In optics, focusing properties of optical fields are always very important, and the research of tight focusing properties have attracted more and more interest. A variety of tight focusing results of vector optical fields with more complex states of polarizations (SoPs) have been presented. As the symmetry property of the focused field is one of the most important properties, we propose a method to discuss the relation of the symmetry of the focused fields and the incident optical fields, and the vector optical fields of local linear polarization can be generated in the experimental setup as shown in Fig. 1. We also give the expansion of the theory, including the discussion of the polarization, intensity, phase, weak focusing, central singularity and so on. Some examples of the tight focusing calculations are also proposed in order to prove the validity of our theory and help us to reform the SoPs of the incident vector fields in order to get desired symmetry of the tightly focused fields. One representative example is the vector optical fields of kaleidoscope, which is shown in Fig. 2. From this figure we can see pretty focusing patterns similar to the kaleidoscope we have seen when we were children, which proves that certain symmetry of the tight focusing fields can be gained from our theory. To conclude, we believe that the analysis of the symmetry of tightly focused fields and the method to design the vector optical fields can help us to flexibly use the tight focusing properties in order to get more applications, including optical trapping, optical machining and so on.
PS: Figure 1 is the schematic of experimental setup for generating the desired vector optical fields of local linear polarization. Figure 2 is one simulated example of the designed states of polarization and the corresponding tight focusing fields with certain symmetry.
Figure 1. Schematic of experimental setup for generating the desired vector optical fields of local linear polarization.
Figure 2. One simulated example of the designed states of polarization and the corresponding tight focusing fields with certain symmetry.