4. Tensor properties of the anharmonic oscillator model. Starting from Eq. (1.4.52), rele- vant to a collection of isotr

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4 Tensor Properties Of The Anharmonic Oscillator Model Starting From Eq 1 4 52 Rele Vant To A Collection Of Isotr 1 (49.06 KiB) Viewed 65 times

4. Tensor properties of the anharmonic oscillator model. Starting from Eq. (1.4.52), rele- vant to a collection of isotropic, centrosymmetric, anharmonic oscillators, show that the nonlinear susceptibility possesses the following tensor properties: X1122 = X1212 = X1221 = X1133 = X1313 = X1331 = X2233 = X2323 = X2332 = X2211 = X2121 = X2112 = X3311 = X3131 = X3113 = X3322 = X3232 = X3223 = $x111 = {x2222 = $x3333, (1.7.15) with all other elements vanishing. Give a simple physical argument that explains why the vanishing elements do vanish. Also, give a simple physical argument that ex- plains why Xijkl possesses off-diagonal tensor components, even though the medium is isotropic