Wave Propagation in a 3-D Optical Waveguide

In this paper we study the problem of wave propagation in a 3-D optical fiber. The goal is to obtain a solution for the time-harmonic field caused by a source in a cylindrically symmetric waveguide. The geometry of the problem, corresponding to an open waveguide, makes the problem challenging. To solve it, we construct a transform theory which is a nontrivial generalization of a method for solving a 2-D version of this problem given by Magnanini and Santosa.\cite{MS} The extension to 3-D is made complicated by the fact that the resulting eigenvalue problem defining the transform kernel is singular both at the origin and at infinity. The singularities require the investigation of the behavior of the solutions of the eigenvalue problem. Moreover, the derivation of the transform formulas needed to solve the wave propagation problem involves nontrivial calculations. The paper provides a complete description on how to construct the solution to the wave propagation problem in a 3-D optical waveguide with cylindrical symmetry. A follow-up article will study the particular cases of a step-index fiber and of a coaxial waveguide. In those cases we will obtain concrete formulas for the field and numerical examples.Comment: 35 pages, 3 figure

Nanoscale Metamaterial Optical Waveguides with Ultrahigh Refractive Indices

We propose deep-subwavelength optical waveguides based on metal-dielectric multilayer indefinite metamaterials with ultrahigh effective refractive indices. Waveguide modes with different mode orders are systematically analyzed with numerical simulations based on both metal-dielectric multilayer structures and the effective medium approach. The dependences of waveguide mode indices, propagation lengths and mode areas on different mode orders, free space wavelengths and sizes of waveguide cross sections are studied. Furthermore, waveguide modes are also illustrated with iso-frequency contours in the wave vector space in order to investigate the mechanism of waveguide mode cutoff for high order modes. The deep-subwavelength optical waveguide with a size smaller than {\lambda}0/50 and a mode area in the order of 10-4 {\lambda}02 is realized, and an ultrahigh effective refractive index up to 62.0 is achieved at the telecommunication wavelength. This new type of metamaterial optical waveguide opens up opportunities for various applications in enhanced light-matter interactions.Comment: 22 pages, 8 figure

Harmonic oscillations and their switching in elliptical optical waveguide arrays

We have studied harmonic oscillations in an elliptical optical waveguide array in which the coupling between neighboring waveguides is varied in accord with a Kac matrix so that the propagation constant eigenvalues can take equally spaced values. As a result, long-living Bloch oscillation (BO) and dipole oscillation (DO) are obtained when a linear gradient in the propagation constant is applied. Moreover, we achieve a switching from DO to BO or vice versa by ramping up the gradient profile. The various optical oscillations as well as their switching are investigated by field evolution analysis and confirmed by Hamiltonian optics. The equally spaced eigenvalues in the propagation constant allow viable applications in transmitting images, switching and routing of optical signals.Comment: 14 pages, 5 figure

Nonlinear optics and light localization in periodic photonic lattices

We review the recent developments in the field of photonic lattices emphasizing their unique properties for controlling linear and nonlinear propagation of light. We draw some important links between optical lattices and photonic crystals pointing towards practical applications in optical communications and computing, beam shaping, and bio-sensing.Comment: to appear in Journal of Nonlinear Optical Physics & Materials (JNOPM

Steering between Bloch oscillation and dipole oscillation in parabolic optical waveguide arrays

We study the optical oscillations of supermodes in planar optical waveguide arrays with parabolically graded propagation constant in individual waveguide interacting through nearest neighbor couplings. In these arrays, we have identified a transition between a symmetric dipole oscillation (DO) and a symmetry-breaking Bloch oscillation (BO) under appropriate conditions. There exist obvious correspondences between gradon localization and various optical oscillations. By virtue of an analogue between the oscillation of optical system and that of a plane pendulum, we propose a shift of the graded profile to cause a transition from BO to DO. We confirm the optical transition by means of Hamiltonian optics, as well as by the field evolution of the supermodes. The results offer great potential applications in optical switching, which can be applied to design suitable optical devices.Comment: Submitted to JOSA B for publication

Steering between Bloch oscillation and dipole oscillation in parabolic optical waveguide arrays

We study the optical oscillations of supermodes in planar optical waveguide arrays with parabolically graded propagation constant in individual waveguide interacting through nearest neighbor couplings. In these arrays, we have identified a transition between a symmetric dipole oscillation (DO) and a symmetry-breaking Bloch oscillation (BO) under appropriate conditions. There exist obvious correspondences between gradon localization and various optical oscillations. By virtue of an analogue between the oscillation of optical system and that of a plane pendulum, we propose a shift of the graded profile to cause a transition from BO to DO. We confirm the optical transition by means of Hamiltonian optics, as well as by the field evolution of the supermodes. The results offer great potential applications in optical switching, which can be applied to design suitable optical devices.Comment: Submitted to JOSA B for publication

Nonlinear properties of AlGaAs waveguides in continuous wave operation regime

Aluminum Gallium Arsenide (AlGaAs) is an attractive platform for the development of integrated optical circuits for all-optical signal processing thanks to its large nonlinear coefficients in the 1.55-μm telecommunication spectral region. In this paper we discuss the results of the nonlinear continuous-wave optical characterization of AlGaAs waveguides at a wavelength of 1.55 μm. We also report the highest value ever reported in the literature for the real part of the nonlinear coefficient in this material (Re(γ) ≈521 W<sup>−1</sup>m<sup>−1</sup>)