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1.
Opt Lett ; 39(7): 2129-32, 2014 Apr 01.
Article in English | MEDLINE | ID: mdl-24686692

ABSTRACT

We study nondiffracting accelerating paraxial optical beams in periodic potentials, in both the linear and the nonlinear domains. In particular, we show that only a unique class of z-dependent lattices can support a true accelerating diffractionless beam. Accelerating lattice solitons, autofocusing beams and accelerating bullets in optical lattices are systematically examined.

2.
Phys Rev Lett ; 109(2): 023602, 2012 Jul 13.
Article in English | MEDLINE | ID: mdl-23030159

ABSTRACT

We demonstrate that light propagating in an appropriately designed lattice can exhibit dynamics akin to that expected from massless relativistic particles as governed by the one-dimensional Dirac equation. This is accomplished by employing a waveguide array with alternating positive and negative effective coupling coefficients, having a band structure with two intersecting minibands. Through this approach optical analogues of massless particle-antiparticle pairs are experimentally realized. One-dimensional conical diffraction is also observed for the first time in this work.

3.
Phys Rev Lett ; 109(11): 113905, 2012 Sep 14.
Article in English | MEDLINE | ID: mdl-23005632

ABSTRACT

We demonstrate, for the first time, that photonic lattices support a new type of laser filaments, called lattice filaments (LF). The LF attributes (length, width, and intensity) can be tailored by both varying the photonic lattice properties and also dynamically through the interaction between filaments. This opens the way for extensive all-optical control of the nonlinear propagation of intense ultrafast wave packets. Our approach is generic and applicable to all transparent media, with potential strong impact on various photonic applications.

4.
Opt Lett ; 37(11): 1892-4, 2012 Jun 01.
Article in English | MEDLINE | ID: mdl-22660064

ABSTRACT

We predict that surface optical Bloch oscillations can exist in semi-infinite waveguide arrays with a linear index variation, if the array parameters close to the boundary are appropriately perturbed. The perturbation is such that the surface states obtain the Wannier-Stark ladder eigenvalues of the unperturbed infinite array. The number of waveguides, whose parameters need to be controlled, decreases with increasing ratio of index gradient over coupling. The configuration can find applications as a "matched" termination of waveguide arrays to eliminate the distortion of Bloch oscillations due to reflection on the boundaries.

5.
Phys Rev E Stat Nonlin Soft Matter Phys ; 84(3 Pt 2): 036601, 2011 Sep.
Article in English | MEDLINE | ID: mdl-22060516

ABSTRACT

We analyze the 1D focusing nonlinear Schrödinger equation in a finite interval with homogeneous Dirichlet or Neumann boundary conditions. There are two main dynamics, the collapse which is very fast and a slow cascade of Fourier modes. For the cubic nonlinearity the calculations show no long-term energy exchange between Fourier modes as opposed to higher nonlinearities. This slow dynamics is explained by fairly simple amplitude equations for the resonant Fourier modes. Their solutions are well behaved so filtering high frequencies prevents collapse. Finally, these equations elucidate the unique role of the zero mode for the Neumann boundary conditions.

6.
Opt Express ; 19(11): 10057-62, 2011 May 23.
Article in English | MEDLINE | ID: mdl-21643264

ABSTRACT

Femtosecond filamentation inside a periodic lattice in air is numerically shown to form intense dynamic bullets. The long propagation distance of the bullet structure is primarily attributed to the effect of the lattice that regulates the competition between linear and nonlinear spatiotemporal effects in the region of normal dispersion.

7.
Phys Rev Lett ; 92(22): 223901, 2004 Jun 04.
Article in English | MEDLINE | ID: mdl-15245225

ABSTRACT

We predict the existence of random phase solitons in nonlinear periodic lattices. These solitons exist when the nonlinear response time is much longer than the characteristic time of random phase fluctuations. The intensity profiles, power spectra, and statistical (coherence) properties of these stationary waves conform to the periodicity of the lattice. The general phenomenon of such solitons is analyzed in the context of nonlinear photonic lattices.

8.
Opt Lett ; 26(24): 1978-80, 2001 Dec 15.
Article in English | MEDLINE | ID: mdl-18059751

ABSTRACT

The performance of switching junctions in two-dimensional discrete-soliton networks is analyzed theoretically by coupled-mode theory. Our analysis can be used for the design of routing junctions with specified operational characteristics. Appropriately engineering the intersection site can further improve the switching efficiency of these junctions. Our analytical results are verified by numerical simulations.

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