## 4 Discussion  
A 3D printing method is successfully used to fabricate CSPAs in this paper. Its theoretical processing accuracy is \(\sim\)150 nm, and the actual processing accuracy \(\sim\)200 nm according to practical measurements of the surface roughness. Due to the machining accuracy, the final stepped surface is not ideally smooth but already satisfy the requirement for generation a needed vortex light field. Considering the precision of focused ion beam (FIB) processing can reach an accuracy of \(\sim\)4 nm, it can be expected that the CASPs will present a very smooth and entire surface through FIB technique. However, if the processing area being 150\(\times\)150 \(\upmu\)m or even larger and the etching depth being more than \(\sim\)6 \(\upmu\)m, the FIB processing will be time-consuming and expensive. It can be seen that the 3D printing technology has achieved a better balance between processing accuracy and fabrication cost for manufacturing large-area micro-optical devices.  
It should be noted that from the light field characters and the light intensity distribution shown in Figures 9 and 11, the secondary bright rings in addition to the main bright rings also exist at the focal plane. From the perspective of sidelobe suppression, the main bright rings are created by the diffraction of incident light beams passing through the outer circle area of the CSPA. The ineffective secondary bright rings or the sidelobe are caused by the diffraction of incident beam going through the central small region of each vortex phaser of the CSPA. Therefore, as long as an annular spiral phaser with an appropriate width being used, the operation of eliminating the sidelobe of the vortex beam should be achieved. In the follow-up work, we plan to hollow out the small central region of each vortex phaser of the CSPA in order to obtain the best annular light field.  
Next we discuss the relationship between the bright ring radius and the wavelength of the incident light beam. In formula (2), \(r\) is the radius of the bright ring, and \(l\) the TC, and \(w_{0}\) the beam waist radius of the Gaussian beam, and \(z\) the transmission distance, and \(k\) the wave number [46].  
\[r^{2}=\frac{||l||\Big{(}k^{2}w_{0}^{4}+4z^{2}\Big{)}}{2k^{2}w_{0}^{2}} \tag{2}\]  
Considering the safe optical power range that the detector can withstand and the convenience of matching the light source with the structural region, a beam expander is added behind the laser, so the planewave light source used in the experimental measurement. Since a planewave light being used, there is no corresponding parameter of the Gaussian beam, so it is impossible to draw an accurate relationship between the wavelength and the radius of the bright ring from the above formula. According to measurement results, the bright ring radius of beams including the red, the green, and the blue light, are obtained, which are 10.75 \(\upmu\)m, 11.25 \(\upmu\)m and 12.58 \(\upmu\)m, respectively. We plot a relationship between the central wavelength of the incident light beams and the radius of the bright ring to obtain Figure 14. From the figure, we can see that as the wavelength increasing, the radius of the bright ring gradually decreased and then the decreasing trend tends to be gentle gradually. According to the following relation curve, the variation trend of the radius of the bright ring with the central wavelength of the incident beam is understood, which is convenient for predicting the bright ring radius corresponding to the incident beam with a wider wavelength range, and clarifies a good direction for in-depth exploration of the vortex optical field distribution.