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凹(平)面衍射光栅稳定共振腔的近似分析

周国生

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凹(平)面衍射光栅稳定共振腔的近似分析

周国生

AN APPROXIMATE ANALYSIS ON CONCAVE (PLANE) GRATING-MIRROR STABLE RESONATOR

ZHOU GUO-SHENG
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  • 本文从自洽的费涅耳衍射积分方程出发,利用费涅耳数近似趋于无穷,计算了凹(平)面锯齿形和截端锯齿形衍射光栅稳定共振腔的共振模特性。结果指出:当光栅槽很浅,满足光栅自准直条件,在一定的角度范围内,腔内的场振幅分布近似与光栅的闪耀角无关。垂直于光栅槽方向(x方向)的场分布由m阶厄米-高斯函数和微扰项(m+1阶和m-1阶厄米-高斯函数)表示。微扰项随光栅倾角的增大而增大。当微扰项可以忽略不计时,倾斜的光栅可以和垂直于光轴、曲率半径为Γ1cos3θ(x方向)和Γ1cosθ(y方向,平行于栅槽方向)的长条凹镜等效。文中给出了栅、镜面上的场分布、稳定性条件、频谱分布及输出场特性。
    The self-consistent integral equation for the field distribution of the resonant modes in a concave (plane) grating-mirror stable resonator is solved in the limit of infinite Fresnel numbers and under Littrow (collimate) configuration. Under the conditions above mentioned the field distribution is approximately independent of the blazing angles of the grating. In the direction parrallel to the grooves of the grating (y direction) the inclined grating can be equivalent to the concave mirror which has the radius of curvature ry-r1·cosθ and is perpendicular to the axis of the resonator (z axis). In the x direction the field distribution can be described in terms of Hermit-Gaussian function and the perturbation term. The perturbation term which is proportional to tangent of the incline of the grating introduces astigmatism to the field. When the perturbation can be neglected, the inclined grating would be equivalent to a concave mirror of radius rx=r1-cos3θ, which is also perpendicular to the axes of the resonator.The resonant condition, the stabilty condition, the field distribution and other charecteristies of the field distribution are obtained.
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  • 文章访问数:  6005
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  • 被引次数: 0
出版历程
  • 收稿日期:  1977-12-28
  • 刊出日期:  1978-03-05

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