轴棱锥顶点离轴加工误差对贝塞尔光束的影响

Influence of Axicon Vertex off Axis Machining Error on Bessel Beams

理论推导了轴棱锥顶点离轴加工误差的透射率函数。在惠更斯-菲涅耳衍射积分理论和稳相近似法的基础上,推导出顶点离轴轴棱锥后的衍射光场表达式,分析了顶点离轴加工误差对贝塞尔光束的影响。对顶点离轴轴棱锥后衍射光场进行数值模拟,结果表明,当为理想加工轴棱锥时,轴棱锥后的光场分布为近似理想贝塞尔光束;当存在加工误差时,衍射光斑对半分离。相同距离处,分离程度随顶点离轴误差的增加而增加;相同的顶点离轴误差下,分离程度随传输距离的增加而增加。同时,还研究了这种元件的加工厚度对光斑分离程度的影响,结果表明,随着加工厚度的增加,光斑分离程度也会逐步增大。研究结果对轴棱锥加工、贝塞尔光束应用等具有一定的指导意义。

The transmittance function of the axicon vertex off axis machining error is derived theoretically. Based on Huygens-Fresnel diffraction integral theory and stationary phase method, the expression of diffraction field behind the vertex off axis machining error is derived and the influence of the vertex off axis machining error in an axicon on the Bessel beams is analyzed. The expression of diffraction field behind the axicon is simulated numerically. Results show that if the axicon is ideal manufactured, the field distribution behind the axicon is approximately an ideal Bessel beam, and if the machining error exists, the diffraction beam pattern will split in half. At the same distance, the separation of the beam pattern will increase with the increasing of the vertex off axis machining error, with the same vertex off axis machining error, the separation of the beam pattern will increase with the increasing of the transmission distance. Meanwhile, the influence of the thickness of the element on the separation of the beam pattern is also studied. The results show that the separation degree of the beam pattern increases gradually with the increasing of the thickness. The findings offer some guidance for axicon machining and the application of Bessel beams, and so forth.