Manifestation of Weak Localization and Long-Range Correlation in Disordered Wave Functions from Conical Second Harmonic Generation

Abstract

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.

Geometry of classical periodic orbits and quantum coherent states in coupled oscillators with SU(2) transformations

“…Equation (16) indicates that the probability distributions of the coherent states | (t; υ 1 ,υ 2 ) are concentrated exactly on the Lissajous-trochoid transformed curves shown in Eq. (5).…”

“…Modern laser cavities have been employed extensively to serve as an analogous system to provide an experimental visualization in an optical context to confirm many quantum effects such as quantum chaos phenomena [14,15], disorderinduced wave localization [16], geometric phases [17], and quantum tunneling [18]. Spatial structures of laser modes in broad-area resonators have been of interest for a long time because they offer much insight into the pattern formation of natural waves [19][20][21][22][23][24][25][26][27].…”

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

“…In experiments the disordered wave functions were measured in a microwave cavity to show the influence of chaos and localization in disordered quantum billiards. 13 In 2006, Chen et al 26 demonstrated the spatial structure of two-dimensional (2D) disordered wave functions from exploring the near-field patterns of conical second-harmonic generation (SHG) in a GdCa 4 O(BO) (GdCOB) nonlinear crystal with moderate defect domains. So far, experimental results for the disordered wave functions only covered a partial WL regime and did not provide a comprehensive analysis of the transition from extended to prelocalized states.…”

Model of commensurate harmonic oscillators with SU(2) coupling interactions: Analogous observation in laser transverse modes

“…Consequently, the electromagnetic radiation modes in the optical resonator or waveguide are analogs of the wave functions of a quantum system [10][11][12]. The tight connection between the paraxial beam propagation and quantum mechanics has been extensively exploited to study wave chaos phenomena [11,13,14], disorder induced wave localization [15], semiclassical physics [16,17], and transient dynamics of quantum states [18][19][20].…”