The numerical aperture (NA) of a microscope objective nominally represents the angular range of light rays accepted at its pupil. High NA objectives are particularly useful for tight focusing of beams and have many applications in bio-imaging at improved resolution, particle trapping as in optical tweezers, etc. Since early studies by Richards and Wolf (1959), it is known that the focal field profiles for high NA apertures are strongly dependent on the polarization state of the fields in the pupil plane. Theoretical calculations of focal fields for high NA systems requires full vectorial diffraction theory as the longitudinal component of the field cannot be ignored. The complete control of the polarization and phase in the pupil plane becomes important when a high NA microscopy system is to be tailored for specific applications.

The paper by Kenny, Lara, Rodriguez-Herrera and Dainty presents a technique for achieving full polarization control using 2 spatial light modulators (SLMs) and a third SLM for full phase control. It is well known that starting with a linearly polarized light, achieving any arbitrary state of polarization requires two independent retardations. In the Poincare sphere representation, every polarization state of light is represented by a point on the surface of a sphere. Going from one fixed starting point to any other on the surface of sphere requires two independent rotations (e.g. azimuthal and polar rotations) which are equivalent to the two retardations above. The experimental setup used in this paper makes use of two SLMs to make the two retardances spatially variable pixel-by-pixel. Starting with a plane beam with uniform polarization profile the technique can provide a beam profile where every point (x,y) can have a pre-specified arbitrary polarization state. The authors further introduce a third SLM in their setup to give a pre-specified phase profile to the beam to achieve full polarization and phase control over the beam. The authors have shown theoretical calculations using McCuthchen's method for calculating focal field profiles and the corresponding experimental results. A number of interesting field profiles (e.g. spatially separated orthogonally polarized spots) have been demonstrated in the paper and the technique has a great potential for achieving custom focal field profiles for specific applications.

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