Exact bidirectional X-wave solutions in fiber Bragg gratings

We find exact solutions describing bidirectional pulses propagating in fiber Bragg gratings. They are derived by solving the coupled-mode theory equations and are expressed in terms of products of modified Bessel functions with algebraic functions. Depending on the values of the two free parameters the general bidirectional X-wave solution can also take the form of a unidirectional pulse. We analyze the symmetries and the asymptotic properties of the solutions and also discuss about additional waveforms that are obtained by interference of more than one solutions. Depending on their parameters such pulses can create a sharp focus with high contrast

Bessel-like optical beams with arbitrary trajectories

A method is proposed for generating Bessel-like optical beams with arbitrary trajectories in free space. The method involves phase-modulating an optical wavefront so that conical bundles of rays are formed whose apexes write a continuous focal curve with prespecified shape. These ray cones have circular bases on the input plane, thus their interference results in a Bessel-like transverse field profile that propagates along the specified trajectory with a remarkably invariant main lobe. Such beams can be useful as hybrids between nonaccelerating and accelerating optical waves that share diffraction-resisting and self-healing properties

Advanced trajectory engineering of diffraction-resisting laser beams

We introduce an analytical technique for engineering the trajectory of diffraction-resisting laser beams. The generated beams have a Bessel-like transverse field distribution and can be navigated along rather arbitrary curved paths in free space, thus being an advanced hybrid between accelerating and non-accelerating diffraction-free optical waves. The method involves phase-modulating the wavefront of a Gaussian laser beam to create a continuum of conical ray bundles whose apexes define a prespecified focal curve, along which a nearly perfect circular intensity lobe propagates without diffracting. Through extensive numerical simulations, we demonstrate the great flexibility in the design of a gamut of different beam trajectories. Propagation around obstructions and self-healing scenarios are also investigated. The proposed wave entities can be used extensively for light trajectory control in applications such as laser microfabrication, optical tweezers and curved plasma filamentation spectroscopy

Nonlinear Band Gap Transmission in Optical Waveguide Arrays

The effect of nonlinear transmission in coupled optical waveguide arrays is theoretically investigated via numerical simulations on the corresponding model equations. The realistic experimental setup is suggested injecting the beam in a single boundary waveguide, linear refractive index of which ($n_0$) is larger than one ($n$) of other identical waveguides in the array. Particularly, the effect holds if $\omega(n_0-n)/c>2Q$, where $Q$ is a linear coupling constant between array waveguides, $\omega$ is a carrier wave frequency and $c$ is a light velocity. Making numerical experiments in case of discrete nonlinear Schr\"odinger equation it is shown that the energy transfers from the boundary waveguide to the waveguide array above certain threshold intensity of the injected beam. This effect is explained by means of the creation and propagation of gap solitons in full analogy with the similar phenomenon of nonlinear supratransmission [F. Geniet, J. Leon, PRL, {\bf 89}, 134102, (2002)] in case of discrete sine-Gordon lattice.Comment: 4 pages, 6 figures. Phys. Rev. Lett. (in press

Statistical PT-symmetric lasing in an optical fiber network

PT-symmetry in optics is a condition whereby the real and imaginary parts of the refractive index across a photonic structure are deliberately balanced. This balance can lead to a host of novel optical phenomena, such as unidirectional invisibility, loss-induced lasing, single-mode lasing from multimode resonators, and non-reciprocal effects in conjunction with nonlinearities. Because PT-symmetry has been thought of as fragile, experimental realizations to date have been usually restricted to on-chip micro-devices. Here, we demonstrate that certain features of PT-symmetry are sufficiently robust to survive the statistical fluctuations associated with a macroscopic optical cavity. We construct optical-fiber-based coupled-cavities in excess of a kilometer in length (the free spectral range is less than 0.8 fm) with balanced gain and loss in two sub-cavities and examine the lasing dynamics. In such a macroscopic system, fluctuations can lead to a cavity-detuning exceeding the free spectral range. Nevertheless, by varying the gain-loss contrast, we observe that both the lasing threshold and the growth of the laser power follow the predicted behavior of a stable PT-symmetric structure. Furthermore, a statistical symmetry-breaking point is observed upon varying the cavity loss. These findings indicate that PT-symmetry is a more robust optical phenomenon than previously expected, and points to potential applications in optical fiber networks and fiber lasers.Comment: Submitted to Nature Communications, Pages 1-19: Main manuscript; Pages 20-38: Supplementary material

Discrete Ginzburg-Landau solitons

We demonstrate that discrete solitons are possible in Ginzburg-Landau lattices. As a result of discreteness, we find that this system exhibits a host of features that have no counterpart whatsoever in either the continuous limit or in other conservative discrete models

Lattice solitons in Bose-Einstein condensates

We systematically study the properties of lattice solitons in Bose-Einstein condensates with either attractive or repulsive atom interactions. This is done, by exactly solving the mean-field Gross-Pitaevskii equation in the presence of a periodic potential. We find new families of lattice soliton solutions that are characterized by the position of the energy eigenvalue within the associated band structure. These include lattice solitons in condensates with either attractive or repulsive atom interactions that exist in finite or semi-infinite gaps, as well as nonlinear modes that exhibit atomic population cutoffs

PT\mathcal{PT}-Symmetric Periodic Optical Potentials

In quantum theory, any Hamiltonian describing a physical system is mathematically represented by a self-adjoint linear operator to ensure the reality of the associated observables. In an attempt to extend quantum mechanics into the complex domain, it was realized few years ago that certain non-Hermitian parity-time ($\mathcal{PT}$) symmetric Hamiltonians can exhibit an entirely real spectrum. Much of the reported progress has been remained theoretical, and therefore hasn't led to a viable experimental proposal for which non Hermitian quantum effects could be observed in laboratory experiments. Quite recently however, it was suggested that the concept of $\mathcal{PT}$-symmetry could be physically realized within the framework of classical optics. This proposal has, in turn, stimulated extensive investigations and research studies related to $\mathcal{PT}$-symmetric Optics and paved the way for the first experimental observation of $\mathcal{PT}$-symmetry breaking in any physical system. In this paper, we present recent results regarding $\mathcal{PT}$-symmetric Optic