This is the text of the talk given by Michael D. Stenner at:
CLEO/QELS (Conference on Lasers and Electro-Optics / Quantum Electronics and Laser Science Conference)
Long Beach, California , May 19-24, 2002.
Good morning. My name is Michael Stenner and I’d like to talk to you about Instability Limits to
“Fast” Light Pulse Propagation.
This talk is based on work done by myself and Dan Gauthier in the Duke University Physics
Department. This work is funded by NSF.
The recent developments in “fast” (or superluminal) light have been based on a new technique for creating anomalous dispersion. This technique was proposed by Steinberg and Chiao, and implemented by Wang et al.
The technique uses two gain lines to create a range of frequencies for which there is large anomalous dispersion, but very little gain or absorption. We are interested in the properties of this system in the high gain limit.
The reason the high gain limit is interesting is because high gain is necessary for large group advancement. Note that “group advancement” is analagous to “group delay”. To achieve a large group advancement, one must have steep anomalous dispersion here between the peaks. In order to make this steep, the gain must be made very large. Therefore, high gain is necessary for large advancement using this technique.
Unfortunately, a number of nonlinear optical processes make it very difficult to create this gain and dispersion profile with very high gain.
To understand the optical properties of this system, it is necessary to look more closely at the way the medium is prepared. Here I describe the system that we use in our experiment. The system used by Wang et al.
was very similar.
We apply a strong “pump” beam to a potassium 39 vapor cell. The beam is detuned to the blue from the D
1 line. This beam both optically pumps the atoms into the upper ground state, and provides the pumping field for stimulated Raman scattering. Thus, a probe beam will experience gain when its frequency is greater than the pump’s by the ground state splitting.
We also apply a second pump beam at a slightly different frequency, which in turn creates a second gain frequency. Applied together, these beams create gain at two frequencies, with small gain in between.
If a pulse were then applied with frequency between these two gain frequencies, it would see anomalous dispersion and would experience advancement. However, our experiments involve the pump fields only. For the remainder of this talk, the only beams present are the pumping beams.
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There are several nonlinear optical processes that occur in this system. The most obvious is the one for which the system was designed: the Raman anti-Stokes transition. Due to the ground state inversion created by optical pumping, the Raman anti-Stokes transition experiences amplification, and the amplified light is shifted up in frequency by the ground state splitting. This has the effect of creating new photons with frequency greater than the pumps’ by the ground state splitting.
A related process, the Stokes/anti-Stokes coupling, creates two photons, one shifted up by the ground state splitting, the other shifted down.
Another important process that occurs in our system is the Induced Modulation Instability. In this process, two photons of one pump beam and one photon from the other can interact with the atoms to create a new photon, shifted by the splitting between the pumps. This process can happen in either direction, shifting either up or down, and can happen repeatedly. The resulting photons can have frequencies shifted by any integer multiple of the pump splitting.
This process can happen along with the Raman processes, leading to net frequency shifts equal to the ground state splitting plus some integer multiple of the pump splitting.
In our experiment, we inject two linearly polarized pumping beams into our potassium 39 vapor cell.
We then observe the light that emerges from the cell and passes through a crossed polarizer.
If we plot the power that emerges in the orthogonal polarization asa a function of input power, we find that it grows roughly exponentially. At low power, where the behavior is fairly linear, there is little output light, as expected. However, as we increase the pump power, the output power increases very rapidly.
If we set an arbitrary threshold of 0.1% “conversion” we find that it occurs here at about 12.5
mW per pump, where there’s a Raman intensity gain of about e to the 10 (or 22,000).
When we increase the pump power by a factor of two, we see 10% conversion.
Note that using a bichromatic pump significantly reduces the threshold for the instability, even as a function of the total pump power.
Perhaps most interesting is the optical spectrum of this emerging light. This is a plot of power in the orthogonal polarization as a function of frequency. The pump frequency is here at zero. Most of the light has been shifted up by roughly the ground state splitting. Note these peaks at roughly one ground state splitting down, and 3 ground state splittings up. Also note the breadth and spikey structure of these peaks.
overlay
Our interpretation of this spectrum is based on a combination of the effects described previously.
This large peak is a result of Raman anti-stokes scattering, which shifts the pump light up by one ground state splitting. The smaller peak comes from the Stokes/anti-Stokes coupling, which is a weaker effect.
However, the Raman processes alone create only very narrow peaks. The breadth and spikey structure of these peaks comes from the repeated induced modulation instability.
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Finally, this small peak out there comes from the fact that those Raman processes also repeat, but each step introduces a 90 ◦ polarization rotation. If we rotate the polarizer parallel to the input polarization, we see peaks at even multiples of the ground state splitting, rather than odd multiples.
To get finer resolution in both power and frequency, we also consider the electronic spectrum of the detector output.
Here I show detector output as function of frequency. Note that the power remains well above the noise background out beyond 2.5 GHz. There are peaks roughly at multiples of the ground state splitting.
If we zoom in farther, we see that these peaks are spaced at the pump splitting. What’s interesting is that the power does not drop to the noise floor between peaks. This is a largely continuous spectrum, rather than a discrete comb of peaks, as predicted by the theory that most closely applies to this problem.
Finally, lets consider the temporal evolution of the generated light. Here I show the pwer in the orthogonal polarization as a function of time. Most obvious is the broad pattern repeating at 40 ns, which corresponds to the pump splitting. We also see this fast structure, on the order of a nanosecond, which corresponds toa a frequency of roughly twice our ground state splitting.
These small pulsesappear to be about 500 ps long, but we’re right at the edge of the analog bandwidth of our scope, so we can’t be sure if there’s anything faster present.
Finally, the structure of this signal can change dramatically over time, leading us to wonder if it’s just noisy, or chaotic. We tried to analyze it, but unfortunately, we don’t have enough vertical resolution to carry out a convincing analysis.
To conclude:
We find that the induced modulation instability severely limits this fast light pulse approach.
This is not just because of noise introduced into the pulse, but but because the become severely distorted in the high gain limit, and so the system cannot be prepared as desired.
We also find that this annoying effect is also rather interesting because it leads a very broad continuous spectrum from a narrow pure bichromatic input.
This behavior may be chaotic, but we can’t be sure yet.
This phenomenon privides a slower and more easily measured analog to the ultrafast pulse generation ideas of Harris et. al .
Finally, this is based on some of the same processes using in modern telecom research for tailoring gain profiles in fiber amplifiers.
Thank you for your attention.
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