NMiP Reader

Textbooks

• Computational Photonics : An Introduction with MATLAB by Marek S. Wartak

• Numerical Methods In Photonics by Andrei V. Lavrinenko, Jesper Lægsgaard, Niels Gregersen, Frank Schmidt, Thomas Søndergaard.

Both are availabe online through the CU library.  I have tried to give direct links above, but if those fail, just look them up using the library search tool.  

Optimization

• Original paper by Nelder and Mead on simplex method: J.A. Nelder and R. Mead, “A simplex method for function minimization,” Computer Journal, Volume 7, Issue 4, 1965, pp. 308-313. https://doi.org/10.1093/comjnl/7.4.308
• Concise statement of algorithm plus convergence proof in 1 and 2 dimensions:  J. C. Lagarias, J. A. Reeds, M. H. Wright, P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J. Optim., Vol. 9, No. 1, 1998, pp. 112-147
• Original paper on simulated annealing for finding equilibrium of atoms: Kirkpatrick, S.; Gelatt, C. D.; and Vecchi, M. P. "Optimization by Simulated Annealing." Science 220, 671-680, 1983
• Summary by the authors that applied it to optimization: K. S. Yee, "Numerical Solution of Initial Boundary Value Problems Involving Maxwell's Equations in Isotropic Media,'' IEEE Trans. on Antennas and Propagat., vol. 14, pp. 302-307, May 1966.

FDTD Method

Boundary conditions for the FDTD method

• K. S. Yee, "Numerical Solution of Initial Boundary Value Problems Involving Maxwell's Equations in Isotropic Media,'' IEEE Trans. on Antennas and Propagat., vol. 14, pp. 302-307, May 1966.
• G. Mur, "Absorbing Boundary Conditions for the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations," IEEE Trans. on Electromagnetic Compatibility, Vol. EMC-23, November 1981, pp. 377-382
• B. Engquist and A. Majda, "Absorbing boundary conditions for the numerical simulation of waves", Math. Comput., vol. 31, pp. 629-651, 1977.

Dispersive materials in FDTD method

• R. J. Luebbers, F. Hunsberger, K. S. Kunz, R. B. Standler, and M. Schneider., “ A frequency-dependent finite-difference time-domain formulation for dispersive materials”, IEEE Trans. on EM Compat, V 32, N 3, Aug 1990

Anisotropic materials in the FDTD method

• J. B. Schneider and S. Hudson, ``The finite-difference time-domain method applied to anisotropic material,'' IEEE Trans. Antennas Propagat., vol. 41, pp. 994-999, July 1993

Nonlinear materials in the FDTD method

• G. W. Zheng and K. S. Chen, “Transient analysis of dielectric step discontinuity of microstrip lines containing a nonlinear layer,“ Int. J. Infrared Millim. Waves, vol. 13, no. 8, pp. 1127-1137, 1992
• P. M. Goorjian and A. Taflove, “Direct time integration of Maxwell's equations in nonlinear dispersive media for propagation and scattering of femtosecond electromagnetic solitons,” OpticsLett., B 17, pp. 180-182, Feb. 1992.

Gaussian Beam Superposition Method

• J. Arnaud, “Representation of Gaussian beams by complex rays,” Applied Optics, Volume 24, Issue 4, 538- February 1985
• R. P. Herloski, S. Marshall, R. L. Antos, „Gaussian beam ray-equivalent modeling and optical design,”Applied Optics, Vol. 22 Issue 8 Page 1168 (April 1983)
• A. W. Greynolds, “Propagation of generally astigmatic Gaussian beams along skew ray paths,” SPIE Vol560, Diffraction Phenomenon in Optical Engineering Applications, 1985.

FFT Beam Propagation Method

• M. D. Feit and J. A. Fleck, Jr., "Beam nonparaxiality, filament formation, and beam breakup in the sel-focusing of optical beams," J Opt Soc Am B., Vol. 5, No. 3, pp. 633-640, March 1988
• M. D. Feit and J. A. Fleck, Jr., "Computation of mode properties in optical fiber waveguides by a propagating beam method," Applied Optics, Vol. 19, No. 7, pp. 1154-1164, 1 April 1980
• N. Delen, B. Hooker, “Free-space beam propagation between arbitrarily oriented planes based on full diffraction theory: a fast Fourier transform approach,” JOSA A, Volume 15, Issue 4, 857-867, April 1998
• D. Yevick, J. Yu, Y. Yayon, “Optimal absorbing boundary conditions,” J. Opt. Soc. Am. A,Vol. 12, No. 1, January 1995
• R. R. McLeod, Notes on gyrotropic materials
• Robert R. McLeod and Kelvin H. Wagner, "Vector Fourier optics of anisotropic materials," Adv. Opt. Photon. 6, 368-412 (2014)

Finite Difference Beam Propagation Method (FD BPM)

• D. Yevick, B. Hermansson, “Split-step finite difference analysis of rib waveguides,” Electronic Letters, Vol. 25, No. 7, pp. 461-462

Coupled Mode Equations applied to Bragg holography

• N. Uchida, "Calculation of diffraction efficiency in hologram gratings attenuated along the direction perpendicular to the grating vector," JOSA 63, March 1973, pp. 280-287

Mode Propagation Method

Method

• Good summary: D. F.G. Gallagher, T.P. Felici, “Eigenmode Expansion Methods for Simulation of Optical Propagation in Photonics – Pros and Cons,” Photonics West, San Jose, 2003. Paper 4987-10
• All of the details: P. Bienstman Ph.D. dissertation, U. Gent, 2000

Applications

• Shani Y, Henry CH, Kistler RC, Kazarinov RF, Orlowsky KJ. "Integrated optic adiabatic devices on silicon." IEEE Journal of Quantum Electronics, vol.27, no.3, March 1991, pp.556-66
• Henry CH, Shani Y. "Analysis of mode propagation in optical waveguide devices by Fourier expansion." IEEE Journal of Quantum Electronics, vol.27, no.3, March 1991, pp.523-30.