Filtering of matter symmetry properties by circularly polarized nonlinear optics

We propose a direct readout of symmetry information in matter using nonlinear optics. From combinations of circularly and longitudinally polarized optical fields, we construct irreducible spherical field tensors for second- and third-order nonlinear processes. The coupling of these field tensors to the matter susceptibility tensors allows filtering out of the susceptibility symmetries independently of the sample orientation in the laboratory frame. Experimental demonstrations are conducted on microcrystals, in a microscopy configuration compatible with symmetry order imaging.

Figure 1

(a) SHG raw images of TTB crystals with dipolar (${\widehat{e}}_1{\widehat{e}}_1{\widehat{e}}_1)$ and octupolar (${\widehat{e}}_{-1}{\widehat{e}}_1{\widehat{e}}_1)$ polarization sets. (b) White light image and selected area for polarization-resolved SHG images. (c) Ratio between third and first orders (see text) and (d) its histogram. Scale bars: 10 $\mu \text{m}$.

Figure 2

(a) FWM raw images of NaCl microcrystal surrounded by oil with its isotropic (${\widehat{e}}_1{\widehat{e}}_1{\widehat{e}}_1{\widehat{e}}_1$), second- (${\widehat{e}}_{-1}{\widehat{e}}_1{\widehat{e}}_1{\widehat{e}}_1$), and fourth-order (${\widehat{e}}_{-1}{\widehat{e}}_1{\widehat{e}}_1{\widehat{e}}_{-1}$) contributions. (b) White light image of three NaCl crystals with different orientations in the sample plane. (c) Ratio between fourth and zero orders and (d) its histogram. Scale bars: 10 $\mu \text{m}$.