Fresnel equations and the refractive index of active media

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 73, Issue 2, 2006, Pages

  Skaar, Johannes ^a  

^a NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

NONLINEAR EQUATIONS; VECTORS; VELOCITY MEASUREMENT;

ACTIVE MEDIA; EXCITATION SOURCES; FRESNEL EQUATIONS;

REFRACTIVE INDEX;

EID: 33644502567     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.73.026605     Document Type: Article

References (16)

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13. If the medium is conducting at zero frequency, the electric χ is singular at ω=0. Although χ is not square integrable in this case, relations similar to Eq. 2 can be derived.
14. Let F(s) be the Laplace transform of the Laplace transformable function f(t). A well-known result in the theory of Laplace transforms states that if F(â iω)exp(â iωÏ.,)â†' 0 as Im ωâ†' â, then the inverse transform of F is zero for t<Ï., (see, for example, Ref.).
15. Any physical excitation is real and can be represented by two complex terms, e.g., u(t)exp(â i ω1 t)+u(t)exp(i ω1 * t). This excitation would require the substitution 1â •(i ω1 â iω)â†' 1â •(i ω1 â iω)+1â •(â i ω1* â iω) in Eq. 10. For clarity it is often convenient to consider the positive frequency excitation separately.
16. One may argue that the asymptotic form of Ïμâ 1 for large ω is different from the usually assumed dependence 1â • ω2. Without significantly altering g in the region ⠣ωâ ω0 ⠣≠2Î" this can be fixed for instance by letting gâ†' (g+ FÌf) ωÌf 02 â • (ωÌf 02 â ω2 â iω Î"Ìf) where â £ FÌf â £âa¡1, ωÌf 0 âa¢ ω0, and 0< Î"Ìf âa¡ ωÌf 0 â ω0.