Preferential-order waveguide grating couplers: a comparative rigorous analysis using the finite-difference time-domain method

We rigorously analyze and compare preferential-order waveguide grating output couplers using the finite-difference time-domain method in the total-field/scattered-field formulation for TE and TM polarizations. Four kinds of preferential-order grating couplers are studied: volume holographic grating couplers, slanted parallelogrammic surface-relief grating couplers, double-corrugated surface-relief grating couplers, and reflecting-stack surface-relief grating couplers. The outcoupling efficiencies and branching ratios of the couplers, revealing their preferentiality, are calculated and compared with the rigorous coupled-wave analysis leaky-mode method. In addition, their performance is examined in terms of the main design parameters and the excitation wavelength.     

Design of polarization-independent optical couplers composed of three parallel slot waveguides

The characteristics of directional couplers and power splitters based on three-guide optical couplers in slot waveguide structures are analyzed in detail by a three-dimensional full-vectorial beam propagation method. The numerical results show the achievement of a compact three-guide directional coupler operating as polarization independent with a length of 58.0 microm and having almost evenly spaced propagation constants of the three lowest order modes for quasi-TE and quasi-TM modes. Thus, a high coupling efficiency from one outside waveguide to the other outside waveguide is demonstrated and is over 99.5% for both polarization states. For a three-guide power splitter, multiple sets of waveguide parameters for achieving polarization-independent operation are presented. Tolerances to operating wavelength and structural parameters are also analyzed, and the evolution of the injected field along the propagation distance through the proposed devices is demonstrated.     

Lossy multilayer channel optical waveguides analyzed by the transmission line matrix method

We demonstrate that the three-dimensional vectorial transmission line matrix (TLM) method is applicable to the analysis of lossy multilayer optical waveguiding structures. Any lossy multilayer waveguide geometry, including sharp discontinuities in the transverse plane, can be treated taking into account the coupling between all optical field components. The complex propagation constants (propagation constants and the attenuation coefficients) for the fundamental TE-like and TM-like modes can be determined. These parameters of the fundamental TM-like mode of a typical lossy multilayer rib dielectric waveguide are obtained as functions of free-space wavelength. Calculation of the electric-field pattern is also included. Numerical comparisons with the argument principle method (for the case of lossy multilayer slab waveguides) and the spectral-index technique (for the case of lossy multilayer rib waveguides) are also included, and it is shown that the application of the TLM method to lossy multilayer optical waveguides is accurate.     

Application of the symplectic finite-difference time-domain method to light scattering by small particles

A three-dimensional fourth-order finite-difference time-domain (FDTD) program with a symplectic integrator scheme has been developed to solve the problem of light scattering by small particles. The symplectic scheme is nondissipative and requires no more storage than the conventional second-order FDTD scheme. The total-field and scattered-field technique is generalized to provide the incident wave source conditions in the symplectic FDTD (SFDTD) scheme. The perfectly matched layer absorbing boundary condition is employed to truncate the computational domain. Numerical examples demonstrate that the fourth-order SFDTD scheme substantially improves the precision of the near-field calculation. The major shortcoming of the fourth-order SFDTD scheme is that it requires more computer CPU time than a conventional second-order FDTD scheme if the same grid size is used. Thus, to make the SFDTD method efficient for practical applications, one needs to parallelize the corresponding computational code.     

Application of the transmission line matrix method to the analysis of slab and channel optical waveguides

The applicability of the three-dimensional vectorial transmission line matrix (TLM) method to the analysis of optical waveguiding structures is demonstrated. Any waveguide geometry, even incorporating anisotropic materials, can be treated by taking into account the coupling between all optical field components. The application of the TLM method to optical waveguides is shown to be both efficient and accurate. The dispersion curve for the fundamental TE-like mode of a typical rib dielectric waveguide as well as its electric-field pattern is obtained by the use of the TLM method. Numerical comparisons with the integral-formulation technique, the effective-index method, the finite-difference analysis, the spectral-index method, and the beam-propagation technique are also included.     

Analysis of far-infrared horns, lightpipes, and cavities containing patterned conductive films

A scheme is described for calculating the scattering parameters of patterned conductive films in waveguide. The films can have non-uniform, non-isotropic, and non-local sheet impedances. Once the scattering parameters are known, they can be combined with the scattering parameters of paths, dielectric slabs, and waveguide steps to build up models of complicated components comprising patterned films in profiled lightpipes and cavities. It is then straightforward to calculate the Stokes fields of the total reception pattern, the natural optical modes to which the component is sensitive, the Stokes fields of the individual natural modes, and the spatial state of coherence. The method is demonstrated by modeling an absorbing pixel in a length of shorted multimode waveguide. The natural optical modes change from being those of the waveguide to those of a free-space pixel as the size of the absorber is reduced.     

A procedure to obtain the complete electromagnetic scattering properties at discontinuities between integrated optical waveguides

Abstract

A method to obtain the complete electromagnetic scattering properties of discontinuities between arbitrary integrated optical waveguides is presented. The method involves a new generalized scattering matrix concept, together with the generalized telegraphist equations formulism and the modal matching technique. Radiation losses, as well as reflection and transmission coefficients between proper modes, can be obtained. Single and multiple discontinuities in planar and channel optical waveguides have been analysed. Numerical results of complex scattering coefficients are given. The possibilities of the method for analysing waveguide photonic crystals, as well as optical devices in waveguide periodic waveguide structures, are demonstrated.     

Quasi-analytic formalism for mode characteristics in highly overmoded rectangular dielectric waveguide bends

A fast and simple quasi-analytic method to simulate mode characteristics in highly overmoded rectangular dielectric waveguide bends is presented. Fast mode-based bend models are necessary, since overmoded rectangular waveguides have become very popular in optical interconnects on printed circuit boards. The proposed method combines a simple mode solver with the formalism that was proposed by Melloni et al. [J. Lightwave Technol. 16, 571 (2001)], yielding to a very convenient and accurate quasi-analytic formalism for the bend transfer function based on matrix notation. For that purpose, a simple method to approximate leaky modes is introduced. The model offers the ability to predict individual modal phases and amplitudes within a given bend as well as the calculation of coupling losses and was validated using three-dimensional beam-propagation-method simulation software.     

Analysis of mode size transformation with a tapered directional coupler

A simple tapered directional coupler with a five-layered structure is employed for mode conversion between a single-order and higher-order modes. We investigate coupling from higher-order modes to a single-order field theoretically and experimentally. As a result, we confirm that the first two modes in the tapered waveguide are coupled with a single-order mode in another waveguide by computer simulation using the beam propagation method. Furthermore, we fabricated the actual device and observed the streak patterns of the first three modes.     

Equivalent-optical-waveguide model for the analysis of optical waveguides by means of an asymptotic effective-index method

We present a theoretical method that makes it possible to analyze three-dimensional (3-D) integrated optical waveguides with arbitrary refractive-index profiles. With this method it is easy to obtain effective indexes, propagation constants, and coupling-switching properties of planar and channel optical waveguides. This theoretical approach involves one's modeling the original optical waveguide by means of an equivalent optical waveguide whose effective index is evaluated by the application of a technique that we call the asymptotic effective-index method. The numerical values show good convergence and accuracy for effective indexes, propagation constants, and coupling-switching characteristics. Theoretical and experimental results are given.     

Analysis of piezoelectric ultrasonic transducers attached to waveguides using waveguide finite elements

A finite-element modeling procedure for computing the frequency response of piezoelectric transducers attached to infinite constant cross-section waveguides, as encountered in guided wave ultrasonic inspection, is presented. Two-dimensional waveguide finite elements are used to model the waveguide. Conventional three-dimensional finite elements are used to model the piezoelectric transducer. The harmonic forced response of the waveguide is used to obtain a dynamic stiffness matrix (complex and frequency dependent), which represents the waveguide in the transducer model. The electrical and mechanical frequency response of the transducer, attached to the waveguide, can then be computed. The forces applied to the waveguide are calculated and are used to determine the amplitude of each mode excited in the waveguide. The method is highly efficient compared to time integration of a conventional finite-element model of a length of waveguide. In addition, the method provides information about each mode that is excited in the waveguide. The method is demonstrated by modeling a sandwich piezoelectric transducer exciting a waveguide of rectangular cross section, although it could be applied to more complex situations. It is expected that the modeling method will be useful during the optimization of piezoelectric transducers for exciting specific wave propagation modes in waveguides.     

Whispering gallery modes of a curved antiresonant reflecting optical waveguide

The whispering gallery modes of a curved antiresonant reflecting optical waveguide are described and analyzed. We present a ray analysis method that can be used to derive an eigenmode equation and to analyze the loss characteristics of a waveguide in rectangular coordinates by using conformal transformation. With an optimized design of an antiresonant reflecting optical waveguide structure, the propagation loss of such a waveguide can be significantly reduced.     

Transverse electric modes in planar slot waveguides

Transverse electric (TE) modes in symmetrical planar slot waveguides are analytically solved, and a comprehensive knowledge about them is provided. It has been shown that there are four types of TE modes in planar slot waveguides just as the TM modes. Their field solutions, characteristic equations and cut-off conditions are derived. The cut-off conditions and the power confinement factors of the TE and TM modes are compared. It is demonstrated that there may be degeneration points between TE and TM modes. Because a three-dimensional waveguide has similar modal characteristics as its planar counterpart, our work presents a foundation of recognizing and utilizing the three-dimensional slot waveguides.     

Sensitivity of Traveling Wave Photodetectors in Superconducting Box-Shaped Plasmon-Polariton Optical Waveguides

A very sensitive superconducting traveling wave photodetector made of a modified box-shaped waveguide, which includes two high index layers and an active superconducting layer, is studied. The optical propagation constants and the power absorption efficiency for guided modes are determined using the finite element method; the results show that by acting only on the waveguide geometry, different confinement regimes of the light in the absorption superconducting layer can be achieved and optimized.     

Nonlinear optical responses in two-dimensional photonic crystals

A two-dimensional (2D) highly nonlinear lithium niobate (LN) photonic crystal (PhC) waveguide is fabricated with the aim of studying its nonlinear optical properties. We show a large enhancement of the second-harmonic generation (SHG) in the 2D LN PhCs, originating from resonance between the external pump laser field and a photonic band mode. The SHG enhancement results agree well with the experimental photonic band structure obtained by an angle-dependent optical reflectivity and the theoretical band structure generated by three-dimensional finite-difference time-domain calculations. These results open new possibilities for the use of 2D LN PhC waveguide in integrated nonlinear optical applications.     

Performance analysis of a multimode waveguide-based optical disk readout system

We propose a method to improve the optical resolution to read out optical disks, without making the spot size on the disk smaller than the diffraction limit. The idea is to reconstruct the bit pattern from the complete field profile (including amplitude and phase) of the light reflected from the disk. We measure the phase and amplitude information by picking up the wave front into different modes of a bimodal waveguide. Once picked up, these modes can be split by a photonic integrated circuit to be measured by separate detectors. By combining the information from the responses from the different modes, we can improve the bit error rate substantially.     

A slab optical waveguide with negative effective thickness

Two new asymmetric slab optical waveguides with a left-handed media (LHM) cover or substrate are studied. The effective thickness is derived by using normalized waveguide parameters. An analytical method is then proposed to calculate the universal effective thickness. We show that negative effective thickness exists in the waveguide with a LHM substrate, unlike in conventional waveguide or other LHM waveguides studied previously. However, for the waveguide with a LHM substrate, the shape of high-order mode behaves like that of a traditional slab waveguide, and neither the fundamental mode nor the other higher order modes have the novel phenomena of negative effective thickness. Both TE and TM modes are discussed.     

Power Absorption Efficiency in Superconducting Box-Shaped Optical Waveguides

A very sensitive superconducting traveling wave photodetector made of a modified box-shaped waveguide, which includes two high index layers and an active superconducting layer, is studied. The optical propagation constants and the power absorption efficiency for guided modes are determined using the finite element method; the results show that by acting only on the waveguide geometry, different confinement regimes of the light in the absorption superconducting layer can be achieved and optimized.     

Modal Characteristics of Five-Layered Slab Waveguides with Double-Clad Metamaterials

The guided modes are investigated in a five-layered slab waveguide with double claddings of metamaterials using a new graphical method. The dispersion equations in the symmetric and asymmetric five-layered slab waveguide are derived from the presented graphical method, and corresponding field distributions are plotted for the oscillating guided and surface guided modes. The energy flux distribution along the axis is plotted for the surface TE₁ mode.     

Integration of micrometer-sized polymer elements at the end of optical fibers by free-radical photopolymerization

A simple method of manufacturing micrometer-sized polymer elements at the extremity of both single-mode and multimode optical fibers is reported. The procedure consists of depositing a drop of a liquid photopolymerizable formulation on a cleaved fiber and using the light that emerges from the fiber to induce the polymerization process. After exposure and rinsing a polymer tip is firmly attached to the fiber as an extension of the fiber core. It is shown that the tip geometry can be adjusted by the variation of basic parameters such as the geometry of the deposited drop and the conditions of drop illumination. When this process is applied to a multimode fiber three-dimensional molds of the fiber's linearly polarized modes can be obtained. The process of polymer-tip formation was simulated by a numerical calculation that consisted of an iterative beam-propagation method in a medium whose refractive index is time varying. It is shown that this process is based on the gradual growth, just above the fiber core, of an optical waveguide in the liquid formulation. Experimental data concerning two potential uses of the tipped fibers are presented.