A Month In Paris

So we've all been here a while. I'm getting pretty accustomed to the lifestyle. I definitely plan on adopting the fork in left hand, knife in right thing among other things. The plan now though is to work hard and take advantage of the city on the weekends. So expect pictures and posts.
Last Sunday Robyn and I dipped are hot feet into the cool fountains at the Louvre, walked around the Champs-Élysées, stood beneath the Arc de Triomphe, and visited a place that is not so popular it seems, the Grande Arche. It's at La Defense, last stop of the M1. This area is the financial district of the city so the buildings are shiny and tall. It was really a soothing place and the density of people very tolerable.

The Past 5 Days: Shopping, Fete de la Musique, and 50 yrs of the Laser Celebration

Pardon moi, mes amis! Didn't mean to take such a long time to make a post. These past couple of days have been a whirlwind. Let me recount them briefly

Saturday 19-06
Michelle, Robyn, and I went shopping. I found a neat running shoe store, Boutique Marathon, and got some reasonably priced baskets. We covered a lot of ground and I think it's safe to say we were all satisfied. Interesting things, at Châtelet – Les Halles it seems they have an ode to Modern Physics, and a Royal avec fromage is delicious.

Sunday 20-06
Went out with everyone to Luxembourg and got some neat postcards I plan to fill out in French and send to some folks back in the states.

Monday 21-20
50 ans du LASER! The festivities commenced at the Louvre with some of the pioneers of Laser science and technology rounded up by Bianca, John Nees, Pat, and myself for guided tours of the museum. Pat and I attended the Delacroix tour and it was awesome. Let me just say Le Louvre is the bee's knees, it's exquisite, and I want to live there. Delacroix's artwork was extremely interesting, very political, avant-garde as our guide said, and requires a lot more contemplation than I previously thought. He went into a lot of detail that I will spare you here but if you want to know more I'd be more than happy to discuss it. After the tour we gathered to hear a talk by Costas Fotakis director of IESL among other organizations. He and his crew are best known for their work in artifact and artwork preservation through the use of lasers. He brought up many different methods including THz TDRS as a tool for acquiring information of the artwork and he also discussed laser cleaning through the use of ultrashort pulses and ablation. I am glad Patrick got to ask him a question.

Later that evening a group of us went to Notre Dame to celebrate Fête de la Musique. People were playing music and dancing all along the Seine River. We walked around while enjoying some delicious sorbet. Before heading back home we followed the sound of cheering only to see in the distance naked people dancing in a large fountain. It was an interesting experience to say the least.

Tuesday 22-20
The 50th Anniversary of the Laser continued on at Ecole du Louvre. The day was spent listening to many important speakers the first of which was Charles Townes. At 95 years of age, the creator of the MASER, who paved the way for the laser and all of the science that have gushed out of such a tool, was sharp, funny, and above all else truly wise. His talk was an encouraging one, telling us all to share what we know and keep an open mind. Kathleen Maiman, wife of the late LASER inventor Ted Maiman, talked on behalf of her husband. She kind of reiterated something touched by Townes and a couple of other Nobel Laureates, which was: people, even experts, will tell you you're nuts and that it can't be done. Well we know where that got Charles Townes and Ted Maiman. The following talks were interesting covering topics like laser manipulation of atoms, seeing in 4D, and attosecond pulses to name a few.

Wednesday 23-20
50 ans du laser was celebrated at Ecole Polytechnique as well. There were presentations, posters, and interactive demonstrations for high school students. Nobel Laureates and revered Physicists and Engineers took the stage and gave more technical talks about their work. I know that there was a lot of filming going on. I definitely hope to find some of the recordings online and share them with you all.

Fun filled five days, no? It's back to work for me!

Notes on "Carrier Dynamics and THz radiation in Photoconductive Antennas"

Zhisheng Piao et al's paper consists of calculating the effects of certain parameters (capture time, carrier density, momentum relaxation time, etc) on THz waveforms generated and detected by photoconductive (PC) antennas. They mention how their results agree with experimental work shown in other papers.

• Interaction between electrons e^- and holes h⁺
• Carrier trapping in mid-gap states (due to material defects)
  
• Scattering of carriers
• Dynamical space-charge effects (particularly screening)

Their conclusions were
Using the Drude-Lorentz model (electron pinball classical treatment) for carrier transport in semiconductors they discuss

• Major contributor to THz radiation is due to ultrafast change in n (carrier density)
• At high n the local electric field (active area of PC antenna between the electrodes) oscillates and induces E&M radiation
• When using a PC antenna as a detector there is a discrepancy between the transmitted and detected THz signal.

Why are PC antennas a good source of THz

They exhibit instantaneous polarization arising from optical excitation, and transport of photoexcited carriers in E field. Low temperature grown gallium arsenide, LT GaAs, in particular has short carrier lifetime, high mobility, and high break down E field. These characteristics lead to intense, large bandwidth THz radiation.

How does the THz radiation come about

The radiation arises from an ultrafast change in semiconductor photocurrent. The change in photocurrent can be attributed to

• Change in n (via optical pumping)
• Carrier acceleration (E^­_loc ~bias + polarization effects)

Calculations
Assumptions include

• free carrier trapping time is much smaller than carrier recombination time thus carrier trapping time determines carrier lifetime
  
• neglect LT GaAs nonlinear absorption effects
  

Based on Maxwell's equations and Hertzian Dipole far-field regime the transmitted THz field can be defined asThe different terms in this equation can be related to different material, pump pulse, and bias parameters.

Results

You definitely want to view this in a separate window

1. Plots (a) and (b) show the effect of varying the capture time on dn/dt and dv/dt. A larger effect can be observed in the dv/dt plots. The dn/dt plot (shape and magnitudes) reveals how much more influential the change in carrier density is to the THz signal. Without the inclusion of a bias, E&M radiation can still be emitted from the PC antenna as long as dn/dt does not equal 0. However the inclusion of a bias allows for a shortening of the time scale, which in turn leads to wider bandwidths.
2. Plots (a) and (b) show the effect of carrier density on the local E field and THz signal. As n₀ increases the THz signal starts to oscillate. This is due to screening caused by the polarization term in E_loc. The field becomes comparable to the restoring force between the electrons and holes and thus causes them to move around switching the polarization of the field (positive and negative peaks).
   
3. Plots (a) and (b) show temporal and spectral profiles of THz signals when the pump laser pulse width is varied. Here you can see the shorter the pulse duration, the wider the spectrum. This can be exploited for spectroscopic experiments.
4. Plot (a) shows an emitted THz pulse profile and the detected pulse with varying detector capture times. As you can see, the shorter the capture time, the truer to the original the detected pulse is. This is because the detector has a faster response time to changes in photocurrent supplied by the THz radiation. There is distortion because the photocurrent response is a convolution of the detected E field and the detector's carrier density and lifetime. In plot (b) it seems that a longer capture time leads to a better spectral profile. I am not particularly sure why just yet. In practice the detector can act as a filter, cutting off a part of the signal. The THz pulse has a Gaussian distribution with shorter wavelengths towards the center and longer wavelengths towards the outer rim (so usually smaller frequencies can get cut off).

This paper answers a lot of important questions on how these PC antennas work, what's the source of the THz radiation and how it's influenced by different parameters, and what to be conscious of especially when doing spectroscopy. So that is what I know!

Under Construction: A More In Depth Explanation of the the Pump and Probe Lines

Salut Tout le Monde,

Bianca and I discussed the pump-probe setup for THz measurements and I feel more confident explaining what I know.

The equipment used to acquire THz signals can have response times on the order of milliseconds, microseconds at best, but certainly not picoseconds. The THz signals themselves are of a couple picoseconds duration. Thus collecting these waveforms is a tricky matter; but with the introduction of a probe beam path with an optical delay line the system can have enough time to take data.

Each individual femtosecond pulse centered at 800 nm is split by a beam splitter and the resulting pulses travel the pump and probe paths respectively. It is essential that these pulses originate from the same pulse for temporal and spatial coherence's sake. If the pulses used were from different lasers, for example, the THz signal would not be detected. The pulses along the pump line interact with a photoconductive transmitter to produce THz radiation that then is either transmitted or reflected by a sample and finally arrive at a receiver similar to the transmitter. The pulses along the probe line can be delayed, travel a longer path than the pump line, and arrive at the receiver. (Note that the same can be true for the pump line. Just a difference in length between the two paths is needed.) The probe pulses reach mirrors on a mechanical scanner, which translates in the direction of pulse propagation. The probe pulse is used to inject carriers into the receiver and the THz radiation from the sample supplies a transient electric field (i.e., bias) needed to produce a current across the receiver's electrodes that is then detected by the measuring equipment.The way in which the gate sampling/delay line works is that it allows for an incremental measurement of the THz radiation waveform. Looking at the figure above: The probe path is increased in step sizes equal to a. At each step the mechanical scanner pauses for however long it takes for your measuring equipment to respond to a current change in the detector (e.g. , 30 ms). Distance a corresponds to a position along the transmitted waveform. So the probe pulses will strike the receiver giving the equipment enough time to acquire one amplitude and time value off of the waveform. For the case of a 5 ps transmitted pulse and steps of a = 150μm, corresponding to a 1ps delay (~2a= c*Δt), you can acquire the waveform in 5 steps. In this way the THz signal profile can be pieced together. For finer resolution, a can be much shorter. The total sampling window size is determined by l. (There are limitations to the mechanical scanner so if resolution is important, it is probably best to make your sampling window shorter, collecting just the waveform, and then minimize your step size.) One thing to note is that the pauses and system response are much larger than the pulse duration, but the transmitted THz pulses strike the detector every 12.5 ns (80 MHz repetition rate). Each time a measurement is made, it is essentially of a different THz pulse. However, the waveform measurements are done repeatedly and each collected point is an average of multiple readings.

Concerning the types of scans:
Rapid scan allows for shorter time intervals between measurements, (this is dictated by system response time) but does not have good signal to noise ratio, might cut out some signal frequencies, and is not very stable (e.g., can introduce vibration to the setup). Its speed is beneficial in large sample imaging because it reduces the time you would have to sit around and wait.
When it comes to accuracy, stability, resolution, and bandwidth (which are essential in spectroscopy) a slower scan proves more useful.