We present time-resolved cyclotron resonance spectra of holes in p-Ge measured during single magnetic field pulses by using a rapid-scanning, fiber-coupled terahertz time-domain spectroscopy system. The key component of the system is a rotating monolithic delay line featuring four helicoid mirror surfaces. It allows measurements of THz spectra at up to 250 Hz repetition rate. Here we show results taken at 150 Hz. In a single 900 ms measurement 135 cyclotron resonance spectra were recorded that fully agree with what is expected from literature.
© 2010 Optical Society of America
Terahertz (THz) measurements of cyclotron resonance (CR) in pulsed magnetic fields were so far mostly performed at fixed excitation frequencies from multiple microwave or laser line sources [1–4]. Since femtosecond-laser-pumped THz time-domain spectroscopy (TDS) systems, in contrast, emit and detect broadband radiation, they offer the advantage of measuring continuous spectra as has been shown at constant magnetic field [5–7]. The disadvantage of these systems with pulsed magnetic fields has in the past been the long data acquisition time limited by slow mechanical scanning of the delay stage. Here we introduce rapid mechanical scanning, based on a rotary delay line, which enables high-speed THz TDS. Moreover, we demonstrate the usefulness of 1.5 m free-space propagation inside the cryostat, and approx. 0.5 m outside. In this way we still benefit from the flexibility provided by fiber-coupled THz components as used before , but find the emitter and detector performance relatively unimpeded by a rapidly changing magnetic field even up to 40 T. To verify the applicability of our system, we present measurements of well-known cyclotron resonance of holes in p-doped germanium (p-Ge).
2. Experimental setup
The setup of our system is shown in Fig. 1. The output of a femtosecond fiber laser emitting approx. 100 mW at 805 nm center wavelength is prechirped by a transmission grating stretcher providing a high efficiency of about 65 %. The fiber-guided radiation is then split into two fibers. The emitter arm contains, in a free-space section, the rapid-scanning delay line capable of scanning a delay of 140 ps at up to 250 Hz repetition rate. Coupling to the standard dipole antennas is achieved by gluing the fibers directly to the LT-GaAs substrates. Si and TPX lenses are used to couple and collimate the THz radiation. We use a reflection setup to measure twice the transmission through a 0.6 mm thick p-Ge sample, by Au-coating its back side, and by inserting a 10 mm thick high-resistivity Si beam splitter in the cryogenic holder, together with a flat mirror and a home-made off-axis parabolic mirror. The assembly was placed inside a He cryostat and inserted in a LN-cooled magnet coil with a bore diameter of 30 mm. Single magnet pulses up to 40 T with pulse durations of approx. 500 ms were generated by discharging a 1 MJ capacitor bank.
3. High-speed delay line
The key component of our THz spectroscopy system  is the mechanical delay line based on a rotating element. It features four helicoid reflecting surfaces wound around a cylinder, all made out of one block. The monolithic assembly guarantees a balanced mass distribution and therefore allows for high rotation speed. Although helicoid surfaces disturb the beam profile, a fiber-coupling efficiency of about 10 % was achieved. A sketch of the delay line is given in Fig. 2.
The helicoid surfaces are inclined at about 11 degrees from the plane of rotation. In contrast to previous delay lines based on helicoid surfaces , the use of two opposing helicoid surfaces guarantees a stable center ray. The cylinder has a diameter of 50 mm, the thickness of the wedges built by the reflecting surfaces is 10 mm. The DC-motor driven device causes a time delay of 140 ps with repetition rates up to 250 Hz.
The principle of this specific delay line is scalable in various parameters. Increase of the repetition rate could be achieved by adding more helicoid surface pairs to the two pairs used here. When keeping the same outer dimensions and inclination angle of the reflecting surfaces, however, this could lower the achievable time delay. By scaling the outer dimensions or increasing the inclination angle this could be compensated for. In conjunction with the intended field of use, one can freely choose these parameters to achieve the best set of characteristics as described above.
The measurement presented here was taken with a repetition rate of the delay line of 150 Hz. Three different time windows of a sample data set are shown in Fig. 3. Each repetition of the delay line provides a set of at least three THz pulses, which arise from multiple reflections inside the sample. The first pulse from the front side of the sample is not evaluated by our analysis, but could help to determine the sample thickness. The dashed box in the lower plot of Fig. 3 marks the 0.5 ms time window used for Fourier transformation, corresponding to a time delay of about 16 ps.
The influence of the magnet pulse launch on the time-domain traces is shown in Fig. 4 where a section of approx. 1 ms duration is apparently affected. The induced spike around 175 ms is caused by the abrupt rise of the magnetic field driven by shortened capacitors. By chance, this does not interfere with the evaluated THz pulses here and lies in between two transients. In our presented measurement no triggering of the magnet pulse initiation with respect to the delay line is used, but is feasible for future experiments.
The change of the THz amplitude absorbance, induced by the magnetic field, is shown in the lower plot of Fig. 5. As reference, the average of 10 THz spectra before the pulse initiation is taken. In the upper plot, the measured magnetic field is shown as a function of time. With a 0.6 mm thick, p-doped Ge sample having a hole concentration of 1014 cm−3 oriented with the  crystal direction along the magnetic field, strong spectral absorption peaks are seen in individual spectra at frequencies that follow the magnetic field.
Ge has two prominent light and heavy hole cyclotron resonance absorption lines that shift linearly in frequency with the magnetic field (ω = eB/m*). This translates into two major absorption features best seen during the relatively slow downsweep of the magnetic field. These lines provide, after scaling, light and heavy hole effective masses of 0.04 m0 and 0.3 m0, respectively. The additional weak third line accounts for quantum effects in the cyclotron resonance of valence band holes . A linear dependence of the resonance frequency on the applied magnetic field can clearly be verified as shown in Fig. 6.
The ultimate performance of our system in terms of narrow linewidth measurement is set by the delay line time window (Δν = 1/τ). Since the cyclotron resonance linewidth is fixed by the hole scattering time along the cyclotron orbit, it follows that scattering times as large as 140 ps can be measured, assuming that multiple reflections inside the sample are suppressed. This limitation, when translated in terms of holes mobility (μ = eτ/m*), gives light and heavy holes values of 6 ·106 cm2/Vs and 7 · 105 cm2/Vs respectively. These values are much higher than currently achievable in Ge, therefore the delay line time window does not impact the measured cyclotron linewith here. Another detrimental line broadening mechanism is caused by the magnetic field drift during the acquisition of a spectrum. In our experiment a maximum rate of 70 T/s on the downsweep of the magnet pulse occurs. For a scanning repetition rate of 150 Hz and 0.5 ms Fourier-transformed time window, the magnetic field drift here is 35 mT. This corresponds to an upper mobility measurement limit of approx. 3 · 105 cm2/Vs, which is still above the mobility values of the holes of our sample. For samples with sharper linewidth, this measurement limit can be raised by increasing of the delay line repetition rate.
Our CR data fully agree with the established results of reference . Further developments now in progress are aimed at increasing the scanning speed of the delay line as well as the intensity and the frequency range of the THz pulses. This work paves the way to routine THz TDS measurement of both complex conductivity or susceptibility over the THz frequency range at low temperatures and magnetic fields supplied by 60 T coils.
We presented a THz TDS system with a novel high repetition rate mechanical delay line, and proved its applicability to single-event measurement tasks aiming at millisecond dynamics. The measured cyclotron resonance spectra of p-Ge fully agree with literature-based expectations. This also demonstrates the robustness of the applied fiber-coupled, partly free-space system. The principle of the novel delay line introduced here allows to specifically tailor both the spectral resolution and the acquisition time per spectrum. A future achievement of even higher repetition rates is straightforward.
Part of this work has been supported by the EuroMagNET II program under the EU contract number 228043. Supported by the Deutsche Forschungsgemeinschaft through the Cluster of Excellence “Munich-Centre for Advanced Photonics”.
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