Probing the reciprocal lattice associated with a triangular slit to determine the orbital angular momentum for a photon.

The orbital angular momentum conservation of light reveals different diffraction patterns univocally dependent on the topological charge of the incident light beam when passing through a triangular aperture. It is demonstrated that these patterns, which are accessed by observing the far-field measurement of the diffracted light, can also be obtained using few photon sources. In order to explain the observed patterns, we introduce an analogy of this optical phenomenon with the study of diffraction for the characterization of the crystal structure of solids. We demonstrate that the finite pattern can be associated with the reciprocal lattice obtained from the direct lattice generated by the primitive vectors composing any two of the sides of the equilateral triangular slit responsible for the diffraction. Using the relation that exists between the direct and reciprocal lattices, we provide a conclusive explanation as to why the diffraction pattern of the main maxima is finite. This can shed a new light on the investigation of crystallographic systems.

Strong correlations between incoherent vortices.

We establish a correlation rule of which the value of the topological charge obtained in intensity correlation between two coherence vortices is such that this value is bounded by the topological charge of each coherence vortex. The original phase information is scrambled in each speckle pattern and unveiled using numerical intensity correlation. According to this rule, it is also possible to obtain a coherence vortex stable, an integer vortex, even when each incoherent vortex beam is instable, non-integer vortex.

Unveiling a truncated optical lattice associated with a triangular aperture using light's orbital angular momentum.

We show that the orbital angular momentum can be used to unveil lattice properties hidden in diffraction patterns of a simple triangular aperture. Depending on the orbital angular momentum of the incident beam, the far field diffraction pattern reveals a truncated optical lattice associated with the illuminated aperture. This effect can be used to measure the topological charge of light beams.

Hermite-Bessel beams and the geometrical representation of nondiffracting beams with orbital angular momentum.

We investigate theoretically and experimentally the decomposition of high-order Bessel beams in terms of a new family of nondiffracting beams, referred as Hermite-Bessel beams, which are solutions of the Helmholtz equation in Cartesian coordinates. Based on this decomposition we develop a geometrical representation of first-order Bessel beams, equivalent to the Poincaré sphere for the polarization states of light and implement an unitary transformation within our geometrical representation using linear optical elements.

Fast light, slow light, and phase singularities: a connection to generalized weak values.

We demonstrate that Aharonov-Albert-Vaidman weak values have a direct relationship with the response function of a system, and have a much wider range of applicability in both the classical and quantum domains than previously thought. Using this idea, we have built an optical system, based on a birefringent photonic crystal, with an infinite number of weak values. In this system, the propagation speed of a polarized light pulse displays both superluminal and slow light behavior with a sharp transition between the two regimes. We show that this system's response possesses two-dimensional, vortex-antivortex phase singularities. Important consequences for optical signal processing are discussed.

Demonstration of superluminal effects in an absorptionless, nonreflective system.

We present an experimental and theoretical study of a simple, passive system consisting of a birefringent, two-dimensional photonic crystal and a polarizer in series, and show that superluminal dispersive effects can arise even though no incident radiation is absorbed or reflected. We demonstrate that a vector formulation of the Kramers-Kronig dispersion relations facilitates an understanding of these counterintuitive effects.

Soliton propagation in a medium with Kerr nonlinearity and resonant impurities: a variational approach.

Using a variational approach we have studied the shape preserving coherent propagation of light pulses in a resonant dispersive medium in the presence of the Kerr nonlinearity. Within the framework of a combined nonintegrable system composed of one nonlinear Schrödinger and a pair of Bloch equations, we show the existence of a solitary wave. We have tested our analytical solution through numerical simulations confirming its solitary wave nature.

Superluminal effects and negative group delays in electronics, and their applications.

The causality principle does not forbid negative group delays of analytic signals in electronic circuits; in particular, the peak of a pulse can leave the exit port of a circuit before it enters the input port. Furthermore, pulse distortion for these "superluminal" analytic signals can be negligible in both the optical and electronic domains. Here we suggest a possible extension of these ideas to microelectronics. The underlying principle is that negative feedback can be used to produce negative group delays. Such negative group delays can be used to cancel out the positive group delays introduced by transistor latency, as well as the propagation delays due to the interconnections between transistors. Using this principle, it may be possible to speed up computer systems.

Soliton interaction in a nonlinear waveguide in the presence of resonances.

The simultaneous propagation of two optical pulses through a nonlinear dispersive medium composed of a resonant three-level system is investigated. By choosing a soliton of area 4 pi and order N=2 at the pump frequency, together with a weaker pulse with a sech profile at the signal frequency, we show that the pump soliton breaks up into a pair of solitary waves which are cloned to the signal frequency. Due to a combination of coherent population trapping and nonlinear dispersive effects, the pair interacts in a repulsive fashion so that the taller wave travels faster than the shorter one.

Interference of traveling nondiffracting beams.

We study numerically the interference resulting from the superposition of two Bessel beams propagating in free space. We discuss how to obtain such beams and show the existence of the self-imaging effect during propagation. The evolution of the superimposed Bessel beams is analyzed on the basis of the evolution of the individual beams. Our exact numerical predictions contradict previous approximated analytical treatments, showing that they can lead to quantitatively wrong results and misleading conclusions.

Experimental observation of interfering Bessel beams.

We experimentally verified the interference resulting of the superposition of two Bessel beams propagating in free space and showed for first time the self imaging effect using nondiffracting beams. Our results are supported by numerical simulations and possible applications are discussed.

Two-photon-resonant photoinduced second-harmonic generation in Er(3+)-doped germano-aluminosilicate optical fibers pumped at 1.319 microm.

The growth of a two-photon-resonant photoinduced second-harmonic signal at 660 nm in Er(3+)-doped GeO(2)-Al(2)O(3)-SiO(2) single-mode optical fibers pumped by a Nd:YAG laser at 1.319 microm is reported. Defect states in the band gap are optically excited through a resonant two-photon absorption process connecting the (4)I(15/2)-(4)F(9/2) energy levels of the erbium ions present in the fiber core. As a result a periodic X((2)) grating is formed, and efficient second-harmonic generation takes place. For erbium-free GeO(2)-doped silica test fibers no second-harmonic signal has been detected, even after hours of seeded preparation process.

Cross-phase modulation of incoherent light in single-mode optical fibers.

When two optical incoherent beams copropagate in an optical fiber, the intensity-dependent refractive index couples the two beams through a nonlinear process known as cross-phase modulation. We show, for the first time to our knowledge, experimental evidence on cross-phase-modulation-induced correlation time reduction and a concomitant growth of the frequency components of the two copropagating incoherent waves in a singlemode optical fiber. Theoretical analysis agrees well with experimental data.