Influence Of Astigmatic Lens On The Beam Parameters Of Laser Beams

There are two cases when laser beams passing through optical system. One is perfect system, the other is nonideal system. When laser beams passing through nonrealitical optical system such as atmosphere, nonlinal media and aberrated lens the wave front will distort .But the influence on optics field of aberrated system can be described by a phase exp( ?iφ) multiplying the original optical field.The paper is taking the second-order-moment and power in the bucket as the beam width definition, changes in the beam parameters such as the beam width and far-field divergence angle of Gaussian beams after the passage through an astigmatic lens are studied both analytically and numerically. It is found that the relative errors of the beam width and far-field divergence angle introduced by the astigmatism depend on the astigmatic coefficient C2, Rayleigh range z0 and focal lengths f of the lens. For the beam width the errors are additionally dependent on the propagation distance z. At the geometrical focal plane the relative errors in the x and y directions are equal. The results are of practical interest for the design of laser-optics systems.Starting from the generalized Huygens-Fresnel diffraction integral, the relative errors of the beam parameters, such as the beam width and far-field divergence angle of cosh-Gaussian(ChG) beams after passing through an astigmatic lens are studied. It is shown that the relative errors of the beam width and far-field divergence angle introduced by the astigmatism mainly depend on the astigmatic coefficient C2, decentered parameterα, Rayleigh range z0 and focal lengths f of the lens. The relative errors of the beam widths in the x and y directions at the geometrical focal plane are equal, while at the waist plane in the image space they are different, and dependant on the astigmatic coefficient C2 and decentered parameterα. In addition, the relative errors of the beam width dependend on the propagation distance z. The far-field divergence angles in the x and y directions are not equal due to the astigmatism and dependant on the decentered parameterα..