What was the motivation for investigating electro–optic sampling?

Michael Woerner, Peter Gaal and Klaus Reimann (from left to right) in their lab at the Max-Born-Institut in Berlin, Germany. Credit: MAX-BORN-INSTITUT

Our group specializes in ultrafast spectroscopy of solids, mainly semiconductors. We wanted to find a method that enables time-resolved measurements of emission from quantum-cascade lasers that operate in the mid-infrared and terahertz regions. The conventional method for these types of measurements relies on nonlinear optics and up-conversion. Short probe pulses around the 800-nm range are mixed with the mid-infrared signal under analysis, and the intensity of the resulting sum-frequency signal is then measured as a function of a time delay. The problem is that it is very difficult to get good results with a large signal-to-noise ratio. We decided to investigate other methods and this lead to the idea of using electro–optic sampling to see if it helped.

What is the principle behind electro–optic sampling?

The idea is that one measures the electric field coming from the laser. Certain semiconductor crystals such as ZnTe are electro–optic and become birefringent when subjected to an electric field. We use femtosecond probe pulses to 'sample' the birefringence that is induced in such a crystal by the signal beam's electric field. After leaving the crystal the probe pulses pass through a quarter waveplate and polarizer and then strike two detectors. If there is no signal beam there is no electric field and thus no birefringence, and the probe becomes circularly polarized and each detector receives the same signal. However if there is a signal beam, the crystal changes its refractive index and the light becomes elliptically polarized, so that unequal intensities are received by the detectors. The difference in the detector readings is proportional to the strength of the electric field and by taking a Fourier transform of these measurements it is possible to obtain the signal laser's emission frequency. This means that our technique can determine both the signal's temporal and spectral characteristics. For our first attempt we used a CO2 laser [operating at 10 μm] as a signal laser to make these measurements, but the final goal for us is to do these measurements on a quantum-cascade laser and analyse the time structure of its emission, such as its modulation behaviour.

What determines the measurement range?

The duration of the probe pulses needs to be shorter than half the period of the signal emission frequency that is being measured. For example, pulses of 12 fs enable measurements of a signal wavelength of 7.5 μm or longer. On the other hand, the frequency bandwidth of any one measurement is given by half the repetition rate of the probe laser. This means that the linewidth of the emission that is being measured needs to be smaller than half the repetition rate. As a result our scheme is well suited for analysing lasers but could not be applied to broadband spectroscopy.

It is important to have a probe laser with a high and very stable repetition rate. Fluctuations of the repetition rate cause a loss of frequency resolution. With a perfectly stable probe laser, the inverse of the measurement time yields the frequency resolution, for example 2 Hz for a measurement time of 0.5 s.

What are the main benefits of your approach?

Our technique can be used to measure any wavelength longer than the minimum allowed by the pulse-length limit. This means that we have the potential to make measurements in the range of 2–10 THz, which is hard to address by other means. Also if the signal to be analysed has a very narrow frequency range (emission linewidth) then the signal-to-noise ratio can be very high — 106 or more. This means that we can measure a signal of just 1 μW for a narrowband signal.

How could the technique be improved or refined?

There are several aspects that could be improved. Noise, mainly shot noise in the detectors, limits the sensitivity and performance of the measurements. Using higher-power probe pulses — we only use around 50 mW or so at present and this could be improved by a factor of ten or so — would reduce noise by a factor of three. However, the probe power must not be made too strong or unwanted nonlinear effects are induced, such as white-light generation. Using a thicker ZnTe crystal to improve sensitivity is another possibility, provided that the probe and signal wavelengths are adequately phase-matched within the crystal. A third option could be to use other electro–optic crystals, such as GaSe, which give larger signals, but that would depend on the wavelength range of operation.

Reimann and his co-workers have a letter on electro–optic sampling on p577 of this issue.