Computing the flow of light : nonstandard FDTD methodologies for photonics design The finite difference time domain (FDTD) method computes the time evolution of a system at discrete time steps and periodically visualizing the results lets us view the time evolution yielding valuable physical insights. FDTD and FDTD like methods can be used to solve a wide variety of problems including but not limited to the wave equation Maxwells equations and the Schrödinger equation. In addition to introducing useful new methodologies this book provides readers with analytical background and simulation examples that will help them develop their own methodologies to solve yet to be posed problems. The book is written for students engineers and researchers grappling with problems that cannot be solved analytically. It could also be used as a textbook for a mathematical physics or engineering class. An accompanying CD provides supplemental Mathcad and pseudocode programs 1. Finite difference approximations 2. Accuracy stability and convergence of numerical algorithms 3. Finite difference models of the simple harmonic oscillator 4. The 1D wave equation 5. FDTD Algorithms for the 1D wave equation 6. Program development and applications of FDTD algorithms in one dimension 7. FDTD algorithms to solve the wave equation in two and three dimensions 8. Review of electromagnetic theory 9. The Yee algorithm in one dimension 10. The Yee algorithm in two and three dimensions 11. Example applications of FDTD 12. FDTD for dispersive materials 13. Photonics problems 14. Photonics design Appendix A. Supplemental research Appendix B. List of programs