Two-beam SHG from centrosymmetric media
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We report a comprehensive study of quadrupolar second-harmonic generation (SHG) from centrosymmetric materials. Because of symmetry, quadrupolar SHG from centrosymmetric materials is forbidden in the forward direction, and is extremely weak when it is obtained using a traditional single-beam SHG geometry. A two-beam geometry is found to enhance quadrupolar SHG greatly compared to single-beam SHG. Two orthogonally polarized laser beams create wavelength-scale, forward-radiating gradients in the second-harmonic polarization that enhance SHG. The radiation pattern of two-beam quadrupolar SHG is observed to have a TEM00 mode, different from single-beam quadrupolar SHG which has a TEM01 mode. The quantitative study of quadrupolar SHG is done with a two-beam geometry on an isotropic glass slide. The polarization of the two-beam quadrupolar SHG is found to be normal to the plane determined by the two crossed fundamental beams, and the SHG intensity depends on the orthogonally polarized fundamental electric fields. Quadrupolar SHG from a glass slide with two tightly focused laser beams appears surface-like – SHG peaks sharply when the glass surfaces are centered on the two-beam overlap region, but vanishes when the overlap is totally immersed in glass bulk. Quasi-phase-matched quadrupolar SHG from two glass slides (and two pellicle films) is demonstrated. Enhanced and phase-matched two-beam SHG from a centrosymmetric and birefringent crystal – calcite – is also realized. Preliminary studies on the application of two-beam SHG in microscopy are done with a scratched glass slide. We find that dipolar SHG and quadrupolar SHG can be selectively imaged by choosing different polarization combinations of the fundamental laser beams. Macroscopically centrosymmetric silicon nanocrystal composites embedded in glass are studied by single-beam and enhanced two-beam SHG. Both techniques are sensitive to the nano-interface chemistry, but two-beam SHG gives rise to a signal that is several orders stronger. Multiple signal discrimination techniques are developed to separate the nanocrystal SHG from the glass SHG which is also enhanced by the two-beam geometry. The enhanced two-beam SHG enables spectroscopy and time resolved studies of silicon nano-interfaces.