William Angerer - Department of Physics and Astronomy - University ...

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approximation. The agreement between the magnitudes of the calculated and experimental
second-order susceptibility elements is quite good. Note that the calculated
data exhibits a larger dispersion in the second-order susceptibility elements than the
experimental data. In addition, the calculated X~~x
lacks a resonance at 2.80 e\".
vVe speculate this feature may result from virtual transitions involving an intrinsic
midgap defect state. Since, the calculation of the dispersion of X~~x
includes only
bulk band structures, the calculation cannot predict spectral features that couple to
defect states.
6.5 Possible Origin of the 2.80 eV Resonance
By analyzing the nature of a resonance in Xl~k,
the magnitude of this feature, and the
symmetry of states that may participate in this resonance. we are able make some
speculative suggestions about the nature of this feature. First, we consider possible
origins of the feature at a two photon energy of 2.80 eV. The second order non linear
susceptibility for second-harmonic generation is derived from quantum statistical
mechanics as [46]
(2) (, =? ) = _ jU e 3 ""' [ (ghln)(nlrjln')(n'lrklg) + 1 (0) (6 36)
Xl}k W _Wo • v 2 ~ ( 'r )( .) ... Pg .'
h g, n , n' W - Wng + Z ng Wo - Wn'g + zr n'g
where N is the number of electrons per unit volume: Ig), In), and In') are states of
the system, hWng is the energy difference between states nand g; r ng is a dephasing
term; p~O) is the equilibrium density of the initial state g; -erk is the dipole operator
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