Analysis of Phase Distribution of Focused Light in High Numerical Aperture Systems

Abstract:

High numerical aperture focusing is becoming increasingly important for nanotechnology related applications. Rigorous, vector evaluation of the focused field, in such cases, is usually performed using the Richards-Wolf method which is based on the Debye approach. The resulting field is known to have a piecewise quasi planar phase. A corresponding result, produced by a Fresnel-Kirchhoff integral for aplanatic optical systems of medium and low numerical apertures, leads to the well known physical fact that a quadratic phase exists when the entrance pupil is not located at the front focal plane. Yet, the amplitudes produced in both ways are in a good agreement. In this work we investigated the difference, presented above, in a 2D system with the help of the Stratton-Chu diffraction integral. The amplitude obtained by the Stratton-Chu integral was quite similar to the classic results while the phase exhibited a quadratic behavior, with the quadratic coefficient depending on the numerical aperture of the optical system. For lower numerical apertures it approached the result obtained by the Fresnel-Kirchhoff integral while for higher numerical apertures it was approaching the Richards-Wolf result. A mathematical expression for the quadratic coefficient was derived and verified for various values of numerical aperture.

• Periodical: Key Engineering Materials (Volume 437)
• Pages: 616-620
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.437.616
• Online since: May 2010
• Authors: Alexander Normatov, Boris Spektor, Joseph Shamir
• Keywords: High Numerical Aperture Focusing, Numerical Analysis, Optical Propagation

References

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DOI: 10.1007/s003400000451

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