I Plane wave decomposition method in scalar optics

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The discussion centers on the plane wave decomposition method in scalar optics, particularly its application in predicting the distribution of an optical scalar wave traveling in the Z direction. Fourier Optics allows for the decomposition of a scalar wave into plane waves, but this process overlooks the varying polarization directions of these components. While scalar diffraction is a good approximation for many scenarios, it may not suffice in cases requiring vectorial diffraction, such as high-numerical aperture lens imaging, where polarization effects become significant. The conversation also touches on the conditions under which polarization differences can be ignored, suggesting that limiting plane wave components to small angles with the Z axis may simplify analysis. Overall, the method's effectiveness hinges on the context and specific optical requirements.
HUANG Huan
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Suppose an optical scalar wave traveling in Z direction. Using the diffraction theory of Fourier Optics, we can predict its new distribution after a distance Z. The core idea of Fourier Optics is to decompose a scalar wave into plane waves traveling in different directions. But this decomposition process ignores the polarization factor of different plane wave components, i.e. each plane wave has a different polarization direction, which is not necessarily in XY plane. So, if we consider the polarization directions when adding all plane wave components, we may not obtain the original scalar wave.

why can we use plane wave decomposition method of Fourier Optics? Is it because it is a scalar wave? Or if we demand that all the plane wave components make a small angle with z axis, then it is possible to ignore the polarization direction differences? Thank you!
 
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HUANG Huan said:
why can we use plane wave decomposition method of Fourier Optics? Is it because it is a scalar wave? Or if we demand that all the plane wave components make a small angle with z axis, then it is possible to ignore the polarization direction differences? Thank you!

Scalar diffraction is usually a very good approximation, so that's why it's often used. When vectorial diffraction is required, for example imaging with a high-numerical aperture lens, a variety of polarization effects can be obtained, for example depolarization. Similarly, when calculating the efficiency of a diffraction grating, polarization (s- and p- polarization states) matters.

some references: Gu, "advanced Optical Imaging Theory" and the Richardson Grating Lab "Diffraction Grating Handbook".
 
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