Observation of disordered wave functions with conical second-harmonic generation and verification of transition from extended to prelocalized states in weak localization

Abstract

We experimentally acquire the disordered wave functions from the conical second-harmonic generation to explore the variation of weak localization from extended to prelocalized states. We numerically verify that the experimental density distributions with different extents of weak localization can be excellently analyzed with a reduced version of the nonlinear σ model (RV-NLS model). Moreover, we demonstrate that the χ -square distributions with fractional degrees of freedom are practically equivalent to the density distributions of the RV-NLS model. Our finding indicates that the concept of fractional degrees of freedom can be applied to the statistical properties of disordered wave functions.

Pattern formation of second harmonic conical waves in a nonlinear medium with extended defect structure

“…3(f Figure 4 demonstrates another kind of SH wave pattern formed by the interference of dozens of Bessel-like beams that originate randomly from different layers inside the crystal. This SH wave pattern has been called the extended state which has its intensity distribution widely spreading over the space [5,13]. It is clear seen that the extended state displays the propagation behavior of the random pattern associated with the quasi-linear ridge structure [27].…”

“…However, SHG is not restricted to the collinear interactions; non-collinear schemes can be realized as well. Though the noncollinear geometries are not suitable for efficient frequency doubling, scientists have taken great interests in their physics and applications on material characterization [2][3][4][5][6][7][8][9][10][11][12][13].…”

“…Figure 1 shows the experimental setup of a diode-pumped actively Q-switched Nd:YAG laser with intracavity SHG in a GdCOB crystal. The same experimental scheme has been presented in [5,13]. The active medium is a 0.8-at.…”