Tricomi–Gauss beam and its propagation characteristics

Tricomi beams are structured light beams that belong to the general class of non-diffracting light beams. The cross-section of an ideal Tricomi beam extends upto infinity and hence the energy distribution in the transverse plane (beam cross-section) is not finitely bounded. But all real-world systems are finitely bound, which causes inconvenience in studying Tricomi beams practically. To overcome this issue we introduce Tricomi–Gauss beam for the first time, which possesses similar characteristics to Tricomi beams but with a finite beam cross-section. In this study, we derive the general expression for the Tricomi–Gauss beam and its propagation. We show that the derived equation can be used to study the propagation properties of a family of Bessel–Gauss beams only by setting the appropriate parameters to the derived equation. Simulation results show the intensity and phase profiles of the beams as they propagate through (i) free space (ii) lens system and (iii) fractional Fourier transform system. Interesting propagation characteristics were observed, especially in the case of the asymmetric Bessel–Gauss beam, which can be attributed to the choice of parameters. The advantages of Tricomi–Gauss beam are verified by practically generating the beams using computer-generated holography technique.