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Abstract
We present a fiber-coupled terahertz quasi time-domain spectroscopy system driven by a laser with a central wavelength of 1550 nm. By using a commercially available multimode laser diode in combination with state-of-the-art continuous wave antennas, a bandwidth of more than 1.8 THz is achieved. The peak signal-to-noise ratio is around 60 dB. A simulation based on the optical spectrum of the laser diode and the transfer function of the THz path is in agreement with the experimental results. The system is used to extract the refractive index from two different samples and the results indicate that the performance is up to 1.8 THz comparable to a terahertz time-domain spectroscopy system.
© 2017 Optical Society of America
1. Introduction
Over the last years terahertz (THz) time-domain spectroscopy (TDS) systems have evolved into reliable, commercially available products [1–3]. Nevertheless, for many industrial applications the cost of these systems still hinders their widespread use. The most expensive component of a THz TDS system is the femtosecond laser which is needed to excite the photoconductive THz antennas. Hence, it is highly desirable to find a more cost-effective light source. The potential cost savings are up to 50% of the total system cost [4]. In contrast to THz TDS systems, continuous wave (cw) THz systems can be realized using low cost diode lasers. One of the advantages of cw THz systems is their high spectral resolution which depends on the laser linewidth [5]. Besides, if only one frequency is detected, fast imaging is possible [6]. Yet, a high frequency resolution calls for wavelength stabilization of the driving lasers. This makes the system more complex and expensive.
A promising alternative is quasi time-domain spectroscopy (QTDS). This measurement technique is based on photomixing of the optical beat signal caused by the multiple modes of a laser diode [7–10]. With this technique it is possible to generate pulse-like signals in the time-domain similar to what is obtained from a THz TDS system. Thus, a single measurement contains the information over the full spectral bandwidth. So far, only free-space systems have been demonstrated utilizing optical excitation at 800 nm. Reported signal-to-noise ratios are around 50 dB with bandwidth smaller than 1 THz. Molter and associates [11] used a more complex setup with two laser diodes in an external resonator and achieved around 1.5 THz bandwidth. A THz QTDS system has also been used for imaging applications [12].
Due to the availability of reliable and cost-effective components at 1550 nm from the telecommunications industry, commercially available photoconductive THz antennas often utilize this wavelength. There are high-performance fiber-coupled THz antenna modules available [13]. Consequently, very robust systems can be designed which are suited for applications in industrial environments [3]. Therefore, to achieve compatibility with the aforementioned fiber-coupled THz antennas, we use a multimode laser diode emitting at a central wavelength of 1550 nm.
Here, we demonstrate a THz QTDS system with a bandwidth of 1.8 THz with a dynamic range of 60 dB for frequency components below 300 GHz. This constitutes a considerable improvement compared to previous QTDS measurements [7,9] and shows the potential of this measurement technique.
2. Theoretical background
2.1 Photomixing mechanism
The photomixing process employed in this work generates THz radiation by modulating the photoconductivity of the emitter antenna [10]. Together with an applied bias voltage the laser-induced conductivity modulation creates a varying current Jemi in the antenna’s active region. The accelerated charge carriers lead to the emission of THz radiation:
Assuming sufficiently small carrier lifetimes/transit times within the emitter antenna, the conductivity (and in turn, the current) approximately follows the envelope Ieff of the incident laser intensity I:When using a laser diode with multiple longitudinal modes, the laser light is the sum of many individual oscillations with a difference frequency Δω, given by the round-trip time of the laser. Due to the dependence on the laser intensity photomixing is comparable to a non-linear process: it generates constant terms, second harmonics, sum frequencies and difference frequencies. However, the electrons in the antenna can only follow the slowly oscillating frequency components, turning the emitter antenna into a lowpass filter. In effect, all terms but the difference frequencies can be neglected in the resulting expression:Here, Ai, ωi, and φi denote amplitude, frequency and phase of the i-th laser mode. In total, there are N laser modes. Δφij is the phase difference between modes i and j.The resulting THz signal will thus consist of multiples of the difference frequency Δω of the laser light used for excitation. The largest achievable frequency component is (N-1)Δω, i.e. it is approximately given by the bandwidth of the laser used for excitation.
Detection is done coherently with a photoconductive antenna. The same laser beam that is used for emission is also used for detection, only a variable time shift between both is introduced. Assuming all the above approximations, the resulting current signal is proportional to the convolution of the THz electrical field with the laser-modulated conductivity σ of the detector antenna [10]:
The last relation arises from the above expression for and the approximation that the conductivity follows the laser intensity. As the authors of Ref [10]. have derived, in the frequency-domain this can be expressed asThe cross-correlation thus removes all phase information which is contained in the laser light, only the amplitude information remains. This results in a pulse-like shape of the detected signal in the time-domain. Only the phase which is introduced by the THz beam path remains in the signal.2.2 Simulating the detected signal
To calculate the expected shape of the signal, the above expression for the detector current in the frequency-domain in Eq. (5) is used as a starting point. The only information that we then need is the optical spectrum of the laser diode and the transfer function of the THz beam path. This information is sufficient to calculate the expected THz QTDS time-domain trace.
A model optical spectrum is generated from the actual measurement of the laser’s spectrum with an optical intensity spectrum analyzer. The laser’s line shape is assumed to be Gaussian, for the simple reason that convolution operations on Gaussians are mathematically very simple and fast:
The laser’s intensity in the frequency-domain can then be derived from the definition in the time-domain:The calculation is then continued according to the expression derived for the detector antenna current, but also taking an additional complex transfer function H(ω) of the THz beam path into account:The transfer function is extracted from a cw THz measurement using the same emitter and detector as in the subsequent QTDS measurements. Due to phase noise, the noise resistant phase unwrapping algorithm presented in [14] is applied twice with parameters τ1 = 0.988 and τ2 = 0.614.Typically, measured optical spectra do not have the required resolution to accurately determine the spectral line width of the individual modes. Therefore, the spectral line width needs to be optimized so that the envelope of the simulated THz signal matches the envelope of the measurement.
3. Experimental setup
In order to conduct the QTDS measurements at 1550 nm, we use the experimental setup shown schematically in Fig. 1. To demonstrate the feasibility of a low-cost laser we use a commercially available multimode laser diode (Thorlabs FPL1055T) with a central wavelength of 1550 nm. The emitted radiation is coupled into a single mode fiber using a fiber collimator. A fiber-based 50:50 beam splitter divides the optical radiation into two arms. To sample the emitted THz signal, a fiber-coupled free-space delay unit is incorporated into the optical arm leading to the detector. Since the emitter and detector antenna are sensitive to the polarization of the irradiating light, they are connected with polarization maintaining (PM) fibers. This requires the use of a fiber-based polarization controller and polarization filter beforehand. The emitted THz radiation was collimated and then focused onto the detector by two off-axis parabolic mirrors with a focal length of 76.2 mm. The total length of our THz path is approximately 0.3 m.
Fig. 1 Schematic of the experimental setup used for the QTDS measurements. The setup consists of a commercially available multimode laser diode which is coupled into a single mode (SM) fiber and split into two optical arms. The optical arm leading to the detector (THz-Rx) contains an optical delay unit. The THz emitter (THz-Tx) and detector require linearly polarized light and are fiber-coupled with polarization maintaining (PM) fibers. In order to ensure the correct polarization, we use a polarization controller and filter.
In this setup, we use THz antennas that are optimized for the generation and detection of cw THz radiation. Since QTDS is the extension of photomixing from two to multiple frequencies, these antennas should be well-suited for the generation and detection of multi-cw THz radiation. The emitter utilizes an InGaAs-based pin-photodiode combined with a bow-tie antenna [13]. The bias voltage of the emitter photodiode is −1.5 V. It is modulated at 15 kHz to enable lock-in detection. For the detector a photoconductor based on low-temperature grown Be doped InGaAs is used [13]. This photoconductive material exhibits ultrafast carrier trapping so that the THz radiation can be sampled with a high temporal resolution. The photoconductive gap of the detector has a width of 10 µm and contains interdigitated fingers [13]. The details of the experimental setup used for the cw THz measurements are described elsewhere [15]. The spatial position of the THz antennas and the THz beam path were kept unchanged for both cw and QTDS measurements.
4. Experimental results and discussion
In this section, we present our measurement results. First, we discuss the operating conditions of the multimode laser diode and analyze its optical spectrum. We investigate the effect of low optical power on the performance of our THz antennas in cw THz measurements. Then we turn to the actual QTDS measurements and investigate the obtained THz signal in the time and frequency domain. We compare these QTDS measurements with the results obtained from cw THz measurements using the same THz photomixers and show that our simulation of the QTDS signal is in good agreement with the measured data. Finally, we show that thickness measurements are one possible application for our QTDS setup and compare the results to a state-of-the-art THz TDS system.
The maximum suitable injection current for the employed multimode laser diode is 500 mA. The laser diode drive current was limited to 490 mA in order to avoid damaging the laser diode and obtain the largest possible output power. Directly after collimation we measured 80 mW of optical power. With a coupling efficiency of 50%, we were able to couple 40 mW average power into the single mode fiber. The spectrum of the multimode laser diode was measured with a spectral resolution of 0.06 nm (approx. 7.5 GHz) using an optical spectrum analyzer (84610B by Agilent Technologies) and is shown in Fig. 2. As can be seen, the laser diode emits multiple modes with a constant frequency spacing of approx. 45 GHz. The full width at half maximum (FWHM) of this spectrum is roughly 8.8 nm which corresponds to 1.1 THz (see inset of Fig. 2). Thus, we expect frequency components of at least 1 THz in our QTDS spectrum.
Fig. 2 Optical spectrum of the multimode laser diode at an injection current of 490 mA. The spectral resolution of this measurement is 0.06 nm which corresponds to approx. 7.5 GHz. The inset illustrates the FWHM of 8.8 nm.
Due to the accumulation of losses in the QTDS setup, originating from insertion losses into the fiber, the optical delay unit and losses due to the polarization controller and filter, the maximum available optical power at the emitter and detector antenna is only 9 mW and 3.5 mW, respectively. However, the optimal operating conditions for the THz antennas are 30 mW of optical power at the emitter and detector. Therefore, we checked the performance of the THz antennas in cw THz measurements for low optical excitation power. Figure 3 shows a comparison between a measurement with 30 mW at the emitter and detector (black curve) and with 9 mW at the emitter and 3.5 mW at the detector (red curve). The horizontal lines correspond to the measured noise current in the illuminated detector with a deactivated emitter. Both spectra were obtained with an integration time of 300 ms and a frequency step size of 1.25 GHz in a setup as described in [13]. As can be seen in Fig. 3, the cw THz spectrum at 3.5 mW at the detector is identical to the spectrum at 30 mW, only shifted to lower power.
Fig. 3 Measured cw THz spectra for two different optical excitation powers. For both measurements the emitter is biased with −1.5 V at 15 kHz. The optical power at the detector is given in the figure. An integration time of 300 ms is used. For the black spectrum the optical power at the emitter is 30 mW, for the red spectrum 9 mW. The horizontal lines correspond to the noise level of the illuminated detector antenna without any incident THz radiation.
The lower optical power at the emitter reduces the emitted THz power and thus the measured current in the detector antenna. However, as shown in Fig. 3, at the same time the lower optical power reduces the noise level and partly offsets the lower THz power in terms of signal-to-noise ratio (SNR). Therefore, also at the lower optical power available from the multimode laser diode the THz antennas show an excellent performance with a bandwidth of greater than 3 THz and more than 80 dB SNR around 300 GHz. Consequently, the application of these THz antennas in our QTDS setup seems promising.
The alignment of the antennas is done with our cw THz setup for which reference spectra exist. After the initial alignment and the measurements described above with the cw setup, the position of the antennas is kept unchanged for the QTDS measurements. Therefore, we are able to use the cw THz measurements to extract the antenna characteristics of the emitter and detector as well as the characteristics of the THz path. These results will be used later on for our theoretical model.
As the next step, we use the setup as illustrated in Fig. 1 and couple the multimode laser diode into the THz system. Exemplary results are shown in Fig. 4. As in the cw THz measurement, we use a bias voltage of −1.5 V modulated at 15 kHz to drive the emitter. The detector signal is additionally amplified by a transimpedance amplifier for the lock-in process. We used an integration time of 30 ms and a step size of 100 fs for the optical delay unit. One measured time-domain pulse trace is exemplarily shown in Fig. 4(a) and its Fourier transform in Fig. 4(b). As can be seen, the optical beat signal caused by the interference of the multiple modes of the laser diode is translated into a periodic, pulse like THz signal in the time-domain. The period of this signal is approx. 23 ps and is caused by the length of the laser resonator, i.e. the round trip time of the laser diode. From the corresponding Fourier spectrum it can be seen that multiple discrete frequencies have been created by the mixing of the multiple modes. These discrete components have a spacing of approx. 43.5 GHz which corresponds to the frequency spacing of the laser diode. For the first time, we were able to detect frequency components up to 1.8 THz with a QTDS setup.
Fig. 4 Quasi time-domain spectroscopy measurements in the time- (a) and frequency-domain (b) for 9 mW at the emitter and 3.5 mW at the detector. The lock-in integration time is 30 ms and the step size of the optical delay unit 100 fs. A bandwidth greater than 1.8 THz and a SNR of 60 dB at 300 GHz is achieved.
For the lock-in integration time of 30 ms a peak signal-to-noise ratio of 60 dB is demonstrated below 300 GHz from a single measurement as shown in Fig. 4(b).
Furthermore, we simulated the QTDS signal using only the measured optical spectrum of the laser diode and the extracted antenna and THz path characteristics from the previous cw THz measurements. In Fig. 5 we show the comparison between the measured and the simulated QTDS signals. As can be seen, our model accurately predicts both the pulse trace in the time-domain and the corresponding spectrum.
Fig. 5 Comparison between the measured data (black) obtained by QTDS and the simulated data (red) based on the optical spectrum and the extracted antenna and THz path characteristic both in the time- (a) and frequency-domain (b). As can be seen, measurement and simulation are in good agreement.
The main difficulty in reproducing the measured signal in the simulation is the extraction of the phase characteristic of the THz transmission path. Phase noise and water absorption lines in the cw THz measurement have considerable impact on the phase unwrapping algorithm. Hence, the noise-resistant phase unwrapping algorithm presented in [14] has been applied twice to the acquired cw THz phase, first with a weak filter influence and then with a stronger filter characteristic. The algorithm effectively acts as a first-order infinite impulse response low-pass filter with control parameter τ≤1 during phase unwrapping. τ controls the bandwidth of the filter: smaller values will decrease the bandwidth, whereas τ = 1 disables the filtering characteristic of the algorithm.
In this work, we have used a Nelder-Mead minimization algorithm to find the filter coefficients producing the best match between simulation and measurement [16]. We obtained τ1≈0.988 and τ2≈0.614 for the two iterations. Manual experiments with the filter coefficients have shown that too little filtering will produce seemingly noise-like time-domain traces, while too much filtering will produce distinct, but unrealistic, periodic waveforms. Thus, there seems to exist a “sweet-spot” of filter coefficients which makes the simulation approach the measurement. As would be expected, the filter only affects the phase spectrum. The power spectrum is the same regardless of whether the noise-resistant phase-unwrapping is used or not.
Finally, to prove the applicability of our low-cost THz system to non-destructive testing problems, we confirm that the QTDS approach is able to perform thickness measurements with a high resolution. This is due to the pulse-like nature of the QTDS signal and the large bandwidth of our signal. The device under test will cause a delay of the pulses in the time-domain and a reduction of the amplitude as the THz radiation will be reflected and absorbed. Figure 6 shows the extracted refractive index of a polyoxymethylene (POM) sample and of a thin ceramic film. The refractive index was calculated both from QTDS measurements and for comparison from a conventional THz TDS measurement. As can be seen, both approaches yield the same refractive index of approx. 1.4 for the POM sample and 3.1 for the ceramic film. The extracted refractive index for both samples is nearly constant over the frequency range from 0 to 1.8 THz. These results confirm that the QTDS approach is useful for non-destructive testing. The fiber-coupled 1550 nm THz QTDS system has significantly lower cost than typical THz TDS systems. In turn, for an industrial production process with a material system with known refractive index this implies that QTDS measurements can accurately determine sample thickness.
Fig. 6 Extracted refractive index of a polyoxymethylene (POM) sample and a ceramic film. The refractive index was calculated from both QTDS and TDS measurements. As can be seen, both approaches yield the same values of the refractive index over the full frequency range for both samples.
5. Conclusion
We have presented a THz QTDS system with fiber-coupled antennas. The commercially available multimode laser diode was fiber coupled and had an optical 3 dB bandwidth of 1.1 THz with a central wavelength of 1550 nm. The measured THz signal had a bandwidth of up to 2.0 THz with a peak SNR of 60 dB around 300 GHz. The experimental data could be successfully reproduced by a numerical model which used the optical spectrum of the laser diode and the transfer function of the THz path as input quantities. The transfer function of the THz path was retrieved from a cw THz measurement with two frequency controlled laser diodes.
The QTDS system was used to determine the refractive index of a ceramics and a POM sample. The results were compared to the data retrieved from a state-of-the-art THz TDS system (see e.g [3].). The evaluated refractive index from both systems showed similar refractive indices up to 1.8 THz. The SNR was limited in this experiment by the low optical power at the emitter (9 mW) and detector (3.5 mW). We expect an increase in SNR and bandwidth if more power is delivered to the antennas. This can be achieved by using a laser diode with a higher output power or through the use of PM only components.
A drawback of THz QTDS is the discrete frequency resolution originating from the large mode spacing of the employed monolithic laser diode. The frequency spacing between the discrete THz lines can be reduced by using monolithic laser diodes with a longer cavity or an external resonator [17]. However, for many applications like the determination of the thickness of painting layers or the water content in diesel oil, a high spectral resolution is not required [18,19]. In conclusion, we demonstrated that THz QTDS systems are an interesting low-cost alternative to established THz TDS systems.
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