When light interacts with matter, it normally passes through (or is absorbed or scattered by) the material; but, if the light is high intensity (> 10$12W/cm2$), then the light actually changes the matter it is interacting with. For more information on this, see our page on High Intensity Light-Matter Interactions. If the Light is intense enough, the light will actually rip off the electrons of the atoms it is interacting with. When this occurs, the ripped-off electron absorbs upwards of 45 - 50 photons all at once. This normally happens in two steps: First, the electron absorbs enough photons (thus gaining enough energy) to be excited into a high-lying Rydberg state. Next, the electron will absorb another number of photons and leave the atom with a certain amount of kinetic energy. If the electron absorbs only one photon after being in the excited state, the process is called Multi-Photon Ionization (MPI) since the electron is just barely ionized. If the electron absorbs more than one electron after being in the excited state, the process is called Above-Threshold Ionization (ATI) since the electron has absorbed more photons above the minimum energy it needed to be ionized. For more information on MPI and ATI, see our page on MPI and ATI.

For this experiment, we shined High Intensity, Short-Pulsed laser light on Xenon. The light is generated from pumping a Ti:Sapphire crystal; the light emitted is 800 nm in wavelength. To obtain high intensities, we generate short pulses of light. Each pulse is approximately 110 fs (thats 1.1 x 10$-13$ s). Each pulse can have up to 850 mJ of energy and our repetition rate is 1 kHz. The pressure in our chamber is adjusted to be high enough to get fairly good signal-to-noise ratios yet low enough to avoid space-charge effects. Our focused-down intensities are upwards of 10$14W/cm2$. Below is a typical spectrum.

Note that the laser polarization angle for this spectrum is 0 degrees. An explanation of polarization angle now follows. Our experiment is set up such that the laser beam enters (and exits) a vacuum chamber (backing pressure is approximately 4 x 10$-10$ torr). The chamber is filled (to small pressures) with Xenon. The electrons we observe travel perpendicularly to the laser pulses down a flight-tube to our Micro-Channel Plate (MCP) detector. Now, if the electric field of the laser points in the same direction of the flight tube, this is 0 degrees polarization. The bulk of the electrons are ionized in this direction (and 180 degrees from there). By passing the laser beam through a Half-Wave Plate, we can turn the polarization through whichever angles we choose. When the polarization of the electric field is perpendicular to the flight tube, this is 90 degrees polarization; for certain intensities, we even see electrons at 90 degrees!

For this set of experiments in particular we are intested in how a spectrum changes with a change in angle. Below is an example. If we just look at at the 5g peak in the MPI order, we can display a radial plot of how the peak height changes with respect to angle. The blue diamonds are our data points, and the red line is a fit to our data using the scheme talked about below.

As you can see, the distribution is not simply "all of the electrons come out at 0 degrees". In fact, there are "jets" of electrons that come out at 36 degrees and 72 degrees. Now, what exactly does this mean? Well, it just so happens that one can model this system such that the data can be fit with a sum of even (subscripted by 2L) Legendre Polynomials. The subscript of the polynomials, L, according to the model, are related to the quantum angular momenta of the electrons when they are in the Rydberg State (the intermediate state in which they exist just before they are fully ionized). Actually, a backwards fit needs to be done to figure out how the terms in the 2L-Legendre Polynomials correspond to the coefficients of the "proper" expansion. The reason we use this expansion is that when we combine all the terms of the physically meaningful sum, the coefficients are all inter-related, which make it difficult for fitting routines to handle. On the other hand, the expansion we are currently using is also correct, just not as physically meaningful -- and, since no terms share coefficients with each other, fitting routines have an easy time fitting the data. In the future, we will work backwards from the fits we have to the more physically meaningful terms.

In the meantime, there is some information we can get out of our fits. Our fitting parameters do apply to physically meaningful quantities if we assume no interference between Rydberg states. Below are shown, for the fit above, which L's contribute to the angular momentum of the 4.3 x 10$13W/cm2$, 800 nm, 100 fs, MPI order 5g peak.

Evidently, there is a lot going on here. Mainly, we have a bunch of L=5, with a good bit of L=0, 1, and 2 and a bit less of 3, 4, and 6. If, as stated earlier, we assume no interferneces, we can see that having L=5 makes sense: the electron started in the L=4 (g) state, and absorbed one photon, so there should be mostly L=5 (which there is). What is difficult to see is why there exist bunches of the other terms. When we later work back to the "meaningful" coefficients, that should shed some light ont this. By then looking at what happens as we move from the 5g peak to the 6g peak to the 7g peak, &c. we can try to figure out better what the mechanisms of ionization are and what processes are taking place. We can also look from order to order to see how the distributions change. Another way to look at the data is to look how the distributions change for a single peak (say, the 5g of the MPI order) when we change the intensity.

Next, a word needs to be said regarding fitting the data and error bars. Since our data comprise counted electrons, the percent uncertainty for each point is 1/sqrt(Number of counts for that point). The horizontal error bars are +/- 1¡. Since we have 16 data points for each plot, we fit our data using 15 paramters so that we are neither critically nor over parameterized. Below is the fit of the same data shown in the previous two figures, where signal (normalized) is plotted vs. angle for the given energy.

Plainly, the two jets seen in the radial plot up above are real, given our error bars.

Finally, given the above data corresponding to a peak energy you may be wondering how accurate our other, non-peak angular distributions are. Below you will find a radial graph and its partner fitting plot, with error bars. The specific energy value is 7.88 eV (for the same intensity as the above graphs), which lies somewhere between photon orders; hence, the electron counts here are smaller than those found at a peak energy.

One might argue that the 3rd, 4th, and 5th points from the left in the data have an "uneeded" or "extra" bump present in the fit. However, even if this "extra" bump were taken out, there would be some large feature between those points that would stick out from the rest of the distribution. The same can be said of those points near 40¡: here, a straight line could be drawn through them. Our fitting routine puts some minor bumps and wiggles in those points, but no one can doubt that the main bumps/jets, near 20¡, 40¡, and 80¡ ought to be included in the fit.

The movies you can view show what happens to the angular distributions when you keep the intensity the same, and scan in energy.