Nonlinear optical measurements in the excitonic region of CdS at 4.2 K

Second-harmonic generation, two-photon absorption, and $k$-vector spectroscopy were performed as a function of frequency in the excitonic region of CdS at 4.2 K. The measured second-harmonic intensities were compared with intensities calculated from an anharmonic-oscillator model. The relative strengths of the excitonic contribution to the second-order nonlinear susceptibility were determined for each input polarization. The results of two-photon absorption measurements were interpreted in terms of direct and indirect processes. For the direct process $p$-exciton peaks of the $A$ and $B$ exciton series were observed and the splitting of the $P_{x,y}$ and $P_z$ components of the $A$, $n=2\mathrm{}$ exciton could be resolved. Observed relative $p$-exciton band strengths could be modeled with a many-band model of two-photon absorption. Indirect two-photon absorption, a two-step process involving phase matching, was verified by combining two-photon absorption and second-harmonic intensity measurements. Phase-matched two-photon absorption was then used in a third series of experiments with two crossed beams overlapping in the CdS samples to measure part of the dispersion curve of the exciton-polariton near the $B$-exciton photon energies $k$-vector spectroscopy). A model including spatial dispersion (i.e., the nonlocality of the dielectric constant) was found to give a better fit to the measured dispersion curve. By simultaneously measuring second-harmonic power, two-photon absorption, and the dispersion curve a consistent set of theoretical parameters could be determined for CdS and various checks on experimental results could be performed.