In the presence of astigmatism, the three-dimensional distribution of rays in the image region passes through two orthogonal lines, the vertical sagittal foci and the horizontal tangential foci. With increasing astigmatic behaviour of the imaging system, the sagittal and tangential foci will be farther removed from each other and the separation between these two planesserves as the measure of astigmatism. Midway between these planes, i.e., corresponding to the defocus term, 𝑊20 = − 𝑊22⁄2 , where 𝑊22 is the co-efficient of astigmatism, the intensity spread is found to be minimum and the transverse plane passing through this point is referred to as the plane of minimum aberration variance. For a diffraction-limited imaging system, the IPSF on this plane is the Airy pattern. In our study, each sector of the azimuthal Walsh aperture is masked by suitably oriented linear polarizers. The polarization phase introduced is a function of the state of polarization (SOP) of the input beam, the transmission axis of orientation of the masking polarizer and the orientation of the analyzer. A feasible method to assess the degree of astigmatic compensation is to compute the IPSF at the plane of minimum astigmatic variance and compare the intensity distribution with that of airy pattern. IPSFs for different values of 𝑊22 are computed with the presence of compensating polarization masked azimuthal Walsh filters at 0° and 90° with input beam parameters a=b=1 , 𝛿 = 90° and analyser kept at a particular angle. The results are compared with IPSFs computed for an unmasked lens and airy pattern.
In this paper, we propose illumination beam shaping using azimuthal Walsh filters derived from azimuthal Walsh functions, in and around the focal plane of a rotationally symmetric imaging system and studied for finding out self-similar groups and sub-groups for different orders to examine self-similarity existing between them and their corresponding transverse intensity distributions at the far-field plane. The unique rotational self-similarities observed in 2D intensity distributions at the transverse far-field plane for adjacent orders of azimuthal Walsh filters are also presented. Practical implementations of these filters are achievable by the availability of high speed spatial light modulators (SLMs) which can be successfully used to code and control illumination in and around the tightly focused field and coupling of light into metamaterials, plasmonic structures and waveguides. Further scope of research is intended to develop a new photonics platform based on dielectric surface wave harvesting model controlled by the dynamically variable illumination using azimuthal Walsh filters. Surface waves such as Bloch Surface Waves (BSW) and Surface Plasmons (SP) can be considered as the future enabling tools using this concept for probable applications in Photonics Research as well as in Industrial sectors, namely, quantum optics, telecom, sensing, computing, security, imaging and medical applications.
Conference Committee Involvement (9)
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