By Manthos G. Papadopoulos (Editor), Andrzej J. Sadlej (Editor), Jerzy Leszczynski (Editor)

Microscopic conception of nonlinear optics.- exact nonlinear optical homes for small molecules.- decision of vibrational contributions to linear and nonlinear optical properties.- SOS tools in calculations of digital NLO houses

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**Sample text**

57) we could identify the matrix element describing two-photon absorption. If we now consider one higher order of response as well as one higher order residue, we can identify the expression for the matrix element describing two-photon absorption between two excited states, say g and f . The following double residue of the second-order hyperpolarizability needs to be considered: (68) lim 2 →− g0 = = = g0 + lim 2 3→ f0 m 2 3 m − 1 3 1 g ˆ m m ˆ f mg + 1 1 1 − m − 1 3 3 0 ˆ g g ˆ m m ˆ f f ˆ 0 − f0 m0 + 1 3 f0 − 0 ˆ g f ˆ 0 g ˆ m m ˆ f g ˆ m m ˆ f + mf − 1 mg + 1 0 ˆ g f ˆ 0 Out of the 24 permutations in Eq.

The three-photon absorption matrix element, symmetrized in the dummy indices, can thus be written as (79) 3 M0f = 1 2 123 mn 0 ˆ m m ˆ n n ˆ f n0 − 1 − 2 m0 − 1 where the operator 1 2 3 denote that the summation of terms obtained by permuting the pairs 1 , 2 , and 3 is performed. The connection to the first-order residue of the second-order hyperpolarizability in Eq. (67) is verified by explicit comparison of the six terms in each case. We see that the probability of three-photon absorption depend on the light intensity to the third power.

There are also physical interactions between the quantum mechanical system and the environment that may be described by a dielectric continuum model and which can be included in a self-consistent field approach (see Chapter 4). Let us return to the problem of solving the response of the quantum mechanical system to an external electric field. The zeroth-order wave function of the quantum mechanical system is obtained by use of any of the standard approximate methods in quantum chemistry and the coupling to the field is described by the electric dipole operator.