The carrier effects on the change of refractive index for n-type GaAs at λ=1.06,1.3, and 1.55 μm

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Abstract
A numerical Kramers–Kronig analysis is used to calculate the refractive‐index change Δn caused by the injection/depletion of free carriers in various doped n‐type GaAs. The analysis makes use of a carrier‐related absorption spectrum, which is established by using quantum theory as well as empirical relations and is confirmed by the experimental absorption data in the literature. We obtain the Δn values for various doping concentrations ND and carrier concentrations N at three wavelengths; λ=1.06, 1.3, and 1.55 μm. The Δn value is positive for low‐N region, and increases gradually to its maximum which is around 10−4 for λ=1.06 μm. Thereafter, Δn decreases rapidly to 0 as N increases. The linear relation between Δn and N, as predicted by the Drude theory, only happens when N is beyond a certain value. In this region, the Δn value may attain to −10−2 at N=5×1018 cm−3 for λ=1.55 μm. Because of this significant Δn value and its linear relation with N, the free‐carrier induced index‐change effect may find the applications in integrated optics and optical probing.