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Abstract
We investigate the performance of terahertz (THz) quasi time-domain systems (QTDS) driven by electrically pulsed multi-mode laser diodes operating at 659 nm. We show that at the same average output power, a reduced duty cycle considerably increases the obtained bandwidth. In the presented experiment, the high frequency performance is improved by 50 dB/THz. We identify the broadening of the optical spectrum caused by pulsing the laser source to be responsible for the increased THz bandwidth.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
THz time-domain spectroscopy (TDS) has made tremendous progress since the early demonstrations by Grischkowsky and coworkers [1]. While the early THz-TDS systems in the 1990s where mainly operated by mode-locked titanium sapphire lasers with low-temperature grown GaAs antennas most modern THz spectrometers rely on ultrafast fibre lasers operating at the telecom wavelength with antennas based on InGaAs [2–5]. Meanwhile, many practical applications for THz-TDS systems have been discussed ranging from monitoring of industrial production processes (see [6] for a review) to quality control for sugar beet seeds [7].
Yet, the market for THz-TDS systems is still rather small as they cost several tens of thousands of Euros [8]. The most expensive component is the femtosecond laser source. Experiments with mode-locked laser diodes have either the problem of a complex setup of the laser source [9,10] or reduced performance due to the high repetition rate [11]. A cost-effective alternative to THz-TDS is THz quasi time-domain spectroscopy (THz-QTDS) where the femtosecond laser is replaced by a simple multimode semiconductor laser diode [12, 13]. Since the emitted modes of the laser diode have an equidistant frequency spacing, the THz signal shows a periodic pulse-like structure produced by a multi-frequency photomixing scheme. Hence, this scheme leads to waveforms that are similar to those in a THz-TDS setup. The first demonstrations used laser diodes around 800 nm or even shorter wavelength [12,13]. Recently, Kohlhaas et al. demonstrated a fiber-coupled THz QDTS system driven by a laser with a central wavelength of 1550 nm [14]. By using state of the art continuous wave (CW) emitter and detector antennas a bandwidth greater than 1.5 THz with a peak signal to noise ratio (SNR) of 60 dB was obtained. While this result is impressive for the QTDS concept, its performance falls short of state of the art THz-TDS system with a bandwidth greater than 6 THz and a peak SNR of 90 dB [4,5]. In light of prior experiments by Shibuya et al. [15], our original idea was to increase the THz amplitude by electrically pulsing the laser diode to consequently improve the SNR. Pulsed laser operation is achieved by modulating the injection current with a pulse wave at different duty cycles.
Contrary to our initial expectations based on Shibuya’s results, the actual THz amplitude did not increase by much. Instead, early results showed a broadened THz spectrum with many more frequency components. Hence, in this work, we quantitavily investigate the performance of a THz-QTDS system with a modulated laser diode. Specifically, the laser diode was driven by current pulses with a low duty cycle and a high peak amplitude, such that the average output power is kept constant. This allows for a comparison of the performance at various duty cycles.
2. Experimental setup
The experimental setup is very similar to a typical free space THz-TDS or THz-QTDS setup [13], as shown in Fig. 1. The difference is the light source: For this experiment, we used a Rohm RLD65PZB5 type 659 nm semiconductor laser diode driven by a PicoLAS LDP-V 80-100 V3 short pulse current source. The short pulse driver is able to deliver up to 80 A peak current in a 12 ns pulse at a repetition rate of 2 MHz. The pulse duration and repetition rate were controlled via an external function generator and are variable. The peak current was also controlled via an externally applied voltage.
Fig. 1 The laser diode is driven by a short pulse current source at a repetition rate of 2 MHz. Besides, the setup is very similar to THz-TDS or THz-QTDS setups: the laser beam is split in two and guided to the photoconductive transmitter (Tx) and receiver (Rx) antennas, respectively. The laser beam of the detector arm can be delayed to sample the THz time-domain waveform.
Regarding the THz components, we used a 200 µm dipole antenna as the emitter and a 50 µm dipole antenna as the detector. Both antennas are based on low temperature grown gallium arsenide (LT-GaAs).
For investigating the effects of pulsed laser operation, we measured THz quasi time-domain traces for different duty cycles (i.e. the ratio of the on-time of the laser pulse to the pulse period) at a constant average output power. In order to prevent the destruction of the laser diode at high injection currents, we set the average output power to a comparatively low value of about 15 mW. After losses due to the optical path, each antenna was excited with about 7 mW (whereas the antenna’s damage threshold exceeds 30 mW). Single shot THz traces were repeatedly measured and then averaged in order to improve the signal to noise ratio (SNR). The number of averages N was chosen for each duty cycle so as to achieve a separation of peak intensity at 220 GHz to noise floor of at least 40 dB (N ≥ 30).
The laser’s repetition rate was set to 2 MHz. It is important to note that pulsed laser operation produces very intense harmonics of the repetition rate in the detector’s current signal, even when no THz signal is present. Some care had to be taken to not record any beating or aliasing effects of these harmonics.
In our setup, we used a Stanford Reserch SR830 lock-in amplifier with a bandwidth of about 100 kHz and a modulation frequency of about 10 kHz. The 2 MHz pulse repetition rate is well outside its bandwidth and thus sufficienctly suppressed by the input’s low-pass filters. As a result, any aliasing and beating effects from the generated harmonics were eliminated from the signal.
The integration time for each measurement was set to 100 ms at a delay line movement speed of 1.25 ps/s.
3. Results
3.1. THz bandwidth
Figure 2(a) shows the THz spectra at duty cycles D = 3.5% and D = 50%, with the duty cycle defined as the relation between the time span that the power is switched on and the total cycle period: D = T on/T cycle. The spectra were obtained from a discrete Fourier transform of the time-domain data. To improve the peak visualization, the data was zero-padded to 10x the original length. As in all time-domain systems, the frequency resolution is determined by the length of the acquired time window. The graph shows a significantly broader spectrum for lower duty cycles, reaching a bandwidth (defined as the frequency where the signal vanishes in the noise floor) of 1 THz at D = 3.5%, whereas the bandwidth at D = 50% is limited to about 550 GHz at the same noise level.
Fig. 2 a) Comparing the THz spectra at two far-apart duty cycles reveals the effect of pulsed laser diode operation. The maximum amplitude stays approximately the same, but the total bandwidth is considerably increased. By performing a fit through the peaks after the maximum at about 0.22 THz, the roll-off constant fRO can be determined (examplary fits are visualized with dashed lines).
b) Quantifying the roll-off shows that it closely follows a saturation model when plotted against the reciprocal duty cycle. The model’s parameters from Eq. (1) can be extracted from a fit to the data. A more thorough discussion can be found in the running text.
The discrete nature of the acquired THz spectra does not change and is still solely determined by the relatively short cavity roundtrip time of about 41 ps of the laser diode.
After reaching the peak intensity at around 0.22 THz all recorded spectra fall off with an exponential decay P ∝ exp (− f / fRO). The decay constant (or roll-off frequency) fRO is determined from a fit through the peaks after the frequency of maximum intenstity. Figure 2(b) depicts fRO against duty cycle. The curve follows a simple saturation model of
where fRO,0 is the maximum achieveable bandwidth for D → 0, M is the increase of bandwidth at small duty cycle, D, and D3dB is the 3 dB compression point.The fit provides us with values for all of these parameters. However, all of our data points are on the initial steep slope of the curve so that small errors in the roll-off already have a big impact on the fitted parameter’s accuracy. This also shows in the parameters covariance, which is taken as the basis for the expressed uncertainties:
The noticeably large error bar of fRO,0 is due to a lack of data for low duty cycles. In our experiment, this could not be realized, because shorter (and consequently more intense) current pulses have led to the destruction of the laser diodes.
3.2. Correlation to optical bandwidth
The minimum duty cycle used in the experiment of D = 3.5% leads to a pulse duration of 17.5 ns. Hence, we can exclude spectral broadening due to the pulse duration, which would only yield a spectral increase in the range of 17.5 ns−1 ≈ 57 MHz which is orders of magintude smaller than the achieved bandwidths. However, the duty cycle affects the laser spectrum beyond a simple Fourier analogy. We therefore investigate the laser diode’s optical spectrum at different duty cycles. Examplary spectra are shown in Fig. 3. Evidently, short duty cycles increase the spectral width of the multimode laser diode and further shift the central wavelength. One effect that leads to spectral broadening can be band gap filling: Due to Pauli exclusion, higher injection currents fill more energy levels in the gain medium and thus a wider range of frequencies are radiated [16].
Fig. 3 Examplary optical spectra for low and high duty cycles. A lower duty cycle and correspondingly higher peak current in the diode leads to a broader optical spectrum. The 10 dB widths are marked.
Of note are also the intensity “spikes” that appear in the optical spectrum at high duty cycles. Theses spikes can probably be attributed to mode competition in the laser diode [17–20]. The displayed spectrum is then a time average of a dynamic behavior. Schmidtke et al. demonstrate that this process happens on time scales of a few 10 ns [17]. Since the current pulse duration at low duty cycles is in the same order of magnitude, it stands to reason that the pulsed operation influences, if not outright dampens, the mode competition processes in the laser diode. As a result, a flatter optical spectrum at low duty cycles is expected. Moreover, optical modes that would otherwise be suppressed by mode competition are radiated and can contribute to a broader average optical spectrum.
Since the involved time scales are much shorter than those of the measurement electronics (some few 10 ns vs. 100 ms, respectively), we do not expect the dynamics of this effect to be visible in the terahertz spectra.
A plot of the 10 dB width of the optical spectrum together with the THz spectral roll-off as depicted in Fig. 4 suggests a strong correlation between both parameters. The Pearson correlation coefficient evaluates to R = 0.9676, indicating an almost linear relationship.
Fig. 4 The roll-off frequencies of the THz spectra at different duty cycles correlate strongly with the 10 dB widths of the corresponding optical spectra (Pearson correlation coefficient R = 0.9676).
Theory [21] states that the measured current at the detector antenna is approximately
where is the average optical intensity and ωH (ω) is the propagation and antenna factor. For thorough theoretical calculations it is important to note that the equation includes approximations which might not necessarily hold in our case. One such approximation is the completely linear and spatially uniform response of the THz antennas to the laser intensity, altough actual photoconductors can saturate. Moreover, the optical spectra not only change their width, but also their overall shape, along with significantly varying peak output power.Still, Eq. (5) provides an approximate explanation of the the system’s response. Qualitatively, the data confirms the prediction that a broader optical spectrum leads to an increased THz bandwidth. The large correlation coefficient further indicates that the optical bandwidth is the major driver behind the decreasing THz roll-off in our experiment.
4. Conclusion and outlook
We have shown a feasible method to effectively enhance the THz bandwidth in THz-QTDS setups. The effect is achieved by employing an electrically pulsed laser diode, demonstrated with repetition rates up to 2 MHz and duty cycles as low as 3.5%. The increased THz bandwidth is highly correlated to an increase of the width of the laser spectrum due to operation at low duty cycles.
We expect that the performance can be further increased by using laser diodes which are specially designed for pulsed operation. These should allow for even higher peak currents and consequently broader optical spectra.
While the usual trade-off of a discrete THz spectrum as a result of cheap laser source is still made, the proposed scheme can help offset the typically small bandwidth of THz-QTDS compared to classical TDS systems. The improvement does not depend on overly expensive equipment so the comparably low price of THz-QTDS can be maintained.
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