Taco D. Visser

Phase singularities of the coherence functions in Young's interference pattern

We analyze the coherence properties of a partially coherent field emerging from two pinholes in an opaque screen and show that the spectral degree of coherence possesses phase singularities on certain surfaces in the region of superposition. To our knowledge, this is the first illustration of the singular behavior of the spectral degree of coherence, and the results extend the field of singular optics to the study of phase singularities of correlation functions.

Absorption and scattering correction in fluorescence confocal microscopy

In three‐dimensional (3‐D) fluorescence images produced by a confocal scanning laser microscope (CSLM), the contribution of the deeper layers is attenuated due to absorption and scattering of both the excitation and the fluorescence light. Because of these effects a quantitative analysis of the images is not always possible without restoration. Both scattering and absorption are governed by an exponential decay law. Using only one (space‐dependent) extinction coefficient, the total attenuation process can be described. Given the extinction coefficient we calculate within a non‐uniform object the relative intensity of the excitation light at its deeper layers. We also give a method to estimate the extinction coefficients which are required to restore 3‐D images. An implementation of such a restoration filter is discussed and an example of a successful restoration is given.

Singular behavior of the spectrum in the neighborhood of focus.

In a recent paper [Phys. Rev. Lett. 88, 013901 (2002)] it was shown that when a convergent spatially coherent polychromatic wave is diffracted at an aperture, remarkable spectral changes take place on axis in the neighborhood of certain points near the geometrical focus. In particular, it was shown that the spectrum is red-shifted at some points, blueshifted at others, and split into two lines elsewhere. In the present paper we extend the analysis and show that similar changes take place in the focal plane, in the neighborhood of the dark rings of the Airy pattern.

The structure of partially coherent fields

Publisher Summary The general framework of optical coherence theory is now well established and has been described in numerous publications. This chapter provides an overview of recent advances, both theoretical and experimental, that have been made in a number of areas of classical optical coherence. These advances have been spurred on by the introduction of the space-frequency representation of partially coherent fields, and an increased emphasis on the spatial coherence properties of wave fields. The fundamental experiment to measure spatial coherence is Youngs double-slit experiment. A number of important optical processes are influenced by the coherence properties of the wave field. Results relating to the propagation of partially coherent wavefields highlight some of the significant results relating to optical beams. The influence of coherence on focusing is summarized and reviewed, along with the scattering of partially coherent wave fields and its relation to inverse scattering problems is discussed. It has been shown that spatial correlation functions have interesting topological properties associated with their phase singularities; these properties and the relevant literature are discussed. The coherent mode representation and its applications are described and several techniques for the numerical simulation of wave fields with a prescribed statistical behavior are explained.

Polarization singularities of focused, radially polarized fields

The state of polarization of strongly focused, radially polarized electromagnetic fields is examined. It is found that several types of polarization singularities exist. Their relationship is investigated, and it is demonstrated that on smoothly varying a system parameter, such as the aperture angle of the lens, different polarization singularities can annihilate each other. For example, the evolution of a lemon into a monstar and its subsequent annihilation with a star is studied. Also, the quite rare collision of a C-line and an L -line, resulting in a V-point, is observed.

Comparison of different theories for focusing through a plane interface

We consider the problem of light focusing by a high-aperture lens through a plane interface between two media with different refractive indices. We compare two recently published diffraction theories and a new geometrical optics description. The two diffraction approaches exhibit axial distributions with little difference. The description based on geometrical optics is shown to agree well with the diffraction optics results. Also, some implications for three-dimensional imaging are discussed.

Modal analysis of a planar waveguide with gain and losses

In this study, we analyze the waveguiding properties of a planar waveguide amplifier in which losses and gain can be present simultaneously. It is found that the subsequent modes comprise both loss and gain modes. Also, the dependence of the gain on the state of polarization turns out to be significant for realistic dielectric structures. For strong losses or gain, the standard transfer matrix approach may become numerically unstable, therefore, a scattering matrices formalism is employed. A semiconductor-like gain profile enables us to study the gain as a function of /spl omega/ for realistic laser amplifier structures. >

Can spatial coherence effects produce a local minimum of intensity at focus

It is demonstrated that, for high-Fresnel-number focusing systems illuminated by certain classes of partially coherent light, it is possible to produce a local minimum of intensity at the geometrical focus. Such an effect is possible even though the average intensity in the entrance plane of the lens is uniform. An explanation is offered for this effect, and potential applications are considered.

Defocusing of a converging electromagnetic wave by a plane dielectric interface

We study how a converging spherical wave gets distorted by a plane dielectric interface. The fields in the second medium are obtained by evaluating the m-theory diffraction integral on the interface. The loss of intensity and the form of the intensity distribution are investigated. Examples are presented for various refractive-index contrasts and depths of focus. In general the intensity gets spread out over a volume that is large compared with the case without refractive-index contrast. It was found that moving the focusing lens a distance d toward the interface does not result in an equal shift of the intensity profile. This latter point has important practical implications.

Focal shifts of converging diffracted waves of any state of spatial coherence

We analyze the focusing of wave fields of any state of coherence by systems with low Fresnel numbers. We study the optical intensity on the axis in the focal region. The dependence of the focal shift and of the maximum on-axis intensity on the state of coherence is examined for some model fields.