# Rewritable Binary Recording of the Photon Spin State in Chiral Liquid Crystals

Nicolas Bruni, Charles Loussert, Mushegh Rafayelyan, Tetiana Orlova, Delphine Coursault, Etienne Brasselet

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Nicolas Bruni, Charles Loussert, Mushegh Rafayelyan, Tetiana Orlova, Delphine Coursault, et al. "Rewritable Binary Recording of the Photon Spin State in Chiral Liquid Crystals." Physical Review Letters, 2025, 134 (22), pp.223804. 10.1103/pqdp-x2vr. hal-05337424

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# Rewritable Binary Recording of the Photon Spin State in Chiral Liquid Crystals

Nicolas Bruni, Charles Loussert, Mushegh Rafayelyan, Tetiana Orlova, Delphine Coursault, and Etienne Brasselet

University of Bordeaux, CNRS, Laboratoire Ondes et Matière d'Aquitaine, F-33400 Talence, France

<figure><img src="image_2.png" /></figure>

We experimentally demonstrate that the spin state (up or down) of circularly polarized light can be reliably encoded as a polar structural state (up or down) in chiral liquid crystals, with high selectivity. This enables a spin-driven, nonvolatile binary liquid crystal memory, which can be optically written and electrically erased on demand. The underlying mechanism involves an orientational buckling instability, whose direction depends on whether the handedness of light matches or opposes that of the chiral medium. This optical poling effect arises from a chiral light-matter interaction during the propagation of light through the twisted anisotropic medium.

**Introduction**—Using light to store and retrieve information from matter is a long-standing technological goal, with the first patent dating back nearly a century [1]. Optical data storage has since evolved into a variety of solutions that rival or surpass electronic ones [2]. Particles with nonzero spin, like photons and electrons, have inspired encoding binary information in matter via spin states, with magnetic materials being prime candidates [3–6]. Beyond magnetism, spin angular momentum of light enables data encoding in solids and fluids, from irreversible chiral writing in solid-state media [7] to reversible structuring in achiral liquid crystals [8]. Here, by combining the optical reorientation of liquid crystals [9] with the structural multistability of frustrated chiral phases [10–12], we experimentally demonstrate a spin-driven binary liquid crystal memory. The recorded unit of information, termed a spin bit, highlights a strongly selective binary process controlled by the photon spin state. Notably, spin bits are both rewritable and non-volatile, positioning liquid crystal-based optical memories [13] within the scope of spin-dependent photonics [14].

**Chiral light-matter system**—We use chiral nematic liquid crystals, characterized by a helical orientational order of pitch $p$ (the distance over which the director **n** rotates by $2\pi$) and a handedness (right or left). Confined between plane-parallel substrates enforcing perpendicular anchoring, a uniform helix cannot form. When confinement is strong ($p/L \gtrsim 1$, with $L$ the cell thickness), frustration unwinds the helix completely [15], yielding a stable uniform director $n_0$ normal to the film plane (see Supplemental Material Sec. I [16]). For $p \approx L$, long-lived, particlelike elastic excitations can coexist with $n_0$, a phenomenon known since the 1970s [10–12]. Numerous topologically distinct excitations, some with supramolecular polarity, have since been identified via 3D director reconstruction [27–29]. While polarity can arise from up or down symmetry breaking due to geometric constraints [30], on-demand generation of polar excitations had not been

demonstrated. Here, we achieve it using a paraxial circularly polarized Gaussian beam (waist $w$) at normal incidence. As illustrated in Fig. 1, the spin bit state (up or down) is determined by the match or mismatch between light and matter chirality.

**Writing, erasing, and storing spin bits**—Experiments are conducted at room temperature under nominal conditions with $w \approx p \approx L$, where $L$ ranges from 3 to 50 µm [31] and the liquid crystal birefringence $dn$ from 0.06 to 0.22. A continuous-wave 532 nm laser beam with sufficient power $P$ induces distortions in the director field, enabling the storage of particlelike elastic excitations. Figure 2

<figure><img src="image_3.png" /><figcaption>FIG. 1. Schematic representation of the four possible chiral light-matter interaction scenarios, each leading to the generation of particle-like elastic excitations with either up or down orientation and left-handed or right-handed twist (depicted by twisted arrows). The diagram highlights enantiomeric (mirror-image) pairs, with $L$ and $R$ indicating the handedness of the light and the liquid crystal. Chiral light: circularly polarized light characterized by a helical electric field trajectory along the direction of propagation, shown at a fixed moment in time. Chiral liquid crystal: medium with a uniformly twisted (helical) director field.</figcaption></figure>
<figure><img src="image_4.png" /></figure>

FIG. 2. XPOL images of recorded spin bits written with *L* and *R* circularly polarized pump beam for samples of various thickness (a) and birefringence (b). The arrowed cross refers to the orientation of the linear polarizer (dark color) and analyzer (light color). Observations are made for *L* chiral nematics using halogen lamp illumination and long pass color glass filter ($\lambda_{probe} > 590$ nm). (a) E7 nematic material. (b) Nematics R237, MLC6608 and E7 for increasing *dn* at *L* = 10 µm. See also videos 1–4 showing the spin bit writing process for *L* = 10 µm and E7 material. Scale bars: *L*.

illustrates the results: crossed linear polarized (XPOL) images show recorded excitations generated by either right- or left-handed circular polarization, for various *L* at fixed *dn* [Fig. 2(a)] and various *dn* at fixed *L* [Fig. 2(b)]. Remarkably, the swirling XPOL intensity pattern (clockwise or counterclockwise) depends solely on the polarization handedness, indicating that different structures are written depending on the spin state of the incident light. We refer to Supplemental Material, Sec. I to IV, for complementary data [16].

This spin-driven phenomenon occurs regardless of the handedness of the chiral liquid crystal and is not restricted to a specific surface anchoring, though the latter is known to influence the structural stability of particlelike elastic excitations [32]. The recorded structures can be erased on demand using an electric field in materials with positive dielectric anisotropy, allowing reproducibility tests that confirm high fidelity. Spin bit storage is also long lived, with some samples remaining stable for over two years. We refer to Supplemental Material, Secs. V and VI for additional support of these remarkable properties [16]. Next, we address key questions: what structural features are shared or distinct between spin bits generated with different optical and material chirality, and how are they related? While 3D director mapping via linear or nonlinear microscopy is possible [33], we instead use standard polarization imaging, which is well suited for this study.

**Spin bits structural features**—The invariance of the XPOL pattern under in-plane rotation of the sample around

<figure><img src="image_5.png" /></figure>

FIG. 3. XPOL z-scan intensity maps in the (*r*, *z*) plane for the four possible chiral light-matter interaction scenarios, highlighting mirror-image configurations. After spin bit generation, the sample is either kept in its original orientation (“sample upside”) or flipped (“sample downside”). Insets: thumbnails as defined in Fig. 1. Scale bars: 10 (horizontal), 50 µm (vertical). The maps result from azimuthal averaging of the axisymmetric radial intensity profile at each *z* position, denoted $\langle\cdot\rangle_{\phi}$, and are normalized to their own maximum: $\overline{\langle I \rangle}_{\phi} = \langle I \rangle_{\phi}/\max_{r,z}\langle I \rangle_{\phi}$. Experimental conditions: chiral nematic films with *L* = 10 µm and *dn* ≈ 0.22 (E7 nematic); probe illumination from a halogen lamp spectrally filtered at 633 nm; imaging with a microscope objective of numerical aperture NA = 0.25.

the normal to the sample indicates that the transverse structure of spin bits is axisymmetric (see Supplemental Material, Sec. VII [16]). To probe their longitudinal structure, we image spin bits at different *z* positions before and after flipping the sample upside down, using crossed circular polarizers (XCPOL) imaging for the four chiral light-matter scenarios. As shown in Fig. 3, meridional intensity maps in the (*r*, *z*) plane (obtained via azimuthal averaging) reveal distinct upside and downside patterns, indicating a broken symmetry along the *z* axis. Moreover, for a given material chirality, spin bits written with *L* and *R* chiral light yield upside maps that match the downside maps of spin bits written with opposite optical handedness. This demonstrates that spin bits possess a supramolecular polar structure pointing up or down depending on the optical chirality of the writing beam. Comparing both material chiralities shows that LL and RL configurations yield enantiomers of those from RR and LR, respectively, with identical orientation. Additional measurements with orthogonal XCPOL settings support these findings (see Supplemental Material, Sec. VII [16]). Overall, spin bits behave as polar refractive elements, enabling straightforward optical readout of their up or down state through their light redistribution signature (see Supplemental Material, Sec. VIII [16]).
<figure><img src="image_6.png" /><figcaption>FIG. 4. Experimental probability to generate up (black upward-pointing triangle) or down (downward-pointing triangle) spin bit vs $s_3^{in}$ for the four possible chiral light-matter interaction scenarios, over 50 events for each value of $s_3^{in}$ by 0.1 step, for $L = 10$ µm and E7 nematic. Discriminatory recording with high fidelity fails for $|s_3^{in}| \lesssim 0.1$. Insets: thumbnails as defined in Fig. 1.</figcaption></figure>

The discriminatory optical recording of spin bits also applies to elliptically polarized light beams, provided the ellipticity is large enough. This is shown in Fig. 4, which presents the probability of generating up or down spin bits as a function of the third reduced Stokes parameter $s_3^{in}$ [34], where $s_3^{in} = \pm 1$ corresponds to $L$ and $R$ circular polarization states and $s_3^{in} = 0$ to linear polarization state. Lower values of $Ldn$ result in reduced discrimination for intermediate values of $|s_3^{in}|$.

**Optical writing mechanism**—To better understand the optically induced formation of spin bits, we performed a time-resolved polarimetric analysis of the director reorientation (see Supplemental Material, Sec. IX [16]). This reveals the spatial structure of the director field in the $(x, y)$ plane at the onset of the writing process, showing the emergence of an axisymmetric localized chiral umbilic [35], see Fig. 5. In particular, this inhomogeneous orientation differs from the uniform alignment typically expected from purely optical reorientation phenomenon [9]. This deviation arises from photothermal effects induced by residual optical absorption in the electrodes. Local heating reduces the frustration level, quantified by $p/p_c$ where $p_c = 2(K_2/K_3)L$ and $K_{2,3}$ are the twist and bend elastic constants (see Supplemental Material, Sec. X [16]). This leads to a localized axisymmetric elastic torque that triggers axisymmetric reorientation. Since a chiral umbilic is apolar, this suggests that the polarization state of the writing beam plays a key role in the subsequent symmetry breaking. The transition occurs around $P \sim 300$ mW (see Supplemental Material, Sec. XI [16]), an optical power value consistent with the destabilization threshold of the most unstable reorientation mode in the purely optical regime. This supports a two-step writing mechanism: (i) initial formation of an apolar, topologically trivial axisymmetric reorientation seeded by photothermal effects and enhanced by

<figure><img src="image_7.png" /><figcaption>FIG. 5. Polarimetric analysis of the director field at the beginning of the writing process for both $L$ and $R$ circular polarization states for a left-handed chiral sample ($L = 10$ µm, E7 nematic), where $\Delta$ (a) refers to the birefringent phase retardation and $\psi$ (b) to the slow axis orientation of an effective optically anisotropic slab describing the reoriented director field. Inset: sketch of the corresponding typical 3D director profile in the plane $(x, y)$. Scale bar: 10 µm.</figcaption></figure>

optical torque, followed by (ii) a topological transition into a polar axisymmetric structure that relaxes into a stable spin bit after the beam is turned off.

We now provide a quantitative model of the spin-driven supramolecular poling mechanism. For analytical tractability, we consider a translation-invariant perturbation of the director field with $\theta(z) = \theta_1 \sin(\pi z/L)$ and $\phi(z) = 2\pi\chi(K_2/K_3)(z/p)$, where $\chi = \pm 1$ denotes the material chirality ($R$ or $L$) [36]. Within this framework, we identify a source of light-induced asymmetry that accounts for the spin bit selection rule and provides information about the writing dynamics. The approach consists in evaluating the spatial distribution of the light-induced time derivatives of $\theta$ and $\phi$, to the leading order in $\theta$, building on previous studies of light-driven director reorientation in nematics and long-pitch cholesterics [37,38]. The resulting expressions are proportional to the incident light intensity and read as

$$ \left. \frac{\partial \theta}{\partial \tau} \right|_{\text{opt}} = \sin 2\theta (n_e/n_o)^4 |A_e|^2, \quad (1) $$

$$ \left. \frac{\partial \phi}{\partial \tau} \right|_{\text{opt}} = 2(n_e/n_o)^2 \text{Re}(A_e A_o^* e^{i\psi}), \quad (2) $$

where $A_o$ and $A_e$ refer to the ordinary and extraordinary complex amplitudes of the electric light field satisfying

$$ \frac{\partial A_o}{\partial z} = - \frac{\partial \phi}{\partial z} \frac{n_e}{n_o} e^{i\psi} A_e, \quad (3) $$

$$ \frac{\partial A_e}{\partial z} = - \frac{1}{2n_e} \frac{\partial n_e}{\partial z} A_e + \frac{\partial \phi}{\partial z} \frac{n_o}{n_e} e^{-i\psi} A_o, \quad (4) $$

where $n_e(z) = n_\parallel n_\perp [n_\parallel^2 \cos^2\theta(z) + n_\perp^2 \sin^2\theta(z)]^{-1/2}$ and $n_o = n_\perp$ are the extraordinary (e) and ordinary (o)
<figure><img src="image_8.png" /><figcaption>FIG. 6. (a),(b) Typical spatial distribution of the light-driven time derivative for the director angles $\theta$ and $\phi$ calculated from Eqs. (1) and (2), for the four possible chiral light-matter interaction scenarios with $\theta_1 = 20^\circ$. (c), (d) Experimental snapshots at times $t_{1,2}$, with the writing beam activated at $t=0$, of the morphogenesis dynamics observed under XPOL imaging. Scale bars: 10 µm. $t_1 = (0.3 \text{ s}, 0.5 \text{ s})$ and $t_2 = (0.5 \text{ s}, 1.1 \text{ s})$ for panels (c) and (d).</figcaption></figure>

refractive indices, $\Psi(z) = k \int_0^z [n_e(\zeta) - n_o] d\zeta$ is the adiabatic birefringent phase retardation accumulated between the *e* and *o* waves after a propagation distance $z \in [0, L]$ and *k* is the pump beam wave vector in vacuum. Also, $\tau = t/t_{\text{elast}}$ is the time normalized to the characteristic elastic relaxation time [39]. In addition, the boundary conditions are that of incident circular polarization state, $A_o(0) = i\sigma E_0/\sqrt{2}$ and $A_e(0) = E_0/\sqrt{2}$, where $\sigma = \pm 1$ refers to $L/R$ chiral light. Using the material parameters of E7 with $p = L = 10 \text{ µm}$ (which corresponds to the main experimental conditions studied) at room temperature, we obtain the typical results shown in Figs. 6(a) and 6(b) for the four possible light-matter scenarios $(\sigma, \chi) = (\pm 1, \pm 1)$ and we refer to Supplemental Material, Sec. XII, for additional simulations [16]. Note that including light-induced temperature elevation has only a minor impact on these results.

Light-induced asymmetry across the sample mid-plane is observed for both polar and azimuthal director components. The asymmetry in the polar angle depends on the product $\sigma\chi$, which is consistent with the spin bit polarity that depends only on $\sigma\chi$, see Figs. 3 and 4. Moreover, the quantity $(\partial\theta/\partial\tau)_{\text{opt}}$ is larger for contrahanded ($\sigma\chi = +1$) than for cohanded ($\sigma\chi = -1$) configurations, suggesting different morphogenesis pathways. Indeed, the optical

power above which a spin bit can be written is found to be about 10% larger for $\sigma\chi = -1$ than for $\sigma\chi = +1$ (see Supplemental Material, Sec. XI [16]). Accordingly, recalling that we deal here with a fixed writing beam power, the distorted state grows faster for $\sigma\chi = +1$ than for $\sigma\chi = -1$, as shown in Figs. 6(c), 6(d) and videos 1–4. These observations align with previous experimental and numerical studies showing distinct bifurcation scenarios for different $\sigma\chi$ values [38,40].

In summary, we have identified a supramolecular optical poling effect initiated by photothermal reduction of frustration and driven by spin-dependent nonadiabatic propagation of light. Moreover, light-induced twisted director distortions, previously reported under circularly or elliptically polarized laser beams, likely plays a complementary role in shaping the reorientation dynamics [37,41–44].

*Concluding remarks*—Five decades after the discovery of bistable particlelike elastic excitations in frustrated chiral liquid crystal films [10–12], we have shown that the spin of photons can be used to generate such excitations, whose up or down polar structure is determined by whether the handedness of the chiral light matches (cohanded interaction) or opposes (contrahanded interaction) that of the chiral medium. While the optical angular momentum includes both spin and orbital parts [45], our work raises the question of whether an orbital counterpart to spin bits exists. Previous study with optical vortex beams [27] suggests that there is no unambiguous link between the orbital state of the writing beam and the recorded structure’s nature or polarity, highlighting the role of the spatial extent of the optical stimulus [46]. This leaves the orbital counterpart open for future investigation.

We believe that combining different light degrees of freedom (e.g., phase, amplitude, polarization) could enable new types of light-driven directional recording. Recent work on light-induced imprinting of topological information in achiral nematics [47] is a step in this direction. A next step would be to combine the topological diversity of 3D particlelike elastic excitations in chiral liquid crystals [48] with advances in generating 3D particlelike electromagnetic structures [49,50], whose potential in optomechanics has been discussed [51]. This could lead to transferring optical knots and links [52] to matter as structural knots and links in confined chiral nematic crystals [53], or transferring 3D polarization textures like Möbius strips [54,55] and skyrmions [56]. Such developments could result in new soft topological optical memories, manipulable by external fields [57–59].

Finally, in nonlinear optics, we recall that quadratic optical orientational nonlinearities arise from noncentrosymmetric director field configurations, whether spontaneous or field-induced [60,61]. Therefore, as noncentrosymmetric structures, spin bits offer potential for developing nonlinear optical materials with spatially varying quadratic nonlinearities, expanding the scope of singular optics of liquid crystal defects [62].
Acknowledgments—We acknowledge the support of French National Research Agency Project No. ANR-21-CE24-0014-01 and IdEx University of Bordeaux/Grand Research Program GPR LIGHT. We also thank Emma Furlanetto and Samlan Chandran Thodika for their experimental assistance.

[1] J. L. Baird, Improvements in or relating to the recording of views of objects or scenes, or optical images or the like, British Patent GB289104 (1928).

[2] T. Alexoudi, G. T. Kanellos, and N. Pleros, Optical RAM and integrated optical memories: A survey, Light Sci. Appl. 9, 91 (2020).

[3] C. Stanciu, F. Hansteen, A. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, All-optical magnetic recording with circularly polarized light, Phys. Rev. Lett. 99, 047601 (2007).

[4] N. Romming, C. Hanneken, M. Menzel, J. E. Bickel, B. Wolter, K. von Bergmann, A. Kubetzka, and R. Wiesendanger, Writing and deleting single magnetic skyrmions, Science 341, 636 (2013).

[5] R. Wiesendanger, Nanoscale magnetic skyrmions in metallic films and multilayers: A new twist for spintronics, Nat. Rev. Mater. 1, 16044 (2016).

[6] A. V. Kimel and M. Li, Writing magnetic memory with ultrashort light pulses, Nat. Rev. Mater. 4, 189 (2019).

[7] T. Omatsu, K. Miyamoto, K. Toyoda, R. Morita, Y. Arita, and K. Dholakia, A new twist for materials science: The formation of chiral structures using the angular momentum of light, Adv. Opt. Mater. 7, 1801672 (2019).

[8] E. Brasselet, Singular optical manipulation of birefringent elastic media using nonsingular beams, Opt. Lett. 34, 3229 (2009).

[9] N. Tabiryan, A. Sukhov, and B. Y. Zel'dovich, Orientational optical nonlinearity of liquid crystals, Mol. Cryst. Liq. Cryst. 136, 1 (1986).

[10] W. E. L. Haas and J. E. Adams, Electrically variable diffraction in spherulitic liquid crystals, Appl. Phys. Lett. 25, 263 (1974).

[11] W. E. Haas and J. E. Adams, New optical storage mode in liquid crystals, Appl. Phys. Lett. 25, 535 (1974).

[12] M. Kawachi, O. Kogure, and Y. Kato, Bubble domain texture of a liquid crystal, Jpn. J. Appl. Phys. 13, 1457 (1974).

[13] J. Prakash, A. Chandran, and A. M. Biradar, Scientific developments of liquid crystal-based optical memory: A review, Rep. Prog. Phys. 80, 016601 (2016).

[14] F. Cardano and L. Marrucci, Spin-orbit photonics, Nat. Photonics 9, 776 (2015).

[15] F. Fischer, Critical pitch in thin cholesteric films with homeotropic boundaries, Z. Naturforsch. 31, 41 (1976).

[16] See Supplemental Material at http://link.aps.org/supplemental/10.1103/pqdp-x2vr, which includes Refs. [17–26], for additional information about the material parameters, experimental methods, supporting experimental observations, numerical simulations, and illustrating videos.

[17] J. Li and, C.-H. Wen, S. Gauza, R. Lu, and S.-T. Wu, Refractive indices of liquid crystals for display applications, J. Disp. Technol. 1, 51 (2005).

[18] J. F. Strömer, E. P. Raynes, and C. V. Brown, Study of elastic constant ratios in nematic liquid crystals, Appl. Phys. Lett. 88, 051915 (2006).

[19] A. Varanytsia, G. Posnjak, U. Mur, V. Joshi, K. Darrah, I. Muševič, S. Čopar, and L.-C. Chien, Topology-commanded optical properties of bistable electric-field-induced torons in cholesteric bubble domains, Sci. Rep. 7, 16149 (2017).

[20] P. Oswald and P. Pieransky, *Nematic and Cholesteric Liquid Crystals: Concepts and Physical Properties Illustrated by Experiments* (Taylor & Francis, CRC, Boca Raton, FL, 2005).

[21] H. Hakemi, E. F. Jagodzinski, and B. D. Dupré, Temperature dependence of the anisotropy of turbidity and elastic constants of nematic liquid crystal mixture E7, Mol. Cryst. Liq. Cryst. 91, 129 (1983).

[22] B. T. Hallam and J. R. Sambles, Optically guided mode study of nematic liquid crystal alignment on a zero-order grating, Phys. Rev. E 61, 6699 (2000).

[23] H. Chen, R. Zhu, J. Zhu, and S.-T. Wu, A simple method to measure the twist elastic constant of a nematic liquid crystal, Liq. Cryst. 42, 1738 (2015).

[24] P. D. Brimicombe, C. Kischka, S. J. Elston, and E. P. Raynes, Measurement of the twist elastic constant of nematic liquid crystals using pi-cell devices, J. Appl. Phys. 101, 043108 (2007).

[25] H. Wang, T. X. Wu, S. Gauza, J. R. Wu, and S.-T. Wu, A method to estimate the Leslie coefficients of liquid crystals based on MBBA data, Liq. Cryst. 33, 91 (2006).

[26] B. Yang and E. Brasselet, Study of elastic constant ratios in nematic liquid crystals, J. Opt. 15, 044021 (2013).

[27] I. I. Smalyukh, Y. Lansac, N. A. Clark, and R. P. Trivedi, Three-dimensional structure and multistable optical switching of triple-twisted particle-like excitations in anisotropic fluids, Nat. Mater. 9, 139 (2010).

[28] P. J. Ackerman, R. P. Trivedi, B. Senyuk, J. van de Lagemaat, and I. I. Smalyukh, Two-dimensional skyrmions and other solitonic structures in confinement-frustrated chiral nematics, Phys. Rev. E 90, 012505 (2014).

[29] P. J. Ackerman and I. I. Smalyukh, Diversity of knot solitons in liquid crystals manifested by linking of preimages in torons and hopfions, Phys. Rev. X 7, 011006 (2017).

[30] G. Park, A. Suh, H. Zhao, C. Lee, Y.-S. Choi, I. I. Smalyukh, and D. K. Yoon, Fabrication of arrays of topological solitons in patterned chiral liquid crystals for real-time observation of morphogenesis, Adv. Mater. 34, 2201749 (2022).

[31] We found that the level of discrimination with respect to the incident optical spin state decreases beyond the reported range for the helical pitch *p*, leaving room for further study to extend it.

[32] J.-S. B. Tai and I. I. Smalyukh, Surface anchoring as a control parameter for stabilizing torons, skyrmions, twisted walls, fingers, and their hybrids in chiral nematics, Phys. Rev. E 101, 042702 (2020).

[33] T. Lee, B. Senyuk, R. P. Trivedi, and I. I. Smalyukh, Optical microscopy of soft matter systems, in *Fluids, Colloids and Soft Materials: An Introduction to Soft Matter Physics* (Wiley, New York, 2016), pp. 165–185.

[34] M. Born and E. Wolf, *Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light* (Elsevier, New York, 2013).
[35] A. Rapini, Umbilics: Static properties and shear-induced displacements, J. Phys. 34, 629 (1973).

[36] I. I. Smalyukh, B. Senyuk, P. Palffy-Muhoray, O. Lavrentovich, H. Huang, E. Gartland Jr, V. Bodnar, T. Kosa, and B. Taheri, Electric-field-induced nematic-cholesteric transition and three-dimensional director structures in homeotropic cells, Phys. Rev. E 72, 061707 (2005).

[37] E. Brasselet, T. Galstian, L. J. Dubé, D. O. Krimer, and L. Kramer, Bifurcation analysis of optically induced dynamics in nematic liquid crystals: Circular polarization at normal incidence, J. Opt. Soc. Am. B 22, 1671 (2005).

[38] E. Brasselet, D. Krimer, and L. Kramer, Light-induced instabilities driven by competing helical patterns in long-pitch cholesterics, Eur. Phys. J. E 17, 403 (2005).

[39] The characteristic time of a nematic sample with perpendicular orientational boundary conditions is usually defined as $t_{elastic} = \gamma_1 L^2 / (\pi^2 K_3)$, where $K_3$ is the bend elastic constant and $\gamma_1$ is the orientational viscosity.

[40] P. Maddalena, G. Arnone, G. Abbate, L. Marrucci, and E. Santamato, Optically induced reorientation in nematics doped by chiral agents, Mol. Cryst. Liq. Cryst. 261, 113 (1995).

[41] E. Santamato, G. Abbate, P. Maddalena, L. Marrucci, and Y. R. Shen, Laser-induced nonlinear dynamics in a nematic liquid crystal film, Phys. Rev. Lett. 64, 1377 (1990).

[42] A. S. Zolot'ko and A. P. Sukhorukov, Fréedericksz transition induced in nematic liquid-crystal by circularly polarized-light wave, JETP Lett. 52, 62 (1990), http://jetpletters.ru/ps/1152/article_17438.pdf.

[43] L. Marrucci, G. Abbate, S. Ferraiuolo, P. Maddalena, and E. Santamato, Self-stimulated light scattering in nematic liquid crystals: Theory and experiment, Phys. Rev. A 46, 4859 (1992).

[44] D. O. Krimer, L. Kramer, E. Brasselet, T. Galstian, and L. J. Dubé, Bifurcation analysis of optically induced dynamics in nematic liquid crystals: Elliptical polarization at normal incidence, J. Opt. Soc. Am. B 22, 1681 (2005).

[45] A. M. Yao and M. J. Padgett, Orbital angular momentum: Origins, behavior and applications, Adv. Opt. Photonics 3, 161 (2011).

[46] C. Loussert and E. Brasselet, Multiple chiral topological states in liquid crystals from unstructured light beams, Appl. Phys. Lett. 104, 051911 (2014).

[47] M. El Ketara, H. Kobayashi, and E. Brasselet, Sensitive vectorial optomechanical footprint of light in soft condensed matter, Nat. Photonics 15, 121 (2021).

[48] I. I. Smalyukh, Knots and other new topological effects in liquid crystals and colloids, Rep. Prog. Phys. 83, 106601 (2020).

[49] D. Sugic, R. Droop, E. Otte, D. Ehrmanntraut, F. Nori, J. Ruostekoski, C. Denz, and M. R. Dennis, Particle-like topologies in light, Nat. Commun. 12, 6785 (2021).

[50] D. Ehrmanntraut, R. Droop, D. Sugic, E. Otte, M. R. Dennis, and C. Denz, Optical second-order skyrmionic hopfion, Optica 10, 725 (2023).

[51] R. Droop, D. Ehrmanntraut, and C. Denz, Transverse energy flow in an optical skyrmionic hopfion, Opt. Express 31, 11185 (2023).

[52] W. T. Irvine and D. Bouwmeester, Linked and knotted beams of light, Nat. Phys. 4, 716 (2008).

[53] D. Seč, S. Čopar, and S. Žumer, Topological zoo of free-standing knots in confined chiral nematic fluids, Nat. Commun. 5, 3057 (2014).

[54] I. Freund, Multitwist optical möbius strips, Opt. Lett. 35, 148 (2010).

[55] T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, Observation of optical polarization möbius strips, Science 347, 964 (2015).

[56] Y. Shen, Q. Zhang, P. Shi, L. Du, X. Yuan, and A. V. Zayats, Optical skyrmions and other topological quasiparticles of light, Nat. Photonics 18, 15 (2024).

[57] T. Porenta, S. Čopar, P. J. Ackerman, M. Pandey, M. Varney, I. I. Smalyukh, and S. Žumer, Topological switching and orbiting dynamics of colloidal spheres dressed with chiral nematic solitons, Sci. Rep. 4, 7337 (2014).

[58] J.-S. B. Tai, P. J. Ackerman, and I. I. Smalyukh, Topological transformations of hopf solitons in chiral ferromagnets and liquid crystals, Proc. Natl. Acad. Sci. U.S.A. 115, 921 (2018).

[59] Ž. Kos and J. Dunkel, Nematic bits and universal logic gates, Sci. Adv. 8, eabp8371 (2022).

[60] M. Čopič and T. Ovsenik, Second-harmonic scattering on orientational fluctuations in nematics, Europhys. Lett. 24, 93 (1993).

[61] S. Trashkeev, N. Vasenin, S. Vatnik, I. Vedin, A. Ivanenko, and V. Klementyev, Harmonic generation in a nematic liquid crystal, Laser Phys. Lett. 17, 075002 (2020).

[62] E. Brasselet, Singular optics of liquid crystal defects, *Liquid Crystals: New Perspectives*, edited by P. Pieranski and M. H. Godinho (John Wiley & Sons, Hoboken, 2021), pp. 1–79.
# Supplemental Material

## Rewritable binary recording of the photon spin state in chiral liquid crystals

Nicolas Bruni, Charles Loussert, Mushegh Rafayelyan, Tetiana Orlova, Delphine Coursault, and Etienne Brasselet*

Univ. Bordeaux, CNRS, Laboratoire Ondes et Matière d'Aquitaine, F-33400 Talence, France.

## CONTENTS

<table><tr><td>I. Liquid crystal samples</td><td>1</td></tr><tr><td>II. Optical setup</td><td>2</td></tr><tr><td>III. Writing beam conditions for Fig. 2</td><td>2</td></tr><tr><td>IV. General information on imaging conditions</td><td>2</td></tr><tr><td>V. Reproducible and generic character of spin bits</td><td>3</td></tr><tr><td>VI. Stability and robustness of spin bits</td><td>3</td></tr><tr><td>VII. Structural features of spin bits</td><td>6</td></tr><tr><td>VIII. Binary optical readout of spin bits</td><td>7</td></tr><tr><td>IX. Polarimetric analysis of the optically induced reorientation</td><td>8</td></tr><tr><td>X. Laser induced heating effects</td><td>8</td></tr><tr><td>XI. Optical power to record a spin bit</td><td>10</td></tr><tr><td>XII. Simulated (∂θ/∂τ)opt and (∂φ/∂τ)opt</td><td>11</td></tr><tr><td>XIII. Description of supplementary videos</td><td>11</td></tr><tr><td>References</td><td>12</td></tr></table>

## I. LIQUID CRYSTAL SAMPLES

Right- and left-handed chiral nematic mixtures are prepared by doping achiral nematic liquid crystals, respectively with R811 and S811 chiral molecular dopants (from Merck). Three kinds of commercial nematic mixtures are used:

* E7 (from Merck) whose refractive indices parallel and perpendicular to the director are $n_‖ = 1.746$ and $n_⊥ = 1.522$ at 20°C and at 589 nm wavelength [1], and whose splay, twist and bend Frank elastic constants are $K_1 = 10.3$ pN, $K_2 = 7.4$ pN, $K_3 = 16.5$ pN, respectively [2].

* MLC6608 (from Licristal) whose refractive indices parallel and perpendicular to the director are $n_‖ = 1.5595$ and $n_⊥ = 1.4768$ at 20°C and at 589 nm wavelength [1].

* R237 (from BEAM Co.) whose birefringence at room temperature provided by the manufacturer is $n_‖ - n_⊥ = 0.058$ at 532 nm wavelength, which is close to our homemade measurement giving $n_‖ = 1.503$ and $n_⊥ = 1.450$.

We use cells with nominal thickness $L = (3, 10, 50)$ µm (from EHC Co. Ltd) provided with indium-tin-oxide (ITO) electrodes with either polyimide (PI) LX-1400 [for $L = 10$ µm and 50 µm] or cetyltrimethylammonium bromide (CTAB) [for $L = 3$ µm and 10 µm] anchoring treatment. The nominal cell thicknesses from the manufacturer are verified by reflection spectrum measurement and the cholesteric pitch is measured by using the Cano wedge technique in order to ensure consistent preparation of the samples that all satisfy $p \simeq L$. The samples are then prepared by capillary filling at room temperature, at which all the experiments are performed. See Fig. S1(a) and S1(b) for a sketch of the frustrated liquid crystal sample under illumination and the definition of the director.
<figure><img src="image_9.png" /></figure>

**Fig. S1 | Experimental framework.** (a) Frustrated chiral nematic sample lying in the (x, y) plane, where (x, y, z) refers to the laboratory frame and (X, Y, Z) to the sample frame. The writing of spin bits is made by using a normally incident circularly polarized Gaussian laser beam with a beam waist radius w ≃ p ≃ L located in the mid-plane of the frustrated chiral liquid crystal (FCLC) slab. The probe light is prepared from a halogen lamp and observations are made using direct polarized imaging [see panel (c)]. (b) Director definition using polar (θ) and azimuthal (φ) spherical angles: undistorted, **n**₀ = **z**, and distorted, **n**(*θ*, *φ*). (c) Writing of structures in the sample is made using a fully polarized pump laser beam (PC: polarization controller). The dashed line indicates the facet on which impinges (or ‘has impinged’ at the imaging step) the writing beam. Imaging of the recorded particle-like elastic excitations (here depicted as a heart-like shape) is carried out by illuminating the sample with a probe light provided by a halogen lamp, which is possibly spectrally filtered (SF: spectral filter). The reported images are obtained by placing the sample between crossed linear or circular polarizer (P) and analyzer (A), to which we refer to as XPOL and XCPOL observations, respectively. MO: microscope objective whose numerical aperture (NA) is adapted to the need. The solid (dash) line refers to input (output) plane with respect to the incident writing pump beam. When imaging the sample or performing z-scan, the sample is either left as is ('sample upside') or flipped upside down relative to its position when a spin bit is recorded ('sample downside').

## II. OPTICAL SETUP

The pump writing beam is a continuous-wave laser beam operating in the fundamental Gaussian mode at 532 nm wavelength (G5, from Coherent). The beam divergence of the pump beam is ≃ (0.2, 1, 3)° for L = (50, 10, 3) µm and the involved light-matter interaction can therefore be considered in the framework of paraxial light. The white light source used for imaging the sample is a halogen lamp. The polarization state assessment for the dependence of the spin bit recording as a function of the incident polarization state is made using a free space visible polarimeter (PAX1000VIS, from Thorlabs). Sketches of the optical setup for writing and imaging spin bits as well as how the sample is placed for imaging are shown in Fig. S1(c).

## III. WRITING BEAM CONDITIONS FOR FIG. 2

The data in Fig. 2(a) [E7 nematic] is obtained for an optical pump beam power P ≈ (120, 300, 1000) mW for L = (3, 10, 50) µm and irradiation time T ≈ (0.5, 1, 10) s, respectively. The data in Fig. 2(b) [L = 10 µm] is obtained for an optical pump beam power P ≈ (350, 600, 300) mW and T ≈ 1 s for the nematic material R237, MLC6608, and E7, respectively. See videos 1–4 showing the spin bit writing process for L = 10 µm and E7 material for the four possible types of chiral light-matter interaction.

## IV. GENERAL INFORMATION ON IMAGING CONDITIONS

The definition of the imaging plane for XPOL imaging and the dependence of XPOL images with respect to the imaging wavelength are shown in Fig. S2(a) and S2(b), respectively.
<figure><img src="image_10.png" /><figcaption>**Fig. S2** | Determining the observation plane for XPOL imaging and the role of the wavelength. (a) XPOL images of a pair of spin bits recorded using L and R circularly polarized writing beam as a function of the observation plane location along the *z* axis. We identify *z* = *z*\* as the location giving the sharpest image noting that it does not necessarily correspond to the mid-plane of the sample [3]. Here the probe illumination light is from a halogen lamp spectrally filtered at 500 nm wavelength. Images are recorded using the same irradiation intensity and acquisition time. The brightness is then enhanced in a similar way for all images in order to optimize the global visual rendering. (b) XPOL images at *z* = *z*\* using various wavelengths selected from interference filters (with 10 nm full-width half-maximum bandwidth). In this figure, all reported data correspond to a 10 µm-thick R chiral nematic liquid crystal sample prepared with E7 nematic, using 20× microscope objective with NA = 0.25 for the imaging. Scale bars: 10 µm.</figcaption></figure>

## V. REPRODUCIBLE AND GENERIC CHARACTER OF SPIN BITS

The reproducibility of the phenomenon is summarized in Fig. S3, which demonstrates that the writing of a spin bit can be performed at various location in the sample [panel (a)], see also the corresponding videos 5 and 6] and that a spin bit is rewritable after having been erased by electrical means [panel (b)], see also the corresponding videos 7 and 8]. spin bits are obtained whatever the material chirality and are nonspecific to the homeotropic anchoring treatment, as shown in Fig. S4.

## VI. STABILITY AND ROBUSTNESS OF SPIN BITS

The level of stability of the recorded spin bits is very high, as illustrated in Fig. S5 that demonstrated storage duration over 2 years. Moreover, spin bits are resilient to a realigning electric field, at least up to a threshold value $U = U^*$ for the applied voltage difference between the electrodes of the sample. For $U < U^*$ the spin bit is squeezed in a reversible manner [Fig. S6(a)] while for $U > U^*$ the spin bit is irreversibly erased [Fig. S6(b)], see also the corresponding videos 9 and 10. This implies the existence of an energy barrier to be overcome for the erasure process to be effective, which is consistent with the observed long-term storage. Similar erasure dynamics consisting of a sequence of three distinct regimes are observed for the four possible types of chiral light-matter interaction. The first regime corresponds to electrically driven orientational squeezing of the axisymmetric particle-like elastic excitation at fixed structural topology, the second one is associated with electric field driven topological structural transition for the director field that eventually breaks the axisymmetry [see Fig. S6(b) at *t* = 2.08 s], and the third one refers to electric field assisted elastic relaxation of an axisymmetric topologically trivial director field [see Fig. S6(b) at *t* = 2.12 s]. All these observations suggest that spin bits are associated with identical, topologically nontrivial, 3D axisymmetric elastic energy landscapes, irrespective of the chirality of the writing light and matter.
<figure><img src="image_11.png" /></figure>

**Fig. S3** | **spin bits writing and write-and-erase statistics.** (a) Writing statistics summary for left-handed and right-handed chiral pump light at distinct positions. Top panels display portfolio of 49 independent spin bits recorded at distinct positions **r**ᵢ. Bottom panels display enlarged XPOL images of a single spin bit at *z* = *z*\* (label “1”) and the average XPOL images of the spin bits portfolio (label “⟨·⟩rᵢ”) whose high-fidelity similarity highlights the reproducible character of the spin-optical recording process. (b) Same as in (a) for write & erase statistics at fixed position. The protocol consists in applying a 5 V<sub>rms</sub> voltage difference across the sample for a few seconds in order to erase a spin bit once it has been recorded, and then repeating the optical writing & electrical erasing sequence. The bottom panels highlight the reproducible character of the opto-electrical rewriting process, where the label “⟨·⟩tᵢ” refers to average over spin bits recorded at distinct times tᵢ. In this figure, all reported data correspond to a 10 µm-thick R chiral nematic liquid crystal sample prepared with E7 nematic and the observations are made using a 10× microscope objective with NA = 0.25 using halogen lamp illumination and long pass color glass filter (λ<sub>probe</sub> > 590 nm).

<figure><img src="image_12.png" /></figure>

**Fig. S4** | **Nonspecificity of the material chirality and of the anchoring treatment.** (a) XPOL images of spin bits at *z* = *z*\* for the four possible types of chiral light-matter interactions using PI treatment as is the case in the main text unless stated otherwise. (b) Same as in (a) but for another anchoring treatment, using CTAB treatment. In this figure, all reported data correspond to 10 µm-thick chiral nematic liquid crystal samples prepared with E7 nematic and the observations are made using 10× microscope objective with NA = 0.25, and halogen lamp illumination with long pass color glass filter (λ<sub>probe</sub> > 590 nm). Scale bars: 10 µm.
<figure><img src="image_13.png" /></figure>

**Fig. S5 | Long-term storage of spin bits.** XPOL images of spin bits at $z = z^*$ for a circularly polarized writing beam taken one year apart over two years for a test sample. Time zero is defined as the moment of spin bit writing and $t_0 = 2$ weeks. We note that the sample has been subjected to various daily manipulations, including perturbations associated with outdoor pedestrian and public transport, which highlights the robust nature of the memory beyond its resilience to thermal orientational fluctuations of the director field under nominal usage conditions. In this figure, all reported data correspond to a 10 µm-thick R chiral nematic liquid crystal sample prepared with E7 nematic and the observations are made using 10× microscope objective with NA = 0.25, and halogen lamp illumination with long pass color glass filter ($\lambda_{probe} > 590$ nm). Scale bars: 10 µm.

<figure><img src="image_14.png" /></figure>

**Fig. S6 | Electrical erasing of spin bits.** Typical dynamical response of a spin bit to the application of a quasistatic electric field along the *z* axis below (a) and above (b) the threshold value *U* = *U*\* above which erasure takes place if the field is applied for a sufficiently long time duration. Here, a quasistatic electric field at 10 kHz frequency, is applied at *t* = 0 for L chiral sample with *L* = 10 µm and *dn* = 0.22 (E7 nematic), and R circularly polarized writing beam. The XPOL power refers to the total output probe power extracted from XPOL imaging. In fact, the obtained signal is associated to the 3D elastic energy landscape of the director field. (a) *U* = 0.3 V<sub>rms</sub>. Insets: XPOL images before, during, and after the electric field is applied. (b) *U* = 0.35 V<sub>rms</sub>. Insets: XPOL images during and after the topological transition process. Scale bars: 10 µm.
VII. STRUCTURAL FEATURES OF SPIN BITS

The axisymmetric nature of the 3D director field of a spin bit is experimentally assessed from the observation of XPOL images that are invariant with respect to the rotation of the sample around the *z* axis once the spin bit is written, see Fig. S7.

<figure><img src="image_15.png" /></figure>

**Fig. S7 | Axisymmetric structural nature of the spin bits.** XPOL imaging of a pair of spin bits at $z = z^*$ recorded by using left-handed and right-handed circularly polarized pump beam, as a function of the in-plane orientation angle $\alpha$ of the sample, where the frame $(X, Y)$ refers to that ‘attached’ to the sample and $(x, y)$ to that of the laboratory, see Fig. S1(a). Observed images do not depend on $\alpha$, which demonstrates the axisymmetric supramolecular ordering of spin bits. In this figure, all reported data correspond to a 10 µm-thick R chiral nematic liquid crystal sample prepared with E7 nematic and the observations are made using a 20× microscope objective with NA = 0.25 using halogen lamp illumination spectrally filtered at 633 nm wavelength.

We also report in Fig. S8 a complementary experimental demonstration of the supramolecular polar nature of spin bits retrieved from XCPOL z-scan intensity maps in the plane $(r, z)$ for the four possible types of chiral light-matter interaction, but using XCPOL settings orthogonal to that used in Fig. 3 of the main text.

<figure><img src="image_16.png" /></figure>

**Fig. S8 | Scanning XCPOL imaging of spin bits.** Same as in Fig. 3 of the main text but for orthogonal XCPOL settings, namely, with the circular polarizer being right(left)-handed and the circular analyzer being left(right)-handed for left(right)-handed chiral nematic, respectively.
VIII. BINARY OPTICAL READOUT OF SPIN BITS

The z-scan results shown in Fig. 3 of the main text and Fig. S8 suggest a simple way to read the up or down state of a spin bit without resorting to a tedious optical examination of the 3D structure, by viewing a spin bit as a kind of polar refractive optical element. The idea can be grasped by considering the refraction from a plano-convex lens whose focal spot position indeed depend on the orientation of the lens, see Fig. S9. Under appropriate XCPOL imaging conditions, a highly discriminating redistribution of on-axis light can be obtained at a given plane $z = z_{\text{readout}}$, as shown in Figs. S10(a) and S10(b). Ensuing experimental demonstration of binary spin-orbit optical readout is reported in Fig. S10(c) where the optical readout of 8-bit ASCII encoded letters U and B is shown.

<figure><img src="image_17.png" /><figcaption>**Fig. S9 | Ray optics illustration of the polar lensing effect.** (a) Ray tracing for a hemispheric plano-convex lens with diameter $2p$, thickness $p$ (mimicking the transverse to longitudinal aspect ratio) and refractive index 1.6, immersed in a medium with refractive index 1.5, and illuminated on-axis towards $z > 0$. The focal plane is longitudinally shifted by a distance of about $p$ as the lens is flipped upside down with respect to the propagation axis, as shown in the inset where paraxial (nonparaxial) rays are shown in dark (light) red.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>**Fig. S10 | Binary optical readout of spin bits.** (a) z-scan XCPOL intensity maps obtained for a pair of spinbits with opposite supramolecular polarity for a left-handed chiral nematic film with $L = 10~\mu\text{m}$ and $dn \simeq 0.22$, using a microscope objective with NA = 0.1 and a probe illumination spectrally filtered at 633 nm wavelength. (b) Intensity contrast $C = |\langle(I)_{\phi}^{\sigma=+1} - \langle(I)_{\phi}^{\sigma=-1}\rangle / \langle(I)_{\phi}^{\sigma=+1} + \langle(I)_{\phi}^{\sigma=-1}\rangle|$ between the maps shown in panel (a). (c) Normalized readout image (background subtracted) of 8-bit ASCII encoding of UB acronym, which stands for University of Bordeaux, at the plane $z = z_{\text{readout}}$ for which the readout contrast reaches its maximum value as shown in panel (b).</figcaption></figure>
## IX. POLARIMETRIC ANALYSIS OF THE OPTICALLY INDUCED REORIENTATION

The data shown in Fig. 5(a) is obtained by measuring the reduced Stokes vector $\mathbf{s} = (s_1, s_2, s_3)$ [4], which is carried out by recording six intensity images of the sample plane obtained from the projection of the output field on the horizontal, vertical, diagonal, anti-diagonal, left-handed circular, and right-handed circular polarization states, owing to usual polarization optics. This is done by illuminating the sample at normal incidence by a probe light having circular polarization state with helicity $\sigma_{\text{probe}} = \pm 1$ and wavelength $\lambda_{\text{probe}} = 633$ nm.

Nonzero birefringent phase retardation $\Delta$ experienced by the probe beam is associated to the reorientation of the director, with the typical dependence $\Delta \sim \theta^2$ to the lowest order in $\theta$. In addition, the orientation angle of the major axis $\Psi$ of the output probe polarization ellipse is related to the azimuthal reorientation angle $\phi$ of the director field. More specifically, considering the reoriented sample as an effective slab of uniaxial material associated with spatially varying birefringent phase retardation and spatially varying in-plane optical axis orientation angle $\psi$, and noting that $\max(\Delta) < \pi$ at the early stage of the writing dynamics, one gets

$$ \Delta = \arccos(\sigma_{\text{probe}}s_3), \qquad (S1) $$

$$ \Psi = \frac{1}{2} \arctan \left( \frac{s_2}{s_1} \right), \qquad (S2) $$

and

$$ \psi = \Psi - \sigma_{\text{probe}} \frac{\pi}{4}. \qquad (S3) $$

As such, $\Delta$ and $\psi$ gives a relevant information about the polar ($\theta$) and azimuthal ($\phi$) degrees of freedom for the director field.

## X. LASER INDUCED HEATING EFFECTS

*Laser induced temperature increase.* — The light-induced temperature elevation $dT$ is measured according to the following procedure. The pump beam ($\lambda = 532$ nm), with waist radius $w = 10$ µm and linear polarization state, is directed onto a pure E7 nematic sample with thickness $L = 10$ µm. The sample is placed in a temperature controlled oven, at the temperature $T$ and the sample plane is imaged between crossed linear polarizers using a long pass filter ($\lambda > 590$ nm). As the pump beam heats the sample via absorption by the electrodes (the absorption of each of the two electrodes is measured to be $\simeq 1.7\%$) the XPOL signal becomes nonzero as it approaches the nematic-isotropic melting point temperature $T_{\text{NI}} = 58^{\circ}\text{C}$ due to giant pretransitional orientational fluctuations. In practice, the pump beam power $P$ is increased in 2 mW steps until the XPOL signal suddenly drops off as an isotropic bubble appears, corresponding to a temperature increase $dT = T_{\text{NI}} - T$. The experiment is carried out by gradually increasing the temperature of the oven from $25^{\circ}\text{C}$ to $55^{\circ}\text{C}$ in $5^{\circ}\text{C}$ steps. The results are shown in Fig. S11.

<figure><img src="image_19.png" /><figcaption>**Fig. S11 | Optical power dependence of the temperature elevation.** Light-induced temperature elevation $dT$ as a function of the incident optical power $P$ of the writing beam.</figcaption></figure>
*Temperature induced changes of the level of frustration.* — Recalling that the level of frustration of the chiral nematic sample is given by $p/p_c$ where $p_c = 2(K_2/K_3)L$ where $K_2$ and $K_3$ are the twist and bend Frank elastic constants, it can change due to the temperature dependence of the pitch and/or of the elastic constants. The former is tested by evaluating the pitch using the Cano wedge technique [5] that gives a pitch increase of about 1–2% from room temperature to $T \lesssim T_{NI}$. The latter is assessed from the knowledge of the temperature dependence of the ratio $K_2/K_3$, which increases with temperature [6]. In the latter reference, however, the quantitative assessment requires recalibration as the elastic constants are overestimated, as noted by the authors of that work. Such a recalibration is shown in Fig. S12(a) by exploiting sparse experimental data found in the literature for $K_2$ and $K_3$ [2, 7–10]. It is therefore the temperature changes $p_c$ that dominates over that of $p$ and leads to a decrease of the level of frustration with laser induced heating, see Fig. S12(b).

By affecting the material parameters, the temperature elevation also affects the characteristic optical power associated with the orientational destabilization of the most unstable reorientation mode, above which a fluctuation turns to be unstable in a purely optical situation. This characteristic power, also called the optical Fréedericksz power threshold depends on the dielectric and elastic properties of the liquid crystal as well as on the level of geometric frustration ($p/L$) and the finite size of the incident beam ($w/L$). A fair estimate can be made in the case of incident circular polarization by doubling the value provided in [11] for the case of linear polarization, which gives, accounting for the condition $p = L = w$,

$$P_F = \frac{\pi^3 c n_{\parallel}^2 K_3}{n_{\perp}(n_{\parallel}^2 - n_{\perp}^2)} \left[1 - \left(\frac{2K_2}{K_3}\right)^2\right] \left(1 + \frac{\sqrt{2}}{\pi}\right)^2. \quad (S4)$$

where $c$ is the speed of light. Its value as a function of the temperature is shown in Fig. S12(c), where the knowledge of the material parameters as a function of the temperature is taken from see Fig. S12(a) for the elastic constants $K_2$ and $K_3$, and from [1] for the refractive indices $n_{\parallel}$ and $n_{\perp}$. This tells that the writing beam power $P \sim 300$ mW is about $P_F$ for our system, which is consistent with the observed sudden character of the spin bit writing process (see videos 1–4).

<figure><img src="image_20.png" /><figcaption>**Fig. S12 | Temperature dependence of the elastic constants of E7 and the corresponding level of frustration.**
(a) Temperature dependence of $K_2$ (red color) and $K_3$ (blue color) from room temperature to the melting point. The solid lines correspond to quadratic fits and the markers refer to experimental data from previous works. (b) Corresponding level of frustration. (c) Optical Fréedericksz threshold power $P_F$ evaluated from Eq. (S4).</figcaption></figure>

In addition, we carried out another experiment in order to determine at which temperature the homogeneous defrustration occurs for the representative sample of our study with $p \simeq L$. This is done by placing the sample in a temperature controlled oven, at the temperature $T$, and applying a realigning electric field that makes the director to be aligned along the $z$ axis. Then, the electric field is switched off at $t = 0$ and the XPOL power of the image of the sample is recorded. A rising signal is the signature of defrustration, from which we can identify that $p/p_c$ reaches the critical value 1 at a temperature of about 50°C. The results are summarized in Fig. S13. Together with the local temperature elevation reported in Fig. S11, this provides an additional experimental support of the main text statement that the optical writing mechanism can be described as a two-step process: (i) the generation of an apolar, topologically trivial, axisymmetric reorientation seeded by photothermal effects and enhanced by the optical torque exerted on the director field, (ii) the topological transformation into a polar axisymmetric structure that relaxes into a stable particle-like elastic excitation after the optical stimulus is switched off.
<figure><img src="image_21.png" /><figcaption>**Fig. S13** | Experimental determination of the temperature at which the sample is no longer frustrated. XPOL power as a function of time as an initially realigning electric field is switched off at time zero. Inset: XPOL image at *t* = 1.5 s and *T* = 54°C, for which the defrustrated state exhibits a typical fingerprint texture.</figcaption></figure>

XI. OPTICAL POWER TO RECORD A SPIN BIT

In this section we substantiate the fact that the threshold power above which a spin bit can be written is about 10% larger for $\sigma\chi = -1$ than for $\sigma\chi = +1$, which is mentioned in the main text. This is summarized in Fig. S14, which collects the probability to obtain a given final result (no structure, spin-dependent structure, or spin-independent structure) as function of the incident pump beam power when the laser exposure duration is fixed to 1 s. The shaded areas refer to a probability $\gtrsim 50\%$ to record a spin bit. The minimal power leading to the latter condition is about 10% larger when the optical and material chirality are co-handed compared to the contra-handed situation (noting that here the results refer to a left-handed chiral nematic sample).

Note that, here, the probability to get a spin bit at *P* = 300 mW is not 100% because of the fixed illumination duration condition used to carry out the parametric study. In practice, if one allows for a bit longer exposure (say up to 2 s, which is more than enough) one gets 100% spin-driven writing for both left-handed and right-handed optical chirality. At *P* = 270 mW, spin bits are only observed for the contra-handed situation with 100% probability if one waits for sufficiently long time while nothing is recorded for the co-handed situation.

<figure><img src="image_22.png" /><figcaption>**Fig. S14** | Optical power range for recording spin bits. Probability of the three types of events after relaxation for a laser exposure duration equal to 1 s vs the incident optical power. Data is shown for L (a) or R (b) circularly polarized writing beam using a left-handed chiral nematic sample with *L* = 10 µm made of E7 nematic. In the reported range of power, the three observed events are: nothing is recorded (black), spin-dependent structure is recorded (red) and spin-independent structure is recorded (blue). Scale bar: 10 µm.</figcaption></figure>
## XII. SIMULATED $(\partial\theta/\partial\tau)_{\text{opt}}$ AND $(\partial\phi/\partial\tau)_{\text{opt}}$

Complementary simulations of the spatial distribution of the light-driven time derivative for the director angles $\theta$ and $\phi$ are reported in Fig. S15. This highlights an up/down asymmetry that becomes more pronounced as the amplitude $\theta_1$ of the director initial perturbation increases [see panel (a)], while the asymmetry with respect to the mid-plane of the sample ($z = L/2$) remains unchanged as shown by normalized profiles [see panel (b)].

<figure><img src="image_23.png" /><figcaption>Fig. S15 | Simulated spatial distribution of light-driven time derivatives from Eqs. (1) and (2) of the main text (a,b) Same as Fig. 5 of the main text but for $\theta_1$ from 2° to 20° by 2° step. (c,d) Normalized version of panels (a,b).</figcaption></figure>

## XIII. DESCRIPTION OF SUPPLEMENTARY VIDEOS

* **Video 1.** XPOL recording of the writing dynamics and ensuing elastic relaxation after the pump beam is switched off, for $\sigma = +1$ and $\chi = -1$. The writing beam conditions are that used for Fig. 2(a). Nematic material: E7. Thickness: $L = 10$ µm. Viewing area: 38 µm $\times$ 38 µm. Polarizer is oriented along $y$ axis and analyzer is oriented along $x$ axis.

* **Video 2.** Same as video 1 for $\sigma = -1$ and $\chi = -1$.

* **Video 3.** Same as video 1 for $\sigma = +1$ and $\chi = +1$.

* **Video 4.** Same as video 1 for $\sigma = -1$ and $\chi = +1$.

* **Video 5.** XPOL recording of the writing of 4 spin bits along a row for $\sigma = +1$ and $\chi = +1$. The writing beam conditions are that used for Fig. 2(a). Nematic material: E7. Thickness: $L = 10$ µm. Viewing area: 82 µm $\times$ 82 µm. Polarizer is oriented along $x$ axis and analyzer is oriented along $y$ axis.

* **Video 6.** Same as video 5 for $\sigma = -1$ and $\chi = +1$.

* **Video 7.** XPOL recording of 10 consecutive write & erase cycles at a given position for $\sigma = +1$ and $\chi = +1$. The writing beam conditions are that used for Fig. 2(a). Nematic material: E7. Thickness: $L = 10$ µm. Viewing area: 41 µm $\times$ 41 µm. Each cycle has a duration of 50 s and consists of 10 s illumination with the writing beam followed by 20 s relaxation, then a quasistatic electric field at 10 kHz frequency obtained from a voltage difference of about 5 V$_{rms}$ is applied during 10 s, followed by 10 s relaxation. Polarizer is oriented along $y$ axis and analyzer is oriented along $x$ axis.

* **Video 8.** Same as video 7 for $\sigma = -1$ and $\chi = +1$.

* **Video 9.** XPOL recording of the reversible electrical squeezing of a spin bit, which corresponds to the data shown in Fig. S6(a). Viewing area: 49 µm $\times$ 49 µm.

* **Video 10.** XPOL recording of the irreversible electrical erasure of a spin bit, which corresponds to the data shown in Fig. S6(b). Viewing area: 49 µm $\times$ 49 µm.
[1] J. Li and, C.-H. Wen, S.Gauza, R. Lu, and S.-T. Wu, "Refractive indices of liquid crystals for display applications," J. Disp. Technol. 1, 51–61 (2005).

[2] J. F. Strömer, E. P. Raynes, and C. V. Brown, "Study of elastic constant ratios in nematic liquid crystals," Appl. Phys. Lett. 88, 051915 (2006).

[3] A. Varanytsia, G. Posnjak, U. Mur, V. Joshi, K. Darrah, I. Muševič, S. Čopar, and L.-C. Chien, "Topology-commanded optical properties of bistable electric-field-induced torons in cholesteric bubble domains," Sci. Rep. 7, 16149 (2017).

[4] M. Born and E. Wolf, *Principles of optics: electromagnetic theory of propagation, interference and diffraction of light* (Elsevier, 2013).

[5] P. Oswald and P. Pieransky, *Nematic and Cholesteric Liquid Crystals: Concepts and Physical Properties Illustrated by Experiments* (Taylor & Francis, CRC, Boca Raton, FL, 2005).

[6] H. Hakemi, E. F. Jagodzinski, and B. D. Dupré, "Temperature dependence of the anisotropy of turbidity and elastic constants of nematic liquid crystal mixture E7," Mol. Cryst. Liq. Cryst. 91, 129–136 (1983). 7, 16149 (2017).

[7] B. T. Hallam and J. R. Sambles, "Optically guided mode study of nematic liquid crystal alignment on a zero-order grating," Phys. Rev. E 61, 6699–6704 (2000).

[8] H. Chen, R. Zhu, J. Zhu and S.-T. Wu, "A simple method to measure the twist elastic constant of a nematic liquid crystal," Liq. Cryst. 42, 1738–1742 (2015).

[9] P. D. Brimicombe; C. Kischka; S. J. Elston, and E. P. Raynes, "Measurement of the twist elastic constant of nematic liquid crystals using pi-cell devices," J. Appl. Phys. 101, 043108 (2007).

[10] H. Wang, T. X. Wu, S. Gauza, J. R. Wu, and S.-T. Wu, "A method to estimate the Leslie coefficients of liquid crystals based on MBBA data," Liq. Cryst. 33, 91–98 (2006).

[11] B. Yang and E. brasselet, "Study of elastic constant ratios in nematic liquid crystals," J. Opt. 15, 044021 (2013).