Diffused Channel Waveguides Research Articles

Design of a lossy tunable wavelength demultiplexer utilizing MgO:Ti:LiNbO/sub 3/ depressed index waveguides

Design of an integrated optical tunable wavelength demultiplexer with a stable channel spacing is shown, utilizing software tools suitable for metal-clad diffused channel waveguides. The device, consisting on a three-mode depressed index waveguide with single-mode input and output waveguides has been designed using experimental data of double diffusion of MgO on Ti:LiNbO/sub 3/ waveguides. The BPM simulations show the feasibility of the device, the stable spectral behavior and the narrow separation between channels obtained. It is also shown that the buffer layer between electrodes and waveguides can be eliminated depending on the design parameters.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Wave propagation in integrated acoustooptical anisotropic waveguides

A system of coupled scalar wave equations is derived for anisotropic inhomogeneous media. Conditions of small index gradients, par-axial propagation and moderate anisotropy are used. The equations obtained serve as a basis for a beam propagation method (BPM) algorithm in anisotropic media. The anisotropy slightly modifies the dispersion characteristics of diffused channel waveguides. The BPM algorithm is tested by application to Ti indiffused waveguides in LiNbO3, the principal axes of which are declined against the laboratory coordinate system about an arbitrary angle. Very good agreement with results obtained from a plane wave analysis is confirmed. The method is applied to a combined collinear acoustooptical waveguide with transverse and longitudinal variation of one off-diagonal element of the permittivity tensor. Coupling to radiation modes occurs for sufficiently high off diagonal elements.

An accurate variational analysis of single-mode diffused channel waveguides

We present a procedure based on the variational principle to obtain the modal propagation characteristics of single-mode diffused channel waveguides with arbitrary index profiles. The only assumption in our method, in addition to the scalar approximation, is that the trial field is separable along the depth and the width directions. The method is iterative, with each cycle of iteration requiring the solution of two planar waveguide propagation problems. The convergence is usually achieved within 2–3 cycles of iteration. Comparisons with other methods show that our method gives much better accuracy.

Modeling of Ti:LiNbO/sub 3/ waveguide directional couplers

A simple and accurate method is presented for studying the coupling characteristics of 3D diffused channel waveguide directional couplers. The method is based on the scalar variational principle and differs from other methods as it does not require any assumption for the functional form of the trial field. The authors also propose an equivalent 2D directional coupler that also gives accurate results and, hence, saves considerable computational time, Comparison with experimental and other theoretical results is also presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Rigorous finite-difference analysis of coupled channel waveguides with arbitrarily varying index profile

A rigorous finite-difference formulation for the hybrid-mode analysis of coupled diffused dielectric channel waveguides is presented. The method includes the two-dimensional continuous index profile variations directly in the finite-difference form of coupled equations and avoids the shortcomings inherent in the usual staircase approximations. The formulation in terms of the wave equation for the transverse components of the magnetic field leads to an eigenvalue problem where the nonphysical, spurious modes do not appear. The analysis includes the complete set of hybrid-modes, takes mode-conversion effects and complex waves into account, if they exist, and allows the calculation of dielectric channel waveguides with large index difference levels. Dispersion characteristic examples are calculated for coupled structures suitable for optical integrated circuits. The theory verified by comparison with results available from other methods. >

Finite-difference method without spurious solutions for the hybrid-mode analysis of diffused channel waveguides

Diffused dielectric channel waveguides with an arbitrarily varying refractive index profile in the cross-sectional plane are analyzed with a rigorous finite-difference method. The method is formulated in terms of the wave equation for the transverse components of the magnetic field. This leads to an eigenvalue problem where the nonphysical, spurious modes do not appear. The analysis includes the complete set of hybrid modes, takes mode-conversion effects and complex waves into account, and allows the immediate inclusion of large index difference levels as well as the two-dimensional continuously varying index profile function without the usual staircase approximation. As an example, dispersion characteristics are calculated for structures suitable for millimeter-wave and optical integrated circuits, such as channel waveguides with refractive index variations having stepped, linear, Gaussian, and exponential function profiles. The theory is verified by comparison with results available from other rigorous methods.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Computational modeling of diffused channel waveguides using a domain integral equation

A domain integral equation is proposed for the computational modeling of diffused channel waveguides. In the modeling the propagation properties and the field distributions of the lower order guided modes are computed. The method is used to design the channel waveguides that are realized by an ion-exchange process in glass substrates. In particular, the method is applied to the design of ion-exchanged waveguides with low fiber/chip coupling losses. The aim is to realize modal distributions in the channel waveguides that closely match the rotationally symmetric field distributions of the HE/sub 11/ fiber mode. Some technological aspects of the realization of such ion-exchange waveguides are indicated, and various numerical results relevant to the design process are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Effect of annealing on diffused channel waveguides

Mode size measurements of the Ag(+)-Na(+) ion-exchanged channel waveguides in BK7 glass show a square root dependence on the annealing time in contrast to the linear variation predicted in the literature.

Approximate analysis of mode dispersion in diffused-channel waveguides

We propose an approximate mode analysis using the effective index method for calculating mode dispersion in diffused channel waveguides. The method uses the minimum computing time and gives good agreement with other published results.

Insertion loss reduction between single-mode fibers and diffused channel waveguides

Methods of reducing the insertion loss between single-mode fibers and graded-index channel waveguides, namely, annealing and backdiffusion, are analyzed theoretically and compared. Mode mismatch and misalignment losses are calculated to determine the best method and the optimal conditions for their use. The main result of this paper is that, in the single-mode regime, there is no apparent advantage in using backdiffusion instead of the simpler annealing process, in contrast with the multimode case. In the coupling loss calculation, a numerical simulation of waveguide formation by potassium-sodium ion exchange in glass is used for illustration.

Scalar finite element analysis of electrooptic modulation in diffused channel waveguides and poled waveguides in polymer thin films

Electrooptic modulation with diffused channel waveguides is analyzed by utilizing the approximate scalar finite element approach developed for anisotropic asymmetric slab waveguides. The interaction of the applied electric fields with the optical fields is calculated over the 2-D finite element mesh, and the direct calculation of the waveguide eigenmodes provides the electrooptic changes in the propagation wavenumbers. Applications of this simplified finite element approach to arbitrary index profiles and fields are illustrated for both titanium-indiffused LiNbO(3) and poled waveguides in polymer thin films.

Analysis of propagation characteristics of diffused channel waveguides: weighted residual method

Using the weighted residual method, formulas for calculating the propagation constant and field distributions of diffused channel waveguides are derived. The results obtained are more accurate than those of Marcatili’s method and agree well with those of the finite-element method.

Analysis of optical waveguides and some discontinuity problems

In the paper, using the vector H-field finite element method, we obtain new results for the solution of diffused channel waveguides, the effect of electrodes and buffers for rib waveguides, and the calculation of coupling length for a directional coupler. We also present solutions of discontinuities for optical waveguides by combining the vector finite element method and least-square boundary residual methods. Some basic discontinuity steps, such as vertical misalignment, change of width, and change of rib height for rib wave-guides are illustrated here.

Guided Mode Characteristics of Metal-Clad Planar Optical Waveguides Produced by Diffusion (Short Paper)

Analytical and numerical results for the guided mode characteristics of metal-clad planar waveguides produced by diffusion are developed. Values of the complex propagation constants are obtained numerically and are shown to be in good agreement with the analytical results. These give insight into how waveguide and material parameters determine the loss. Since the profile of the waveguide represents the variation of the refractive index of the diffused-channel waveguide with the depth dimension, the results obtained can be used to reduce the dimensionality of the diffused-channel waveguide and facilitate the application of the effective-index method.

An analysis of intersecting diffused channel waveguides

The coupling characteristics of intersecting diffused channel waveguides are computed for realistic three-dimensional diffusion profiles by means of the propagating beam method (PBM). Both TE and TM polarizations are treated for waveguides formed on z -cut LiNbO 3 . Good agreement between computed and previously reported measured results is found for the TE polarization. Agreement between computed and measured results is not as good for the TM polarization. This is explained by the fact that the applicable 2\Deltan -waveguide supports four modes, which should make coupling characteristics very sensitive to input conditions.

3-D analysis of LiNbO3: Ti channel waveguides and directional couplers

An efficient method of calculation of effective refractive indexes and field distribution of guided optical modes in diffused channel waveguides and directional couplers is presented. Refractive index distribution which follows from the theory of two-dimensional anisotropic diffusion is considered. Experiments which relate the refractive index profile with fabrication parameters are described. Then the coupling length of a directional coupler can be calculated from the fabrication parameters. The results correspond well to recently published experimental data.

Finite-element solution of integrated optical waveguides

A vector <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</tex> -field finite-element method has been used for the solution of optical waveguide problems. The permittivity of the guiding structures can be an arbitrarily tensor, only limited to being lossless. To extend the domain of the field representation, infinite elements have been introduced. To eliminate spurious solutions and to improve eigenvectors, a penalty function method has been introduced. To show the validity and usefulness of this formulation, computed results are illustrated for step channel waveguide, diffused channel waveguide, anisotropic channel waveguide, and channel waveguide directional couplers.

Exact numerical solution for the diffused channel waveguide

We present an exact numerical solution based on a vector integral equation to investigate the diffused channel waveguide. Various examples are given and compared with other numerical and approximate methods. An approximate numerical solution is also given using the effective index method and the integral equation solution for the inhomogeneous slab.

Investigation of an interference modulator based on a multimode channel waveguide in LiNbO3

The parameters of diffused channel waveguides in Y-cut LiNbO3 were determined and the mode field distributions were calculated. Various operating conditions in an interference modulator were analyzed and the values of the control voltage were determined as a function of the distance between electrodes.

Interferometric method for measuring diffused channel waveguide-index profile

An interferometric method for measuring the distribution of refractive-index change in diffused channel waveguides is described. It is based on Young's fringes generated by the interference between a point light source and its reflection from the surface of the waveguide substrate and requires the same experimental arrangement as that used for end-fire coupling. The technique allows a nondestructive measurement of the surface-index change and the lateral dependence of the index distribution if the depth diffusion constant and the diffusion time are known. When used in conjunction with successive removal of substrate layers, the method can in theory be used to measure both the depth and lateral dependencies. Experimentally measured surface-index changes and lateral dependencies of index change distributions in 5-, 9-, and 21-microm wide channel waveguides fabricated by diffusion of 195- and 390-A thick Ti films into Z-cut LiNbO(3) for 6 h at 1000 degrees C are given. Maximum surface ordinary index changes were 4.2 x 10(-3) and 8.5 x 10(-3) for the two Ti thicknesses. Measured lateral dependencies agree with the theoretical sum of error function profiles calculated using a lateral diffusion coefficient of 1.0 x 10(-12) cm(2)/sec.