Vector diffraction algorithm based on optical vector decomposition synthesis and Huygens-Fresnel

A technology of Fresnel diffraction and diffraction algorithm, applied in the field of vector diffraction algorithm based on light vector decomposition and Huygens-Fresnel, can solve the problems of inconvenient calculation and unintuitive physical meaning

Pending Publication Date: 2022-03-25
杨翼
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  • Application Information

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Problems solved by technology

Richard-Wolf vector diffraction is based on the superposition of plane wavelets. Its theoretical basis is the angular spectrum theory of plane waves. Its physical meaning is not intuitive, and it...

Method used

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  • Vector diffraction algorithm based on optical vector decomposition synthesis and Huygens-Fresnel
  • Vector diffraction algorithm based on optical vector decomposition synthesis and Huygens-Fresnel
  • Vector diffraction algorithm based on optical vector decomposition synthesis and Huygens-Fresnel

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Embodiment 1

[0063] This embodiment considers the objective lens of NA=0.5 (α=30°), considers that the incident photoelectric vector is linearly polarized light in the x direction, and the x and y total light intensity distributions on the focal plane of the objective lens are shown in the appendix image 3 . Among them, the solid line is the result of Richard-Wolf vector diffraction (formula (11)), and the dotted line is the result of vector Huygens-Fresnel diffraction (formula (4)). It can be seen that the light intensity distribution in the x and y directions of the vector Huygens-Fresnel diffraction results and the Richard-Wolf vector diffraction results almost completely coincides. attached Figure 6 The first row (α = 30°) shows the light intensity distribution for the x, y and z components of the vector Huygens-Fresnel diffraction. attached Figure 7 The first row (α = 30°) shows the comparison of vector Huygens-Fresnel diffraction and Richard-Wolf vector diffraction logarithmic ...

Embodiment 2

[0065] This embodiment considers the objective lens of NA=0.87 (α=60°), considers that the incident photoelectric vector is linearly polarized light in the x direction, and the x and y total light intensity distributions on the focal plane of the objective lens are shown in the appendix Figure 4 . Among them, the solid line is the result of Richard-Wolf vector diffraction (formula (11)), and the dotted line is the result of vector Huygens-Fresnel diffraction (formula (4)). It can be seen that the light intensity distribution in the x and y directions of the vector Huygens-Fresnel diffraction results and the Richard-Wolf vector diffraction results almost completely coincides. attached Figure 6 The second row (α = 60°) shows the light intensity distribution for the x, y and z components of the vector Huygens-Fresnel diffraction. attached Figure 7 The second row (α = 60°) shows the comparison of the logarithmic contours of the vector Huygens-Fresnel diffraction and the Rich...

Embodiment 3

[0067] This embodiment considers the objective lens of NA=0.97 (α=75°), considers that the incident photoelectric vector is linearly polarized light in the x direction, and the x and y total light intensity distributions on the focal plane of the objective lens are shown in the appendix Figure 5 . Among them, the solid line is the result of Richard-Wolf vector diffraction (formula (11)), and the dotted line is the result of vector Huygens-Fresnel diffraction (formula (4)). It can be seen that the vector Huygens-Fresnel diffraction results and the Richard-Wolf vector diffraction results almost completely coincide in the light intensity distribution in the x direction, and almost completely coincide in the central part of the light intensity distribution in the y direction, only in the first sub-peak part. nuance. attached Figure 6 The third row (α=75°) shows the light intensity distribution of the vector Huygens-Fresnel diffraction x, y and z components. attached Figure ...

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Abstract

The invention provides a vector diffraction algorithm based on light vector decomposition and synthesis and Huygens-Fresnel, which comprises the following steps that incident light polarized along the x direction is propagated to any point (x, y) on a detection surface, the electric field intensity Ex in the x direction is decomposed into s light Es and p light Ep, the direction of the Es is not changed when the incident light is propagated to the detection surface, and the direction of the Ep is changed; vector synthesis is carried out on the direction-changed Ep and the direction-unchanged Es again to obtain components E'x, E 'y and E' z in the x direction, the y direction and the z direction; and substituting the expressions of the components E'x, E 'y and E' z into a Huygens-Fresnel diffraction formula to obtain vector Huygens-Fresnel diffraction. According to the method, the huygens-Fresnel diffraction formula and the Richardd-Wolf vector diffraction formula of the obtained vector are subjected to simulation comparison, the difference between the huygens-Fresnel diffraction formula and the Richardd-Wolf vector diffraction formula is small, the difference is slight only under the high numerical aperture, and the algorithm is simple and clear in theoretical principle and convenient to calculate.

Description

technical field [0001] The invention relates to the technical field of vector diffraction in physical optics, in particular to a vector diffraction algorithm based on light vector decomposition synthesis and Huygens-Fresnel. Background technique [0002] In the field of general imaging, scalar diffraction theory is a good approximation, but for high numerical aperture (NA) objective lens imaging, it is necessary to consider the vector characteristics of light. For example, the numerical aperture of the objective lens used in lithography machines is generally relatively high in order to improve the resolution. In this case, the analysis of the focus spot size and light intensity distribution cannot only be approximated by scalar diffraction theory, but vector diffraction analysis must be used. In addition, when the incident light is not naturally polarized, but linearly polarized, radially polarized, or elliptically polarized, the light intensity distribution after passing th...

Claims

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Application Information

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IPC IPC(8): G02B27/00
CPCG02B27/0012
Inventor 杨翼
Owner 杨翼
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