Fundamental Mode Field Research Articles

Accurate prediction of the propagation characteristics of single-mode graded-index fibers by a novel approximation of the fundamental modal field

We propose a novel approximation of the fundamental modal field in single-mode graded-index fiber and present a variational analysis to investigate the propagation parameters of practical interest. Employ- ing the formulated fundamental modal field, we prescribe analytical ex- pressions for normalized Petermann I spot size, group delay, and modal dispersion parameter for single-mode graded-index fiber. With the ex- amples of step- and parabolic-index fibers, we show that these param- eters as evaluated by our formalism match excellently with the available exact ones over a wide range of V values. Particularly in the low V region, where the Gaussian approximation is not accurate, our results are found to predict the propagation characteristics accurately. Thus the validity of our formalism is justified. Much less computation is required than with previous methods. The approximation will be useful in the analysis of nonlinear and doped-fiber amplifiers. © 2002 Society of Photo-

Approximate analytical description for fundamental-mode fields of graded-index fibers: beyond the Gaussian approximation

An approximate analytical description for fundamental-mode fields of graded-index fibers is explicitly presented by use of the power-series expansion method, the maximum-value condition at the fiber axis, the decay properties of fundamental-mode fields at large distance from the fiber axis, and the approximate modal parameters U obtained from the Gaussian approximation. This analytical description is much more accurate than the Gaussian approximation and at the same time keep the simplicity of the latter. As two special examples, we present the approximate analytical formulas for the fundamental-mode fields of a step profile fiber and a Gaussian profile fiber, and we find that they are both highly accurate in the single-mode range by comparing them with the corresponding exact solutions.

A Simple Method for Studying Single-mode Graded Index Fibers in the low V Region

Based on a simple series expansion method involving Chebyshev technique, we predict the cladding decay parameter (W) and the fundamental modal field inside the core as well as cladding in case of single-mode graded index fiber in the low normalised frequency (V) region. The method involves formulation of linear relationship of K 1 (W)/K 0 (W) with 1/W for a few intervals of W, where W < 0.6. With examples of step and parabolic index fibers we show that said predictions by our simple formalism agree excellently with the available exact results. Thus the accuracy of our formalism is established.

Analytical approximations for fundamental-mode field and dispersion equation of planar waveguides through the Stevenson-Pad� approach

Analytical approximations for fundamental-mode field and dispersion equation of planar waveguides through the Stevenson-Pad� approach

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.

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

Analysis of Fundamental Modal Field Excitation and Confinement in Single-mode Graded-index Fibers Involving a Novel Simple Function

Article Analysis of Fundamental Modal Field Excitation and Confinement in Single-mode Graded-index Fibers Involving a Novel Simple Function was published on October 1, 1998 in the journal Journal of Optical Communications (volume 19, issue 5).

Variational analysis of single‐mode graded‐index fibers based on a novel approximation of the fundamental modal field

Gautam DasS. N. SarkarUniversity of CalcuttaDepartment of Electronic ScienceCalcutta 700 009, IndiaE-mail: sns@cucc.ernet.inAbstract. A novel and extremely accurate near Gaussian approxima-tion for the fundamental mode in single-mode fibers having arbitrary in-dex profiles is proposed and verified by the variational method. The spotsize calculated from our approximation matches closely the analyticaland exact numerical results for step and parabolic index fibers over alarge range of values of the normalized frequency V. For the low Vregion where the Gaussian approximation is not accurate, our results aresuitable to accurately predict the propagation characteristics of devicessuch as directional couplers involving evanescent field coupling.

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.

Variational analysis of single-mode graded-core W-fibers

A new trial function is proposed to obtain the propagation constant, the normalized group delay, and the modal dispersion parameter of single-mode graded-core W-type fibers. This function uses only simple elementary functions to approximate the fundamental modal fields. In many cases of study, we show that the present trial function gives a significant improvement over the existing trial functions and is very useful in the analysis of fibers and related devices.

A theoretical study of a Ti-diffused Er:LiNbO/sub 3/ waveguide laser

A detailed theoretical procedure of determining the mode sizes of fundamental mode field distribution in a coaxially pumped Ti-diffused Er:LiNbO/sub 3/ waveguide laser has been described. The mode sizes, effective refractive indexes, effective pump area, and coupling efficiency as a function of the initial Ti stripe width W were numerically calculated for the waveguide with 95- and 100-nm initial Ti stripe thicknesses, respectively. The results indicated that the threshold pump power is severely affected by the stripe width, while slope efficiency is hardly changed as W; both show little difference between 95- and 100-nm stripe thickness. In addition, the stimulated emission cross section of Er/sup 3+/ in Er:LiNbO/sub 3/ channel waveguide versus the wavelength were calculated directly from its fluorescence spectra using the /spl beta/-/spl tau/ method. Subsequently, threshold pump power and slope efficiency were evaluated.

A novel waveguide Mach-Zehnder interferometer based on multimode interference phenomena

A novel form of Mach-Zehnder interferometer based on multimode interference (MMI) phenomena in multimode waveguides is predicted and demonstrated. The interferometer is based on symmetrically feeding fundamental mode fields from two square waveguides, 2 a×2 a, in cross section, into a multimode rectangular guide, 2 a×2 b, ( b > a). As a result of multimode interference phenomena, depending on whether the input fields are “in” or “out of” phase, two completely different forms of resultant field pattern are produced at a distance of 2 b 2/λ c, along the multimode guide. The predictions are verified experimentally at 10.6 μm with hollow dielectric guides, but the underlying design concepts are considered to be much more broadly applicable.

Extended Gaussian approximation for single-mode graded-index fibers

A new trial function which extends the generalized Gaussian method for the study of weakly guiding single-mode fibers is presented. This function uses only simple elementary functions to approximate the fundamental modal fields. In many cases of study, we show that the present trial function gives a significant improvement over the existing trial functions, and it is very useful in the analysis of fibers and related devices. >

Calculation and minimization of transition losses in arbitrarily curved waveguides

Presented is a formula for calculating transition losses for arbitrary deviations from a straight line path of an otherwise uniform single-moded waveguide. The formula is not restricted to any particular index profile and utilizes only two parameters of the fundamental mode field. Using it several methods for minimizing transition losses in bent waveguides are investigated and their degree of effectiveness is predicted.

Effects of nonlinear mode field changes in optical switching using directional couplers

In nonlinear applications of waveguide couplers the nonlinear effect on the fundamental mode field is usually quite small. Hence it is generally believed that nonlinear effects in such applications can be analyzed accurately even though the nonlinear modal shape changes are neglected. However, we show that, even in devices with small nonlinear coefficients or low intensities, the nonlinear modal shape change can be significant in the application of nonlinear waveguide couplers to all-optical switching.

Waveguide beam splitters and recombiners based on multimode propagation phenomena

Novel waveguide beam splitters and recombiners based on multimode propagation phenomena in hollow step-index waveguides are predicted and demonstrated. The splitter designs are based on symmetrically feeding the fundamental-mode field from a square cross-section waveguide, 2a × 2a, into a multimode rectangular guide, 2a × 2b (b &gt; a). As a result of multimode superposition phenomena, unique transverse-field patterns representing different-order multiway splitting of the input field occur at predictable positions along the rectangular-guide axis. The predictions are verified experimentally at 10.6 μm with hollow dielectric waveguides but are considered to be more widely applicable.

Analytical expressions of the guided mode field distribution: analysis and comparison

Methods for determining the parameters of the three different approximate solutions for the fundamental mode field distribution of Ti:LiNbO/sub 3/ optical waveguides by using the variational technique are presented. This analysis gives closer approximation not only to the field distribution, but also to the propagation constant. Comparison with the exact results for the exponential index distribution in depth shows that these trial functions are closer to the real solution. It is also shown that these solutions are as accurate as the effective index method for Ti:LiNbO/sub 3/ strip waveguides. The analysis provides an approach for comparing and assessing these solutions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Generalized Gaussian approximation for single-mode fibers

A variational method is presented that generalizes well-known Gaussian method for single-mode fibers. This method uses only simple elementary functions to approximate the fundamental mode fields. By applying it to practical cases such as step index and clad parabolic index fibers, where exact solutions can be found, it is demonstrated that the method is essentially simple and that it is accurate for the analysis of single-mode fibers and devices. This approximation provides much better eigenvalues and, in particular, evanescent fields than the traditional Gaussian. Significantly, the present approximation's range of applicability covers the whole single-mode range, while being only slightly more complicated than the modified Gaussian method. >

Far-from-core Field of Bound Modes on Non-circular Weakly Guiding Optical Waveguides

The principal behaviour of the far-from-core fields of bound modes on non-circular weakly guiding optical waveguides with infinite uniform cladding is investigated. The field function can be split into a purely radial factor, decaying nearly exponentially with the distance from the core similarly to the fundamental-mode field on circular fibres, and a purely azimuthal factor, which retains its shape at all large distances. However, the relative non-circularity of the field vanishes at infinity. Coupling coefficients for parallel waveguides are calculated from two-dimensional Gaussian approximations for the fields and the refractive-index distributions.

Influence of field shape change in nonlinear fibre couplers

In the usual analysis of optical waveguide couplers for alloptic switching, the nonlinear influence on the fundamental mode field shape is neglected. Using an accurate approximation method, the nonlinear modal field effect in these couplers is investigated. It is found that the nonlinear mode field effect can be significant, and that it should be considered in the analysis and design of nonlinear waveguide couplers.