Arbitrary Multiplication and Division of the Orbital Angular Momentum of Light.

Multiplication and division of the orbital angular momentum (OAM) of light are important functions in the exploitation of the OAM mode space for such purposes as high-dimensional quantum information encoding and mode division multiplexed optical communications. These operations are possible with optical transformations that reshape optical wave fronts according to azimuthal scaling. However, schemes proposed thus far have been limited to OAM multiplication by integer factors and require complex beam-copying or multitransformation diffraction stages; a result of the limited phase excursion 2πℓ around the annulus of an OAM state exp(iℓθ).

Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes.

Mode sorting is an essential function for optical multiplexing systems that exploit the orthogonality of the orbital angular momentum mode space. The familiar log-polar optical transformation provides a simple yet efficient approach whose resolution is, however, restricted by a considerable overlap between adjacent modes resulting from the limited excursion of the phase along a complete circle around the optical vortex axis. We propose and experimentally verify a new optical transformation that maps spirals (instead of concentric circles) to parallel lines.

Nondiffracting chirped Bessel waves in optical antiguides.

Chirped Bessel waves are introduced as stable (nondiffracting) solutions of the paraxial wave equation in optical antiguides with a power-law radial variation in their index of refraction. Through numerical simulations, we investigate the propagation of apodized (finite-energy) versions of such waves, with or without vorticity, in antiguides with practical parameters. The new waves exhibit a remarkable resistance against the defocusing effect of the unstable index potentials, outperforming standard Gaussians with the same full width at half-maximum.

Curved singular beams for three-dimensional particle manipulation.

For decades, singular beams carrying angular momentum have been a topic of considerable interest. Their intriguing applications are ubiquitous in a variety of fields, ranging from optical manipulation to photon entanglement, and from microscopy and coronagraphy to free-space communications, detection of rotating black holes, and even relativistic electrons and strong-field physics. In most applications, however, singular beams travel naturally along a straight line, expanding during linear propagation or breaking up in nonlinear media.

Temporal cloaking with accelerating wave packets.

We theoretically propose a temporal cloaking scheme based on accelerating wave packets. A part of a monochromatic light wave is endowed with a discontinuous nonlinear frequency chirp, so that two opposite accelerating caustics are created in space-time as the different frequency components propagate in the presence of dispersion. The two caustics open a biconvex time gap that contains negligible optical energy, thus concealing the enclosed events.

Observation of self-accelerating Bessel-like optical beams along arbitrary trajectories.

We experimentally demonstrate self-accelerating Bessel-like optical beams propagating along arbitrary trajectories in free space. With computer-generated holography, such beams are designed to follow different controllable trajectories while their main lobe transverse profiles remain nearly invariant and symmetric. Examples include parabolic, snake-like, hyperbolic, hyperbolic secant, and even three-dimensional spiraling trajectories.

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 pre-specified 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.

Reflection and refraction of an Airy beam at a dielectric interface.

Reflection and refraction of a finite-power Airy beam at the interface between two dielectric media are investigated analytically and numerically. The formulation takes into account the paraxial nature of the optical beams to derive convenient field evolution equations in coordinate frames moving along Snell's refraction and reflection axes. Through numerical simulations, the self-accelerating dynamics of the Airy-like refracted and reflected beams are observed.

Caustic design in periodic lattices.

We study curved trajectory dynamics and design in discrete array settings. We find that beams with power law phases produce curved caustics associated with the fold and cusp type catastrophes. A parabolic phase produces a focus that suffers from spherical aberrations.

Fourier-space generation of abruptly autofocusing beams and optical bottle beams.

We demonstrate analytically and experimentally that a circular abruptly autofocusing (AAF) Airy beam can be generated by Fourier-transforming an appropriately apodized Bessel beam whose radial oscillations are chirped by a cubic phase term. Depending on the relation between the chirp rate and the focal distance of the Fourier-transforming lens, it is possible to generate AAF beams with one or two foci, the latter case leading to the formation of an elegant paraboloid optical bottle.

Traveling waves in two parallel infinite linear point-scatterer arrays.

Traveling waves in two coupled parallel infinite linear point-scatterer arrays are studied analytically for the first time to our knowledge. The two arrays are considered to be generally offset in the axial direction. It is found that slow quasi-even/odd supermodes are supported, as a result of the coupling-induced splitting of the modes of the single array, in direct analogy to standard optical waveguide couplers.

Pre-engineered abruptly autofocusing beams.

We introduce a new family of (2+1)D light beams with pre-engineered abruptly autofocusing properties. These beams have a circularly symmetric input profile that develops outward of a dark disk and oscillates radially as a sublinear-chirp signal, creating a series of concentric intensity rings with gradually decreasing width. The light rays involved in this process form a caustic surface of revolution that bends toward the beam axis at an acceleration rate that is determined by the radial chirp itself.

Magnetic field integral equation analysis of surface plasmon scattering by rectangular dielectric channel discontinuities.

The scattering of a surface plasmon polariton (SPP) by a rectangular dielectric channel discontinuity is analyzed through a rigorous magnetic field integral equation method. The scattering phenomenon is formulated by means of the magnetic-type scalar integral equation, which is subsequently treated through an entire-domain Galerkin method of moments (MoM), based on a Fourier-series plane wave expansion of the magnetic field inside the discontinuity. The use of Green's function Fourier transform allows all integrations over the area and along the boundary of the discontinuity to be performed analytically, resulting in a MoM matrix with entries that are expressed as spectral integrals of closed-form expressions.

Magnetic field integral equation analysis of interaction between a surface plasmon polariton and a circular dielectric cavity embedded in the metal.

A rigorous integral equation (IE) analysis of the interaction between a surface plasmon polariton (SPP) and a circular dielectric cavity embedded in a metal half-space is presented. The device is addressed as the plasmonic counterpart of the established integrated optics filter comprising a whispering gallery (WG) resonator coupled to a waveguide. The mathematical formulation is that of a transverse magnetic scattering problem.

Modes of the infinite square lattice of coupled microring resonators.

The infinite square lattice of coupled microring optical resonators is studied for what we belive to be the first time. Using the standard matrix formalism and the classical Bloch's theorem for propagation in periodic optical media, the dispersion equation and the amplitudes of propagating Bloch modes are derived analytically. It is found that the dispersion equation omega(kx,ky) of this 2D microring array is expressed as the sum of two independent dispersion equations of the 1D microring array with wavenumbers kx and ky.

Properties of regular polygons of coupled microring resonators.

The resonant properties of a closed and symmetric cyclic array of N coupled microring resonators (coupled-microring resonator regular N-gon) are for the first time determined analytically by applying the transfer matrix approach and Floquet theorem for periodic propagation in cylindrically symmetric structures. By solving the corresponding eigenvalue problem with the field amplitudes in the rings as eigenvectors, it is shown that, for even or odd N, this photonic molecule possesses 1 + N/2 or 1+N resonant frequencies, respectively. The condition for resonances is found to be identical to the familiar dispersion equation of the infinite coupled-microring resonator waveguide with a discrete wave vector.

Analysis of scattering by a linear chain of spherical inclusions in an optical fiber.

The scattering by a linear chain of spherical dielectric inclusions, embedded along the axis of an optical fiber, is analyzed using a rigorous integral equation formulation, based on the dyadic Green's function theory. The coupled electric field integral equations are solved by applying the Galerkin technique with Mie-type expansion of the field inside the spheres in terms of spherical waves. The analysis extends the previously studied case of a single spherical inhomogeneity inside a fiber to the multisphere-scattering case, by utilizing the classic translational addition theorems for spherical waves in order to analytically extract the direct-intersphere-coupling coefficients.

Transformation of radially traveling cylindrical waves between two skew cylindrical coordinate systems.

The transformation of radially traveling cylindrical waves between two cylindrical coordinate systems with skew (nonparallel) axes is derived for the first time to our knowledge. The analytical procedure is based on the complex integral representation of the Hankel function and appropriate contour deformation and change of variables to obtain a final Fourier transform expression of the cylindrical wave in the new system. Scalar and vector waves are considered.

Integral equation analysis of scattering by a spherical microparticle coupled to a subwavelength-diameter wire waveguide.

A rigorous integral equation analysis of the coupling between a fiber waveguide and an adjacent spherical particle is developed. The solution is obtained by applying the entire-domain Galerkin technique, based on Mie-type spherical wave expansion of the field in the sphere and the use of dyadic Green's function of the fiber waveguide. The conversion between cylindrical and spherical wave functions is done through classic analytical formulas.

Green's-function method for the analysis of propagation in holey fibers.

A Green's-function method is employed to provide a rigorous analysis to the propagation and coupling phenomena in holey fibers. The analysis is carried out for an arbitrary grid of circular air holes of the fiber guide, while the electromagnetic field is taken to be a vector quantity. Application of the Green's-function concept leads to a coupled system of equations incorporating as unknowns the field expansion coefficients to cylindrical wave functions within the air holes.

Transmission and radiation in a slab waveguide coupled to a whispering-gallery resonator: volume-integral-equation analysis.

The excitation of a whispering gallery resonator by a surface wave guided in a dielectric slab is analyzed with a rigorous volume-integral-equation approach. The analysis is based on the Green's function concept and the application of the entire-domain Galerkin technique through expansion of the electric field in the resonator in terms of cylindrical wave functions. The algorithm developed yields highly accurate results for the transmission and reflection coefficients in the waveguide.

Analysis of coupling between two slab waveguides in the presence of ring resonators.

The coupling phenomena between two slab waveguides in the presence of ring resonators are investigated through a rigorous integral equation analysis. A Green's-function-theory approach is utilized to develop the integral equation formulation. The solution is obtained by applying an entire-domain Galerkin technique, using the orthogonality properties of involved wave functions in the ring resonators.