Equivalent refractive index of MQW waveguides

In this paper, we have proposed some new numerical and semi-analytical methods for developing an equivalent three-layer model of an MQW waveguide. The waveguiding properties like effective index, field distribution, and fractional power within the core of the waveguide of these equivalent structures are compared with those of previously reported equivalent methods. These results are also compared with the results obtained from the exact multilayer analysis of the MQW waveguide. The waveguiding properties are accurately predicted by the semi-analytical method using variational analysis, and the computational effort is significantly reduced. The use of the three-layer equivalent is illustrated in obtaining an estimation of the waveguide losses and is used to study the effect of nonlinearity     

Evaluation of refractive index approximations used for modedetermination in multiple quantum well slab waveguides

Approximations commonly used to determine the effective indexes of the guided modes of optical waveguides formed using multiple quantum well (MQW) materials are compared to the exact solutions in the slab waveguide model. Modeling the quantum well region as a single homogeneous layer with an average index of refraction is shown to produce results in close agreement with exact values of the effective index. A geometrically weighted average of the indexes provides the most accurate approximation for typical values of index and layer thickness of GaAs-Al_xGa_1-xAs quantum well waveguides     

Refractive index reconstruction of graded-index buried channelwaveguides from their mode intensities

The refractive index distribution has been determined for a number of graded-index, single-mode, buried channel waveguides, formed by irradiation with a high energy focused ion beam. The refractive index has been calculated from the waveguide's mode field intensity at a wavelength of 670 nm, via an inversion of the scalar wave equation. Waveguides with doses in the range 0.7×10¹⁵-4.1×10¹⁵ ions·cm^-2 exhibited a peak refractive index change increasing linearly with ion dose, in the range 0.01-0.08%, and the results are consistent with profiles derived from TRIM simulations     

Method of refractive index profile reconstruction from effectiveindex of planar optical monomode waveguides: Application to potassiumion-exchanged waveguides

A simple nondestructive method for determination of refractive index profile of single-mode waveguides using the measured effective refractive indexes is proposed. The method is based on the extraction of the additional data about the waveguide profile from the investigation of its evolution with the duration of fabrication process. The profile reconstructions are carried out using an appropriate algorithm in the frames of the WKB approximation. The method is applied for few- and single-mode waveguides, obtained by K⁺-Na⁺ field assisted ion exchange. The results are corroborated with the reconstruction from the effective refractive indexes measured at a shorter wavelength, as well as with profile study by means of step-by-step etching     

Refractive index data from GaxIn1?xAsyP1?y films

We have measured the refractive index versus wavelength of several compositions of GaInAsP grown by vapour phase epitaxy on InP. The self-consistent data show reasonable agreement with existing theories for wavelengths larger than the absorption edge. However, at and below the band edge, detail is measured that is not predicted by the simple theories.     

An inverse algorithm to calculate the refractive index profiles ofperiodically segmented waveguides from the measured near-fieldintensities

In this paper, the refractive index profiles of the periodically segmented waveguides (PSWs), which are fabricated in soda-lime glasses by the K⁺-Na⁺ ion-exchanged technique, are reconstructed from the measured transmitted near-field (NF) intensity combined with an inverse method. Through the proposed inverse method, the model Δn'=ηΔn, which characterizes the behavior of the PSWs, is also verified. In the numerical process, a finite-difference method is used to discretize the governing equation, and then a linear inverse model is constructed to identify the unknown refractive index profiles. The approach used is to rearrange the matrix form of the governing differential equation and estimate the unknown index profiles of the waveguides. Then, the linear least-squares error method is adopted to find the solutions. The results show that the accuracy of index determination can be accessed even when the measured noise is considered. In contrast to the traditional approach, the advantages of this method are that no prior information is needed on the functional form of the unknown index profiles, no initial guesses are required, no iterations in the calculating process are necessary, no intensity smoothing is required in advance, and the inverse problem can be solved in a linear domain. Furthermore, the existence and uniqueness of the solutions can easily be identified     

Piecewise linear implementation of nonlinear dynamical systems: from theory to practice

It is shown how to implement by a mixed-signal circuit a continuous-time dynamical system. The chosen case study is the Hindmarsh-Rose model of a biological neuron, but the design strategy can be applied to a large class of continuous-time nonlinear dynamical systems. The system nonlinearities are first approximated by using piecewise-linear functions and then digitally implemented on a field programmable gate array. The linear part of the system is completely analogue and is implemented by using operational amplifiers. Measurement results show that the circuit can reproduce the main dynamics of a biologically plausible neuron.     

An iterative method of solving a system of linear equations and its physical interpretation from the point of view of scattering theory

The iterative method is useful to find the approximate solution of large systems of linear equations when the exact method becomes too expensive to be implemented. One well-known iterative method is the Gauss-Seidel method. The author presents an alternative algorithm which has certain simplicity in its formulation. He uses the system of linear equations encountered in the theory of coupled antennas to illustrate this method and give a physical interpretation of the successive approximations from the point of view of scattering theory. A simple numerical example is given to compare the products resulting from this method and those obtained by the Gauss-Seidel method