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# Sensitive vectorial optomechanical footprint of light in soft condensed matter

## Abstract

Among the properties of light that dictate its mechanical effects, polarization has held a special place since the mechanical identification of the photon spin1. Nowadays, little surprise might be expected from the mechanical action of linearly polarized weakly focused (paraxial) beams on transparent and homogeneous dielectrics. Still, here we unveil vectorial optomechanical effects mediated by the material anisotropy and the longitudinal field component inherent to real-world beams2,3. Experimentally, this is demonstrated by using an elastic anisotropic medium prone to exhibit a sensitive and reversible effect, that is, a nematic liquid crystal, and our results are generalized to vector beams4. This represents an alternative to irreversible damaging approaches restricted to strongly non-paraxial fields5. The reported creation of multiple self-induced lenses from a single beam also open up topology assisted all-optical information routing strategies. Moreover, our findings point out the transverse internal optical energy flows (spin and orbital)6 as novel triggers to tailor structured optical nonlinearities.

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## Data availability

The data that support the findings of this study are available on request from the corresponding author.

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## Acknowledgements

This work has been partially funded by the Research Foundation for Opto-Science and Technology and JSPS KAKENHI (grant no. 20K05364).

## Author information

Authors

### Contributions

E.B. conceived and supervised the project. All authors contributed to the experimental and theoretical results. E.B. wrote the manuscript with contributions from other authors.

### Corresponding author

Correspondence to Etienne Brasselet.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Extended data

### Extended Data Fig. 1 Calculated transverse optical torque density inside the unperturbed anisotropic slab.

Calculated transverse spatial profiles of the normalized optical torque density Cartesian components Γx and Γy for an incident Gaussian field having a linear polarization state oriented along the x axis and propagating along the z axis, where 0≤ξL refers to the propagation distance along the optical axis of the crystal from its input facet that defines ξ = 0. Two values of the internal Gaussian beam divergence angle are considered: θ0 = 1 (a) and θ0 = 10 (b). Each box is centered on (x, y) = (0, 0) and covers an area δL × δL where δ = 2w(z)/L. Each plot is normalized to the maximal value of the plot at ξ = L on the same row and $$\max ({\varGamma }_{x}{| }_{\xi = L})=1.2\times 1{0}^{-3}\max ({\varGamma }_{y}{| }_{\xi = L})$$ for θ0 = 1 whereas $$\max ({\varGamma }_{x}{| }_{\xi = L})=0.60\max ({\varGamma }_{y}{| }_{\xi = L})$$ for θ0 = 10. Parameters: δ = 1.5, L = 57μm, n = 1.756 and n = 1.528. See Methods for details.

### Extended Data Fig. 2 Detailed experimental setup.

Extended version of the illustrative experimental setup shown in Fig. 2(a). BS: non-polarizing beamsplitter for the probe beam. Note that Fig. 2(a) only summarizes the main instrumental ingredients used in practice. Namely, the lens L2 in Fig. 2(a) is an imaging lens for the probe beam in order to observe the director field at the mid-plane of the liquid crystal sample, which corresponds to the 10 × objective lens as shown here. Also, the lens L3 in Fig. 2(a) refers to a collimating lens for the pump beam, which corresponds to a lens system made of a 10 × objective lens followed by a plano-convex lens (f = 100, 150, 200 mm) as shown here. See Methods for details.

### Extended Data Fig. 3 Experimental reconstruction of the director field perturbation for incident light with uniform linear polarization state.

Reconstructed spatial distribution of the director field in the mid-plane of the cell $${\tilde{{\bf{n}}}}_{\perp }=({\tilde{n}}_{x},{\tilde{n}}_{y},0)$$ as in Fig. 2(b) but for another set of parameters: θ0 = 8. 0, δ = 2.0 and P = 250 mW. Here $$\max | {\tilde{n}}_{y}| /\max | {\tilde{n}}_{x}| \simeq 0.88$$. This demonstrates the robustness of the effect versus the diameter of the beam. We notice that the required power to reach the same magnitude for the material response increases with δ whereas choosing δ > 1 facilitates the observations. The latter point can be understood from the fact that the nonlocal character of the nematic response is strengthened as δ decreases 44.

### Extended Data Fig. 4 Transverse intensity profiles of the incident vector beams.

Testing the Laguerre-Gaussian lineshapes of the prepared vector beams. Markers: azimuthally-averaged radial intensity profiles measured just before the focusing lens, a × 10 microscope objective with a numerical aperture NA = 0.4. Solid curves: best fit using the Eq. (4).

### Extended Data Fig. 5 Pump and probe optical characterization of the customary light-induced Fréedericksz instability.

Experimental determination of the customary optical Fréedericksz instability for θ0 = 1. 6 and δ = 1.7 from the pump beam analysis (a) and from probe beam analysis (b). Set of selected power values that corresponds to the transverse intensity profiles shown in the top row: PA = 231 mW, PB = 235 mW, PC = 246 mW while Pth = 233 ± 1 mW . In panel (a), case C, the luminance has been enhanced on the right side of the image in order to better visualize the self-phase modulation intensity rings.

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El Ketara, M., Kobayashi, H. & Brasselet, E. Sensitive vectorial optomechanical footprint of light in soft condensed matter. Nat. Photonics 15, 121–124 (2021). https://doi.org/10.1038/s41566-020-00726-2

• Accepted:

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• DOI: https://doi.org/10.1038/s41566-020-00726-2

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