1. Introduction

The most prominent principle for accessing the terahertz frequency range is time-domain spectroscopy (TDS) [1]. Its applicability to various measurement tasks has been proven in the last decades [2–11]. The most common implementation of TDS systems is realized by using photoconductive antennas as emitter and detector in combination with ultrashort pulses from femtosecond lasers. Already about 20 years ago, Morikawa et al. impressively demonstrated, that a conventional TDS system can be driven by the laser output of multimode diode lasers, resulting in signals similar to the output of systems driven by mode-locked lasers [12, 13]. Since then, several implementations of these cross-correlation spectroscopy systems have been demonstrated [14–21]. Applications range from imaging [22] to low-cost realizations for monitoring the water content of leafs in vivo [23] or semiconductor characterization [24]. These systems rely on the superposition of the laser source’s spectral components in the photomixing devices. This superposition leads to a beat and therefore to a modulation of the charge carriers in the terahertz frequency range, which then can be used for terahertz generation by acceleration of the charge carriers and terahertz detection via cross-correlation in the detector photomixing device. However, the laser nature of the used sources in these systems always leads to the formation of a spectrum with discrete modes, resulting from the individual modes of the laser cavity itself. We already demonstrated an implementation to overcome this comb structure by implementing two modulated diode lasers [25]. This approach leads to a continuous terahertz spectrum, but is technically rather complex.

In this paper, we demonstrate the terahertz cross-correlation principle by using natively incoherent light from a superluminescent diode (SLD), which has no cavity and therefore no specific modes. Using this light source results in a truly combless terahertz cross-correlation signal applicable to all common measurement tasks of TDS systems. This is to the best of our knowledge the first implementation of this measurement principle without the use of a laser light source.

The basic principle of the proposed system is closely related to that of white light interferometry [26], where incoherent light sources are used as well. For white light interferometry, the incoherent light is split up and brought to interference after one of the split fractions has interacted with a sample. In the case of the terahertz cross-correlation spectroscopy system with incoherent light as proposed here, there is another step added to translate one of the branches into the terahertz domain. Instead of interferometry, a cross correlation is carried out in the detector of the system. The coherence length of the light source only influences the accessible spectral range, as itself is defined by the spectral width of the incoherent light source. Samples that generate a signal lasting or delayed more than the native coherence length of the employed light source are measurable due to the generation of an identical copy of the light field at the employed beam splitter. This is the same principle as in white light interferometry or Fourier-transform infrared spectroscopy, where scanning ranges of several meters in combination with incoherent light sources are employed to achieve a high spectral resolution [27].

2. Experimental setup

The experimental setup of our approach is shown in Fig. 1.

 

Fig. 1 Experimental setup: The output of the superluminescent diode (SLD) is optionally bandpass filtered (BP) and amplified by an EDFA. Afterwards, the light is sent to a standard TDS-like setup consisting of a beam splitter (50:50), delay section, terahertz receiver (Rx) and emitter (Tx) as well as reflective terahertz optics. Photomixers for CW terahertz generation and detection are used.

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As light source, we are using a superluminescent diode providing light around 1.55 μm with a -3 dB-bandwidth of 46 nm. The light is coupled into a polarization-maintaining fiber followed by an optical isolator. The broad spectrum is optionally filtered by an optical bandpass filter (BP) limiting the bandwidth to a value, which can be efficiently used by the photomixers to generate and detect terahertz radiation. Furthermore, the performance of the system can be enhanced by amplification of the filtered light with an Erbium-doped fiber amplifier (EDFA). The output of the EDFA (or the plain SLD) is fed into a fiber-optic 50/50 splitter. One output of the splitter is directly connected to the fiber-coupled photomixing terahertz emitter. The second output of the splitter is guided to the optical delay line, followed by the detector photomixer. The detector photomixer current is amplified by a transimpedance amplifier (TIA) by a factor of ${10}^7\frac{V}{A}$ with an electrical bandwidth of 50 kHz. The output of the TIA is sampled with a rate of 200 kS/s and 16 bit accuracy. A voice-coil driven retroreflector is used as the delay line, providing a delay of about 100 ps at an oscillation frequency of 14 Hz. The delay-dependent signals presented in this work are acquired in 1 s each, consisting of 28 individual delay traces. To evaluate the average dynamic range, sets of 20 reference and 20 noise measurements (1 s measurement time each) are used. The averaging of these 20 sets is used to smooth the dynamic range data, but does not raise the dynamic range values. To directly compare our proposed technique to a standard laser-diode driven terahertz cross-correlation spectroscopy systems, a multimode laser diode at a wavelength of 1.55 μm was used instead of the SLD. It provides discrete spectral lines with a spacing of about 1.1 nm, corresponding to a frequency spacing of 140 GHz. The output of this laser is filtered and amplified in the same manner as the output of the superluminescent diode. A benefit of the proposed approach is the unnecessity of dispersion compensation. The fiber-optical branches after the splitter have to be equally long, but the absolute lengths of them do not matter. This enables the use of long fiber branches (in comparison to TDS systems driven by pulsed lasers), which might be beneficial for certain applications.

3. Results

The optical spectrum of the plain SLD (without bandpass filter or EDFA) is shown in Fig. 2(a) and exhibits a continous and smooth spectrum.

 

Fig. 2 (a) Optical spectrum of the plain SLD (without the optional bandpass or EDFA). (b) The obtained terahertz cross-correlation signal and (c) the achieved mean dynamic range. The isolated peak in the delay domain already indicates the spectral continuity in the terahertz range. A peak dynamic range of 30 dB at 100 GHz and a bandwidth of 1.3 THz are achieved.

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In Fig. 2(b), the delay-dependent cross-correlation signal using only the plain SLD is shown. In this case, the optical power at the photomixers is limited to about 8 mW each. A peak dynamic range of 30 dB at a frequency of 100 GHz and a spectral bandwidth of 1.3 THz is achieved and shown in Fig. 2(c). Based on the missing laser cavity the SLD light source provides a continuous optical spectrum, whose conversion to the terahertz frequency range leads to a continuous spectrum and consequently an isolated delay-dependent cross-correlation signal. This is the first proof, that no laser light is required for driving a terahertz cross-correlation spectroscopy system.

The cross-correlation spectroscopy signal can be significantly enhanced by optical filtering and amplification. In Fig. 3(c), the signal is shown for a filter bandwidth of 21.7 nm along with the results obtained with the multimode laser diode (d).

 

Fig. 3 Comparison of the optical spectra ((a) and (b)) and the delay-dependent terahertz cross-correlation signal ((c) and (d)) when using the setup with a SLD and a multimode laser diode (MMLD), each in combination with the same bandpass filter and EDFA. In contrast to the multimode laser diode source, a truly isolated cross-correlation maximum is observable when using the SLD. This behavior results from the continuous optical spectrum provided by the SLD.

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The amplification is chosen to provide about 20 mW at the photomixers. In this arrangement the signal is enhanced by a factor of more than 20, compared to using just the plain SLD (10 nA as shown in Fig. 2 in comparison to more than 200 nA here). Following the equation

 

Fig. 4 Influence of the bandpass width (a) on the dynamic range and bandwidth of the recorded terahertz spectrum (b). A tradeoff between dynamic range at low frequencies and bandwidth can be found.

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By changing the spectral width of the bandpass filter in front of the EDFA, the characteristics of the system can be influenced within limits. We employed four different bandpass filter widths ranging from 21.7 nm (2.7 THz) down to 4 nm (0.5 THz). The results obtained using the different filters are shown in Fig. 4. For each setting, the EDFA was adjusted to supply the same optical power to the experiment. As expected, the spectral width of the acquired terahertz spectrum depends on the spectral width of the used bandpass filter. Besides the spectral width, the peak dynamic range is influenced as well. For the broadest bandpass width, a terahertz spectral width of about 1.7 THz is achieved. The narrow bandpass exhibiting a width of 4 nm leads toa peak dynamic range of about 60 dB and a bandwidth of about 0.5 THz. The results from the intermediate bandpass filter widths consistently fit to this trend. The spectral resolution of the proposed method depends only on the scanned delay range.

To prove the basic applicability of the proposed system to standard terahertz measurement tasks, we have carried out transmission spectroscopic measurements on samples of α-Lactose monohydrate and para-aminobenzoic acid (PABA). These substances are well-known and widely used for terahertz measurements, as they show characteristic absorption features in this frequency range. The presented spectra are an average of 20 measurements each acquired in 1 second. A comparison to the results obtained with our presented approach to the results of a standard TDS measurement system is shown in Fig. 5.

 

Fig. 5 Demonstration of the applicability of the presented approach to spectroscopic measurement tasks. The well-known terahertz simulants para-aminobenzoic acid (PABA, shown in (a)) and α-Lactose monohydrate (b) were measured with the SLD-drivensetup and are compared to the spectra acquired with a standard TDS system. The terahertz beam path was not purged in the SLD-driven setup, so artefacts from water vapor absorptions are present. Within the limited bandwidth, the spectral features are consistent.

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The obtained spectra agree well within the accessible spectral range. In case of the SLD-driven setup, no purging of the terahertz beam path was used (in contrast to the standard TDS measurements), which leads to some artefacts at terahertz frequencies ofwater vapor absorption lines (e.g. around 1.1 THz).

 

Fig. 6 Comparison of a HITRAN-based simulation of a terahertz spectrum with water-vapor absorption and the spectrum of the SLD-driven CCS system employing a highly accurate delay unit. The differing slopes and absolute amplitudes of the spectra are due to the systems characteristics. The agreement of absolute frequencies as well as the linewidths of the absorption features demonstrate the applicability to gas spectroscopy.

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To demonstrate the applicability of the proposed measurement principle to gas spectroscopy, we replaced the rather inaccurate voice-coil-driven delay line used for the measurements so far with an accurate stepper-motor-based delay line and measured the well-known absorption features of water vapor in ambient air. A cutout of the acquired spectrum is shown in Fig. 6 along with a simulated terahertz spectrum using the HITRAN database [28]. The absolute frequencies as well as the spectral width of the absorption features agree within the given signal quality. The widths of water-vapor absorption lines under ambient conditions are in the range of a few GHz, which clearly demonstrates the advantage of the proposed setup compared to CCS systems with multimode laser diodes, whose free spectral range are in the range of several tens of GHz to more than 100 GHz. These systems clearly couldn’t resolve these narrow features. The employment of even more accurate delay units [29] and demonstration on gases with spectrally narrower absorption features is a future task.

4. Conclusion and outlook

We have demonstrated a spectrally continuous terahertz spectroscopy system by using temporally incoherent light for driving a terahertz cross-correlation spectroscopy setup. The output of a superluminescent diode, which is inherently continuous (due to the lack of an optical cavity) was used for demonstrating this principle, but can replaced with any incoherent light source of comparable spectral width and sufficient optical power. The use of the spectral filter and the EDFA is not mandatory for this measurement principle, but improves efficiency and provides the flexibility to adapt the accessible terahertz spectral range. The fundamental applicability to standard terahertz measurement tasks was demonstrated by spectroscopic measurements of well-known samples. The systems performance is not yet comparable to that of standard TDS systems, but broadens the conceivable methods for terahertz spectroscopy. Further improvements of the systems performance can be expected from the development of terahertz sources and detectors for CW photomixing. The improvement of spectral quality will be achieved by employing more accurate delay units [29].