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Effect of Kerr nonlinearity on an Airy beam  

International Nuclear Information System (INIS)

The effect of Kerr nonlinearity on an Airy beam is investigated by using the nonlinear Schroedinger equation. Based on the moments method, the evolution of the Airy beam width in the rms sense is analytically described. Numerical simulations indicate that the central parts of the major lobe of the Airy beam initially give rise to radial compression during propagation in a focusing medium, even though the rms beam width broadens. The partial collapse of the center parts of the major lobe of the beam appear below the threshold for a global collapse. The evolutions of the field distributions of the Airy beams are different during propagation in different Kerr media while the beams still travel along the parabolic trajectory just as the beam propagates in free space.

2010-10-01

2

Interpolation between Airy and Poisson statistics for unitary chiral non-Hermitian random matrix ensembles  

CERN Document Server

We consider a family of chiral non-Hermitian Gaussian random matrices in the unitarily invariant symmetry class. The eigenvalue distribution in this model is expressed in terms of Laguerre polynomials in the complex plane. These are orthogonal with respect to a non-Gaussian weight including a modified Bessel function of the second kind, and we give an elementary proof for this. In the large $n$ limit, the eigenvalue statistics at the spectral edge close to the real axis are described by the same family of kernels interpolating between Airy and Poisson that was recently found by one of the authors for the elliptic Ginibre ensemble. We conclude that this scaling limit is universal, appearing for two different non-Hermitian random matrix ensembles with unitary symmetry. As a second result we give an equivalent form for the interpolating Airy kernel in terms of a single real integral, similar to representations for the asymptotic kernel in the bulk ...

2010-01-01