## 2 Micro-Actuator Fabrication  
### Principle of Two-Photon Polymerization  
TPP can be explained by the non-linear optical property of TPA described by [PERSON] in 1931 [22]. TPA is the interaction between a single atom/molecule and multiple photons during a single quantum event, which occurs in the photo-excitation process from a lower quantum state to an excited quantum state of an atom (or molecule). When a single photon has energy above the bandgap of the material, photon energy is absorbed by the excitation of electrons from the valence band (VB) to the conduction band (CB) by single-photon absorption. However, even if the photon energy is less than the bandgap, electrons can be excited by multiple photons through a virtual state when a very high photon density is provided to a material. Therefore, the simultaneous/sequential action of two photons provides enough energy to induce this transition during the TPA process [23]. Since TPA requires very high energy, it can be induced by using femtosecond (fs) laser with a short pulse duration, which makes it possible to obtain a sufficient optical electric field for TPA to be feasible. TPA can be explained by two mechanisms: sequential TPA and simultaneous TPA (Figure 1a). Sequential excitation is an electronic transition to an excited energy state via an intermediate state. The absorbed species are transferred to the actual intermediate state by first photon absorption, and this species is transformed into an excited state by the subsequent absorption of the second photon [23]. The excited electrons in the intermediate state are excited to a higher quantum state by absorbing a second photon with the same energy. In contrast, electrons are excited to a higher state by simultaneously absorbing two photons in one quantum state without the excited intermediate state in simultaneous TPA. The absorption process is considered the initial interaction of atoms/molecules and photons, and it form a temporary virtual energy state above the ground state. When the second photon arrives before the decay of the photon in the virtual state within a short time period, the two photons can be absorbed at the same time, thereby becoming exited to the higher state and transcending the energy bandgap. When the TPA process takes place on photocurable resin materials, photo-induced polymerization reactions occur, which allow for 3D micro/nanoscale structure fabrication. For TPA polymerization, two photons are simultaneously absorbed within a tightly focused small focal volume using a high numerical aperture (N.A.) objective lens in a photocurable resin, which causes a chemical reaction between the photo-initiator molecule and the monomers by femtosecond pulses with an ultrahigh-peak intensity and a very short pulse duration [24,25]. A general photocurable resin is composed of a photoinitiator (PI) for radical generation, a monomer or oligomer to form the bonding between molecules, crosslinkers, photosensizers, quenchers, and solvents for dilution [26]. Looking at the properties of the photocurable resin's components in detail, the PI can be classified into two types--radical and cationic, depending on what material needs to be generated. The monomers or oligomers, constituent units of the polymer network, determine the physical/chemical and mechanical properties of the photo-polymerized structure. The solvent can control the viscosity of the photocurable resin, which is an important component for the stability of a photo-polymerized structure. By using photocurable resin with a high viscosity, the photo-polymerized structure can be stably maintained, but it takes a long time in the development process. In contrast, the mechanical stability of a photo-polymerized structure is not guaranteed, but the development process can be completed in a short time with a low-viscosity photocurable resin. To achieve an efficient fabrication process, it is necessary to consider the factors required for each component.