Kasimir Blomstedt

Polygon approximation of the fringes of diffractive elements

In the electron-beam fabrication of interferogram-type diffractive elements, such as diffractive lenses, continuous fringes are often approximated by polygons to reduce the data volume. Local wave-front errors are then generated that scatter light and give rise to background noise. A roughness parameter beta is introduced to quantify local phase errors in polygon-encoded diffractive structures. An efficient numerical method is developed to compute the Fresnel diffraction pattern of a polygon aperture. Polygon-approximated diffractive axicons and lenses are then investigated to determine the dependence of the signal fidelity on beta. It is found, e.g., that the maximum local phase error must be as large as pi/6 rad before the Strehl ratio S of a paraxial diffractive lens reduces below S = 0.9. However, much smaller errors can noticeably break the circular symmetry of the diffraction pattern.

Effective degree of coherence : general theory and application to electromagnetic fields

The concept of overall or effective degree of coherence has proven useful and insightful in the scalar theory of light. In this paper we extend the concept to fields represented over arbitrary vector (Hilbert) spaces. We show that the effective degree of coherence remains unaltered by scaled unitary mappings, which describe for instance many physical interactions. In the context of random, vector-valued electromagnetic fields the invariance implies that the effective degree of coherence assumes the same value in commonly used representation spaces. Thereby, in contrast to the local degree of coherence, this quantity can be taken as an intrinsic property of the electromagnetic wave field. In particular, the effective degree of coherence does not change when the field is scattered by a lossless medium and it can be determined from the far-field pattern. Hence the effective degree of coherence of electromagnetic fields is readily measurable.

Surface-profile optimization of diffractive 1:1 imaging lenses

Local optimization of surface-relief profiles of diffractive high-numerical-aperture imaging lenses is considered in the 1:1 imaging geometry for both linearly polarized illumination and unpolarized illumination by using the transition points of a four-level grating as design parameters. In the imaging geometry the optimized surface profiles differ considerably from those optimized previously for focusing or collimation geometries. Binary surface-relief grating structures are shown to provide high local diffraction efficiencies (up to 95%) in the outer regions of a high-numerical-aperture diffractive imaging lens because of the near-Littrow configuration.

Coherent modes of random electric and magnetic fields in a spherical volume

Whereas the coherent-mode representation of scalar fields has proven valuable from both theoretical and practical points of view, the coherent modes of vector-valued optical fields have received much less attention. We demonstrate that the coherent-mode structures of a stationary, random electric field and the corresponding magnetic field in a source-free, finite, spherical volume are, in general, not equivalent, i.e., the coherent modes of the magnetic field are not obtained from those of the electric field directly via Maxwell equations and suitable normalization. We also show that the converse holds when the volume is large compared to the wavelength. Similar results are further presented for arbitrary free fields, whose sources are at infinity, and for homogeneous free fields. A homogeneous and isotropic free field in a spherical volume is then considered, and the connection between its electric and magnetic coherent-mode decompositions is derived. An example of such a field is blackbody radiation.

Complementarity and Polarization Modulation in Photon Interference

We derive two general complementarity relations for the distinguishability and visibility of genuine vector-light quantum fields in double-pinhole photon interference involving polarization modulation. The established framework reveals an intrinsic aspect of wave-particle duality of the photon, not previously reported, thus providing deeper insights into foundational quantum interference physics.

Novel method for analyzing signal errors caused by polygonal approximations in the fabrication of diffractive elements

We develop a novel and efficient method to simulate diffraction patterns in the far field and in the Fresnel region when the phase counters of a quantized diffractive optical element are approximated by arbitrary polygons. Approximation causes signal errors whose effects have not been extensively studied so far. We take the polygonal shapes into account without any further approximations in the simulation, in contrast to calculations based on direct application of the Fast Fourier Transform. The method is applied to diffractive Fresnel lenses, axicons and gratings with finite size.