Focusing regions evolution under linear transformations in the boundary condition

机译：边界条件下线性变换下的聚焦区域演化

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The properties of optical surfaces generated by diffraction are studied analyzing the changes in the curvature function of the boundary condition. The study leads to establish a classification for the optical fields as elliptical, hyperbolical or parabolic. The elliptical regions are separated from hyperbolic regions by a region of parabolic type, which corresponds to optical focusing regions. The main result of the analysis leads us to describe and to control bifurcations and vortices effects allowing to geometrize and to control the topological properties of the optical field. For this feature is important to control the geometry of the parabolic region, obtained by controlling the curvature function in the boundary condition. The model is implemented experimentally applying a linear transformation in transmittances of zone plate type. The experimental results corroborate the theoretical predictions.

机译：通过分析边界条件曲率函数的变化，研究了由衍射产生的光学表面的特性。该研究导致将光学场分为椭圆形，双曲形或抛物线形。椭圆区域与双曲线区域之间由抛物线型区域隔开，该区域对应于光学聚焦区域。分析的主要结果使我们描述并控制了分叉和涡旋效应，从而可以几何化并控制光场的拓扑特性。对于此功能而言，重要的是控制抛物线区域的几何形状，该几何形状是通过在边界条件下控制曲率函数获得的。该模型是通过在波带片类型的透射率中应用线性变换来实验实现的。实验结果证实了理论预测。

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《Current developments in lens design and optical engineering XVII》|2016年|99471B.1-99471B.6|共6页
会议地点 San Diego CA(US)
作者
A. Garcia-Guzman; S.I. De los Santos-Garcia; M. A. Torres; J. Munoz; G. Martinez-Niconoff;
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Instituto Nacional de Astrofisica Optica y Electronica INAOE, Dpto. de Optica, Postal 51 y 216, Puebla, Mexico;

Instituto Nacional de Astrofisica Optica y Electronica INAOE, Dpto. de Optica, Postal 51 y 216, Puebla, Mexico;

Instituto Nacional de Astrofisica Optica y Electronica INAOE, Dpto. de Optica, Postal 51 y 216, Puebla, Mexico;

Instituto Nacional de Astrofisica Optica y Electronica INAOE, Dpto. de Optica, Postal 51 y 216, Puebla, Mexico;

Instituto Nacional de Astrofisica Optica y Electronica INAOE, Dpto. de Optica, Postal 51 y 216, Puebla, Mexico;

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3. Generalized solution of a one-dimensional quasilinear boundary value problem of the hydriding type with nonlinear boundary conditions and state evolution [J] . Chernov I.A. Differential equations: A translation of differensial'nye uraveniya . 2011,第4期

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4. Focusing regions evolution under linear transformations in the boundary condition [C] . A. Garcia-Guzman, S.I. De los Santos-Garcia, M. A. Torres, Conference on current developments in lens design and optical engineering XVII . 2016

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Focusing regions evolution under linear transformations in the boundary condition

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