In this paper, reflection and transmission coefficients at dielectric fractal-fractal interface are discussed. The ratio of permittivity of the two dielectric fractal media is kept constant, while the dimension is varied in order to get the desired results. Conventional results are recovered for the integer dimensions. The proposed expressions are useful to study the behavior of electromagnetic waves for non-integer dimensions, multiple fractal interfaces and waveguides. Moreover, it is also helpful to understand the variation in the magnitudes of reflection and transmission coefficients with the difference in dimensionality at interface of the two fractal media.
2. Vicsek, T., "Fractal models for diffusion controlled aggregation," J. Phys. A: Math. Gen., Vol. 16, No. 17, 1983.
3. Wagner, G. C., J. T. Colvin, J. P. Allen, and H. J. Stapleton, "Fractal models of protein structure, dynamics and magnetic relaxation," J. Am. Chem. Soc., Vol. 107, No. 20, 5589-5594, 1985.
4. Stillinger, F. H., "Axiomatic basis for spaces with noninteger dimension," J. Math. Phys., Vol. 18, No. 6, 1224-1234, 1977.
5. Bollini, C. G. and J. J. Giambiagi, "Dimensional renormalization: The number of dimensions as a regularizing parameter," Nuovo Cimento B, Vol. 12, 20-26, 1972.
6. Baleanu, D. and S. Muslih, "Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives," Phys. Scripta, Vol. 72, No. 23, 119-121, 2005.
7. Tarasov, V. E., "Electromagnetic fields on fractals," Modern Phys. Lett. A, Vol. 21, No. 20, 1587-1600, 2006.
8. Palmer, C. and P. N. Stavrinou, "Equations of motion in a non-integer-dimensional space," J. Phys. A, Vol. 37, 6987-7003, 2004.
9. Tarasov, V. E., "Continuous medium model for fractal media," Physics Letters A, Vol. 336, No. 2-3, 167-174, 2005.
10. Martin, O.-S., "Electromagnetism on anisotropic fractals,", 2011,Eprint arXiv: 1106.1491.
11. Muslih, S. and D. Baleanu, "Fractional multipoles in fractional space," Nonlinear Analysis: Real World Applications, Vol. 8, 198-203, 2007.
12. Baleanu, D. and A. K. Golmankhaneh, "On electromagnetic field in fractional space," Nonlinear Analysis: Real World Applications, Vol. 11, No. 1, 288-292, 2010.
13. Zubair, M., M. J. Mughal, Q. A. Naqvi, and A. A. Rizvi, "Differential electromagnetic equations in fractional space," Progress In Electromagnetic Research, Vol. 114, 255-269, 2011.
14. Zubair, M. , M. J. Mughal, and Q. A. Naqvi, "The wave equation and general plane wave solutions in fractional space," Progress In Electromagnetics Research Letters, Vol. 19, 137-146, 2010.
16. Zubair, M. , M. J. Mughal, and Q. A. Naqvi, "An exact solution of the cylindrical wave equation for electromagnetic field in fractional dimensional space," Progress In Electromagnetics Research, Vol. 114, 443-455, 2011.
17. Zubair, M., M. J. Mughal, and Q. A. Naqvi, "An exact solution of spherical wave in D-dimensional fractional space," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 10, 1481-1491, 2011.
18. Zubair, M., M. J. Mughal, and Q. A. Naqvi, "Electromagnetic fields and waves in fractional dimensional space," Springer Briefs in Applied Sciences and Technology, XII, 76, Springer, Germany, Jan. 28, 2012.
19. Mughal, M. J. and M. Zubair, "Fractional space solutions of antenna radiation problems: An application to Hertzian dipole," 2011 IEEE 19th Conference on Signal Processing and Communications Applications (SIU), 62-65, Apr. 20-22, 2011, doi:10.1109/SIU.2011.5929587.
20. Hira, A., M. Zubair, and M. J. Mughal, "Reflection and transmission coefficients at dielectric-fractional interface," Progress In Electromagnetics Research, Vol. 125, 543-558, 2012.
21. Balanis, C. A., Advanced Engineering Electromagnetics, Wiley, New York , 1989.