# Generating Bessel-Gaussian Beams with Controlled Axial Intensity Distribution
## 3 Experimental Implementation of the Bessel-Gaussian Beam
### Results and Analysis  
The axial field intensity distributions were acquired with a step of 1 mm along the optical axis. The effect of a diaphragmed Gaussian beam on the axial intensity and length of the Bessel zone is shown in Figure 3a-d. The dots denote the experimental data, and the solid line denotes the approximated experimental data. It can be seen that the experimental results are in good agreement with the theoretical calculations presented in Section 2.  
Figure 3: _Cont._  
For the \(z_{\text{AP}}\) sections corresponding to the region of abrupt change in axial field intensity (vertical dashed lines in Figure 3a-d), the cross-sections of field intensity are shown in Figure 4. The results of calculating the gradient of the function are presented in yellow lines in Figure 3. The most interesting area from the entire dependence of the axial intensity distribution of the Bessel zone was the leading and trailing edges. When a Gaussian beam hit an axicon without a mask, the gradient of the function had equal rise and fall times, Figure 3a. In the case when the outer or inner part of the Gaussian beam was diaphragmed, only one edge of the Bessel beam field intensity changed, as described in Section 2. With the external diaphragm, the leading edge in the function remained unchanged, and with the internal diaphragm, the trailing edge remained unchanged. In this case, the rate of change of the intensity distribution profile in the studied areas increased by more than 4 times. In Figure 3b,c, one can see these jumps in the gradient speed. After installing the mask with annular aperture, two sharp changes in axial intensity were obtained, Figure 3d. The rate of change also increased by more than 4 times.  
Figure 4: _Cont._  
Figure 3: Axial intensity distributions of a zero-order Bessel beam and gradient from the longitudinal coordinate \(z_{\text{AP}}\) for various parameters of the binary mask in front of the axicon: (**a**) without binary mask, \(d=0\) mm, \(D\rightarrow\infty\); (**b**) with binary mask, \(d=4\) mm, \(D\rightarrow\infty\); (**c**) with binary mask, \(d=0\), \(D=7\) mm; (**d**) with binary mask, \(d=4\), \(D=7\) mm.  
As mentioned earlier, Figure 4 shows the cross sections of the field intensity distribution of the Bessel beam. As a reference distribution, we took the cross section that corresponded to Figure 4a, when a Gaussian beam with a diameter of 4 mm without apodization fell on the axicon. It can be seen that there were features of the zero-order Bessel function in each distribution that are of interest. The absolute value of field intensity in the analysis plane for the cases in Figure 4b-e corresponds to the intensity profile shown in Figure 3a. Apodization of the beam incident on the axicon did not in any way affect the size or shape of the central maximum (the nucleus of the Bessel zone).  
The change in relative position of the Bessel zone core in Figure 4 was associated with camera positioning accuracy during the registration of the cross section of the field intensity distribution. However, this fact did not affect the analysis and interpretation of the results. The same can be said about the triple symmetry of the first maximum, the origin of which has nothing to do with the amplitude diaphragm set in front of the axicon, and can be explained by the presence of aberrations in the afocal optical system located after the axicon.