Lithium Niobate - Sellmeier Equations

Sellmeier Equations

The Sellmeier equations for the extraordinary index are used to find the poling period and approximate temperature for quasi-phase matching. Jundt gives

$n^2_e = 5.35583 + 4.629 \times 10^{-7} f + {0.100473 + 3.862 \times 10^{-8} f \over \lambda^2 - (0.20692 - 0.89 \times 10^{-8} f)^2 } + { 100 + 2.657 \times 10^{-5} f \over \lambda^2 - (11.34927 )^2 } - 1.5334 \times 10^{-2} \lambda^2$

valid from 20-250 °C for wavelengths from 0.4 to 5 micrometers, whereas for longer wavelength,

$n^2_e = 5.39121 + 4.968 \times 10^{-7} f + {0.100473 + 3.862 \times 10^{-8} f \over \lambda^2 - (0.20692 - 0.89 \times 10^{-8} f)^2 } + { 100 + 2.657 \times 10^{-5} f \over \lambda^2 - (11.34927 )^2 }- (1.544 \times 10^{-2} + 9.62119 \times 10^{-10} \lambda) \lambda^2$

which is valid for T = 25 to 180 °C, for wavelengths λ between 2.8 and 4.8 micrometers.
In these equations f = (T-24.5)(T+570.82), λ is in micrometers, and T is in °C.

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