In this section, the transceivers are characterized as sensor heads in THz TDS measurements in reflection geometry. In
Section 3.1, we investigate THz transceiver chips with varying gap sizes in order to determine the optimal combination for high bandwidth emission and high dynamic range. Furthermore, the performance of the THz TRX is compared with a THz reflection head consisting of separate, state-of-the art emitter and receiver modules. In
Section 3.2, the TRX is employed for THz imaging experiments. Due to the confocal geometry of the THz transceiver, the focal length of the parabolic mirror used for focusing the THz radiation on the DUT can be changed easily in order to increase the lateral resolution of the image.
3.1. Characterization of the THz Transceiver
In this section, THz transceivers with three different photoconductive gap sizes are compared. In order to facilitate the optical coupling of the transceiver chip inside the sensor head, the gap size of the emitter and the receiver part of the TRX were chosen to be equal (cf.
Figure 2). In
Figure 3a, the measurement setup that was used for all THz TDS measurements in reflection geometry with fiber-coupled THz transceiver modules is shown: the emitted radiation, which is divergent with an angle of ±15°, is collimated by a parabolic mirror with 3″ focal length and reflected from a planar, gold-coated mirror back onto the transceiver.
Figure 3b compares the THz spectra for InGaAs:Fe based transceivers with a gap size of 15 µm (light green), 20 µm (dark green), and 25 µm (black), respectively. Note that all InGaAs:Fe based transceivers exhibit a bandwidth of more than 6 THz and a peak spectral power ≥80 dB in comparison to the high frequency noise floor >7 THz. This is a significant improvement compared to the best transceiver results published so far: in [
14], a similar, monolithically integrated THz transceiver based on low-temperature-grown, Be doped InGaAs was presented. This LTG-InGaAs:Be based transceiver achieved a bandwidth of 4.5 THz and a peak power of 70 dB. For comparison, the THz spectrum of such a transceiver is shown in
Figure 3b in blue. Thus, the InGaAs:Fe TRX presented here increases the bandwidth and spectral power by more than 1.5 THz and up to 20 dB, respectively. These improvements stem from the superior electrical and dynamic properties of the InGaAs:Fe photoconductive material as discussed in
Section 2.1.
As shown in
Figure 3b, the difference between 20 and 25 µm wide gaps is relatively small, whereas a significant increase (≈10 dB) in spectral power is obtained for the smallest employed gap size of 15 µm. For this antenna geometry, a bandwidth of 6.5 THz in combination with a normalized spectral power of 90 dB at 1 THz is achieved.
In order to analyze the properties of the presented THz transceiver further, we characterized emitter and receiver part of the TRX separately. First, we studied the emitted THz pulse amplitudes of the emitter part detected by a separate, state-of-the-art LTG-InGaAs:Be/InAlAs:Be based THz receiver. As shown in
Figure 4a, the emitted amplitude as a function of optical power is higher for the TRX with the 15 µm wide gap versus 20 µm gap size. Furthermore, as
Figure 4b shows, the detected THz pulse amplitudes are also larger for the smaller photoconductive gap. Since the noise level is approximately equal for the two gap sizes (cf.
Figure 4c), the transceiver with the smaller gap size shows the overall best performance (cf.
Figure 3b). Since the applied bias field was kept constant at 40 kV/cm for the emitter, we attribute the higher emitted THz pulse amplitudes to the higher carrier density induced by the optical excitation due to the smaller gap size. For the receiver part, we attribute the higher detected THz pulse amplitudes to the higher induced carrier density and also to a higher induced field in the antenna for a given incoming THz field strength. Both carrier density and induced field strength are increased due to the smaller photoconductive gap size.
Second, since the midpoints of the TX and RX photoconductive gaps on the TRX chip are separated by 45 µm only (see
Figure 2), we investigated the influence of an active emitter part on the performance of the receiver part of the TRX. For these measurements, we split the optical beam leading to the emitter part of the TRX into two arms with equal optical power. While one of these arms kept exciting the emitter part of the TRX, the other optical beam was used to drive a separate, fiber coupled emitter. In this configuration, we can characterize the receiver part of the TRX with the separate emitter, while the emitter part of the TRX could be switched on and off.
Figure 5a shows the time-domain signal detected by the receiver part, when the separate emitter was switched off and the emitter part of the TRX was on (light green) or off (dark green). As can be seen, the active emitter part leads to a pronounced background in the receiver signal, which is caused by direct cross-talk between the emitter and the receiver through the substrate of the TRX chip. However, the peak-to-peak amplitude of this background is less than 5% of the THz pulse amplitudes shown in
Figure 4a,b. In addition, the background is static and, therefore, it can be subtracted from the measurement signal. This procedure is applied for the measurements shown in
Figure 5b: first, the THz path between the separate emitter and the TRX receiver was blocked in order to record the background when the emitter part is switched on and off. Next, this background was subtracted and the noise floor was determined by measuring the same configuration with a blocked THz path again. In
Figure 5b, the noise floor for the emitter part switched on (black) and off (blue) is shown. As can be seen, the spectral noise floor of the TRX with the emitter part switched on (black) is spectrally flat between 1.5 and 8 THz. Hence, the dynamic range in in this frequency range remains almost as high as for the deactivated TRX emitter part. Below 1.5 THz, an activated TRX emitter causes excess noise reducing the dynamic range in this range. The dynamic range is calculated by dividing the power spectra by the noise spectra, which were obtained by blocking the THz path after subtracting the static background.
Finally, we compare the transceiver module with a reflection head consisting of an individual, state-of-the-art InGaAs:Fe based THz emitter and a LTG-InGaAs:Be/InAlAs:Be based receiver module.
Figure 6a shows a photograph of the reflection head next to the fiber coupled transceiver module. The reflection head uses four parabolic mirrors to collimate the emitted THz radiation, focus it onto the sample and redirect the reflected pulse toward the THz receiver. Thus, the THz path within this reflection head is angled. Note that with a diameter of only 30 mm the fiber coupled transceiver module is significantly smaller than the reflection head.
In
Figure 6b the normalized pulse traces detected with the reflection head (dark green) and the transceiver (light green) are compared. The shape of the two pulse traces is almost identical although the reflection head uses two individual THz modules and has an angled THz beam path, while emitter and receiver are integrated in very close proximity to each other on the TRX chip. This is mainly because InGaAs:Fe photoconductors from the same wafer were used for the individual THz modules and the THz transceiver. In addition, transceiver and reflection head were operated under the same excitation conditions with the same THz TDS system. Hence,
Figure 6b clearly demonstrates that the integrated transceiver does not have any detrimental effect on the THz pulse trace. The small differences between the two pulse traces are attributed to differing optical coupling schemes inside the fiber-coupled modules leading to slightly different optical excitation powers in the reflection head and the transceiver, respectively.
Figure 6c shows the corresponding dynamic range over the whole THz spectrum. The dynamic range is calculated by dividing the power spectra by the noise spectra, which were obtained by blocking the THz path after subtracting the static background. Both reflection head and transceiver show a THz bandwidth of >6 THz. The peak dynamic range of the reflection head is 80 dB at 1.25 THz, while the transceiver reaches 75 dB peak DNR at 1.25 THz. Note that this is a record-high value for integrated THz transceivers. In comparison to the LTG-InGaAs:Be based transceiver presented in [
14], the TRX presented in this paper features a 20 dB higher dynamic range and a 1.5 THz higher bandwidth. In comparison to the reflection head, the dynamic range of the transceiver is only 5 dB lower. In addition to the increased cross-talk between emitter and receiver, which has been discussed above, the single chip transceiver requires another important compromise: for individual antennas, the best performance could be achieved when the photoconductive gap of the emitter is larger (25 µm wide) than the gap of the receiver (10 µm wide). However, the optical coupling scheme with the polymer waveguide chip in the TRX creates optical spot sizes with equal diameters. Hence, equal gap sizes have to be used for emitter and receiver on the TRX chip, which reduces the performance of the TRX slightly. In addition, the simultaneous alignment of two photoconductive gaps in the TRX is more challenging than aligning a single gap for individual emitters and receivers. Regardless of all these challenges in the design and packaging of a fiber-coupled transceiver head, the performance of the TRX is quite close to the reflection head. In addition, the transceiver benefits from its collinear THz beam path and its small footprint, which makes it a perfect tool for reflection measurements in industrial environments. In the next paragraph, we will show how an integrated transceiver with collinear geometry can facilitate terahertz imaging experiments significantly.
3.2. THz Imaging with a THz Transceiver Module
Many interesting samples for THz imaging allow measurements in reflection geometry only. Without employing advanced near-field techniques to break the diffraction limit, the lateral resolution of THz images is inherently limited by the relatively long wavelengths corresponding to the THz frequency range: in air, the frequencies between 100 GHz and 5 THz correspond to wavelengths of 3 mm to 60 µm.
Here, we employ the fiber-coupled THz transceiver in a THz imaging setup in reflection geometry and demonstrate an improved lateral resolution compared to the reflection head with separate THz modules and angled beam path. The benefit of the integrated transceiver for this measurement is its collinear geometry, which means that only two parabolic mirrors are needed for measurements in reflection geometry: the first mirror collimates the emitted radiation; the second focusses it on the sample, from where the THz pulses are reflected back onto the receiver part of the TRX. Thus, in contrast to two individual THz modules, no angled beam path or beam splitter is necessary. Furthermore, the collinear geometry of the transceiver allows for changing the focal length of the focusing parabolic mirror without major changes of the THz beam path. Thereby, the lateral resolution of the image can be increased due to a smaller beam waist for a shorter focal length.
In the THz imaging setup, a flat sample is raster scanned with an x-y-stage with a pixel spacing of 50 µm. Full pulse traces with a duration of 70 ps were recorded for each pixel. The sample consists of a ceramic substrate patterned with a relief-like structure (see photograph in
Figure 7, top row). The bright squares in the photograph are elevated by 0.5 mm compared to the dark background. The top row of
Figure 7 compares the amplitude images for 4″, 2″, and 1″ focal lengths. Note how the resolution of the THz image is improved for parabolic mirrors with shorter focal length. The second row of
Figure 7 shows the photograph and THz image of a gold-coated ceramic sample. For all of the shown THz images we used a Bessel type high-pass filter at 1.5 THz, leading to an effective spectral maximum around 1.7 THz. Only with the new InGaAs:Fe based transceiver, which exhibits a spectral maximum around 1.2 THz and significantly increased spectral power for frequency components above 1.5 THz, this high-pass filtering becomes feasible.
The minimum beam waist of a Gaussian beam is closely related to the resolution of an image acquired with it. The beam waist radius
w behind a lens/mirror is given by the following equation [
26]:
here,
λ,
f, and
D denote the wavelength, focal length of the mirror, and diameter of the mirror. Thus, the smaller the ratio of focal length to diameter, the smaller the beam waist and the better the lateral resolution. In the reflection head for fiber-coupled THz modules shown in
Figure 6a, a parabolic mirror with 1″ diameter and 4″ focal length is used. For this configuration, for the frequencies 0.5, 1, and 2 THz (corresponding to wavelengths of 600, 300, and 150 µm, respectively) beam waist radii of 1.53, 0.76, and 0.38 mm result. However, with a 1″ focal length these values could be improved by a factor of 4 to 380, 180, and 95 µm, respectively. Note that changing the focal length in the reflection head would also change the angle of incidence of the THz beam. Hence, the reflection head would have to be re-designed completely. In contrast, the collinear geometry of the transceiver allows for improving the lateral resolution, simply by changing the focal length of the focusing parabolic mirror.
To extract a quantitative measure of the resolution from the measurements, we analyzed the reflected amplitude as a function of distance at one edge of the ceramic sample, which corresponds to a d-cut through the confocal point spread function. The square of the measured peak-to-peak pulse amplitude as a function of distance is shown in
Figure 8 for the three focal lengths used. In order to get a quantitative value for the resolution, we fitted the following function to the data:
here, erf(
x) refers to the error function.
P(x),
P0,
x0,
w, and
O denote the intensity as a function of distance, maximum intensity, offset in distance, width of the point spread function, and offset in power, respectively.
P0,
x0,
w, and
O are fit parameters. Usually, Equation (2) is applied for the knife-edge test of a Gaussian beam and results from the integration over a partially blocked Gaussian intensity profile [
27]. Assuming a Gaussian THz beam profile, this equation also applies to the reflected THz power at an edge. Note that
w is an arbitrary measure of the resolution and does not correspond to the real beam waist of the THz beam. Nevertheless, whatever the resolution criterion is, it can be assumed that it scales similarly to
w. The fitted values of
w are 310, 200, and 130 µm (also given in each graph of
Figure 8). Hence, the image resolution could be improved by a factor of 2.4 by simply changing the focal length of the focusing mirror from 4″ to 1″. From Equation (1), optimally, one could have expected an improvement by a factor of four in the THz beam waist, translating into an equivalent improvement in resolution. However, the measured confocal point spread function comprises all the deviations from an ideal geometry of both emitter and receiver, reducing the nominal improvement in resolution. The largest error results from the fact that the dimensions of the edge were too small for the largest focal length used to accurately determine the point spread function. Therefore, this value of
w is not fully comparable to the other two focal lengths. The finite separation between emitter and receiver on the transceiver chip could be an additional source of error. Of course, typical effects of non-ideal optical setups such as cut-off of the beam due to a limited diameter of the mirror are present as well.
Nevertheless, due to its collinear geometry the presented compact, fiber-coupled THz transceiver is a promising tool for high-resolution THz imaging applications.