Influence of the Nonideality of the Axicon and the Input Gaussian Beam on the Quality Parameters and the Fourier Spectrum of the Generated Bessel Light Beam

We investigated the influence of three factors on the formation of a Bessel light beam (BLB) in the scheme of transforming a Gaussian beam by an axicon: the ellipticity of the incident light beam, the ellipticity of the axicon, and the presence of a round tip of the axicon. For this purpose we used the methods of Fourier optics via numerical simulation. The results of the influence of each factor on the structure, quality parameters k_c, k_r, <R²> of the formed BLB and its Fourier spectrum (FSBLB) are shown. We introduced quality parameters of the FSBLB k_Is, k_ws, k_rs, which characterize the spread of amplitude, half-width and average frequency of the conical component of the FSBLB, as well as the parameter η, which determines the ratio of the energy in the conical component to the total energy of the beam. The quality of the FSBLB was analyzed with help of these parameters. The ellipticity of the Gaussian beam incident on the axicon leads to a reduction of the length of the region of existence of the BLB. In this case with increase of longitudinal coordinate all quality parameters decrease and the coefficient of constancy k_c drops most quickly. With increasing eccentricity of the half-widths of the Gaussian beam ε_b, the quality parameters of the FSBLB k_Is, k_ws, which characterize the spread of the intensity and half-width of the conical component of the beam, decrease. The ellipticity of the axicon affects all parameters of the quality of the BLB; most clearly, with an increase in the eccentricity of the axicon ε_a, the coefficient of constancy k_c and the average value of R² decrease. This happens due to oscillations in the ring closest to the axis of the BLB. The shape of the FSBLB with increasing ε_a also changes, moving from circular to elliptical. Because of this the coefficient of constancy of the frequency of the spectrum of the conical component decreases. Regularities in the transverse distributions of the intensity of the BLB, formed in the presence of azimuthal modulation of the cone angle were considered for the case when the number N of complete periods of oscillation of the cone angle is greater than 2. The number of intensity minima in the paraxial ring at a small value of the axicon base angle modulation amplitude B (≤0.05) in the case of odd N is equal to N, and in the case of even N is equal to 2N. For large values of B (>0.05) as in the case of even N, so in the case of odd N, the number of minima in the paraxial ring of the beam is equal to 2N. The spherical tip of an otherwise conical axicon leads to the formation of a separate non-conical component in the spectrum. In the case of a hyperbolic axicon, the conical component of the spectrum broadens in the direction of low spatial frequencies. The results obtained can be used to form special light fields, as well as to assess the quality of manufacturing of axicons and the ellipticity of the beam incident on the axicon.

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