Abstract
We show that the volumetric field distribution in the focal region of a high numerical aperture focusing system can be efficiently calculated with a three-dimensional Fourier transform. In addition to focusing in a single medium, the method is able to calculate the more complex case of focusing through a planar interface between two media of mismatched refractive indices. The use of the chirp z-transform in our numerical implementation of the method allows us to perform fast calculations of the three-dimensional focused field distribution with good accuracy.
Highlights
The field distribution in the focal region of a focusing lens has been studied extensively due to the presence of this element in a large number of optical systems [1]
The Fresnel diffraction integral can be used to calculate the focused field for a lens with low numerical aperture (NA) [2], whereas the scalar Debye integral is a good approximation for a focusing system with higher NA [3]
We show that the DebyeWolf integral can be written as a 3D-FT, simplifying the calculation of the complete volumetric three-dimensional field distribution in the focal region of a high-NA system
Summary
The field distribution in the focal region of a focusing lens has been studied extensively due to the presence of this element in a large number of optical systems [1]. The Fresnel diffraction integral can be used to calculate the focused field for a lens with low numerical aperture (NA) [2], whereas the scalar Debye integral is a good approximation for a focusing system with higher NA [3]. It is well known, that the focused field experiences a change in its polarization state under the high-NA condition [4]. The use of the CZT algorithm in the implementation of our method allows for fast and accurate calculations when compared with the results obtained from direct evaluation of the DebyeWolf integral. We present a number of examples showing the suitability of the 3D-FT method in different scenarios
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