Topological Encoded Vector Beams for Monitoring Amyloid‐Lipid Interactions in Microcavity

Abstract Lasers are the pillars of modern photonics and sensing. Recent advances in microlasers have demonstrated its extraordinary lasing characteristics suitable for biosensing. However, most lasers utilized lasing spectrum as a detection signal, which can hardly detect or characterize nanoscale structural changes in microcavity. Here the concept of amplified structured light‐molecule interactions is introduced to monitor tiny bio‐structural changes in a microcavity. Biomimetic liquid crystal droplets with self‐assembled lipid monolayers are sandwiched in a Fabry–Pérot cavity, where subtle protein‐lipid membrane interactions trigger the topological transformation of output vector beams. By exploiting Amyloid β (Aβ)‐lipid membrane interactions as a proof‐of‐concept, it is demonstrated that vector laser beams can be viewed as a topology of complex laser modes and polarization states. The concept of topological‐encoded laser barcodes is therefore developed to reveal dynamic changes of laser modes and Aβ‐lipid interactions with different Aβ assembly structures. The findings demonstrate that the topology of vector beams represents significant features of intracavity nano‐structural dynamics resulted from structured light‐molecule interactions.


CHARACTERIZATION OF LASER EMISSION 1.Experimental setup
The schematic illustration of the experimental setup was shown in Supplementary Fig. 1. Briefly, the laser emission from the LC droplet was split by a beam splitter and send to a CCD and a spectrometer, thus enabling the simultaneous collection of laser mode imaging and spectra.
The hyperspectral images were collected by keeping the slit widely open. The laser emission was diffracted using a grating and imaged by a thermoelectrically cooled CCD.
The resulting hyperspectral image shows separated laser mode components on a specific wavelength. Figure 1. Illustration of the experimental setup. Inset, the enlargement of the vector beam emitter.

Emission spectra with various pump energy densities
The emission spectra with various pump energy densities were plotted in Supplementary  Fig. 2. The observed peaks in spectra correspond to the longitudinal laser modes.

Supplementary Figure 2.
Laser spectra with various pump energy density. Individual peaks appear with a pump energy density above the lasing threshold. The number of longitudinal laser modes increases with an increasing pump energy density.

Influence of droplet size and cavity size on the laser mode pattern
As illustrated in Supplementary Fig. 1, the critical parameters of this configuration include the droplet size (d) and cavity size (L). The influence of these two parameters on the laser mode pattern is illustrated in Supplementary Figs. 3 to 4.
(1) Droplet size Because of a lower intracavity gain in a small droplet, laser emission can hardly be achieved when the droplet size is below 10 m. As illustrated in Supplementary Fig. 3, when the size of the droplets gets larger, a more complex transverse mode pattern can be observed. Even though more significant changes in transverse mode pattern are expected in a larger droplet size, the complex patterns make the mode identification very hard. The droplet size in the range 18-25 m is preferred for laser mode measurement.
Supplementary Figure. 3. The laser mode pattern from LC droplets with different sizes. Scale bar: 10 m. The doted circles denote the sizes of the droplets. The size of the cavity is kept at 45 M.
(2) Cavity size As illustrated in Supplementary Fig. 4, the cavity size shows no significant influence on the complexity of laser mode pattern. However, because of a higher lasing threshold induce by a larger intracavity loss with a larger cavity size, we do not suggest a cavity size larger than 50 m.
Supplementary Fig. 4. The laser mode pattern with different cavity sizes. The size of droplet is kept at 25 m. Scale bar: 10 m.

Ultrahigh sensitivity of laser modes
The polarized microscopy has been widely used as a gold-standard method for checking the conformation changes of LC. Here, we tried to compare the response of the laser mode to the conformation changes induced by biomolecules with the conventional polarized image. After BSA was induced, continues topological transformation of laser mode can be observed (bottom, Fig. 2f). In contrary, the conventional polarized image remains stable ( Supplementary Fig. 5) all the time. Figure 5. Polarized pattern of LC droplet when 15 nM BSA was induced.

Supplementary
Then, we tried to increase the concentration of BSA to 150 nM and repeat the experiment. The results are given in Supplementary Fig. 6. Because the higher concentration tigers larger conformation changes in LC molecules, a more rapid transformation in laser mode was observed. However, the polarized image remains stable before 116.4 s. At 183.2s, significant changes in polarized image can be observed. In the meantime, the laser modes started to quench, which may come from an increasing intracavity loss in the radial to bipolar transition process. These results indicate that the laser mode possess much higher sensitivity than the polarized image, which is potentially used for molecular interaction investigation. Figure 6. Comparison between the laser mode evolution and the conventional polarized image. The BSA concentration is 150 nM.

INVESTIGATION OF AMYLOID PEPTIDE-LIPID MEMBRANE INTERACTIONS 2.1 Lipid coated LC droplets
A monolayer lipid self-assembled on the LC droplet was used to imitate the biological membrane. As illustrated in Supplementary Fig. 7a, once the 3 M BSA was induced, the conformation of the LC droplet changes to bipolar immediately (within 1 s). However, when the uncoated LC droplet was used (the same as in Fig. 2), the polarized image of the LC droplet shows no significant conformation change ( Supplementary Fig.  7b) even after 15 s. Note that the concentration of BSA is 20 times higher than used in Supplementary Fig. 6, which enables us to observe significant radial to bipolar changes in a shorter time. The result indicates the lipid coated LC droplets are more sensitive to molecular binding than the uncoated ones. Supplementary Figure 7. a, The polarized image showing the conformation of lipid coated LC droplet changes from radial to bipolar when 3 M BSA was added. b, The polarized image of uncoated LC droplet remaining the same after BSA was induced.

Recognition of the laser mode topologies (1) Recognition of laser mode orders
The Laguerre-Gaussian modes are a series of solutions for paraxial wave equations in cylindrical coordinates, which can be written in terms of the Laguerre polynomials as 1 where, m, n is the radial, azimuthal order of LG mode, respectively.
  wz ,   qz is the size and the q-factor of the gaussian beam. LG mode with various orders was plotted in Supplementary Fig. 8, showing "dots" and "flowers" patterns with m and 2n node lines in radial and azimuthal direction. In particular, the observed "circles" in our experiment may be caused by the incoherent superposition of LC modes with different orders, thus making the azimuthal mode order unrecognizable.

Supplementary Figure 8.
LG mode patterns with various orders. The laser mode orders can be easily recognized by the node lines in the radial, azimuthal direction.
(2) Recognition of polarization We have experimentally demonstrated a spatial dependent polarization vector in Fig. 2e.
Here, we try to illustrate the feasibility of recognizing the polarization based on the laser mode pattern through a linear polarizer. In order to describe the polarization state of laser mode, we write the electronic filed of LG mode in a vector form  Supplementary Fig. 10. After passing through a linear polarizer, two symmetry dark regions appear on the laser mode pattern, which is consistent with our experimental result. The polarization of a specific laser mode can be easily recognized by the value of  , which is defined as the angle between the orientation of the maximum intensity and horizontal direction. As shown in Supplementary Fig. 10,

Dynamic laser mode evolution with various A peptide concentration
The laser mode evolution and the decomposition results with various A peptide concentrations were recorded in Supplementary Figs. 11 to 13 and Fig. 3c. The corresponding topology parameters (m, n, P) were recorded in Supplementary Tables 1 to  4. (1) 2.2 nM A peptide Supplementary Figure 11. Evolution of laser mode pattern with the decomposed components (top) and the polarized images (bottom). The concentration of A peptide is 2.2 nM.    (4) 2.2 M A peptide The laser mode evolution and the corresponding polarized images with 2.2 M A peptide is recorded in Fig. 3c.