We simulate the predicted Gouy phase anomaly near astigmatic foci of Gaussian beams using a beam
propagation algorithm integrated with lens design software and compare computational results with experimental
A novel method is described for storing and retrieving the second-order correlation function of partially coherent fields. The key element of the method is an instantaneous hologram that records the superposition of a random field whose correlation function is to be determined and the mutually incoherent reference field, taken over a time interval that is much shorter than the coherence time of the random field. The method is somewhat similar to conventional holography, but differs from it in several important respects.
It is known that only a single-mode beam is completely spatially coherent. In general, beams generated by lasers and other sources consist of several modes and consequently are spatially only partially coherent. In this tutorial paper we first review the basic concepts which are needed to characterize beams of any state of coherence. We then discuss some of their main properties and we show that partially coherent beams can have very rich behavior. For example, two beams may have different spatial coherence properties at the source and yet may give rise to the same intensity distribution in the far zone; or they may have different intensity distributions at the source but may generate far fields with the same spatial coherence properties. We also discuss some recent developments which have demonstrated that the superposition of two beams with broad spectra (low temporal coherence) may result in a light distribution with a completely different spectrum; and that, moreover, the spectrum may be different at different points in the region of superposition. Both theoretical predictions and their experimental verifications are discussed.
During the last few years it has been conclusively demonstrated, both theoretically and experimentally, that the coherence properties of a source affect the spectrum of the emitted radiation.1 Expressed differently it was shown that the spectrum of the field depends not only on the spectrum of the source, but also on the state of coherence of the source. This result holds both for fields generated by primary sources, and for those generated by secondary ones, such as, for example, illuminated apertures or scattering media.
Exact solutions for the focusing of 2D electromagnetic waves through a slit in a perfectly conducting screen are given in a companion paper.1 In this paper, various approximate solutions are compared with the exact solutions to test the validity of each approximate theory. The approximate theories considered are first of all those based on either the Kirchhoff or the Debye approximation. But in addition a more accurate theory is examined, in which only the multiply diffracted waves between the edges of the slit are neglected. In this case the slit problem is treated as two independent half-plane problems and their exact solutions are added. For brevity we consider only the scalar case corresponding to an incident E-field polarised parallel to the edges of the slit.
Energy conservation laws for statistical wavefields are first reviewed based on the following three models: electromagnetic theory scalar wave theory and radiometiy. These laws apply whether or not the coherence properties of the source generate shifts of spectral lines in the emitted radiation. Some subtleties are then noted which indicate why the spectrum of light is in general not conserved on propagation. We illustrate the results by considering fields produced by planar quasi-homogeneous secondary sources and by spherically symmetric sources of different states of coherence. * Research supported by the Department of Energy under grant # DE-FGO2-9OER 14119. The views expressed in this article do not constitute endorsement by DOE. ** Alsowith The Institute of Optics University of Rochester. SPIE Vol. 1319 Optics in Complex Systems (1990) / 59
There is an implicit assumption in all of spectroscopy that the relative energy distribution in
the spectrum of radiation which propagates in free space is independent of the location of the
observer, provided that the observer and the source are at rest relative to each other. That this
assumption is not valid, in general, was suggested by the results of an investigation of Mandel111,
carried out almost thirty years ago. Mandel showed that when light beams from two small
correlated sources which have the same normalized spectra are superposed, the normalized
spectrum in the region of superposition will differ, in general, from the normalized spectrum of
each source. More recently it was predicted theoretically2 and confirmed experimentally soon
therwards3 that the normalized spectrum of light produced by an extended source, will, in
general, differ from the normalized source spectrum (assumed to be the same at every source
point); and that it will depend on the location of the point of observation. The spectral changes
were shown to depend on the correlation properties of the source.