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J. Eur. Opt. Society-Rapid Publ. 22, 8( 2026)
Table 1. Changes in c, l and k affect self-focusing characteristics of RAVB.
Modulation parameter |
c |
l |
k |
Change range |
4 – 8 |
1 – 7 |
100 nm – 380 nm |
380 nm – 780 nm |
Focus depth |
8 cm – 41 cm |
35 cm – 46 cm |
196 cm – 52 cm |
52 cm – 35 cm |
Size of focus spot |
Decreased |
Increased |
Invary |
Invary |
Uniformity of light intensity |
Uniform |
Non-uniform |
Uniform |
Uniform |
in the focus spot |
|
|
|
|
Focus peak intensity |
Increased by ~ 50 times |
Basically unchanged |
Increased by ~ 1.2 times |
Increased by ~ 2.2 times |
also increase. When the value of l is negative, the sign of the topological charge solely influences the rotational direction of the beam.
3.3 The influence of wavelength( k) on self-focusing characteristics of RAVB
When c = 8, l = 1, thevaluesofk are 380 nm, 457.9 nm, 514.5 nm, and 632.8 nm, respectively. The numerical simulation results indicate that the corresponding focus depths z are 52 cm, 43.5 cm, 39 cm and 35 cm, respectively. Equation( 7) demonstrates that the trajectory of the main lobe is dependent on k. For a constant self-bending displacement x, anincreaseink, leads to a reduction in the required propagation distance.
The intensity distributions at the self-focusing plane are illustrated in Figure 4. As k changes, the area of the focus spot varies only slightly. The rotation of the focus spot is quite pronounced at k = 632.8 nm. As the k decreases, the rotation diminishes, and the focus spot approaches a rectangular at k = 380nm. Figure 5 presents the curves depicting both focus depth and focus intensity as functions of wavelength. The data indicates that focus peak intensity increases with increasing wavelength. When k is changed from 100 nm to 800 nm, there is a twofold increase in focus peak intensity. Notably, this variation is markedly more pronounced within the visible spectrum than in the ultraviolet range. Changes in focus depth exhibit an inverse relationship with variations in the corresponding peak intensity. These changes are substantial in the ultraviolet range while remaining minimal within visible light wavelengths.
4 Results and discussion
The results indicate that variations in c, l and k significantly influence self-focusing characteristics of RAVB, as detailed in Table 1.
To achieve a more flexible adjustment of focus depth while maintaining the uniformity of focus spot intensity, c is identified as the most suitable adjustment parameter. The adjustment of c sharply modifies the peak intensity of RAVB, which is conducive to controlling particles. Adjustments to l and k also hold significant application value in some requirements. For instance, where it is essential to maintain a constant size for the focus spot while making minor changes to either the focus depth or peak intensity; this can be accomplished through adjustments to k.
5 Conclusion
In this paper, we present numerical simulations and analyses based on the principle of phase modulation to investigate the effects of modulation parameters on the self-focusing characteristics of RAVB. This research establishes a theoretical foundation for precisely applying and manipulating. The controllable self-focusing property is particularly advantageous for optical lower-NA manipulation micromanipulation. This work provides substantial guidance for applications in laser medicine, scalable patterning, and other optical handling techniques that are independent of polarization. Funding
This study received funding from The Natural Science Foundation of Fujian Province( No. 2024J011214).
Conflicts of interest The authors declare that there are no conflicts of interest.
Data availability statement
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Author contribution statement
All authors have reviewed, discussed, and agreed to their personal contributions. The specific situation is as follows: The simulations and Analysis were performed by Liangqin Gan; Liangqin Gan and Hongyi Lin wrote the article with supervision of Shanggong Yang and Dong Sun.
References
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