Manifestation of weak localization and long-range correlation in disordered wave functions from conical second harmonic generation

We experimentally demonstrate that the near-field patterns of conical second harmonic generation of a laser in random domain structures can be used to explore the spatial structure of two-dimensional disordered wave functions with weak localization. The statistics of the experimental near-field patterns agree very well with the theoretical distributions. In addition to the short-range correlation, the localization effects are found to contribute a nearly constant value to the long-range correlation. The result of this Letter also confirms the possibility of using conical second harmonic generation as a diagnostic tool for topographical characterization of crystals.