Abstract
The second hyperpolarizability (γ) of the H2 molecule was measured by gas-phase electric field induced second harmonic generation at the frequencies of the one-photon resonance for the 3-0 Q(J) overtone transitions (v, J = 0, J → 3, J for J = 0, 1, 2, and 3). The magnitude of the resonant contribution to γ was measured with 2% accuracy using the previously determined non-resonant γ for calibration. Pressure broadening and frequency shift for the transitions were also measured. A theoretical expression for the resonant vibrational γ contribution in terms of transition polarizabilities is compared to the observations. The measured γ resonance strength is 4%-14% larger than the results obtained from this theoretical expression evaluated using ab initio transition polarizabilities.
Highlights
The nonlinear optical (NLO) response of a centrosymmetric molecule is described by the second hyperpolarizability tensor γαβγδ(−ωσ; ω1, ω2, ω3), which is a complicated function of the incident field frequencies ω1, ω2, ω3 and polarizations β, γ, δ due to the electronic, vibrational, and rotational excitations of the molecule
The electronic hyperpolarizability contribution can be described by a universal dispersion formula that applies for all NLO processes,1,2 but the expressions for the vibrational hyperpolarizability are more complicated and differ significantly from one NLO process to the next
The frequency sequence in each scan was shuffled to reduce the effect of slow signal drift during the course of the measurements, and 2, 2, 0, 2, 1 of the scans in Figs. 3(a)–3(e) were done by “triplets.” For these scans, a point about 0.4–1.0 cm−1 offresonance was designated as the internal reference for the scan and measurements at other frequencies designated as the signal
Summary
The nonlinear optical (NLO) response of a centrosymmetric molecule is described by the second hyperpolarizability tensor γαβγδ(−ωσ; ω1, ω2, ω3), which is a complicated function of the incident field frequencies ω1, ω2, ω3 and polarizations β, γ, δ due to the electronic, vibrational, and rotational excitations of the molecule. The electronic hyperpolarizability contribution can be described by a universal dispersion formula that applies for all NLO processes, but the expressions for the vibrational hyperpolarizability are more complicated and differ significantly from one NLO process to the next.. For a homonuclear diatomic molecule, using this expression to calculate the vibrational hyperpolarizability, the electronic hyperpolarizability can be determined from hyperpolarizability dispersion measurements for one NLO process. This allows the dispersion curve for any other NLO processes to be determined. Such an analysis has been applied to hyperpolarizability measurements for H2, D2, N2, and O2.6 some approximations are made in the derivation of this expression for the vibrational hyperpolarizability, and a direct experimental test of the expression has not been performed since the vibrational and electronic contributions are not distinguished in the usual experiments measuring the total molecular hyperpolarizability. The theoretical expression for the resonant vibrational hyperpolarizability is presented, the experiment to measure the resonant overtone vibrational hyperpolarizability in H2 is described, and the experimental results are used to test the theoretical expression for the vibrational hyperpolarizability
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