In this paper, a generalized photon wave function (PWF) which is applicable to electromagnetic problems is introduced. The formulation treats the electromagnetics fields as quantum mechanical entities. The introduced PWF is especially useful for boundaryvalue problems. For instance,the reflection coefficient at a dielectric half space is calculated based on the concepts of PWF and quantum mechanics. With the proposed method, inhomogeneous media, both isotropic and anisotropic, can also be analyzed. It is shown that by defining certain new variables, such as effective charges and effective currents, we will be able to describe the behavior of electromagnetic fields by the proposed photon wave function. At the end of this paper, a new FDTD method based on the notion of photon wave function is introduced and the resonance frequencies of a cubic cavity are obtained.
2. Puccini, A., "About the zero mass photon," Progress In Electromagnetics Research, Vol. 55, 117-146, 2005.
3. Bialynicki-Birula, I., "On the wave function of the photon," Acta Physica Polonica, Vol. 86, 97-116, 1994.
4. Bialynicki-Briula, I., "Photon wave function," Progress in Optics, Vol. XXXVI, 1996.
5. Taflove, A. and M. Brodwin, "Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell's equations," IEEE Trans. MTT, Vol. 23, No. 8, 1975.
6. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd edition, Artech House, Boston, London, 2005.
7. Hadi, M. F. and S. F. Mahmoud, "Optimizing the compact-FDTD algorithm for electrically large waveguiding structures," Progress In Electromagnetics Research, Vol. 75, 253-269, 2007.
8. Georgakopoulos, S. V., C. R. Birtcher, C. A. Balanis, and R. A. Renaut, "Higher-order finite-difference schemes for electromagnetic radiation, scattering, and penetration, part I: Theory," IEEE Anten. Propag. Mag., Vol. 44, No. 2, 134-142, 2002.
9. Kantartzis, N. V. and T. D. Tsiboukis, Higher-Order FDTD Schemes for Waveguide and Antenna Structures, Morgan & Claypool Publishers, San Rafael, CA, 2006.
10. Abd El-Raouf, H. E., E. A. El-Diwani, A. E.-H. Ammar, and F. El-Hefnawi, "A low-dispersion 3-D second-order in time fourthorder in space FDTD scheme (M3d24)," IEEE Trans. Antennas Propag., Vol. 52, No. 7, 1638-1646, 2004.
11. Teixeira, F. L. (ed.), Progress In Electromagnetics Research, Vol. 32, PIER 32, Geometric Methods for Computational Electromagnetics Series, EMW Publishing, Cambridge, MA, 2001.
12. Rosewarne, D. and S. Sarkar, "Rigorous theory of photon localizability," Quantum Opt., Vol. 4, 405-413, 1992.
13. De Raedt, H., et al., "Solving the Maxwell equations by the Chebychev method: A one-step finite-difference time-domain algorithm," IEEE Trans. Antennas Propagat., Vol. 51, No. 11, 2003.
14. Borisov, A. G. and S. V. Shabanov, "Wave packet propagation by the Faber polymomial approximation in electrodynamics of passive media," Journal of Computational Phys., Vol. 216, 391-402, 2006.
15. Bass, F. and L. Resnick, "On the theory of the electromagnetic wave propagation thorough inhomogeneous dispersive media," J. of Electromagn. Waves and Appl., Vol. 19, No. 7, 925-931, 2005.
16. Sakurai, J. J., Modern Quantum Mechanics, 964-03, ISBN 964-03-4473-7..
17. Jackson, J. D., Classical Electrodynamics, 3rd edition, John Wiley & Sons Inc, 1998.
18. Harrington, R. F., Time Harmonic Electromagnetic Fields, McGraw-Hill, 1987.
19. Luo, S. and Z. Chen, "An efficient modal FDTD for absorbing boundary conditions and incident wave generator in waveguide structures," Progress In Electromagnetics Research, Vol. 68, 229-246, 2007.
20. Pozar, D. M., Microwave Engineering, Addison Wesley, 1990.
21. Jancewicz, B., "Plane electromagnetic wave in PEMC," J. of Electromagn. Waves and Appl., Vol. 20, No. 5, 647-679, 2006.
22. Yee, K. S., "Numerical solution of initial boundrary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propagat., Vol. 14, No. 5, 302-307, 1966.
23. Ho, M., "Propagation of electromagnetic pulse onto a moving lossless dielectric half-space: one-dimensional simulation using characteristic-based method," J. of Electromagn. Waves and Appl., Vol. 19, No. 4, 469-478, 2005.