Programmable branched flow of light

Abstract

We demonstrate deterministic control of branched flow of light using anisotropic nematic liquid crystals. By sculpting the director field via photoalignment, we create spatially programmable optical potentials that govern light scattering and propagation. This platform enables configurable, anisotropic branched flow of light and reveals a universal scaling law for its characteristic features, directly connecting disordered photonics with mesoscopic wave transport. Under extreme anisotropy, we observe a pronounced directional channeling effect, driven by anomalous symmetry-breaking velocity diffusion, which concentrates light propagation along preferential directions while suppressing transverse spreading. These findings establish a tunable material platform for harnessing branched flow of light, opening pathways toward on-chip photonic circuits that exploit disorder-guided transport, scattering-resilient endoscopic imaging, and adaptive optical interfaces in complex media.

Figures (4)

• Figure 1: Programmable optical branched flow in nematic liquid crystals (NLC). (a) Tailoring disordered potential of photo-alignment NLC film via potential anisotropy and rotation for controlling anisotropic branched flow. DMD: digital micro-mirror device. (b-d) The simulated optical branched flow fields in the anisotropic disordered NLC film with different potential anisotropy ($A$) and rotation ($\alpha$). The panels (i) are the simulated branched flow fields with a plane-wave excitation, where the insets show the correlation function of the corresponding disordered potential. The panels (ii) are the simulated branched flow fields via a point-source excitation. Here the correlation length $l_x$ is set constant as 15 $\upmu$m. All the scale bars are 200 $\upmu$m.
• Figure 2: Experimental observation of anisotropic branched flow with controllable first-branch distance. (a) Schematic diagram of photo-patterning NLC films with designed disordered director distributions. (b) Experimental setup for excitation and characterization of branched flow in an NLC sample. (c-h) Cross-polarized microscope images (upper panels) of fabricated NLC films with varying potential anisotropy $A$ and potential rotation angle $\alpha$, and their correspondingly measured profiles of the propagating field (lower panels). In (c-e) the disordered potentials are of the same $\alpha=0$, and different $A$-values: (c) $A=1.0$, (d) $A=1.8$. (e) $A=2.6$. In (f-h) the disordered potentials are of the same $A=1.8$, and different $\alpha-$values: (f) $\alpha=0$, (g) $\alpha=\pi/4$, (h) $\alpha=\pi/2$. The insets in the upper panels of (c-h) are the autocorrelation function of the disordered optical potential. The white dashed line in lower panels of (c-h) indicates the measured first-branch distance. All the scale bar is 100 $\upmu$m.
• Figure 3: Quantitative measurement of the first-branch distance on potential anisotropy and potential rotation. (a) The shift of scintillation index curves on varying potential anisotropy. (b) Experimental and simulated results of first-branch distance depending on potential anisotropy. (c) The shift of scintillation index curves on varying potential rotation angle. The potential anisotropy is set as 1.8. (d) Experimental and simulated results of first-branch distance depending on potential rotation angle. The error bars in (b,d) is bandwidth of 98$\%$ peak value of the normalized scintillation index curve.
• Figure 4: Observation of light channeling effect in extreme anisotropic disordered potential. (a) Simulated branched flow field in spatially anisotropic disordered NLC films, with anisotropy of $A=1/1000$. Here $l_y$ is set as 16 $\upmu$m. The scale bar is represented by the correlation lengths. (b-d) The microscope images show the branching of a wide elliptical laser beam propagating through extreme anisotropic potentials ($A=1/1000$) at spatial orientation angles of (b) 0, (c) $\pi/9$, and (d) $\pi/6$. The insets in (a-d) show the autocorrelation function of the disordered potential. The scale bar is 100 $\upmu$m. (e-f) The standard deviation of the velocity angle for propagating light in an extremely anisotropic potential ($A=1/1000$): (e) experimental results, (f) simulated results. The undertint curves are examples of realizations as an illustration for the typical variation in individual realizations of the disordered NLCs. The dashed-blue lines in (e-f) are proportional to $L^{1/2}$ for normal diffusion process, where $L$ is the propagation distance.