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The complex refractive index, m, of a material is related to the dielectric function, ε, of that material by the following equation:
| m2 = με | (1) |
where μ is the magnetic permeability of the material. In most cases με ≅ ε. With this simplification and by following the sign convention adopted in TPDSci for the complex refractive index (m = m' - im") and the dielectric function (ε = ε' - iε"), we have:
| m' 2 - m" 2 = ε' | (2) |
| 2m'm" = ε" | (3) |
These last two equations yield (see problem):
| 2m' 2 = ε' + √(ε' 2 + ε" 2 ) | (4) |
| 2m" 2 = - ε' + √(ε' 2 + ε" 2 ) | (5) |
Note that these results are identical to those for the opposite sign convention in the refractive index and dielectric function (i.e. m = m' + im" and ε = ε' + iε") as can be seen, for example, in Fox M 2010 (his Eq. 1.25 and 1.26). Indeed, this equivalence should be expected from the definition of the square root of a complex number (for example, http://mathworld.wolfram.com/SquareRoot.html) given that Eq. 1 can be written as m = √ε by using the simplifying assumption μ ≅ 1.
| CITATION: Jonasz M. 2010. Refractive index and dielectric function (www.tpdsci.com/Tpc/RIDF.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 06-Nov-2010 Modified: 06-Nov-2010 Peer-reviewed: N/A |
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