Matlab Simulation Code Example for Bessel-Type Vortex Beams

Bessel-type vortex beams are optical beams characterized by helical wavefronts and unique propagation properties, widely used in optical manipulation and communication systems. Implementing their simulation in Matlab typically involves the following core computational steps:

First, construct the helical phase distribution of the vortex beam. This can be achieved in polar coordinates by superimposing the topological charge number with the angular variable, generating a phase factor similar to exp(i*l*θ), where l represents the topological charge and θ is the azimuthal angle. In MATLAB implementation, this requires converting Cartesian coordinates to polar coordinates using [theta, rho] = cart2pol(X, Y) and creating the phase mask with phase = exp(1i * l * theta).

Secondly, superimpose the intensity distribution of Bessel functions. Zero-order or higher-order Bessel functions create the characteristic central dark core and annular intensity pattern, which can be directly computed using MATLAB's besselj function. Key parameters include the beam's cone angle and radial wave number, implemented through k_rho = k * sin(cone_angle) where k is the wave number, and the radial profile is calculated as besselj(l, k_rho * rho).

Finally, simulate the beam propagation through two-dimensional Fourier transform or angular spectrum propagation methods. This requires computing diffraction integrals or implementing far-field/near-field transformations using transfer function methods. The propagation can be coded using fft2 and ifft2 functions with appropriate propagation kernels like H = exp(1i * z * sqrt(k^2 - kx.^2 - ky.^2)) for angular spectrum method, demonstrating the beam's non-diffracting characteristics.

The simulation requires careful attention to the relationship between grid sampling density and beam dimensions to avoid aliasing effects. Typical visualization methods include phase distribution maps (using angle function), transverse intensity profiles, and 3D intensity renderings using surf or mesh functions. This simulation provides a numerical experimental foundation for studying the dynamic properties of optical vortices.