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Chaotic light sources

Published 24 June 2007, 11:07 PM

My previous post was on light sources, and I hope it cleared up the difference between the various sources. Today I am opening Pandora's box: chaotic light sources. Let us see what the experts have to say about this subject:

On page 674 of Optical coherence and quantum optics, Mandel and Wolf write:

We shall call radiation that is derivable from blackbody radiation by any linear filtering process thermal radiation. It has sometimes also been called chaotic radiation.

On page 31 of A guide to experiments in quantum optics, Bachor and Ralph instead write:

In most practical cases classical light will be noisy. Only a perfect oscillator would emit an electro-magnetic wave with perfectly constant amplitude and phase. There are some relatively simple models of realistic light sources. Chaotic light is the idealized approximation for the light generated by independent sources emitting resonance radiation. A practical example is a spectral lamp. In contrast, a thermal light is an approximation of the light emitted by many interacting atoms that are thermally excited and together emit a broad, non resonant spectrum of light. A practical example is a hot, glowing filament.

On page 109 (among others) of Quantum optics—An introduction, Mark Fox finally writes:

The light emitted by a mercury lamp originates from many different atoms. This leads to fluctuations in the light intensity on time-scales comparable to the coherence time. These light intensity fluctuations originate from fluctuations in the number of atoms emitting at a given time, and also from jumps and discontinuities in the phase emitted by the individual atoms. The partially coherent light emitted from such a source is called chaotic to emphasize the underlying randomness of the emission process at the microscopic level.

If we take a vote, then electric discharge lamps (mercury vapor) are chaotic light sources. But now consider this quote from the paper Experimental study of the momentum correlation of a pseudothermal field in the photon-counting regime by Scarcelli, Valencia, and Shih at the University of Maryland:

In principle the term "thermal radiation" should refer only to radiation coming from a blackbody in thermal equilibrium at some temperature T. But in reality, some characteristics of true thermal fields, like the extreme shortness of their coherence time, have imposed serious obstacles to their use in actual experiments, and therefore since the early days of quantum optics there has been a great interest in the realization of more utilizable sources that could simulate the behavior of true thermal fields (gas discharge lamps, randomized lasers, etc.). We usually describe this kind of source as pseudothermal; they are actually all chaotic light sources that can be modeled as a collection of independent atoms emitting radiation randomly […]. The principle of the generation is very simple: coherent laser radiation is focused on a rotating ground glass disk so the scattered radiation is chaotic with a Gaussian spectrum.

So here a electric discharge lamp (e.g., mercury vapor) is pseudothermal. If laser light (which is Poisson) is focused on a rotating ground glass disk it produces a chaotic source with a Gaussian spectrum — very different from the line spectrum of a mercury lamp as plotted below. I do not know about you, but I am confused. Are "gas discharge lamps" and "electric discharge lamps" the same thing? What is a chaotic light source? What is the role of coherence length?

If you can shine some light on this in form of a comment, I would appreciate it very much.

mercury vapor lamp

PS: Links cited in the comments:

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Just to muddy the waters of the 'reflecting pool' a little more ... In this description http://jiejie.spa.umn.edu/projects/S07_PhotonCountingStatistics/apparatus.htm of an apparatus which uses a scintillation disk, the author states:

"A ground glass plate attached to a variable speed, DC motor to create a pseudothermal light source to ensure the detection of Bose-Einstein statistics in the appropriate regime. The speed of rotation of this plate is inversely proportional to the correlation time of the scattered light. Thus, the speed of the plate is altered in order to alter the coherence time."

You didn't mention the B-E distribution in your initial post. How does that fit into the chaos surrounding the terminology of all these light sources?

# Monday, June 25, 2007 03:31 AM by redrooz_at_yahoo_com

RocketRoo, thank you for your comment, but I am not sure where you are heading with this comment. The term "Bose-Einstein statistics in the appropriate regime" is somewhat nebulous.

Usually when I think of Bose-Einstein condensates (BEC), temperatures below a degree Kelvin come to my mind, while we normally do color science at room temperature. Classical experiments with BEC are based on bosons like rubidium isotopes, which condensate into molecules. When you sweep a magnetic field you get a stable condensate due to interference among the atoms, but if the magnetic field strength is too high, you get a "bosenova" implosion, which is something I would not like to happen during a color measurement. ;-)

What is the equivalent of a molecule for a BEC of photons? Is it the slow-light of Lene Vestergaard Hau? She recently had an intriguing letter in Nature 445, 623-626 (8 February 2007) where she was storing photons in "optical dipoles". The amazing result was that two photons stored in two independent BCEs can become indistinguishable, which would be symmetric in time to entanglement.

Getting back to the room temperatures in which we normally work, do you suppose BCE can explain photon bunching? What is the important distinction of light sources with bunched photons versus light sources where the photons are stationary, i.e., have independent arrival times at the detector?

# Monday, June 25, 2007 05:25 PM by Giordano Beretta
The reason I bring BE into the mix is because all light is composed of photons and photons are vector gauge bosons. Therefore, they must obey BE statistics. That, in turn, requires that photons be "sticky" because multiple photons can exist in the same quantum state. Multiple fermions e.g., electrons, cannot because of the Pauli exclusion principle. The BE condensate (a kind of giant boson wavefunction) is a very special case, only realizable at micro-K temperatures and not at all relevant here.

Second point to keep in mind: All light is produced by matter (except perhaps for the Big Bang, but nobody seems to remember what happened there). Therefore, all light is produced by atoms. From the standpoint of QED, that means all light is produced by the electrons in the atoms. Since the electrons are bound to a nucleus, their energies form discrete levels or shells and it is the transitions between these levels that determine the energy (finite frequency) of the emitted photons.

But wait, there's more! BE stats has to do with the NUMBER of emitted photons in a given quantum state. BE predicts that I can see more than one photon emitted at a time, which leads to super-Poisson behavior (cf. your comment about Poisson laser light) or so-called "photon bunching". Can we see this effect? Yes, but not directly. The average number of photons in a given state is the same thing as measuring the intensity of the light (number of photons arriving per unit time). In atomic transitions, the number of photons being emitted is random (or "chaotic") but correlated because of the BE effect. Therefore, the intensities measured at slightly different locations in space or time can appear (weakly) correlated. The eye is only sensitive to the intensity of light, but cannot see intensity correlations. For that you need special equipment to measure the correlations.

For various reasons, there has been an intense(pun?) interest in correlated photons, and that is the unwritten sub-text in the seemingly muddled quotes above. All light produced by atomic transitions is called "chaotic" these days (for better or worse). It also includes the effects due to atomic collisions (Lorentzian line shape) and Doppler shifting of the frequencies (Gaussian line shape).

To summarize so far, all atoms are "chaotic" BE emitters. This, however, begs the question: Why make such a redundant distinction? The reason is that so-called "thermal sources" are not BE emitters. The classic thermal source is essentially a black-body e.g., the sun. But, I hear you ask, "You just got through telling me that all light comes from atoms, and the sun is made of atoms! What gives?" Correct, and I thought you'd never ask.

Black-bodies emit according to the Planck distribution (discussed elsewhere on this blog), which is a continuous spectral distribution. In that case, because of the (nuclear) energies involved, the electrons have been stripped from the hydrogen and helium atoms and are no longer bound to their respective nuclei. Hence, the spectrum is no longer discrete. The electrons no longer act as tiny oscillators. This state of affairs also washes out any BE stats and, indeed, the intensity fluctuations from a black-body source look Poissonian.

And finally, before you put finger to keyboard in response, starlight is black-body radiation (obviously, if the sun is). However, because of Wien's law, the peak spectral wavelength is inversely proportional to the temperature. Hence, distant stars appear colored (even to the naked eye in some cases). With the appropriate filters one can capture their light as if it was "pseudo-thermal" (a term also used more or less synonymously with "chaotic") and once again, detect the BE effects. This is what allowed astronomers to go from Michelson (phase) interferometry to the much more stable and accurate intensity interferometry.

# Thursday, August 16, 2007 04:06 PM by redrooz_at_yahoo_com

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