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.

Figure 1

The experimental configuration for the diode-pumped actively $Q$-switched $\mathrm{Nd}:\mathrm{YAG}$ laser with intracavity SHG in the GdCOB crystal.

Figure 2

(a) The typical far-field pattern of conical SHG. (b) Phase-matching diagram for a conical SHG process in which ${\overline{k}}_1$ is the axial fundamental beam, ${\overline{k}}_1^{\prime }$ is the scattered off-axis fundamental beam, and ${\overline{k}}_2$ is the phase-matched off-axis SHG beam.

Figure 3

Four examples of the near-field wave patterns measured at different transverse positions of the GdCOB crystal.

Figure 4

(a)–(d) The density probabilities $P(I)$ for the experimental data shown in Figs. 3a, 3b, 3c, 3d, respectively.

Figure 5

The measurement of intensity correlation function $C(\Delta r)$ for the experimental wave patterns shown in Figs. 3a, 3b, 3c, 3d. Inset: The difference $C(\Delta r)-C_1(\Delta r)$.