4500HWR01

# 4500HWR01 - Refractive Index Dispersion of Indium Phosphide...

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Unformatted text preview: Refractive Index Dispersion of Indium Phosphide The index of refraction of a dielectric as a function of wavelength may be accu— rately represented using a Sellmeier equation of the form G')‘2 2 k n _, k A2—Ai where A, M, 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: Indium phosphide (InP) is a semi- conductor material that is transparent in the infrared part of the spectrum. For indium phosphide, the Sellmeier equation becomes simply 01A?“ 2 n —A+ , A2—A% where A = 7.255, /\1 = 626.26 nm, and 01 = 2.316. For indium phosphide, considering material dispersion as described above and ig— noring any waveguide dispersion, calculate the refractive index, the ﬁrst derivative of the refractive index with respect to wavelength, the phase velocity, and the group velocity, for A = 1.300 um. Express the refractive index derivative in rum—1. Express the phase velocity and the group velocity in meters / sec. Express all answers accurately to six sig- niﬁcant ﬁgures. Put your ﬁnal answers in the spaces provided. Refractive index = First derivative of refractive index with respect to wavelength 2 ____.______— nm‘1 Phase velocity = _________ meters / sec Group velocity = —_ meters / sec Refractive Index Dispersion of Indium Phosphide The Sellmeier equation is Where A i 7.255, A1 = 626.26 nm, and G1 = 2.316. Therefore for A = 1.30pm n = 320482566 Differentiating dn _ A GIX‘I’ _ -1 a _ — gm — -0.00021876224nm The phase velocity is 1),, = 0/71 = 93, 544,077 m/sec. The group velocity is c =m = 85,919,705771/866. v9 ...
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4500HWR01 - Refractive Index Dispersion of Indium Phosphide...

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