Path-integral analysis of passive, graded-index waveguides applicable to integrated optics

The Feynman path integral is used to describe paraxial, scalar wave propagation in weakly inhomogeneous media of the type encountered in passive integrated-optical communication devices. Most of the devices considered in this work are simple models for graded-index waveguide structures, such as tapered and coupled waveguides of a wide variety of geometries. Tapered and coupled graded-index waveguides are the building blocks of waveguide junctions and tapered couplers, and have been mainly studied in the past through numerical simulations. Closed form expressions for the propagator and the coupling efficiency of symmetrically tapered graded-index waveguide sections are presented in this thesis for the first time. The tapered waveguide geometries considered are the general power-law geometry, the linear, parabolic, inverse-square-law, and exponential tapers. Closed form expressions describing the propagation of a centred Gaussian beam in these tapers have also been derived. The approximate propagator of two parallel, coupled graded-index waveguides has also been derived in closed form. An expression for the beat length of this system of coupled waveguides has also been obtained for the cases of strong and intermediate strength coupling. The propagator of two coupled waveguides with a variable spacing was also obtained in terms of an unknown function specified by a second order differential equation with simple boundary conditions. The technique of path integration is finally used to study wave propagation in a number of dielectric media whose refractive index has a random component. A refractive index model of this type is relevant to dielectric waveguides formed using a process of diffusion, and is thus of interest in the study of integrated optical waveguides. We obtained closed form results for the average propagator and the density of propagation modes for Gaussian random media having either zero or infinite refractive-index-inhomogeneity correlation-length along the direction of wave propagation

Towards efficient three-dimensional wide-angle beam propagation methods and theoretical study of nanostructures for enhanced performance of photonic devices

In this dissertation, we have proposed a novel class of approximants, the so-called modified Padé approximant operators for the wide-angle beam propagation method (WA-BPM). Such new operators not only allow a more accurate approximation to the true Helmholtz equation than the conventional operators, but also give evanescent modes the desired damping. We have also demonstrated the usefulness of these new operators for the solution of time-domain beam propagation problems. We have shown this both for a wideband method, which can take reflections into account, and for a split-step method for the modeling of ultrashort unidirectional pulses. The resulting approaches achieve high-order accuracy not only in space but also in time. In addition, we have proposed an adaptation of the recently introduced complex Jacobi iterative (CJI) method for the solution of wide-angle beam propagation problems. The resulting CJI-WA-BPM is very competitive for demanding problems. For large 3D waveguide problems with refractive index profiles varying in the propagation direction, the CJI method can speed-up beam propagation up to 4 times compared to other state-of-the-art methods. For practical problems, the CJI-WA-BPM is found to be very useful to simulate a big component such as an arrayed waveguide grating (AWG) in the silicon-on-insulator platform, which our group is looking at. Apart from WA beam propagation problems for uniform waveguide structures, we have developed novel Padé approximate solutions for wave propagation in graded-index metamaterials. The resulting method offers a very promising tool for such demanding problems. On the other hand, we have carried out the study of improved performance of optical devices such as label-free optical biosensors, light-emitting diodes and solar cells by means of numerical and analytical methods. We have proposed a solution for enhanced sensitivity of a silicon-on-insulator surface plasmon interference biosensor which had been previously proposed in our group. The resulting sensitivity has been enhanced up to 5 times. Furthermore, we have developed an improved model to investigate the influence of isolated metallic nanoparticles on light emission properties of light-emitting diodes. The resulting model compares very well to experimental results. Finally, we have proposed the usefulness of core-shell nanostructures as nanoantennas to enhance light absorption of thin-film amorphous silicon solar cells. An increased absorption up to 33 % has theoretically been demonstrated

Propagation of an Optical Vortex in Fiber Arrays with Triangular Lattices

The propagation of optical vortices (OVs) in linear and nonlinear media is an important field of research in science and engineering. The most important goal is to explore the properties of guiding dynamics for potential applications such as sensing, all-optical switching, frequency mixing and modulation. In this dissertation, we present analytical methods and numerical techniques to investigate the propagation of an optical vortex in fiber array waveguides. Analytically, we model wave propagation in a waveguide by coupled mode Equations as a simplified approximation. The beam propagation method (BPM) is also employed to numerically solve the paraxial wave Equation by finite difference (FD) techniques. We will investigate the propagation of fields in a 2D triangular lattice with different core arrangements in the optical waveguide. In order to eliminate wave reflections at the boundaries of the computational area, the transparent boundary condition (TBC) is applied. In our explorations for the propagation properties of an optical vortex in a linear and a non-linear triangular lattice medium, images are numerically generated for the field phase and intensity in addition to the interferogram of the vortex field with a reference plane or Gaussian field. The finite difference beam propagation method (FD-BPM) with transparent boundary condition (TBC) is a robust approach to numerically deal with optical field propagations in waveguides. In a fiber array arranged in triangular lattices, new vortices vary with respect to the propagation distance and the number of cores in the fiber array for both linear and nonlinear regimes. With more cores and longer propagation distances, more vortices are created. However, they do not always survive and may disappear while other new vortices are formed at other points. In a linear triangular lattice, the results demonstrated that the number of vortices may increase or decrease with respect to the number of cores in the array lattice. In a nonlinear triangular lattice, however, the number of vortices tends to increase as the core radius increases and decrease as the distance between cores increases. Investigations revealed that new vortices are generated due to the effects of the phase spiral around the new points of zero intensity. These points are formed due to the mode coupling of the optical field between the cores inside the array. In order to understand the dynamics of vortex generation, we examine vortex density, defined as the total number of vortices per unit area of the fiber array. This parameter is to be explored versus the propagation distance, the core radius size and the distance between cores. The Shack-Hartmann wavefront sensor can be employed to find the vortex density and the locations of vortices. Simulation results revealed that the vortex density increases with respect to propagation distance until saturation. It also increases with an increasing radius size but decreases with increasing distance between the array cores for linear and nonlinear regimes

Anderson Localization at the Subwavelength Scale and Loss Compensation for Surface-Plasmon Polaritons in Disordered Arrays of Metallic Nanowires

Using a random array of coupled metallic nanowires as a generic example of disordered plasmonic systems, we demonstrate that the structural disorder induces localization of light in these nanostructures at a deep-subwavelength scale. The ab initio analysis is based on solving the complete set of 3D Maxwell equations. We find that random variations of the radius of coupled plasmonic nanowires are sufficient to induce the Anderson localization (AL) of surface-plasmon polaritons (SPPs), the size of these trapped modes being significantly smaller than the wavelength. Remarkably, the optical-gain coefficient, needed to compensate losses in the plasmonic components of the system, is much smaller than the loss coefficient of the metal, which is obviously beneficial for the realization of the AL in plasmonic nanostructures. The dynamics of excitation and propagation of the Anderson-localized SPPs are addressed too.Comment: 5 pages, 4 figures, to appear in Phys. Rev.