Foreword Preface to the Second Edition Preface 1. Maximization, Minimization, and Motivation 2. Vectors and Matrices 3. Diagonalization and Canonical Forms for Symmetric Matrices 4. Reduction of General Symmetric Matrices to Diagonal Form 5. Constrained Maxima 6. Functions of Matrices 7. Variational Description of Characteristic Roots 8. Inequalities 9. Dynamic Programming 10. Matrices and Differential Equations 11. Explicit Solutions and Canonical Forms 12. Symmetric Function, Kronecker Products and Circulants 13. Stability Theory 14. Markoff Matrices and Probability Theory 15. Stochastic Matrices 16. Positive Matrices, Perron's Theorem, and Mathematical Economics 17. Control Processes 18. Invariant Imbedding 19. Numerical Inversion of the Laplace Transform and Tychonov Regularization Appendix A. Linear Equations and Rank Appendix B. The Quadratic Form of Selberg Appendix C. A Method of Hermite Appendix D. Moments and Quadratic Forms Index.

Introduction to Matrix Analysis. By Richard Bellman. 2nd Edition. Pp. xxiii, 403. £7·50. (McGraw-Hill.)

In this work, a computationally fast, numerically stable, and memory-efficient cascading and doubling algorithm is proposed within the method of lines framework to model long planar waveguide gratings having thousands of periods in the propagation direction. This algorithm can model 2/sup n/ grating periods in n calculational steps and needs N/sup 2/ matrices for N sample points in the problem space. It can model periodic, quasi-periodic, symmetric, and asymmetric gratings efficiently. Different deep waveguide gratings are modeled using this scheme and results for the fundamental TE mode spectral reflectivity are compared with published results showing excellent agreement.

Analysis of deep waveguide gratings: an efficient cascading and doubling algorithm in the method of lines framework

A new method to analyze fiber Bragg gratings

The main purpose of this study is designing a structure with the broadband negative refractive index (NRI) in the wavelengths range of 3–5 μm using multilayer structures. In the proposed structure, actually nanocomposite thin films are used to make multilayer waveguide to show effective NRI. In the composite structure, core-shell nanoparticles including metallic core and a dielectric shell with high refractive index are used. Here, it is shown that by increasing the number of composite layers, the bandwidth for NRI can be increased. Therefore, based on simulation results, in eight-layer waveguide, NRI is available in complete 3- to 5-μm MIR band. In this regard, also, the effect of filling factor (in each thin-film layer) on NRI is studied.

Nanocomposite Multilayer Structure for Broadband MIR Negative Refractive Index

Wide angle and bi-directional beam propagation using the collocation method for the non-paraxial wave equation

We present the reflection characteristics of Bragg gratings using the collocation method and the effect of various parameters such as grating profile, duty cycle of periodic variation, index change and strain on the spectra. Comparisons with the coupled mode theory have also been included.

Reflection characteristics of guided-wave Bragg gratings using the collocation method

We have used the collocation method to model the characteristics of guided-wave Bragg gratings. The collocation method being a total field method, takes into account all modes, guided as well as radiation. We have first studied the effect of the grating structural parameters such as the grating profile and the duty cycle of periodic variation and have shown that these can have significant effect on the Bragg wavelength and the reflection spectrum. We have then obtained the response characteristics of gratings for their use in strain, temperature and pressure sensing. Our results compare very well with available experimental results. Comparisons with the coupled mode theory have also been included.

Ashmeet Kaur Taneja

Papers

Reflection characteristics of guided-wave Bragg gratings using the collocation method

Modelling of guided-wave Bragg gratings and grating sensors using the collocation method