# Amplification of Chirality in Photopatterned 3D Nanostructures of Chiral/Achiral Mixtures
## 1 Introduction  
In general, the term chirality has a broad meaning and chirality in nature is an omnipresent phenomenon. Normally, in chemistry, chirality can be found in organic compounds consisting of one or two carbon atoms with four substituents [1]. In 1850, [PERSON] observed double sodium-ammonium salts and found that their crystals had a tiny facet on one of the edges, oriented to either the right or left. He separated these two types of crystals and identified that they were optically active in solution, with equal rotations in absolute magnitude but opposite direction [2; 3; 4]. Likewise, when two molecules have the same formula but a different state of symmetry of one atom, they are referred to as enantiomers, which are chiral molecules--non-superimposable mirror images of each other [5], as shown in Figure 1.  
Because the optical activity of natural materials is weak, researchers have tried to find enhancements for the characteristics of the materials, which has resulted in the discovery that optical activity can be affected by various factors such as light intensity, electric fields, magnetic fields and temperature [6; 7; 8; 9]. As a reaction to these factors, the optical activity can be changed to the same order of magnitude when phase transitions are involved, and for some cases, the circular birefringence can become large enough to satisfy a negative refractive index [10; 11; 12]. In terms of the chirality parameter \(\kappa\), a material's chirality can be changed. When \(\kappa\) is large enough, a negative index of the material can be realized. If the \(\kappa\)  
Figure 1: An example of non-superimposable mirror images. of the chiral material is larger than the square root of the product of real parts of the \(\varepsilon\) and \(\mu\), which are the permittivity and permeability, respectively, a negative refraction will occur:  
\[\sqrt{\varepsilon\cdot\mu}\ <\ \kappa \tag{1}\]  
\[\text{n}=\sqrt{\varepsilon\cdot\mu}-\kappa \tag{2}\]  
where \(\varepsilon\), \(\mu\), \(\kappa\), and n are permittivity, permeability, the chirality parameter and the refractive index of the material, respectively [13]. \(\pi\)-conjugated conductive polymers, such as polyfluorenes and their copolymers, have received interest [14; 15; 16; 17] as candidates for various applications; solar cells [18; 19; 20; 21], light-emitting diodes [22; 23; 24; 25], bio-imaging [26; 27], optical switches [28; 29; 30; 31], optoelectronics [32] and various synthetic methods of inducing enantioselective interactions of nanoparticles with chiral molecules have been studied [33; 34; 35]. [PERSON] et al. introduced a synthesized chiral polymer, poly(fluorene-alt-benzothiazole) (PFBT), with the addition of gold nanoparticles (AuNPs) and showed that the annealing of the polymer caused an increase in the optical activity [36]. Compared with pure films, the annealed films showed more than three orders of magnitude higher values of chirality, which is an effect that is caused by the structural and plasmonic enhancement of the chirality. Later, the amplification of chirality in a solid phase caused by the dispersion of a chiral polymer in a polymerizable matrix was reported [37]. The helical conformation of PFBT within a polymerized SU-8 matrix excessively enhanced the CD. In addition, the photopatterning of the PFBT/SU-8 mixture was demonstrated successfully using UV exposure with a size of a few hundred \(\upmu\)m [38]. Two-photon polymerization, using a two-photon absorption process, is a fabrication technique for nanopatterns and three-dimensional (3D) structures [39]. This method for nano- and 3D structures is of great interest in various fields, including nanotechnology, biotechnology, photonic crystals and functional applications such as micro-/nano-fluidic devices and micro-/nano-electromechanical systems [40]. Since PFBT/SU-8 showed good optical activity and the potential for usage in applications as a photopatternable material, understanding its characteristics and expanding on its usage are highly required.