4500PR02 - Refractive Index Material Dispersion The index...

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Unformatted text preview: Refractive Index - Material Dispersion The index of refraction of a dielectric as a function of wavelength may be accu- rately represented using a Sellmeier equation of the form where A, Ale, and Gk are called the Sellmeier coefficients. This variation of the refractive index with wavelength represents the material dispersion. It specifies how the velocity of propagation changes with wavelength. The quantities Ak and Gk represent resonant wavelengths and oscillator strengths respectively. For fused quartz, A = 1, A1 = 68.4 nm, G1 = 0.69617, A2 = 116.2 nm, G2 = 0.40794, A3 = 9896.2 nm, 0;; = 0.89748. Calculate, showing all work, the refractive index of fused quartz at freespace wavelengths of 1.0 mm, 1.2 pm, 1.4 pm, and 1.6 ,um. Express refractive indices accurately to five significant figures. Put your final answers in the spaces provided. n()\ : 1.0,um) = n()\ = 1.2 gm) = n()\ = 1.4um) = n(/\ = 1.6,um) = Refractive Index - Material Dispersion From the Sellmeier equation GA 2____ k n —A+Z)\2_/\2 k or GA2 GA2 GA2 2 1 2 3 n —A+ + + /\2-—)\§ A2—A3 A2—Ag andso 02A? A2 — A3 03A? A2 — Ag + Evaluating this numerically for A = 1, /\1 = 68.4 nm, 01 = 0.69617, A2 = 116.2 nm, 02 = 0.40794, A3 = 9896.2 nm, and G3 = 0.89748 gives n()\ = 1.0,um) = 1.450416 n()\ = 1.2 pm) 2 1.448050 n()\ = 1.4 pm) 2 1.445779 ( ) n /\ = 1.6 pm 2 1.443419 ...
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