# Light-Induced Ring Pattern in a Dye-Doped Nematic Liquid Crystal
## 2 Experimental Observations of the Ring Patterns
### Experimental Setup  
Figure 2 shows the experimental setup diagram. The dye-doped liquid crystal cell (DDLCC) undergoes a phototropic transition when it is irradiated by a light source in the absorption band of the guest dye [19; 31]. We used a concentration of methylred methyl ester \(\,1\) wt% as azo-dye guest doping a commercially available E7 NLC (host). The chemical structure and isomers of methylred methyl ester are illustrated in Figure 1c. The absorption spectrum of the methylred methyl ester is depicted in Figure 2b (for details about the chemical synthesis and depration of the azo-colorant, see Section 2.2). The mixture was injected into an antiparallel planned liquid crystal cell with a thickness of 25 \(\mu\)m (Instec Inc., Boulder, CO, USA). A 445 nm Cobolt 90 nW Polarized Laser was used as an exciting irradiation source to generate a phototropic transition. The polarization \(\vec{P}_{B}\) was fixed, and the laser power was used as a tuning or bifurcation parameter. Note that the blue laser wavelength was close to the absorbance peak at 420 nm, enabling us to trigger the isomerization and increase the amount of _cis_ methyl red methyl ester isomer. There was no relevant temperature change in the DDLCC. The experiment was conducted at room temperature, approximately 20 \({}^{\circ}\)C. This meant that only an increase of the _cis_-isomer concentration was responsible for a decrease of birefringence on the liquid crystal. A Kepler telescope \(K_{B}\) with a magnification of \(\times 1/5\) was used to change the waist of the blue laser. The orientational molecular order in the dye-doped liquid crystal interacted with the blue light, making blue light sampling unsuitable for scanning the optical response of the liquid crystal sample. To uncouple the excitation and probing fields, we provided illumination with a 532 nm Verdi V-2 polarized green laser as a probing light. Indeed, the absorbance at 532 nm is negligible for methyl red methyl ester, as seen in Figure 2. Both the green laser polarization \(\vec{P}_{G}\) and its intensity were set fixed. A Kepler telescope with a magnification of \(\times 2\) was used to expand the beam and obtain a more homogeneous illumination. A long-pass dichroic mirror DM (cutoff wavelength at 500 nm) was mounted in a pitch-yaw kinematic mount to  
Figure 2: Experimental setup for the dye-doped nematic liquid crystal phototropic transition with a harmless external illumination. (**a**) A dye-doped liquid crystal cell (DDLCC) is irradiated by a 445 nm blue laser (excitation light beam) \(L_{B}\) and illuminated by a 532 nm green laser (probing light beam) \(L_{G}\). Two pairs of lenses are placed in a Kepler telescope configuration \(K_{B}\) and \(K_{G}\) to expand the laser beam while preserving the collimation. \(\vec{P}_{B}\) and \(\vec{P}_{G}\) are the polarization of the laser sources. A long-wave pass dichroic mirror \(DM\) is used to set both excitation and probing on the same optical line. After the DDLCC, another long-wave pass dichroic mirror is used to filter out the excitation beam. An analyzer in a crossed configuration with respect to \(\vec{P}_{G}\). A set of imaging optics \(IL\) consisting on a \(\times 2\) Kepler telescope and a \(\times 7\) zoom lens is used to enhance the image captured by the \(1/2\)” CCD camera. (**b**) Absorption spectrum of methyl red methyl ester in dichloromethane \(2.0\times 10^{-5}\) mol/L. The solid vertical lines account for the wavelength of the exciting and probing light, respectively. Vertical dashed lines account for the absorption maximum. control the reflection angle and thus the position of the blue laser on the DDLCC. A second dichroic mirror was used to filter out the excitation light from the optical path to the 1/2\" CCD camera. To record the images, a set of illumination optics was used to enhance the image quality. A first pair of lenses in a Kepler telescope configuration with an optical zoom of \(\times 2\) and a secondary zoom lens with a magnification of \(\times 7\) was used.