Modeling the generation and control of Bessel-like beams generated by annular patterns on a digital micromirror device

Bessel beams have been generated using different methods, such as Axicon lens, digital micromirror device (DMD), etc. Due to the infinite energy requirement of ideal Bessel beams in all space, the generated Bessel beams are more appropriately called Bessel-like beams in practice, which are approximations of the ideal Bessel beams. In this work, we theoretically investigated the generation of Bessel-like beams using annular patterns loaded on a DMD based on the scalar diffraction theory. The model predictions were compared and verified with our previous experimental results. For the first time, the theoretical study shows that the DMD-generated Bessel-like beams have an additional amplitude term depending on the annular radius, ring thickness, and incident angle compared with ideal Bessel beams. Furthermore, we modeled the superposition of two Generated Bessel-like beams using two coaxial annular patterns on a DMD, which revealed the periodic intensity distribution along the z axis as predicted previously based on the superposition of two ideal coaxial Bessel beams. Both the simulations and experiments give a similar periodic length that is close to the theoretical values. The modeling results show that the DMD-based method could not only generate a reasonable approximation of the ideal Bessel beams with good controllability and engineering applications but more importantly, provide explicit formulas to guide the design of the annular patterns on the DMD in order to generate and control Bessel-like beams for practical applications.