# Light-Induced Ring Pattern in a Dye-Doped Nematic Liquid Crystal
## 1 Introduction  
The interaction between light and matter has played a fundamental role in the understanding and characterization from the early stages of research [1]. Likewise, the interaction between light and matter has also been the basis of the development of technological elements such as mirrors, lenses, telescopes, microscopes, lasers, and waveguides, among others. The development of more coherent and monochromatic light sources (lasers) accompanied by materials that present stronger nonlinear responses has allowed the creation of a great variety of devices [2; 3; 4; 5; 6]. Liquid crystals are one of the most versatile materials, because of their strong nonlinear response and reorientation capacity through the application of electromagnetic waves and electric and magnetic fields [7; 8; 9; 10; 11]. Liquid crystals are a state of matter in which the molecules have a preferential orientation and can have or not have a positional order; this organization is also known as soft matter [7; 8; 9; 10; 11]. Indeed, this state of matter shares features of solids and liquids. In particular, fluidity, molecular reorientation, and birefringence are characteristic properties of liquid crystals. One of the most studied types of liquid crystals used in technological applications are nematic liquid crystals (NLC). This state is composed of rod-like organic molecules [7; 8; 9; 10; 11]. Because of an intermolecular interaction, these molecules are arranged to have a similar molecularorientation without positional order for specific temperature ranges. This results in a sharp anisotropy of all their physical properties, especially regarding elastic and optical characteristics. Likewise, the ability to reorient the molecular order has allowed the development of many applications, mainly liquid crystal displays (LCDs) and sensors [12]. The LCD is perhaps the best known liquid crystal application by the public today. However, in most of these applications, the control of molecular reorientation is done through electric fields. LCDs therefore require transparent or reflective electrodes, power sources, and other elements. Another manner of achieving molecular reorientation is to consider the application of electromagnetic waves through the liquid crystal sample [13; 14; 15; 16; 17]. However, this type of strategy requires the use of strong electromagnetic fields, which typically need a power on the order of 100 W/cm\({}^{2}\). For these powers, the nonlinear response of the medium is activated [11; 18]. The previous scenario can change radically when one considers the dye-dopant inside the liquid crystal matrix. Indeed, when nematics are doped with azo-dyes, their nonlinear response to opto-electrical perturbations is increased by several orders of magnitude [11; 18]. Indeed, azo-dyes mediate the origin of the coupling of the electromagnetic waves with the liquid crystal; when these molecules are irradiated, they present an isomeric transition. This phenomenon is known as the Janossy effect [19]. This transition is characterized by the fact that the molecule changes from an elongated structure (_trans_-state) to one with a boomerang shape (_cis_-state) when the molecule absorbs a photon. Figure 1 illustrates the typical structure of these molecules. When a sufficiently intense light beam illuminates a thin film of dye-doped nematic liquid crystal, this can induce molecular disorder, generating a transition from a nematic phase to an isotropic one [20]. This type of transition is characterized by the emergence of a front between phases [20]. These fronts are characterized by being a circular spot that gathers in the center of the beam and spreads outwards and stops in the region where both states are energetically equivalent, [PERSON] point. For intermediate light intensities, which do not induce isotropic liquid phase, the emergence of a pattern with a stripe shape has been reported [21; 22]. In fact, these patterns correspond to regions that alternate higher and lower orientational molecular order.