Pulsed terahertz spectrometer PTS‑1
ff-the-shelf terahertz time domain spectroscopy systems (THz-TDS) became available to the scientific community over the last few years. Although such systems differ in layout and various parameters, all of them exhibit relatively low average output power of THz radiation.
In 2013 Tydex decided to design its own THz spectrometer. We applied to a competition held by the Foundation for Assistance to Small Innovative Enterprises in Science and Technology. Our application was funded, and thus we commenced the development of the Pulsed THz Spectrometer PTS‑1 in October 2013. We enlisted employees from the Extreme Light Sources and Application (ELSA) laboratory of N. I. Lobachevsky State University of Nizhny Novgorod as our experts and partners. After some discussion, we decided that PTS‑1 would generate THz radiation by means of optical rectification of femtosecond laser pulses under the condition of Cherenkov phase matching. High-power pumping laser and the aforementioned generation method would ensure high optical-to-terahertz conversion ratio, thus providing high average output power of THz radiation.
A pulsed terahertz spectrometer by Tydex LLC is an integrated solution for broadband terahertz time-domain spectroscopy. The PTS‑1 includes the following (Fig. 1):
• Solid-state femtosecond laser;
• Electro-optical detector of pulsed THz radiation;
• All optomechanical components for the optical and THz path;
• Delay line;
• Electronic control units for the optical delay line, optomechanical modulator and laser;
• PC with pre-installed TydexLN software.
General optical layout of the PTS‑1 is shown in Fig.2. Radiation from an ytterbium solid-state femtosecond laser TeMa‑1050 / 100, which is manufactured by our partners from Avesta LLC, is split into two beams, a pumping beam and a probe beam. A more powerful pumping beam is used to generate THz pulses. The generation occurs when the pumping pulse interacts with 1% MgO:LiNbO3 crystal. The probe beam is used to detect the THz pulse. To detect the THz radiation, the PTS‑1 uses a NIR electro-optical detector manufactured by Tydex. The detection is based on change of polarization of the probe pulse in the presence of THz pulse.
The common feature of all mechanisms is the coherence of optical pulses (both pumping and probe) and the THz pulse. Here the coherence means the correspondence between THz pulse phase and optical pulse intensity. This correspondence is constant in time to a high degree of precision. Fluctuations of laser pulse repetition rate and mechanical vibrations are the same for THz pulse and pumping pulse, and do not affect the coherence. Since pumping pulse and probe pulse replicate the same basic pulse, they are coherent as well. Thus, THz pulse and probe pulse are phase-matched. Due to this matching, the probe pulse always interacts with the same part of the THz pulse within the detector. Probe pulse duration is usually measured in tens of femtoseconds, which is much less than THz pulse period (several picoseconds). Thus, it can be viewed as interaction between the probe pulse and some quasi-constant field. By introducing a time delay between pumping pulse (which is tied to the THz pulse) and probe pulse, one can vary the relative time of arrival of probe and THz pulses to the detector. This method allows detecting various regions of the pulse. Temporal resolution corresponds to the duration of the probe pulse. By scanning along the time delay range using a mechanical delay line, THz pulse waveform can be reconstructed.
Fourier transformation of the waveform gives the spectrum of the THz pulse. For example, to measure the transmission spectrum of a sample, the pulse spectra with and without the sample must be measured. Then divide one by the other. The result will be the transmission spectrum of the sample.
As we mentioned above, it was decided to achieve THz radiation generation in the PTS‑1 by means of optical rectification of femtosecond laser pulses. The optical rectification phenomenon involves formation of nonlinear polarization in a medium exposed to a high-intensity optical pulse. Said polarization follows the envelope shape of the optical pulse.
When radiation propagates through an optical medium with second-order nonlinear susceptibility χ(2), nonzero nonlinear polarization occurs (is induced by electrical field of the radiation) and travels along with the radiation. Whilst at low radiation intensities the nonlinear polarization is proportional to the electric field strength, nonlinear terms become significant at high optical intensities – for example, achieved by a laser pulse. Laser pulse generates a lower-frequency nonlinear polarization wave that propagates with phase velocity V equal to the group velocity of the optical pulse (Fig. 3). Nonlinear polarization wave radiates own optical field at aforementioned frequency.
For laser beams with approximately constant or slowly varying optical power, the quasi-DC (low frequency) nonlinear polarization is usually negligible. In case of ultra-short pulses, however, the strength of the quasi-DC component rises and falls off rapidly, and that leads to emission of an electromagnetic single-cycle pulse with a wide frequency spectrum, ranging roughly from zero frequency to some maximum value, where the overall bandwidth is essentially determined by the inverse of the pulse duration. For an optical pulse with a duration of 100 femtoseconds, for example, the resulting radiation pulse has frequency components going beyond 10 THz.
In crystals with significant second-order nonlinear susceptibility tensor components χ(2), instantaneous nonlinear polarization value is given by:
PNL (t, r) = χ(2) E(t, r) E(t, r),
where E(t, r) is the instantaneous electrical field strength of the laser pulse.
Depending on dispersive properties of the electro-optical crystal, THz wave generation can occur by a variety of mechanisms.
When the velocity of the source (i. e. nonlinear polarization in a nonlinear crystal) coincides with phase velocity of a THz wave at specific frequency, collinear phase matching occurs (see Fig.4 a). When the source propagates faster than the THz wave, another case of phase-matched excitation can occur. The wave propagating at angle θ to the source velocity vector V is also phase-matched to the source. It is known as Cherenkov phase matching (see Fig.4 b).
When the laser beam is focused to a crosswise size about or less than THz wave length, Cherenkov generation becomes efficient. Phase-matched THz waves are generated that propagate at an angle to the laser beam and form the Cherenkov cone .
The THz radiation pulses generated by the PTS‑1 are detected by means of electro-optical sampling using a NIR EOD. The electro-optical sampling utilizes the Pockels effect, change of the optical refractive index of the medium induced by an external electric field (in this case, the field of the THz pulse). In the electro-optical sampling method, the field of the THz pulse changes the orientation of the refractive index ellipsoid of the electro-optical crystal (the crystal becomes birefringent). The NIR EOD uses ZnTe electro-optical crystal. When a linearly polarized probe pulse propagates through the crystal along with THz pulse, is becomes elliptically polarized due to the phase difference between ordinary and extraordinary wave. The ellipticity is proportional to the THz field strength and can be detected with a polarization analyzer. The NIR EOD uses a quarter-wave plate and Wollaston prism as a polarization analyzer. Downstream of the polarization analyzer, the two differently polarized beams are detected using two photodiodes (Fig.5). Detection of difference signal from two diodes allows to suppress laser noise. To increase the sensitivity of the setup, the pumping beam is modulated with a mechanical chopper. A lock-in amplifier built into the NIR EOD helps to detect polarization modulation of the probe beam induced by the THz pulse.
As it was already mentioned, to obtain Cherenkov cone of terahertz waves, optical pulse has to be focused to a crosswise size about or less than THz wave length. To achieve this, the radiation from the pumping laser (average output power 3.14 W, center wavelength 1049 nm, pulse duration ~100 fs, repetition rate 69 MHz) was focused into 10 Ч 10 Ч 1 mm 1% MgO: LiNbO3 crystal using a plano-convex lens with focal length 75 mm (Fig.6). Phase matching is achieved between moving optical pulse and flat terahertz wave propagating at angle θ (40.5°) to the laser beam. To avoid total internal reflection of THz waves in the LiNbO3 crystal, a HRFZ-Si prism was used . To overcome high absorption of THz radiation within LiNbO3 crystal, the pumping laser beam was aligned parallel and in close proximity to the LiNbO3-Si interface.
The radiation produced in the spectrometer was detected by two different means, by electro-optical sampling and with a Golay cell. Waveform of the generated THz pulse, as measured by electro-optical sampling, is shown in Fig.7a. THz pulse spectrum obtained by Fourier transformation of the THz pulse waveform is shown in Fig.7b. Average THz radiation power was measured by means of a calibrated Golay cell. For this purpose, the pumping beam was modulated by an mechanical chopper (modulation frequency was 20 Hz). To suppress any unwanted radiation (such as pumping laser light), the entrance aperture of the Golay detector was equipped with a low-pass filter (LPF) with cutoff frequency 10.9 THz. THz signal amplitude measured at the output surface of the silicon prism was 5.15 V. Golay cell sensitivity at 20 Hz modulation frequency is 24.5 kV / W. Taking into account the LPF losses (TLPF = 70%), we’ve achieved ~300 µW average THz radiation power generated by the PTS‑1.
In this paper we have presented a commercial off-the-shelf THz spectroscopy set PTS‑1 with average output power 300 µW and optical to THz conversion ratio 10–4. PTS‑1 is ideal for scientific research applications due to radiation propagating through free space, flexible optical train and multipurpose software.
This development was supported by Russian Foundation for Assistance to Small Innovative Enterprises (FASIE), contract no. № 12234p / 23287.