Mode Field Profiles Research Articles

Surface plasmon polaritons in metal stripes and wires.

Surface plasmon polaritons (SPPs) are collective electron oscillations coupled to a light field which are propagating along the interface of a metal and a dielectric. As a surface wave, SPP modes feature properties essentially different from light-field modes in all dielectric structures. These properties could allow the realization of novel photonic devices that overcome certain limitations of conventional devices. Specifically, the realization of two-dimensional optics and light-field transport in sub-wavelength SPP waveguides seems feasible. In this review we discuss recent experimental advances regarding SPP waveguides, i.e. laterally confined metal thin films that guide SPPs. Electron-beam lithography is applied to tailor these films with widths ranging from a few micrometres (stripes) to nanoscopic values (wires). We investigate SPP properties such as propagation length, mode field profile and reflection or scattering at interfaces. Various techniques for SPP excitation and detection are discussed.

Gaussian and Sech Approximations of Mode Field Profiles in Photonic Crystal Fibers

We propose using the least square method for approximating the electrical field distribution of the fundamental mode in photonic crystal fibers (PCFs) by using a Gaussian and a hyperbolic-secant (sech) function. It is shown that the mode field can be fitted closely to a Gaussian for large d//spl Lambda/ values (i.e., for strongly guiding structures). For small d//spl Lambda/ values (for weakly guiding structures), a sech function fits the mode field well because the field gradually extends into the cladding region, implying that the analogy of PCFs with step index fibers is not applicable in this regime.

Guiding Properties of a Tapered Photonic Crystal Fiber Compared with Those of a Tapered Single-Mode Fiber

We have fabricated tapered photonic crystal fibers using a fusion splicer and experimentally observed the near-field mode distribution and the beam divergence of it. We have also compared characteristics of the tapered photonic crystal fiber with those of a tapered standard single-mode fiber. Unlike a tapered standard single-mode fiber, the mode field profile of a tapered photonic crystal fiber shows a good confinement of its field within the core region. The numerical apertures of tapered photonic crystal fibers are increased as the diameter of the fiber is decreased.

Improved AWG Fourier optics model

In this paper we present an improved Fourier Optics model to calculate the transmission characteristics between any arbitrary pair of input/output ports (IOPs) of an Arrayed Waveguide Grating (AWG). In this model the input and output sections of the AWG are modeled using the same approximations, thus removing some reciprocity-related inconsistencies present in previously existing models. The expressions which summarize the model are compact and easily interpretable. Simple quasi-analytical expressions are also derived under the Gaussian approximation of the mode field profiles.

Nanotaper for compact mode conversion.

We propose and demonstrate an efficient coupler for compact mode conversion between a fiber and a submicrometer waveguide. The coupler is composed of high-index-contrast materials and is based on a short taper with a nanometer-sized tip. We show that the micrometer-long silicon-on-insulator-based nanotaper coupler is able to efficiently convert both the mode field profile and the effective index, with a total length as short as 40 microm. We measure an enhancement of the coupling efficiency between an optical fiber and a waveguide by 1 order of magnitude due to the coupler.

Experimental observation of longitudinal modulation of mode fields in periodically segmented waveguides

We present what is to our knowledge the first experimental observation by fluorescent visualization, of the evolution of the mode field profile in a periodically segmented waveguide. The experimental observations are then compared with the numerical results obtained by a finite-difference beam propagation method. Good agreement between experimental and numerical results is observed.

A Comparison of Commonly-used Trial Functions in the Variational Analysis of Ti:LiNbO3 Channel Waveguides

Two common trial functions used in the variational method to solve the waveguiding modes of Ti:LiNbO 3 channel waveguides are compared in this paper. The first one has four parameters and the other has just two. The respective modal-field profiles described by them, as well as the respective fiber-to-waveguide coupling efficiencies estimated by these models, are rather different. We propose a self-consistent concept to examine the qualities of the trial fields and then show that the two-parameter model is better.

Mode profile modification of H + ion beam irradiated waveguides using UV processing

Buried channel waveguides made by a direct-write focussed hydrogen ion beam in high quality fused silica were investigated for mode and spectral changes under 193 nm ultra violet irradiation. The guides exhibited a negative index change of approximately 10% of the core cladding difference after a dose of 1 kJ cm −2, and an increase in attenuation at infrared wavelengths. This effect could have application in tailoring the shape of mode field profiles for efficient coupling between waveguides.

TM/TE modal solutions for submicron lossy metal-clad optical fibres

A finite-element approach with the aid of the perturbation technique is used to determine the complex propagation characteristics of lossy metal-clad optical fibres. The fundamental optical modal field profiles of these structures for the pure TE and TM polarisation are investigated. Metal-clad optical fibres of submicron dimensions find an important application in near-field optical scanning microscopy, a technique rapidly developing in recent years, providing high-resolution imaging in the semiconductor industry and in applications in the biological sciences.

Spot size expansion for improved OEIC-to-fibre coupling using directional couplers with 2D confinement

In optical fibre applications, by using an intermediate multiguide directional coupler section, this work has shown that the field profile of the source laser used can be expanded to match that of the receiving optical fibre. The vector H-field finite element method has been employed to determine the modal propagation constants and vector field profiles. An accurate calculation of the excited modal coefficients was achieved by using the least squares boundary residual method, which satisfies the continuity of the transverse field components more rigorously than through the use of the simple overlap integral approach.

FIBERS FOR OPTICAL SCANNING MICROSCOPES

A finite-element approach, with the aid of the perturbation technique, is used to determine the complex propagation characteristics of metal-clad optical fibers. Such structures of sub-micron dimension find an important application in near-field optical scanning microscopy, a technique which has been developing rapidly in recent years, providing high-resolution imaging in both the semiconductor industry and the biological sciences. The fundamental optical modal field profiles of these structures, suitable for optical scanning microscopy applications, for both TE and TM polarisations, are investigated

Theoretical studies of AlGaAs-GaAs multiple-quantum-well optical couplers defined by ion-implantation-induced intermixing

A simple and accurate model is presented for the analysis of ion-implanted AlGaAs-GaAs multiple-quantum-well (MQW) symmetric and asymmetric optical couplers. The modal propagation constants and field profiles of the guided modes of the couplers are solved numerically using a quasi-vector method based on the Galerkin's method. MQW optical couplers defined by ion-implantation-induced intermixing are shown to have similar optical properties as conventional dielectric rib optical couplers. They also provide a more flexible control over the waveguiding and coupling characteristics by changing parameters such as waveguide separation, mask width, ion implant energy, and diffusion time.

Quasi-exact optical analysis of oxide-apertured microcavity VCSELs using vector finite elements

We report a new full vector finite element model for analyzing the optical properties of azimuthally symmetric oxide-apertured vertical-cavity surface emitting lasers (VCSELs). Our model allows for quasi-exact calculation of the lasing mode blueshift, threshold gain, and field profile. Through a detailed analysis of a sample VCSEL, we ascertain the physical effects which determine diffractive or parasitic mode loss. They are: 1) the background density of parasitic modes and 2) the coupling strength between the lasing mode and the parasitic mode continuum. The coupling strength is in turn determined by the relative alignment between the lasing and parasitic mode propagation vectors and the lasing mode penetration into the oxide region. This analysis improves our understanding of the optical physics of apertured VCSELs and should enable the next leap down in lasing threshold.

Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides

Curved, single-mode, silicon oxynitride optical ridge channel waveguides have been characterized by measuring mode field profile alteration, bending loss, and transition loss. The results were compared to theoretical calculations. Near field imaging of the channel mode field profiles showed the effect of bend radius on mode shape. Good agreement was obtained between the measurements and profiles obtained from two-dimensional (2-D) beam propagation method calculations. The exponential dependence of bending loss on bend radius and the variation of transition loss on the lateral offset between channels having different bend radius were successfully modeled by two simple theories.

Local normal-mode analysis of second harmonic generation in a periodic waveguide

A new theoretical analysis method based on the local normal-mode expansion is proposed for analysis of optical second harmonic generation (SHG) under quasi-phase-matching in a waveguide with a periodic structure. Nonlinear coupled mode equations, SHG efficiency, and effective SHG coefficient are derived. In addition, SHG devices quasi-phase-matched with corrugation and with periodic domain inversion are studied analytically and numerically. The results are compared to those obtained by the conventional ideal normal-mode expansion. It is shown that in a corrugated waveguide the local normal-mode expansion method presents a different result from the ideal normal-mode expansion since the periodic variation of the modal field profile is dominant in the quasi-phase-matching process. On the other hand, in the periodically domain-inverted ferroelectric waveguide, it is shown that the variation of the modal field profile is sufficiently small and both expansion methods coincide with each other.

Accurate analysis of multimode interference devices

The accurate analysis of multimode interference devices is demonstrated by using the least-squares boundary residual (LSBR) method. Accurate modal propagation constants and spatial field profiles in the multimode interference (MMI) section can be obtained by using the finite-element method. The accurate calculation of the excited modal coefficients is achieved by using the LSBR, which satisfies the continuity of the transverse field components more rigorously than the simple overlap integrals.

Modal characteristics of graded multilayer optical waveguides

The modal characteristics of graded-step index multilayer planar waveguides for layer thicknesses down to those applicable for quantum well structures have been investigated here. The effects of linear grading of the transverse stepped refractive index profile have been evaluated in terms of the mode field profiles and the modal spectrum. The position of the maximum of the fundamental mode field profile can be moved toward the upper waveguide cladding/core interface with consequential increase in the evanescent field magnitudes.

A finite-difference frequency-domain method that introduces condensed nodes and image principle

A new finite-difference frequency-domain formulation is derived from the integral form of Maxwell's equations. Condensed cubic cell and 3D node are proposed thereby eliminating field discontinuity in the discrete space domain. Deterministic solutions using a reduced 2D condensed node are also presented for standard eigenvalue problems. This method is free from spurious modes by reinforcing electric and magnetic flux conservation among neighboring cells. An image concept is introduced to model field boundaries. Numerical results are presented for the complex propagation constant to demonstrate convergence behavior and accuracy of the proposed approach. Modal field profiles of various guided modes are shown for dielectric waveguides.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Near field measurement of fiber mode field diameters: effects of defocusing

An instrument has been built to measure the mode field profile of optical waveguides by the near field method. It incorporates a confocal microscope that allows accurate focusing of the waveguide end. The instrument has been used to measure the effect of defocus on measured fiber mode field diameters (MFD's). The amount of defocus must be less than a few micrometers if errors in the measured MFD are to be kept less than 0.1 /spl mu/m. Other focusing criteria can give errors of 2% or more. >

Analysis of rectangular waveguide-gratings for amplifier applications

A slow-wave structure composed of a grating inside a rectangular waveguide is analyzed. This type of slow-wave structure is examined for use in a low-voltage amplifier application with a sheet electron beam. Dispersion curves, mode field profiles, and taper designs for the waveguide-grating are presented. The amplifier application places stringent requirements on the taper sections that match the smooth waveguide to the waveguide-grating with minimal reflection.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>