtain solutions describing spatial optical solitons, and their basic properties are determined. The results are compared with those obtained by solving the paraxial nonlinear Schödinger equation. Conditions are found under which these models are mutually inconsistent.     

Ionization spectrum broadening and frequency blue-shift of high-intensity femtosecond laser pulses in gas-filled capillary tubes

. We report on the experimental and theoretical study of spectrum transformation and frequency blue-shift of femtosecond laser pulses with intensities up to 2×10¹⁶ W/cm², propagating in glass capillary tubes under gas ionization. Monomode optical guiding with 45% transmission efficiency is demonstrated in a 100-μm-diameter, 20-cm length capillary. A broadening of the initial spectrum as much as several initial spectrum widths is achieved. Besides the broadening, the mean frequency of the output radiation in the spectrum experiences a blue-shift of up to several initial spectrum widths, caused by the non-stationary, non-linear process of gas ionization. Our numerical simulations, in the form of a simple one-dimensional model for the propagation of intense laser pulses in gas-filled capillaries, are in good qualitative agreement with the experimental results. These simulations show the possibility of significant compression of an output pulse in a simple compression scheme (e.g. a piece of silica glass with normal dispersion), which is very important for obtaining laser pulses with few optical cycles at the millijoule energy level. Received: 25 September 2001 / Revised version: 6 December 2001 / Published online: 25 September 2002 RID="*" ID="*"Corresponding author. Fax: +7-8312/363-792, E-mail: dekart@ufp.appl.sci-nnov.ru     

Strength as a time function in brittle failure

The stress distribution at the vertex of a crack has been derived from the mechanics of brittle failure in terms of the growth of a marginal crack in an elastic half-space. An analytic expression has been derived for the stress-concentration factor for an arbitrary normal load applied to the crack. An expression is also derived for the rate of growth of an edge transverse crack or a strip specimen, which is a function of the length of the growing crack and the constant tensile stress applied to the specimen. A formula is also derived for the time dependence of the strength in terms of the stress at the crack vertex. A numerical calculation for PMMA is in agreement with experiment.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 30–36, February 1978.     

Parametric amplification of soliton steering in optical lattices

We report on the effect of parametric amplification of spatial soliton swinging in Kerr-type nonlinear media with longitudinal and transverse periodic modulation of the linear refractive index. The parameter areas are found where the soliton center motion is analogous to the motion of a parametrically driven pendulum. This effect has potential applications for controllable soliton steering.     

Soliton eigenvalue control in optical lattices

We address the dynamics of higher-order solitons in optical lattices, and predict their self-splitting into the set of their single-soliton constituents. The splitting is induced by the potential introduced by the lattice, together with the imprinting of a phase tilt onto the initial multisoliton states. The phenomenon allows the controllable generation of several coherent solitons linked via their Zakharov-Shabat eigenvalues. Application of the scheme to the generation of correlated matter waves in Bose-Einstein condensates is discussed.     

Multicolor lattice solitons

We report on the existence of multicolor solitons supported by periodic lattices made from quadratic nonlinear media. Such lattice solitons bridge the gap between continuous solitons in uniform media and discrete solitons in strongly localized systems and exhibit a wealth of new features. We discovered that, in contrast to uniform media, multipeaked lattice solitons are stable. Thus they open new opportunities for all-optical switching based on soliton packets.     

Rotary solitons in bessel optical lattices

We introduce solitons supported by Bessel photonic lattices in cubic nonlinear media. We show that the cylindrical geometry of the lattice, with several concentric rings, affords unique soliton properties and dynamics. In particular, in addition to the lowest-order solitons trapped in the center of the lattice, we find soliton families trapped at different lattice rings. Such solitons can be set into controlled rotation inside each ring, thus featuring novel types of in-ring and inter-ring soliton interactions.