THE FREQUENCY-DEPENDENCE OF NONLINEAR-OPTICAL PROCESSES

Explicit formulas are derived for the sum rules for the frequency-depe ndent hyperpolarizability-diagonal-components. These are the counterpa rts to the Cauchy moments for the dynamic polarizabilities. The formul as allow for the frequency dependence of any nonlinear optical process to be expressed as a single general expansion up to terms which are o f fourth power in the optical frequencies, ...,alpha)(n)(-omega(sigma) ;omega(1),...,omega(n)) = X(alpha,alpha,...,alpha)(n)(0) + AW(2) + BW2 2 + B'W-4, where omega(sigma) = Sigma(i) omega(i), W-2 = omega(sigma)( 2) + omega(1)(2) + ... omega(n)(2), and W-4 = omega(sigma)(4) + omega( 1)(4) + ... omega(n)(4) (in conventional notation X(1) = alpha, X(2) = beta, X(3) = gamma, etc.). The advantages of determining the frequenc y dependence of all NLO processes, for a given species, in a single ca lculation are stressed. We focus mainly on the sum rules (A, B, and B' ) for X(3) and X(5). These are applicable to both atoms and molecules (with the exception of X(5) for noncentrosymmetric molecules) and we e valuate them, using near-exact wave functions, for H and He. It is app arent that B' is generally smaller than B and this accounts for the re asonable success of the Shelton-Bishop dispersion formula which is oft en used to fit experimentally-derived dynamic hyperpolarizabilities. ( C) 1996 American Institute of Physics.