The quotient function and its applications

American Journal of Physics

Volumn 66, Issue 3, 1998, Pages 197-202

  Lindell, I V ^a   Sihvola, A H ^a  

^a AALTO UNIVERSITY   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032327139     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18845     Document Type: Article

References (21)

1. It is a special case of the linear-fractional or bilinear function, see CRC Standard Mathematical Tables and Formulae, edited by D. Zwillinger (Chemical Rubber, Boca Raton, FL, 1996), 30th ed., p. 56.
2. It can be easily shown that the most general scalar quotient function whose inverse equals itself is of the form (a-bx)/(b+cx).
3. I. V. Lindell, Methods in Electromagnetic Field Analysis (Oxford U.P., Oxford, 1995), 2nd ed., pp. 237-238.
4. J. A. Kong, Electromagnetic Wave Theory (Wiley, New York, 1986), p. 142.
5. D. K. Cheng, Fields and Wave Electromagnetics (Addison-Wesley, Reading, MA, 1983), p. 454.
6. Reference 4, Sec. 3.3.
7. Reference 5, Sec. 9-6.
8. J. L. Rosner, "The Smith chart and quantum mechanics," Am. J. Phys. 61 (4), 310-316 (April 1993).
9. Reference 4, Sec. 3.2.
10. R. M. A. Azzam, "Relationship between the p and s Fresnel reflection coefficients of an interface independent of angle of incidence," J. Opt. Soc. Am. A 3 (7), 928-929 (July 1986).
11. J. C. Maxwell-Garnett, "Colours in metal glasses and metal films," Trans. R. Soc. London, Sec. A CCIII, 385-420 (1904).
12. Reference 4, Sec. 7.1.
13. It is not difficult to show that, without the minus sign, this kind of requirement leads to a contradiction unless a=0.
14. 2).
15. J. W. Gibbs, Vector Analysis, reprint of the 2nd ed. (1909) (Dover, New York, 1960), Chap. 5, and Ref. 3, Chap. 2.
16. One has to distinguish between the inverse of a dyadic function and the inverse dyadic, which is an algebraic concept.
17. Reference 15, p. 338 and Ref. 3, p. 41.
18. L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge U.P., Cambridge, 1982).
19. I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, Boston, 1994).
20. Reference 19, p. 23.
21. I. V. Lindell, A. H. Sihvola, and K. Suchy, "Six-vector formalism in electromagnetics of bi-anisotropic media," J. Electromagn. Waves Application 9 (7/8), 887-903 (1995).