## 2 Principle of DETL
### Principle of DE  
The core principle of DE to realise the actuation function is mainly the electrostriction effect. When an electric field is applied to the ends of a DE, a series of complex changes occur in the internal microstructure of the material, leading to macroscopic deformation. From a microscopic point of view, there are many polar groups in the molecular chain of DE. In the absence of an electric field, the orientation of these polar groups is randomly distributed. After applying the electric field, the electric field force will prompt the polar groups to rotate and rearrange so that the molecular chain is gradually oriented toward the electric field. This change in the orientation of the molecular chains will change the interaction force between the molecular chains, which will result in stretching or compression of the molecular chains. When the electric field strength is low, the orientation change of molecular chains is relatively orderly, and the deformation of the material is approximately linear with the electric field strength; with the increasing electric field strength, the orientation of molecular chains gradually tends to be saturated, and the growth rate of the deformation of the material is slowly slowed down, and at this time, the deformation of the material shows a nonlinear relationship with the electric field strength [19]. Macroscopically, the electrostriction effect is manifested as the DE shrinks in the thickness direction and expands in the plane direction. This is because under the action of the electric field, the Maxwell stress generated inside the material will compress the material, making it thinner in the thickness direction; according to the principle of conservation of volume of the material, the reduction in the thickness direction is inevitably accompanied by the expansion in the planar direction [20]. Figure 1 shows its driving principle diagram. When the DE is used as the driving element of the tuneable lenses, this expansion in the plane direction will affect the lens, which in turn changes the lens's focal length. Numerous factors affect the electrostriction effect, among which is the electric field strength, which is the most direct and critical factor. Generally speaking, the deformation of the material gradually increases as the electric field strength increases [21; 22]. However, when the electric field strength exceeds the breakdown field strength of the material, electrical breakdown of the material is triggered [23]. DE materials have different breakdown field strengths, usually 10-100 MV/m [24]. In practice, the strength of the applied electric field must be strictly controlled to ensure that it is within the safe working range of the material. The frequency of the electric field also affects the electrostriction effect. Under a low-frequency electric field, the polar groups inside the material have enough time to respond to the change in electric field, and the electrostriction effect can be fully utilised; however, under a high-frequency electric field, the orientation of the polar groups cannot keep up with the rapid change in the electric field, which will lead to the weakening of the electrostriction effect. The response speed of the material will be limited [25]. Figure 1: Principle of DE (author’s original image). In addition, the material's properties, such as temperature, dielectric constant, and cross-linking density, also significantly affect the electrostriction effect. Increasing temperature intensifies the molecular thermal motion and reduces the material's elastic modulus, thus affecting the electrostriction effect [26]. Materials with higher dielectric constants can store more electrical energy at the same electric field strength, resulting in greater electrostriction [27]. The crosslink density determines how closely the molecular chains are connected, and an appropriate crosslink density can enhance the mechanical properties and stability of the material.