The focus of light—linear polarization breaks the rotational symmetry of the focal spot

Abstract

Abstract:We experimentally demonstrate for the first time that a linearly polarized beam is focussed to an asymmetric spot when using a high-numerical aperture focussing system. This asymmetry was predicted by Richards and Wolf [Proc. R. Soc. London A 253, 358 (1959)] and can only be measured when a polarization insensitive sensor is placed in the focal region. We used a specially modified photodiode in a knife edge type set up to obtain highly resolved images of the total electric energy density distribution at the focus. The results are in good agreement with the predictions of a vectorial focussing theory.The ability to control and focus light is at the heart of the interdisciplinary field of optics and for many applications an exact knowledge of the structure of the focal field is required. Many areas in optical sciences make use of a tightly focussed light beam such as confocal microscopy [1] and optical data storage [2]. A highly concentrated and well matched field is also a necessary requirement for coupling to small quantum systems [3] and applying light forces to microscopic particles [4]. In the regime of strong focussing the widely used scalar theories are inadequate to describe the focal field. A vectorial focussing theory is required instead. In the concrete example of a beam which is linearly polarized along the y-axis, the rays propagating in the xz-and in the yz-plane, respectively, contribute differently to the focal field (see figures 1(a), (b)). This has two closely related consequences. The effective numerical aperture in the yz-plane is reduced and the focal spot is elongated in the direction of polarization of the input beam because the rays that propagate in this plane do not add up perfectly at the focus. Associated with this elongation, field components in directions orthogonal to the direction of polarization of the input beam arise. These effects are neglected in scalar descriptions [5], which therefore do not predict the correct spot shape and size. All aspects of the field distribution of a tightly focussed linearly polarized light beam have been studied in theory taking into account the vector properties of the field [6,7,8,9]. The theoretical calculations predict pronounced deviations from the results of the scalar theory. Nevertheless, a major part of the intensity 1 is still predicted to be contained in a field 1 In the following, intensity always refers to electric energy density, which is the part of the field energy that couples to standard photodetectors and photosensitive materials. 1Figure 1: Plane wave model for focussing a beam which is linearly polarized parallel to the y-axis. Cross sections for two planes which contain the optical axis, (a) perpendicular and (b) parallel to the direction of polarization, show that the contribution to the total field of the rays propagating under a large angle to the optical axis is weaker in (b). Calculated intensity patterns for the three orthogonal field components (c-e) and total intensity distribution (f). The direction of polariz...

Complete modeling of subsurface microscopy system based on aplanatic solid immersion lens

“…Figure 4 shows the computed pattern of the intensity distribution when the small gold sphere is placed at the aplanatic point of ASIL for linearly polarized illumination. We note that the intensity pattern of each electric field component has the same shape as the distribution of intensity in the focal region [23,53]. Further, in order to evaluate the profile of image, the FWHM along the x-direction of the normalized x-y intensity profile is given in Fig.…”

Polariton spin whirls

“…In particular, the electric field of a linearly polarized beam, when focused by a high NA objective, acquires non-zero components in the two directions perpendicular to the polarization of the incident field (i.e., at the focus plane the electric field vector sweeps an ellipse) 37,[47][48][49] . For a review see Ref.…”

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