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A THz time-domain spectroscopy-based vector network analyzer for S21-parameter measurements is presented providing THz waveforms as input signal for waveguide-coupled devices under test. We integrate an optical pulse shaper into the emitter arm and fiber-couple the photoconductive antennas to allow for flexible usage. The pulse-shaping capabilities are demonstrated by realizing all 5 bit combinations of a 0.5 THz signal. Furthermore, we can set the center wavelength of the resulting THz spectrum. Finally, we apply the shaped THz waveforms to test the response of a low-noise amplifier.
© 2015 Optical Society of America
1. Introduction
Since the first demonstration of photonic generation of ultrashort electrical signals in 1984 by Auston et al. [1], and the seminal work of Grischkowsky et al. [2] terahertz time-domain spectroscopy (THz-TDS) has been established as a viable tool for spectroscopy [3], destruction free materials testing [4], imaging [5] as well as for security applications [6]. With compact Er-doped fiber lasers replacing the bulkier Ti:Sa oscillators and optical fibers connecting the photoconductive antennas (PCAs) small, inexpensive and robust THz-TDS setups become available and novel applications appear. Recently, we demonstrated the application of THz-TDS for S-parameter measurements of electronic devices [7], moving optical THz generation into the field of electronic measurement techniques. Lately, a single-port VNA using a similar setup with electro-optic detection has been presented [8], based on earlier work employing wire-bonds for connection to the device under test (DUT) [9]. To further extend the range of applications, it is highly desirable to generate almost arbitrarily shaped THz waveforms, allowing for matching of the input signal’s spectrum to the DUT as well as testing of nonlinear systems To also test the temporal response of such systems it is highly desirable to apply temporally shaped waveforms. While shaping of optical pulses is a common technique applied in such diverse fields as, e.g., coherent control [10], pulse compression [11] and communication [12], shaping of THz pulse just recently gained renewed interest [13]. In this work, as well as in the first THz pulse shaping paper by Liu et al. [14], free space propagation has been used.
Here, we combine state-of-the-art optical pulse shaping [15] with PCAs as THz sources to generate arbitrary THz waveforms. In contrast to the setup in [14], our system is based on an inexpensive Er-doped fiber laser and is completely fiber coupled. For better laser power efficiency phase-only pulse shaping is employed. Spatio-temporal coupling as well as dispersion compensation are taken into account to optimize the overall system performance.
2. Experimental setup
Our measurement setup comprises an optical subsystem for pulse-shaping and two fiber-coupled PCAs, one emitter and one detector. Figure 1 shows the pulse-shaping setup: Ultrafast laser pulses are generated with an Er-doped fiber laser (Toptica FemtoFErb) which is coupled into an SHG unit based on a periodically poled LiO3Nb (PPLN), delivering about 30 mW at 780 nm with a pulse length on the order of 50 fs. 25 mW of this laser power are coupled into the pulse shaping unit (blue background), while the remaining 5 mW are used for the detector unit (green background).
The pulse shaper is layed out as a 4f pulse shaper [16] using two transmission gratings with 1764.7 lines/mm. These gratings sit in the focal points of two spherical mirrors with a focal length of 500 mm, forming an 1:1 telescope. In the internal focal plane of this telescope a spatial light modulator (SLM, Jenoptik SLM640d) is placed, containing two displays for independent shaping of spectral phase and polarization. As time domain and frequency domain are connected via the Fourier transform, this spectral shaping leads to a temporal shaping. After the output grating, the light exiting the pulse shaper (Output 1) is coupled into a polarization maintaining (PM) optical fiber and passes through an fiber-coupled polarizer, mapping polarization shaping to amplitude shaping. Control of the amplitude is later used for equalization of the peak electric field of various THz bit-patterns.
Temporally shaping light with the SLM in the focal plane of the 1:1 telescope obviously modifies the imaging properties of this telescope. This induces spatio-temporal coupling, i.e., the spatial intensity distribution is changed by the temporal shaping [17, 18], rendering simple coupling into the optical fiber almost impossible. To circumvent this problem Frei et al. [19] have shown that this effect does not occur if the focal plane of the coupling lens is placed exactly one focal length from the output grating. Hence, we place the collimating lens as close as possible to one focal length from the output grating. The second order dispersion of the fiber connected to Output 1 is additionally to the pulse-shaping compensated with the SLM.
The detector unit contains a motorized delay line and a grating stretcher for pre-compensating the second order dispersion introduced by the PM fiber going to the detector PCA (Output 2).
The optical subsystem is integrated into one housing compatible with 19 inch technology and FC/APC outputs for the PCAs. The electrical part of the system consists of a voltage source delivering a rectangular bias voltage of ±30 V at about 4 kHz, needed for generating the THz-waveforms and a lock-in amplifier, locked to the bias voltage, required for the detection of the THz signals. The fiber-coupled PCAs are mounted on a base with two off-axis parabolic mirrors (OAPM) each, as can be seen in Fig. 2. These bases are freely adjustable allowing for placing both horn antennas of a DUT in focus of the respective OAPMs.
Fig. 2 Schematic overview of the terahertz beam path and fiber connections, FP: fiber-coupled polarizer.
To generate the appropriate phase masks corresponding to the requested optical waveform we implement the Gerchberg-Saxton algorithm [20] for phase mask retrieval. This algorithm requires only up to 10 iterations to calculate phase masks suitable for generating of a waveforms within about 5% error with respect to the target waveforms. 10 iterations are performed in less than 1 s on a standard computer. The algorithm requires the known input spectral intensity and the requested output temporal intensity as input parameters. Finally, in order to cancel the dispersion introduced by the fibers between the pulse shaper and the emitter PCA, a quadratic phase profile is added to the computed phase mask.
3. Results and discussion
Before employing shaped THz waveforms to measure a device under test, we demonstrate the pulse-shaping ability of our setup by generating bit-patterns as well as signals with different central frequencies.
For the bit-patterns we realize all possible 5 bit combinations except 00000. The separation between two bits is 2.15 ps, as indicated by the gray lines in Fig. 3. To equalize the peak electric field strength irrespective of the number of bits set to high to the case of all bits set to high (11111), we attenuate the overall amplitude by polarization rotation according to the overall number of high bits. Otherwise, the overall energy would remain constant, leading to a five-fold higher peak electric field in the case of only one bit set to high. The plot has been normalized by dividing all waveforms by the peak-to-peak amplitude of the 00001 pattern. As can be seen from the plot, the amplitude and peak position of each bit remains rather constant. The different bit-patterns are generated by one run of the Gerchberg-Saxton algorithm with 10 iterations per pattern while keeping the pseudo-random generator’s seed constant for all patterns.
Fig. 3 Bit patterns generated by the setup. All patterns are normalized to the lowest pattern (00001). The position of each bit remains stable, as does the amplitude, regardless of the number of bits in the respective pattern.
To synthesize different frequency bands to increase the available power within this band pulse trains consisting of seven pulses following a Gaussian envelope were generated. Addressing selected frequency bands allows for matching the spectrum required to test a certain DUT. We choose to generate frequencies of 0.5 THz and 0.75 THz, resulting in pulse trains with a pulse interval of 1.5 ps and of 2 ps in the time domain. The resulting spectra as well as the time domain signal are presented in Fig. 4. For comparison, the reference spectrum generated by a single, unshaped pulse is plotted (black dashed line). This clearly demonstrates that parts of the spectrum according to the desired frequency interval are enhanced. They are 18 dB above the next feature of the respective spectrum for both waveforms. Additionally, an enhancement of 3 dB relative to the reference spectrum is visible. An even better suppression of side bands might be achieved in the future for longer pulse trains.
Fig. 4 Spectra of waveforms synthesizing different target frequencies under a Gaussian envelope. Solid blue line: 0.75 THz, dashed red line: 0.5 THz. Long dashed black line: reference spectrum. Inset: time domain signal of the two different frequencies generated.
Finally, we use our setup to evaluate the response of a low-noise amplifier (LNA) operating between 220 GHz and 330 GHz using a shaped waveform as an input signal. Due to the low frequency range, a bit pattern containing five pulses separated by 3.3 ps was generated. In order to retrieve the transmittance (the S21-parameter), the signal is normalized to the signal measured when replacing the LNA with a through-waveguide of identical outer dimensions, canceling the effects of the horn antennas used for coupling into the DUT [7].
The response in the frequency domain, the response of the LNA to a single pulse, as well as the input signal in the time domain, are shown in Fig. 5. Here, a clear deviation in the LNAs response at frequencies below 270 GHz to single-pulse and multi-pulse-excitation can be seen, while a very good match is achieved at higher frequencies, indicating a linear operation of the amplifier even under excitation with fast varying patterns. However, this is expected, as the input spectrum is attenuated at lower frequencies due to the multi pulse waveform as demonstrated above for frequency-band generation.
Fig. 5 Response of a LNA to bit pattern. S21 of LNA measured using a single input pulse (solid red) and a bit pattern (short dashed blue). Features below 270 GHz (gray line) are artefacts due to the lack of information in the reference spectrum (long dashed green, shifted by 50 dB). Above 270 GHz, both S21 measurements agree well. Inset: Bit pattern.
4. Conclusions
In conclusion, we demonstrated a combination of optical pulse shaping with THz-TDS. As phase-only pulse shaping is used, an inexpensive Er-doped fiber laser supplies sufficient laser power. Fiber-coupling of the PCAs to the optical setup allows for flexible usage either with a standard free-space THz beam path or with coupling into rectangular waveguides for characterization of a DUT. Bit-patterns with about 500 GHz bandwidth and pulse trains generating a rather narrow spectrum at different central frequencies are shown. Using a bit-pattern as input signal for an LNA confirms a rather linear response of the device in good agreement with theoretical expectations.
Acknowledgments
This work was supported by the Fraunhofer Internal Programs under Grant No. MAVO 824720 and thank Herman Maßler (Fraunhofer IAF) for providing us with the low-noise-amplifier.
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