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.     

Metal-covered photonic bandgap multilayer for infrared hollow waveguides

Infrared hollow waveguides utilizing a dielectric multilayer are examined by use of a photonic bandgap theory. It is shown that, in the waveguide consisting of quarter-wave film stack, the act of covering the dielectric films with a metal layer is effective in the reduction of the number of film layers. To verify the effect of this design, we fabricated a prototype waveguide with three dielectric layers of SiO2/Ta2O5/SiO2 and a silver layer by using a liquid-phase coating technique. From the loss spectrum of the fabricated waveguide, it is confirmed that, as designed, the waveguide shows wideband low-loss property at the wavelength of Nd:YAG laser light 1.06 microm.     

Characteristic analysis of absorptive multiple-quantum-well optical waveguides

Abstract

By extending the transfer matrix technique from the real domain to the complex, the complex eigenvalue equation is presented for both transverse electric and transverse magnetic modes of absorptive multiple-quantumwell optical waveguides, and a computer program is developed to solve the eigenvalue equation in the complex plane. On the basis of the computed results, the effects of the structural parameters and the refractive index profile on the mode propagation and loss properties are analysed and discussed for In^x Ga^1?xAs/Al^yGa^1?yAs absorptive multiple-quantum-well optical waveguides. The results indicate that, if approximate guided structural parameters and an appropriate refractive index profile are selected, higher-order modes can be controlled and single-mode propagation can be realized in the multiple-quantum-well optical waveguide with lower mode loss.     

Vectorial modal analysis of dielectric waveguides based on a coupled transverse-mode integral equation. II. Numerical analysis

We present numerical implementation and verification of a rigorous full-vector, integral-equation formulation suitable for analyzing modal characteristics of complex, two-dimensional (2D) rectangular-like dielectric waveguides. By dividing the waveguide into vertical slices, a system of integral equations we call vector-coupled transverse-mode integral equations (VCTMIE) is derived. The entire electromagnetic mode fields are completely determined by one-dimensional unknown field functions on the slice interfaces. To further reduce numerical computation, we expand these functions in terms of the guiding modes of a slab waveguide with a large normalized frequency. Through orthogonal projection the resulting nonlinear eigenvalue and eigenvector matrix formulation enables us to obtain the effective mode index with 10(-7) precision and to compute with high resolution the 2D vectorial mode field solutions of an open dielectric waveguide. We show stable and speedy convergence of our method as well as techniques to overcome the Gibbs phenomenon in the reconstruction of the transverse fields.     

包含左手介质的4层平板波导的转移矩阵和模式本征方程

研究了一个芯子层由左手介质构成、其他3层由普通介质构成的4层平板光波导系统。从波动方程出发,根据电磁场的边界条件,得到了TE波的转移矩阵和模式本征方程,并用图解法对这种左手介质4层平板波导中TE波的场分布分别进行了数值模拟。     

Waveguide analysis of organic light-emitting diodes fabricated on surfaces with wavelength-scale periodic gratings

Numerical techniques for the analysis of multilayer waveguide structures were used to study the modes that exist in organic light-emitting diode (OLED) devices. The analysis revealed that waveguide modes of the OLED structure could be grouped, according to the behavior of modal-field profiles in the air cover and the glass substrate, into one of four different "families": (i) bound mode, (ii) semibound modes, (iii) leaky modes, and (iv) nonphysical modes. Four different OLED samples were fabricated on glass substrates on which photoresist gratings had been previously formed. The theory was used to compute the angles at which light from these devices should exit into the air. Theory and data agreed well for the semibound modes for all samples; however, they did not agree so well for the leaky modes. Further investigation revealed that better agreement between theory and data could be obtained with these modes being analyzed as Fabry-Perot cavity modes. The theoretical relation between leaky waveguide modes and Fabry-Perot cavity modes is discussed.     

Vectorial modal analysis of dielectric waveguides based on a coupled transverse-mode integral equation. I. Mathematical formulation

We propose a rigorous full-vector integral-equation formulation for analyzing modal characteristics of the complex, two-dimensional, rectangular-like dielectric waveguide that is divisible into vertical slices of one-dimensional layered structures. The entire electromagnetic mode field is completely determined by the y-component electric and magnetic field functions on the interfaces between slices. These interfacial functions are governed by a system of vector-coupled transverse-mode integral equations (VCTMIE) whose kernels are made of orthonormal sets of both TE-to-y and TM-to-y modes from each slice. To solve for the unknown functions, we construct sets of suitable expansion functions and turn VCTMIE into a nonlinear matrix equation via orthogonal projection. The eigenvectors of the matrix provide the mode field solutions of the complex dielectric waveguide.     

Grating-coupled surface plasmon polaritons and waveguide modes in a silver-dielectric-silver structure

A silver-dielectric-silver structure that supports both waveguide modes and surface plasmon polaritons is explored. The upper interface between the dielectric and the silver is periodically corrugated to allow coupling of visible photons to both types of mode. Such a metallic microcavity leads to plasmonic and waveguide self-interacting bandgaps at Brillouin zone boundaries. In addition there are found other bandgaps from mode crossings within the Brillouin zone. This results specifically in a very flat photonic band due to anticrossings between a surface plasmon polariton and waveguide modes. Characterization of the observed modes in terms of their resonant electromagnetic fields is achieved by using a multilayer, multishape differential grating theory.     

Long-range surface plasmon polariton waveguides embedded in fluorinated polymer

Low-attenuation waveguides based on the propagation of long-range surface plasmon polaritons (LRSPPs) along thin Au stripes embedded in low absorption perfluorocyclobutane (PFCB) polymer are presented. A new low in propagation loss of <2.0 dB/cm was achieved for a 4 microm wide waveguide by optimizing the cladding material and fabrication process. The coupling efficiency between the LRSPP waveguide and the optical fiber is studied theoretically and experimentally for different widths of Au stripes and various cladding thicknesses. Lower coupling loss is found when the cladding thickness is close to the mode diameter of the butt-coupled fiber. Based on the 2D distribution of SPP modes calculated by a finite-difference mode solver, a symmetric structure of multilayer claddings with different refractive indices is proposed to optimize device insertion loss.     

Generalized matrix method for analysis of coherent and incoherent reflectance and transmittance of multilayer structures with rough surfaces, interfaces, and finite substrates

A generalized matrix method is presented for calculating the optical reflectance and transmittance of an arbitrary thin-solid-film multilayer structure on very thick substrates with rough surfaces and interfaces. We show that the effect of roughness and the influence of incoherently reflected light on the back side of a thick layer can be accounted for with a more general transfer matrix that enables the inclusion of modified complex Fresnel coefficients. Coherent, partially coherent, and incoherent multiply reflected light inside the multilayer structure is treated in the same way. We demonstrate the method by applying it to simulated and experimental reflectance spectra of thin epitaxial Si overlayers on very thick SiO(2) substrates and on a separation by ion implantation of oxygen structure with a SiO(2) buried layer exhibiting substantial roughness on both of its interfaces (Si/SiO(2) and SiO(2)/Si).     

Theoretical analysis of hollow ring-core optical fibre for transmitting orbital angular momentum modes

Ring-core optical fibre has been successfully demonstrated to have good performance for lifting mode degeneracy, and maintaining orbital angular momentum (OAM) modes in the first radial order, making it promising for applications of OAM mode multiplexing and generation of cylindrical vector beams. The degeneracy lift can be intensified using a hollow ring-core fibre, i.e. when the innermost layer of waveguide is air. The cut-off ring thickness for supporting the lowest OAM modes in radial order are obtained under various refractive index differences between the transport layer and the cladding. To optimize the design, our analysis addresses the dependence of modal properties on the fibre structure parameters, such as the effective area (A_eff) of respective OAM mode, and the differential mode delay.     

Analysis of general multi-channel planar waveguides

Using the planar waveguide concept in surface acoustic wave (SAW) technology is often advantageous when the modeling of transversely distributed phenomena is indispensable for an accurate design of SAW devices. This is especially true when complex multi-track structures such as transversely coupled resonator filters (TCRFs) are under consideration where, e.g., transverse velocity and stiffness profiles have to be incorporated in the device simulation. The interdigital transducers (IDTs) and the reflector gratings composing those devices behave as planar waveguides, supporting, in principle, all kinds of modes such as bound, semi-bound, and radiation modes. Therefore, to model these SAW propagation effects, we subdivide the SAW structures in transverse direction into several parallel waveguiding channels (N regions), and take, as the wave-describing quantity, a two-dimensional scalar potential function. By doing so, we obtain a complete set of orthonormal modes into which an arbitrary transverse excitation function can be expanded to study its propagation. The general mode spectrum includes a discrete spectrum of bound modes and continuous spectra of semi-bound and radiation modes. We calculate all types of modes by making use of the stack matrix technique. The present work, which arose from the requirement of creating an efficient mathematical tool for the simulation of TCRFs, provides the complete analysis of general SAW multi-channel structures.     

Modulation of Cathodoluminescence by Surface Plasmons in Silver Nanowires

The waveguide modes in chemically-grown silver nanowires on silicon nitride substrates are observed using spectrally- and spatially-resolved cathodoluminescence (CL) excited by high-energy electrons in a scanning electron microscope. The presence of a long-range, travelling surface plasmon mode modulates the coupling efficiency of the incident electron energy into the nanowires, which is observed as oscillations in the measured CL with the point of excitation by the focused electron beam. The experimental data are modeled using the theory of surface plasmon polariton modes in cylindrical metal waveguides, enabling the complex mode wavenumbers and excitation strength of the long-range surface plasmon mode to be extracted. The experiments yield insight into the energy transfer mechanisms between fast electrons and coherent oscillations in surface charge density in metal nanowires and the relative amplitudes of the radiative processes excited in the wire by the electron.     

Artificial anisotropy and polarizing filters

The calculated spectral transmittance of a multilayer laser mirror is used to determine the effective index of the single layer equivalent to the multilayer stack. We measure the artificial anisotropy of photoresist thin films whose structure is a one-dimensional, subwavelength grating obtained from interference fringes. The limitation of the theory of the first-order effective index homogenization is discussed. We designed normal-incidence, polarizing coating and a polarization rotator by embedding anisotropic films in simple multilayer structures.     

Infinite guided modes in a planar waveguide with a biaxially anisotropic metamaterial

We investigate in detail the guided modes in a two-layered planar waveguide where one layer is filled with an ordinary right-handed material (RHM) and the other is filled with a biaxially anisotropic metamaterial. We show that the mode properties are closely dependent on the spatial dispersion relation of the anisotropic medium. When the dispersion equation for the anisotropic medium becomes a two-sheet or a one-sheet hyperbola type, an infinite number of guided modes can be supported simultaneously in the waveguide, which is completely different from the cases of RHM and isotropic metamaterial. We also investigate the mode distributions of the planar waveguide in the lossy case, where we discover that the dominant mode in the waveguide is a forward wave while the higher-order modes are backward waves under the two-sheet hyperbolic dispersion. Numerical results validate our theoretical analysis.     

Tunable wakefield waveguide structure with the possibility of mode selection

The possibility to control the frequency spectrum of Cherenkov radiation in a microwave wakefield dielectric waveguide with the aid of an external ferroelectric layer has been studied. Using the proposed multilayer waveguide structure in combination with a special configuration of control electrodes, it is possible both to adjust the wake field frequency spectrum and to attenuate the modes corresponding to beam-deflecting (defocusing) fields in the waveguide.     

Analysis of characteristics of bent rib waveguides

With a perfectly matched layer boundary treatment, a semivectorial finite-difference method is used to calculate the eigenmodes of a single-mode (SM) or multimode (MM) bent rib waveguide. A detailed analysis is given for the dependence of the bending losses (including the pure bending loss and the transition loss) on geometrical parameters of the bent rib waveguide such as the rib width, the rib height, and the bending radius. The characteristics of the higher-order modes are analyzed. It is shown that the bending loss of the fundamental mode can be reduced effectively by increasing the width and height of the rib. For an integrated device, undesired effects due to the higher-order modes of a MM bent waveguide can be removed by appropriate choice of the geometrical parameters. An appropriately designed MM bent waveguide is used to reduce effectively the bending loss of the fundamental mode, and a low-loss SM propagation in a MM bent waveguide is realized when the bending losses of the higher-order modes are large enough.     

Recent developments in the design and fabrication of visible photonic band gap waveguide devices

In this paper, we present the design, fabrication and initial optical testing of dielectric waveguide devices which incorporate photonic crystals with photonic band gaps (PBG) in the visible region of the spectrum. In the design of our devices we use a full three-dimensional plane wave analysis to solve the photonic band structure simultaneously with the dielectric waveguide boundary conditions for a fixed lattice and waveguide geometry. This takes into account the finite thickness of the waveguide core, and the evanescent wave in the dielectric cladding layers. Furthermore, we explain how the effective Bloch mode index can be extracted from the results. This enables us to tackle important problems associated with mode coupling between the input waveguide and guided Bloch modes within the porous PBG region, such as Fresnel reflections at the interface and up-scattering from the holes. Finally, we present the recent fabrication of quasi-periodic photonic crystals and PBG waveguide bends.     

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.     

Development of interference filters based on multilayer porous silicon structures

Porous silicon (PS) has a great potential in optical applications due to its tuneable refractive index. In particular, multilayer structures consisting of alternating PS layers with different refractive indices can be used as interference filters for applications in the field of optoelectronics and sensors. In the present work, the optical properties of PS single layers and multilayer structures were studied. Since the refractive index of PS varies depending on the air content of the porous matrix, the PS structures were modelled as an homogeneous mixture of silicon and air, according to the effective medium theories (EMTs). By adjusting the refractive index and thickness of each individual layer, we can obtain a stack of PS layers with the desired optical properties, resulting in interference filters of predetermined bandwidth.