Intensity distribution of diffractive axicon with the optical angular spectrum theory

Diffractive axicon is lightweight and easy to be manufactured, it is also efficiently used to produce diffraction-free Bessel beam. But, deducing its expression of the field distribution of light is difficult in theory and the theoretical equation expression has approximation by using the Huygen-Fresnel diffraction integral. Here, the rigorous optical angular spectrum theory that follows the Helmholtz equation is used. The propagation theory of angular-spectrum with fewer approximation, will result in more accurate results. A mathematical model to analyze the field distribution of light of the diffractive axicon is set up. The diffraction intensity distribution of the diffractive axicon with the monochromatic Gaussian beam illumination and multicolor illumination is numerically calculated and discussed. The results of numerical calculation with a monochromatic laser source show that not all the intensity distribution in the focal depth of field has the characteristics of the diffraction-free Bessel beam, and the on-axis diffraction intensity shows direct correlation of the lateral intensity distribution of the incident waves and the period of the diffractive axicon. The extended depth of field of the diffractive axicon with multicolor illumination is increasing as the wavelength reducing. It is expected that our study can provide very useful information for analyzing the diffractive axicon which exists in the optical trapping systems and laser-processing applications and imaging systems.