We consider the waveguiding by thin patterned slabs embedded in a homogeneous medium. In the longwave limit, the wave spectra of slabs are found to be well described by a single frequency-independent parameter, which we call the “guiding power". The guiding power can be evaluated in an effective medium approximation, similar to the Maxwell Garnett theory, but modified for the local field correc...

In the case of tight transverse confinement (cigar-shaped trap) the threedimensional (3D) nonlinear Schrödinger equation, describing superfluid Fermi atoms at unitarity (infinite scattering length |a| → ∞), is reduced to an effective one-dimensional form by averaging over the transverse coordinates. The resultant effective equation is a 1D nonpolynomial Schrodinger equation, which produces resu...

The Bose-Einstein condensate (BEC) of a dilute gas of bosons is well described by the three-dimensional Gross-Pitaevskii equation (3D GPE), that is a nonlinear Schrödinger equation. By imposing a transverse confinement the BEC can travel only in the cylindrical axial direction. We show that in this case the BEC with attractive interaction admits a 3D bright soliton solution which generalizes th...

A “waveguide” is a structure that allows waves to propagate along one (or more) direction(s) while confining them in one or more other “transverse” directions. These arise in many forms in many different wave equations, with a variety of mechanisms for the transverse confinement: silica optical fibers, sound waves propagating down hollow tubes, coaxial transmission lines, and so forth. One comm...

I demonstrate how confinement in Coulomb-gauge QCD makes quark-quark states of the color anti-triplet (diquarks) move out of the physical spectrum. Mesons as color singlet quark-antiquark states, on the other hand have finite masses and for highly excited states in the meson spectra effective restoration of chiral symmetry can be observed. In Coulomb-gauge QCD the 00-component of the gluon prop...

Light-front holographic QCD provides a successful first approximation to hadron spectroscopy in the chiral limit of ($3+1$)-dim light-front QCD, where Schr\"odinger-like equation, with an emerging confining scale, $\ensuremath{\kappa}$, governs confinement transverse direction. In its supersymmetric formulation, holography predicts that each baryon has two superpartners: meson and tetraquark, t...

We analyse the static solutions of attractive Bose-Einstein condensates under transverse confinement, both with and without axial confinement. By full numerical solution of the Gross-Pitaevskii equation and variational methods we map out the condensate solutions, their energetic properties, and their critical points for instability. With no axial confinement a bright solitary wave solution will...

We report on the theoretical analysis of a novel type of vertical-cavity surface-emitting laser (VCSEL) that provides selection of a certain higher-order transverse mode. This selection is based on a spatial variation of the threshold gain by adding an antiphase layer with an etched relief structure. The field intensity profile emitted from this laser is calculated numerically as well as with a...

The spin of light in subwavelength-diameter waveguides can be orthogonal to the propagation direction of the photons because of the strong transverse confinement. This transverse spin changes sign when the direction of propagation is reversed. Using this effect, we demonstrate the directional spontaneous emission of photons by laser-trapped caesium atoms into an optical nanofibre and control th...

We investigate bright and dark solitons with anomalous or normal dispersion and under transverse harmonic confinement. In matter waves, positive atomic mass implies anomalous dispersion (kinetic spreading) while negative mass gives normal dispersion (kinetic shrinking). We find that, contrary to the strictly onedimensional case, the axial and transverse profiles of these solitons crucially depe...