Computational modeling of diffused channel waveguides using adomain 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 HE₁₁ 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     

Modal analysis of strip-loaded diffused optical waveguides by a variational method

The propagating modes supported by strip-loaded three-dimensional diffused optical waveguides are analyzed in detail theoretically by using a variational method. Some typical numerical examples of the propagation constants and the field distributions are illustrated. The dependence of propagation characteristics on the geometrical parameters of the loading dielectric strip is discussed.     

A simple and accurate model analysis of strip-loaded opticalwaveguides with various index profiles

A simple first-order perturbation approach has been developed to study the propagation characteristics of strip-loaded diffused waveguides with various refractive index profiles. Propagation constants of the guided modes of rib waveguides and strip-loaded waveguides with exponential and Gaussian refractive index profiles are obtained. The results are in good agreement with those reported in the literature that were obtained by variational and numerical techniques. The presented technique provides analytical expressions for the modal field profile that should be useful in the design of various integrated optical devices     

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.     

Rigorous finite-difference analysis of coupled channel waveguideswith 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 element analysis of diffused anisotropic optical waveguides

Results are presented for anisotropic waveguides, with an arbitrary permittivity tensor, being diffused in both the transverse directions and by using the finite element method with the vector H-field formulation for the analysis. The importance of considering the waveguide core dimensions to be greater than the diffusion depth in both the transverse directions, the use of extrapolation techniques and of a symmetry plane for anisotropic waveguides are also discussed     

Iterative simplex-finite difference method for the characterizationof optical waveguides

A new method is presented for reconstructing smooth refractive index profiles of optical waveguides from measured effective indexes. It is based on the semivectorial finite difference method to solve the polarized wave equation for a given refractive index profile. An iterative simplex algorithm is used to find the best refractive index parameters that give, as a solution, effective indexes close to the measured ones. The method is applied successfully to Ag⁺-Na ⁺ ion-exchanged glass slab waveguides and to diffused Mg/Ti:LiNbO₃ slab waveguides. Dopant concentration profiles are obtained by using secondary ion mass spectrometry. The relationship between the refractive index change and the dopant concentration is determined for both cases. The iterative simplex algorithm-finite difference method (ISA-FDM) is compared to other index profile reconstruction methods, and the advantages with respect to WKB-based methods are pointed out     

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 onz-cut LiNbO3. 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 applicable2Deltan-waveguide supports four modes, which should make coupling characteristics very sensitive to input conditions.     

Error analysis for refractive-index profile determination fromnear-field measurements

Refractive-index profiles of diffused optical waveguides are determined by analyzing the near-field pattern of the waveguide. For this method, a computer simulation of measurement errors due to noise, quantization, defocusing, and nonlinearity of the camera system is presented by using data of a typical camera measurement system. The simulation procedure includes signal processing of the measurement intensity profile by means of a cubic spline approximation in order to reduce the influence of the measurement system errors. The residual errors associated with this technique are on the order of a few percent when measuring typical Ti:LiNbO₃ waveguides     

Transfer matrix function (TMF) for wave propagation in dielectricwaveguides with arbitrary transverse profiles

A transfer matrix function (TMF) is derived for the analysis of electromagnetic (EM) wave propagation in dielectric waveguides with arbitrary profiles, situated inside rectangular metal tubes. The TMF relates the wave profile at the waveguide output to the (arbitrary profile) input wave in the Laplace space. The TMF consists of the Fourier coefficients of the transverse dielectric profile and those of the input-wave profile. The method is applicable for inhomogeneous dielectric profiles with single or multiple maxima in the transverse plane. The TMF is useful for the analysis of dielectric waveguides in the microwave and the millimeter-wave regimes and for diffused optical waveguides in integrated optics     

铜离子交换单步掩埋BK7玻璃波导的制备与表征

利用Cu离子交换技术制备了BK7玻璃平面光波导,在6328nm波长下,用棱镜耦合技术测量出所制备波导的有效折射率,利用反WKB方法计算并确定了平面光波导的折射率分布,通过对折射率分布进行函数拟合,发现离子交换后的样品折射率分布近似符合改进后的高斯分布,样品的折射率分布似乎是一个掩埋波导的折射率分布,求出所制备玻璃平面光波导在570℃的扩散系数De≈12133×10-14m2s。同时,对所制备波导进行了电子显微镜(EMS)和次级离子质谱(SIMS)测试,得到了铜离子在玻璃表面的浓度分布,从而证明了实验所得到的BK7玻璃平面光波导是掩埋波导。这种掩埋平面波导是由单步Cu离子交换技术得到的。     

Numerical solution of silicon-clad diffused planar optical waveguides

Computer modelling studies indicate that silicon-clad diffused planar optical waveguides exhibit a damped periodic oscillation in their attenuation and phase constant curves and that the attenuation is reduced significantly by reducing the maximum index change.     

高斯折射率分布Cu+-Na+离子交换玻璃波导的制备

利用Cu+ Na+ 离子交换技术制备了玻璃平面光波导 ,在 6 32 8nm波长下 ,用棱镜耦合技术测量出所制备波导的有效折射率 ,利用反WKB方法确定了平面光波导的折射率分布 ,并对折射率分布进行了函数拟合 ,近似符合高斯分布。求出了所制备玻璃平面光波导在 5 80℃的扩散系数为De ≈ 2 2 2 3× 10 -15m2 /s。     

Phase space evaluation of distributed-index branching waveguides

In this paper, we propose a new evaluation concept for characterizing multimode optical branching waveguides. In a ray tracing to simulate multimode branching waveguides, we introduce a phase space expression with the ray position and slope in order to describe the modal distribution of guided light. We have applied this technique for branching waveguides, which have a parabolic distributed-index, and clarified branching characteristics. Experimental results obtained for diffused branching waveguides are compared with theory.     

Formation of lithium niobate-tantalate waveguides

Low loss diffused lithium niobate-tantalate waveguides exhibiting strong electrooptic coefficients have been made by a simple processing procedure. The formation of these waveguides takes place by the conversion of a Nb metal film to Nb oxide at a low temperature, followed by diffusion of Nb into the LiTaO₃ substrate at about 1100°C. The diffused layer has a Gaussxan composition profile. Its measured refractive index is consistent with that calculated by interpolation between the indices of LiNbO₃, and LiTaO₃. The research reported in this paper was jointly sponsored by the Office of Naval Research, Arlington, Virginia and RCA Laboratories, Princeton, New Jersey. This paper is based on a presentation at the Conference on Preparation and Properties of Electronic Materials, Boston, Massachusetts, September 1974.     

Direct index measurements of diffused channel waveguides

A nondestructive method is described for obtaining information about the refractive index profiles of diffused channel waveguides of the type used in integrated optics. The method assumes that the index profile can be approximated as a product of two functions each of which depends on one of the two transverse coordinates. By observing the focusing effect, which the waveguide has on collimated light passing through it transversely to its axis, the shape of the index profile in a direction parallel to the surface of the substrate can be obtained. From measurements of the reflection coefficients we obtain the refractive index at the upper surface of the waveguide. By combining the two measurements the effective depth of the waveguide can be calculated. Results of measurements on multimode and single-mode waveguides formed in glass and lithium niobate are presented.     

Modal analysis of step discontinuities in graded-index dielectricslab waveguides

The modal solutions of the TE- and TM-modes of an arbitrary graded-index dielectric slab waveguide have been derived by applying the generalized telegraphist's equations to the equivalent inhomogeneous parallel-plate waveguide model with electric or magnetic walls. These modal solutions have been employed in a mode-matching procedure to calculate the transmission properties of step discontinuities in arbitrarily graded-index dielectric slab waveguides such as diffused optical waveguides having exponential, Gaussian and complementary error-function index profiles. For slab waveguides containing an abrupt offset, the radiated power is found to increase smoothly with increasing displacement. Power loss calculations for an abrupt change in diffusion depth for which the dominant mode is in the vicinity of cutoff, exhibit a sharp transition from almost zero loss to nearly total radiation loss     

Electro-optically tunable wavelength demultiplexer using depressed index waveguides

A novel configuration of an integrated optical tunable wavelength demultiplexer with a stable channel spacing is proposed. The structure consists of a three-mode depressed index diffused waveguide with single-mode input and output waveguides. The refractive index depression has been designed using experimental data of double diffusion of MgO on Ti:LiNbO/sub 3/ waveguides. The BPM simulation of the structure supports the feasibility of the device and shows a good wavelength tunability.<>     

Diffused waveguides: mode perturbation by thin-film cladding

Normalised parameter plots are given enabling prediction of propagation-constant perturbation in diffused optical waveguides due to a thick dielectric cladding. Refractive-index profiles of Gaussian and complementary-error-function form are treated. The variation of the number of propagating modes with time of diffusion is derived.     

Modes in diffused optical waveguides of arbitrary index profile

A method is presented for numerical calculation of the phase constants of the modes of diffused optical waveguides of arbitrary index profile. For a given bulk and surface index, the phase constants can be plotted against diffusion depth. Graphs giving the number of modes supported by a guide with a particular diffusion depth and index change can also be calculated. Examples are given for complementary error function, Gaussian, and exponential profiles, with indices representative of metal-diffused LiNbO3guides. It is also shown that, by making certain approximations, the modes of a diffused waveguide may be described by just two quantities, a normalized diffusion depth and a normalized mode index. A single universal chart of these two quantities can be made for any diffusion shape, and all diffused guides with this diffusion shape are described by this chart. Charts are given for complementary error function, Gaussian, and exponential shapes. Careful measurement of effective mode indices of Ni-diffused LiNbO3guides fit the universal chart for a complementary error-function shape. A second type of universal chart for each shape relates the number of modes to the diffusion depth and indices of refraction.