Far-Field Perfect Laguerre-Gaussian Beam

We propose a class of vortex beam-the Far-Field Perfect Laguerre-Gaussian Beam (FFPLGB)- which achieves perfect property at the receiving plane in the far-field. Specifically, the beam radius of the FFPLGB is almost invulnerable to orbital angular momentum (OAM), and its radial orders have a minimal impact on the beam radius. We also provide a distance formula that determines the position at which the FFFPLGB begins to acquire its perfect property. This distance formula can improve the practical implementation and operation of the FFPLGB. Quantitative research findings show that the FFPLGB, owing to its unique multi-ring structure, possesses more superior perfect property compared to classical perfect vortex beam. Compared to the declining received probability of Laguerre-Gaussian beam (LGB) with increasing OAM mode, FFPLGB demonstrates the ability to maintain similar OAM spectrum distributions across different OAM modes. Furthermore, the OAM spectrum distribution of FFPLGB remains largely invariant to changes in radial orders, highlighting its robustness and superior performance in optical applications. The perfect property of the FFPLGB effectively surmount the limitations encountered by conventional high-order LGB in various optical applications, and introduce a new developmental direction for LGB.