Abstract
The Debye-Wolf electromagnetic diffraction integral is now routinely used to describe focusing by high numerical (NA) lenses. We obtain an eigenfunction expansion of the electric vector field in the focal region in terms of Bessel and generalized prolate spheroidal functions. Our representation has many optimal and desirable properties which offer considerable simplification to the evaluation and analysis of the Debye- Wolf integral. It is potentially also useful in implementing two-dimensional apodization techniques to synthesize electromagnetic field distributions in the focal region of a high NA lenses. Our work is applicable to many areas, such as optical microscopy, optical data storage and lithography.
Highlights
The calculation of the field distribution in the focal region of a high numerical aperture (NA) lens is an important problem because of the many applications that use tightly focused beams, such as optical microscopy, optical data storage and lithography
When the NA of a lens exceeds approximately 0.5 the field distribution in the focal region can no longer be described in an accurate manner by the scalar diffraction theory so the use of an electromagnetic diffraction theory is necessary
The electromagnetic field distribution at any point in the focal region of a diffraction-limited, high NA incident field of arbitrary uniform polarization is typically obtained by the Debye-Wolf vector integral [1,2,3]
Summary
The calculation of the field distribution in the focal region of a high numerical aperture (NA) lens is an important problem because of the many applications that use tightly focused beams, such as optical microscopy, optical data storage and lithography. Braat et al obtained the field components in the focal region as a series using NijboerZernike functions [10], while Sheppard and Torok obtained the field components as a multipole expansion [11] These two expansions are more physical than those listed above because the Nijboer-Zernike expansion aims at obtaining formulae where the incident and focused fields are represented in terms of aberration functions. The dominant modes are closely connected with the resolution of the optical system, whilst the generalized prolate spheroidal functions are themselves the in-focus eigen field distributions for focusing by a lens Such functions are important since they are unchanged by the focusing operation (to within a scale factor). In contrast to our earlier work [9] which allowed only for one-dimensional (1-D) apodization techniques [12], our current expansion could be used to implement twodimensional (2-D) apodization and masking techniques to synthesize fields at the focal region of a high NA focusing system [13]
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