# Plane wave decomposition method in scalar optics

• I
• HUANG Huan
In summary, using the diffraction theory of Fourier Optics, we can predict the new distribution of an optical scalar wave after traveling in the Z direction. Fourier Optics decomposes the wave into plane waves in different directions, but this ignores the polarization factor of each wave. However, in cases where vectorial diffraction is required, such as imaging with a high-numerical aperture lens, considering polarization is important. References for further reading are "Advanced Optical Imaging Theory" by Gu and "Diffraction Grating Handbook" by Richardson Grating Lab.

#### HUANG Huan

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!

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".

Ibix and berkeman