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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Effects Of Correlation Between Two Fluctuating Sources On The Spectrum Of The Emitted Light

E. Wolf

Published Jan 1, 1987• 0 citations
Publisher

Abstract

It has recently been demonstrated both theoretically1-3 and experimentally4 that contrary to general belief, the spectrum of light emitted by a steady-state source depends, in general, not only on the source spectrum but also on the degree of correlation between the source fluctuations. When the source spectrum consists of a single line centered at frequency wo , the source correlation may cause the spectrum of the emitted light to be a line centered on a lower frequency < wo or at a higher frequency w'o > wA, depending on the particular form of the degree of correla?ion. Thus source correlations provide a new physical mechanism for redshifts or blueshifts of spectral lines. This newly discovered phenomenon is obviously-of particular interest for astronomy, where line shifts observed in the spectra of radiation from stellar objects have up to now always been assumed to be caused either by the motion of the stellar object relative to the observer (the Doppler effect) or as being due to gravitation. Examples of redshifted lines due to source correlations are shown in Fig. 1.

DOI
10.1117/12.967318

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It has recently been demonstrated both theoretically1-3 and experimentally4 that contrary to general belief, the spectrum of light emitted by a steady-state source depends, in general, not only on the source spectrum but also on the degree of correlation between the source fluctuations. When the source spectrum consists of a single line centered at frequency wo , the source correlation may cause the spectrum of the emitted light to be a line centered on a lower frequency < wo or at a higher frequency w'o > wA, depending on the particular form of the degree of correla?ion. Thus source correlations provide a new physical mechanism for redshifts or blueshifts of spectral lines. This newly discovered phenomenon is obviously-of particular interest for astronomy, where line shifts observed in the spectra of radiation from stellar objects have up to now always been assumed to be caused either by the motion of the stellar object relative to the observer (the Doppler effect) or as being due to gravitation. Examples of redshifted lines due to source correlations are shown in Fig. 1.
We recently showed that the spectrum of light emitted by a source depends not only on the spectrum of the source distribution but also on the degree of spectral coherence of the source fluctuations. In this note we show that with a degree of spectral coherence of certain kind, specified by two parameters, the spectrum of the emitted light will be displaced relative to the source spectrum. The displacement will be either toward the lower or toward the higher frequencies, depending on the choice of the parameters.
Abstract : It is generally taken for granted that the spectrum of light does not change on propagation. This belief is implicit in all spectroscopy. In the last few years it was discovered that while such spectral invariance holds for radiation from commonly used sources it does not hold, in general, because the spectrum of emitted radiation depends not only on the source spectrum but also on the coherence properties of the source. It was found that in some cases the induced changes may be appreciable, possibly resulting in frequency shifts of spectral lines. It has also been demonstrated that similar spectral changes may be produced by scattering on random media whose dielectric susceptibility fluctuations are appropriately correlated. Very recently it was shown that under certain circumstances the frequency shifts generated by dynamic scattering may imitate the Doppler effect, even though the source, the scatterer and the observer are all at rest relative to each other. (emk)
It is generally taken for granted that the spectrum of light does not change on propagation. This belief is implicit in all spectroscopy. In the last few years it was discovered that while such spectral invariance holds for radiation from commonly used sources it does not hold, in general, because the spectrum of emitted radiation depends not only on the source spectrum but also on the coherence properties of the source. It was found that in some cases the induced changes may be appreciable, possibly resulting in frequency shifts of spectral lines. It has also been demonstrated that similar spectral changes may be produced by scattering on media whose dielectric susceptibility is appropriately correlated.
It has recently been shown that correlations between source fluctuations throughout the source region can lead to frequency shifts of spectral lines.1,2 We consider the more general problem of modifying the spectrum of the emitted radiation by making a suitable choice of the degree of spatial coherence of the source. To illustrate the potential of this method we consider a simple configuration of two small sources emitting light with identical spectra. We demonstrate that some source correlations can generate multiple spectral lines from a single spectral line of either a Gaussian or Lorentzian profile. Spectral line-shape parameters such as width, amplitude, center frequency, and functional form can also be controlled.
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.