High-speed terahertz time-domain spectroscopy of cyclotron resonance in pulsed magnetic field

We present time-resolved cyclotron resonance spectra of holes in p-Ge measured during single magnetic field pulses by using a rapidscanning, 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 OCIS codes: (300.6495) Spectroscopy, terahertz; (300.6500) Spectroscopy, time-resolved. References and links 1. G. Dresselhaus, A. F. Kip, and C. Kittel, “Cyclotron Resonance of Electrons and Holes in Silicon and Germanium Crystals,” Phys. Rev. 98, 368–384 (1955) . 2. K. Suzuki, and J. C. Hensel, “Quantum resonances in the valence bands of germanium,” Phys. Rev. B 9, 4184– 4218 (1974). 3. D. C. Larrabee, G. A. Khodaparast, F. K. Tittel, J. Kono, G. Scalari, L. Ajili, J. Faist, H. Beere, G. Davies, E. Linfield, D. Ritchie, Y. Nakajima, M. Nakai, S. Sasa, M. Inoue, S. Chung, and M. B. Santos, “Application of terahertz quantum-cascade lasers to semiconductor cyclotron resonance,” Opt. Lett. 29, 122–124 (2004). 4. N. Miura, Physics of Semiconductors in High Magnetic Fields, (Oxford University Press, 2008). 5. D. Some, and A. Nurmikko, “Real-time electron cyclotron oscillations observed by terahertz techniques in semiconductor heterostructures,” Appl. Phys. Lett. 65, 3377–3379 (1994). 6. X. Wang, D. J. Hilton, L. Rein, D. M. Mittleman, J. Kono, and J. L. Reno, “Coherent THz Cyclotron Oscillations in a Two-Dimensional Electron Gas,” Opt. Lett. 32, 2845 (2007). 7. X. Wang, D. J. Hilton, J. L. Reno, D. M. Mittleman, and J. Kono, “Direct measurement of cyclotron coherence times of high-mobility two-dimensional electron gases,” Opt. Express 18, 12354–12361 (2010). 8. S. A. Crooker, “Fiber-coupled antennas for ultrafast coherent terahertz spectroscopy in low temperatures and high magnetic fields,” Rev. Sci. Instrum. 73, 3258–3264 (2002). 9. F. Ellrich, D. Molter, T. Weinland, M. Theuer, J. Jonuscheit , and R. Beigang, “200 Hz Rapid Scan Fiber-coupled Terahertz Time Domain Spectroscopy System,” Proc. IEEE, IRMMW-THz 2008 (2008). 10. Y. Wang, C. Wang, Q. Xing, F. Liu, Y. Li, L. Chai, Q. Wang, F. Fang, and X. Zhang, ”Periodic optical delay line based on a tilted parabolic generatrix helicoid reflective mirror,” Appl. Opt. 48, 1998–2005 (2009). #136983 $15.00 USD Received 27 Oct 2010; revised 25 Nov 2010; accepted 25 Nov 2010; published 30 Nov 2010 (C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 26163


Introduction
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][2][3][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][6][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 [8], 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).

Experimental setup
The setup of our system is shown in Fig. 1.The output of a femtosecond fiber laser emitting Fig. 1.Experimental setup consisting of a commercial fiber laser, a highly efficient transmission grating stretcher, fiber coupling, and the delay line in the emitter arm.The sample is placed inside a helium cryostat inserted into a liquid nitrogen cooled high-field magnet coil.The THz emitter and detector heads are placed outside the cryostat to avoid interference from the high magnetic field.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.

High-speed delay line
The key component of our THz spectroscopy system [9] 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 [10], 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.

Results
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   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 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 10 14 cm −3 oriented with the [110] 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 m 0 and 0.3 m 0 , respectively.The additional weak third line accounts for quantum effects in the cyclotron resonance of valence band holes [2].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 •10 6 cm 2 /Vs and 7 •10 5 cm 2 /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 •10 5 cm 2 /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 [2].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.

Conclusion
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.

Fig. 2 .
Fig. 2. Sketch of the delay line, featuring four helicoid mirror surfaces (two pairs of counter parts) wound around a cylinder.

Fig. 3 .
Fig. 3. Exemplary single time trace of 900 ms duration showing a repetition rate of about 150 transients per second.The magnetic pulse is started by discharging a capacitor bench at about 175 ms after the start of the measurement.From this time, a varying envelope of the time-domain THz traces indicates the absorption caused by the cyclotron resonance.The dashed window marks the evaluated (Fourier transformed) time window of each transient.

Fig. 4 .
Fig. 4. Influence of the magnet pulse start on the THz time-domain signal.An approx. 1 ms section is affected but does not interfere with the THz signal here.

Fig. 5 .
Fig. 5. Pulsed magnet field strength (top) and evolution of THz absorbance spectra of a p-Ge crystal (bottom, color scale bar right), obtained by Fourier transforming all data shown in Fig. 3. Two resonances are clearly seen sweeping through the measured 0.2 -1.2 THz spectral range.A third, weak one in between can just be discerned.The low-frequency part below 200 GHz is grayed out because of a poor SNR.

Fig. 6 .
Fig. 6.Evaluated resonance frequency of light and heavy holes in dependence on the applied magnetic field, which is oriented along the [110] direction of the p-Ge crystal.