Manipulation of Bessel beam

Since the Bessel beam was proposed as an exact solution of propagation-invariant mode to the Helmholtz equation by Durnin in 1987, it has attracted a great deal of research interests. Due to its properties of non-diffraction and self-healing, the Bessel beam has been widely used in the fields of free-space optical interconnects and communications, optical capture and particle manipulation, optical micro-nano machining, optical microscopic imaging, and femtosecond laser processing. Recently, the propagation and manipulation of Bessel beams have become an issue of fundamental importance.

Figure 1. Self-healing process of a Bessel beam with its main lobe blocked.

Self-similar Bessel-like beam

The self-similar beam refers to the beam with overall scaling in transverse profiles during propagation. The most two typical examples are the Laguerre-Gaussian beams and non-diffracting Bessel beams. Recently, researchers have proposed a class of self-similar beams with different scaling factors by solving the paraxial wave equation. The exact solutions of self-similar Bessel beams can be acquired, but there are still restrictions on the scaling factors. The self-similar arbitrary-order Bessel-like beams under tunable stretching transformations have been demonstrated based on the Fresnel integral. The related works either have restrictions in scaling factors or require complicated integral calculations.

The research team of Light Field Manipulation at Northwestern Polytechnical University led by Prof. Sheng Liu and Prof. Jianlin Zhao proposes a new method to construct the arbitrary self-similar Bessel-like beams more straightforwardly, by employing the transverse-longitudinal mapping. This method enables the beam width to vary according to the pre-designed function during propagation for both zero- and higher-order Bessel-like beams, by radially modulating the wave vector cone of the Bessel beam. The relevant work was published in Chinese Optics Letters, Volume 22, Issue 2, 2024 (Yanke Li, Yu Zou, Zhaojin Guo, Sheng Liu, Peng Li, Bingyan Wei, Dandan Wen, Jianlin Zhao. Constructing arbitrary self-similar Bessel-like beams via transverse-longitudinal mapping. [J]. Chinese Optics Letters, 2024, 22(2): 022601) and was selected as the cover of the current issue.

The cover shows the generation of a higher-order self-similar Bessel-like Beam. A higher-order Bessel-like beam with a sinusoidally varying beam width is generated from a plane wave modulated by a special phase.

Figure 2(a) illustrates the design principle of the proposed method. By establishing a relationship between the full width at half-maximum (FWHM) and the transverse wave vector of the Bessel beam, we map the longitudinal variation of the wave vector to the initial phase distribution of the light field. Theoretically, the beam width varying along the propagation direction can be predesigned arbitrarily. By modulating the conical wave vector distribution of the Bessel beam, self-similar Bessel-like beams with different beam width variations described by linear or piecewise functions of propagation distance, are experimentally demonstrated in the paper. When the analytical solution is hard to directly obtain, for example, the self-similar beam with sinusoidal beam width, the initial phase distribution can be numerically calculated, as shown in Figure 2(b). The intensity distribution of the generated self-similar Bessel beams matches well with the Bessel function in different propagation distances. The proposed method is more intuitive and easier to realize, and supports the point-to-point control of the beam width.

Figure 2. Constructing arbitrary self-similar Bessel-like beams via transverse-longitudinal mapping. (a) Scheme of the principle; (b) Zero-order Bessel-like beam with sinusoidal varying beam width.

The proposed approach also enables the generation of self-similar higher-order Bessel-like beams. Figure 3 shows the first- to third-order self-similar vortex Bessel-like beams with sinusoidally-varied beam width, and the results are basically consistent with the theory. The proposed method can be also applicable to other non-diffraction beams containing the conical wave vector, and would be of benefit for exploring applications in the optical manipulation of microparticles and optical imaging.

Figure 3. Propagation process of first- to third-order self-similar Bessel-like beams with sinusoidally-varied beam width. (a-f) Side view of the simulated and experimental propagation process; (g-i) the corresponding beam width vs. propagation distance.