Electro-optic phase modulation was measured along with optical second-harmonic generation in thin films of a new copolymer containing a dicyanovinyl-terminated azo dye side chain. Orientational order was imparted to these films by poling with a corona discharge. Details of the electro-optic measurement technique, in which the real part of the electro-optic coefficient can be determined directly, are presented. Taking advantage of the increased orientation imparted by corona poling and the hindered motion of the nonlinear optical moiety in the side chain of the polymer leads to substantial improvements in both the magnitude and stability of nonlinear optical susceptibilities compared to guest-host polymer systems ordered by electrode poling.

We apply sum rules to answer the question: What is the largest off-resonance electronic nonlinear susceptibility allowed by quantum mechanics? The sum-rule-restricted three-level model shows that the two-level limit yields the absolute maximum susceptibility, which is found to depend only on the first excited state transition energy and number of electrons—in agreement with a large set of second- and third-order susceptibility data from the literature. As such, the sum rules provide a target for the maximum possible off-resonant susceptibilities.

Our approach to the problem of understanding the nonlinear-optical response of a material focuses on fundamental concepts, which are exact and lead to broad results that encompass all material systems. For example, one can calculate precisely and without approximation the fundamental limit of the efficiency of any optical phenomenon. Such limits, in turn, when built into a scale-invariant figure of merit can be used to determine what makes a material optimal for maximizing a desired property, such as its nonlinear-optical response. However, since the results are broad and general (for example, fundamental guidelines for making better quantum systems may demand a particular shape of an electron cloud or energy level spacing), the difficulty arises in implementing such fine tuning using the approaches available to the synthetic chemist or nanotechnologist. Undoubtedly, an intimate interplay of empirical and fundamental approaches will need to be applied to the problem of optimizing molecules and materials. Much of the work in the field of nonlinear optics has by necessity focused on empirical approaches. Our work focuses on the fundamental approach, which is beginning to bear fruit in providing practical guidelines for making new materials. This paper reviews progress made over the last decade.

We apply sum rules to calculate the maximum limit of the resonant two-photon absorption cross section. Comparison of the theory with experimental data from the literature shows that no molecule ever measured exceeds this limit. Molecules with more π electrons have larger two-photon cross sections; but, the two-photon cross sections fall further below the fundamental limit as the number of electrons increases—implying that the additional electrons are not participating efficiently. The sum rules can aid in developing structure property relationships by providing metrics that lead to a deeper understanding of the available data.

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The off-resonant electronic third-order optical susceptibility is derived in the dipole approximation using the method of averages. These results are studied in detail for the two-, three-, and N-level model to determine the origin of the susceptibility with symmetry considerations. If the matrix elements are independent, the third-order susceptibility is shown to be maximized in centrosymmetric structures in the two-level model while, for the general N-level system, weak coupling between the excited states is also required. To address the interdependence of the matrix elements, a two- and three-level system is perturbed to make the molecular potential asymmetric or more asymmetric, and the conditions on the matrix elements for maximizing the third-order susceptibility are derived. The dependence of the third-order susceptibility on the asymmetry of a harmonic oscillator and particle in a box are also discussed.