Optical realization of the two-site Bose-Hubbard model in waveguide lattices

A classical realization of the two-site Bose-Hubbard Hamiltonian, based on light transport in engineered optical waveguide lattices, is theoretically proposed. The optical lattice enables a direct visualization of the Bose-Hubbard dynamics in Fock space.Comment: to be published, J Phys. B (Fast Track Communication

Visualization of Coherent Destruction of Tunneling in an Optical Double Well System

We report on a direct visualization of coherent destruction of tunneling (CDT) of light waves in a double well system which provides an optical analog of quantum CDT as originally proposed by Grossmann, Dittrich, Jung, and Hanggi [Phys. Rev. Lett. {\bf 67}, 516 (1991)]. The driven double well, realized by two periodically-curved waveguides in an Er:Yb-doped glass, is designed so that spatial light propagation exactly mimics the coherent space-time dynamics of matter waves in a driven double-well potential governed by the Schr\"{o}dinger equation. The fluorescence of Er ions is exploited to image the spatial evolution of light in the two wells, clearly demonstrating suppression of light tunneling for special ratios between frequency and amplitude of the driving field.Comment: final versio

Coherent tunneling by adiabatic passage in an optical waveguide system

We report on the first experimental demonstration of light transfer in an engineered triple-well optical waveguide structure which provides a classic analogue of Coherent Tunnelling by Adiabatic Passage (CTAP) recently proposed for coherent transport in space of neutral atoms or electrons among tunneling-coupled optical traps or quantum wells [A.D. Greentree et al., Phys. Rev. B 70, 235317 (2004); K. Eckert et al., Phys. Rev. A 70, 023606 (2004)]. The direct visualization of CTAP wavepacket dynamics enabled by our simple optical system clearly shows that in the counterintuitive passage scheme light waves tunnel between the two outer wells without appreciable excitation of the middle well.Comment: submitted for publicatio

Radially and azimuthally polarized non paraxial Bessel beams

We present a method for the realization of cylindrically polarized non-paraxial beams by constructing exact vector solutions of Maxwell's equations from scalar Bessel beams and combining them together by analogy with the paraxial case

The Hertz vector revisited: a simple physical picture

The polarization potentials, also known as Hertz vectors, are useful auxiliary fields that permit the calculation of the fundamental electromagnetic fields in many cases of practical importance. In this article we show that in a vacuum a single Hertz vector written as the product of a scalar potential and a constant vector, naturally arises as consequence of the transversality of the electromagnetic fields. Thus, our treatment shines a new light on the physical meaning of a Hertz potential

Theory of anisotropic whispering-gallery-mode resonators

An analytic solution for a uniaxial spherical resonator is presented using the method of Debye potentials. This serves as a starting point for the calculation of whispering gallery modes (WGMs) in such a resonator. Suitable approximations for the radial functions are discussed in order to best characterize WGMs. The characteristic equation and its asymptotic expansion for the anisotropic case is also discussed, and an analytic formula with a precision of the order O[nu(-1)] is also given. Our careful treatment of both boundary conditions and asymptotic expansions makes the present work a particularly suitable platform for a quantum theory of whispering gallery resonators

Radially and Azimuthally Polarized Non Paraxial Bessel Beams

We present a method for the realization of cylindrically polarized non-paraxial beams by constructing exact vector solutions of Maxwell's equations from scalar Bessel beams and combining them together by analogy with the paraxial case

Goos-Hanchen and Imbert-Fedorov shifts from a quantum-mechanical perspective

We study the classical optics effects known as Goos-Hanchen and Imbert-Fedorov shifts, occurring when reflecting a bounded light beam from a planar surface, by using a quantum-mechanical formalism. This new approach allows us to naturally separate the spatial shift into two parts, one independent on orbital angular momentum (OAM) and the other one showing OAM-induced spatial-versus-angular shift mixing. In addition, within this quantum-mechanical-like formalism, it becomes apparent that the angular shift is proportional to the beams angular spread, namely to the variance of the transverse components of the wave vector. Moreover, we extend our treatment to the enhancement of beam shifts via weak measurements and relate our results to the recent experiments