Code for Calculating Bessel Beam Phase Distribution

Bessel beams represent a special class of non-diffracting optical fields where phase distribution plays a critical role in understanding propagation characteristics. Calculating Bessel beam phase distributions requires combining mathematical expressions with numerical computation methods. The computational process begins with defining the mathematical expression for Bessel beams. For beams with different topological charges, the order and parameters in the expression vary accordingly. Higher-order Bessel beams exhibit more complex phase structures, particularly featuring phase singularities in the central region. When studying phase distributions in free-space propagation, we must consider the beam's propagation characteristics. During free-space transmission, Bessel beams maintain relatively stable transverse phase distributions while longitudinal phases change with propagation distance. These variations can be investigated by calculating phase distributions at different propagation distances. The core computational approach involves phase extraction from complex amplitude fields. Using numerical methods, we can calculate phase values at each point in the optical field, thereby obtaining complete cross-sectional phase distribution maps. For Bessel beams of different orders, the central regions of phase maps display distinct spiral structures directly correlated with topological charges. When analyzing the effects of different orders, particular attention should be paid to the number and distribution of phase singularities. Higher-order Bessel beams generate multiple phase singularities whose arrangement closely relates to the beam's angular momentum properties. By comparing phase distributions across different orders, we can gain deeper insights into how topological charges influence beam characteristics. For comprehensive study of free-space propagation properties, we recommend implementing a stepwise propagation method to calculate phase distributions at various propagation distances. This approach reveals how phase structures evolve during propagation, which holds significant importance for practical beam control applications. The implementation typically involves Fourier transform-based propagation algorithms and phase unwrapping techniques to handle complex phase discontinuities.