Abstract

We demonstrate a free space two-port photonic vector network analyzer capable of measuring the scattering parameters of devices and materials in the terahertz range with a frequency coverage of 0.2 - 2 THz in a single system. It is based on photoconductive terahertz sources and detectors driven by a telecom-wavelength femtosecond laser. Being able to cover a bandwidth of one order of magnitude, the system is capable of performing S-parameter measurements deep into the terahertz range, beyond frequencies reachable by their electronic counterparts. We demonstrate high performance at three application examples, namely S-parameter measurements of a split ring resonator array and a distributed Bragg reflector, as well as material parameter extraction of several materials.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The Terahertz (THz) range (100 GHz - 10 THz), formerly referred to as the "Terahertz Gap", has long been an almost unexplored area of research. More recently, advances made in generation and detection of terahertz radiation have encouraged many researchers to exploit the opportunities offered in this area. Numerous applications in cross-disciplinary fields, such as, communication [1], biomedical science [2], security [3], imaging [4], industrial sensing [5], spectroscopy [6] etc. show recognition of the importance of terahertz radiation. This growing interest has created a huge demand for devices and components operating in the terahertz range. Nevertheless, the progress in this area of interest is heavily impeded due to a lack of efficient and affordable characterization tools required to benchmark developed devices and components.

In the microwave, millimeter-wave band, and recently the lower end of the terahertz range, the Vector Network Analyzer (VNA) is a well-established instrument for device characterization and development. A VNA measures the amplitude and phase of a reflected or transmitted electromagnetic signal through a device under test (DUT) in the frequency domain. Frequency coverage is usually achieved by sweeping the frequency through the entire band while recording frequency-dependent scattering (S) parameters. Then the S-parameters are compared directly to simulations or used to derive an equivalent circuit of the device to calculate how individual components affect the performance of the device. This provides valuable information regarding potential design errors, which, in turn, helps to improve the layout or components.

Although developed for testing at lower frequencies, VNAs composed of electronic components are now widely used at terahertz frequencies. With the help of frequency extenders, commercially available VNAs can now reach up to 1.5 THz [7]. These extenders include Schottky Diode based frequency doublers and triplers in a hollow core metallic waveguide configuration. They are used in both transmitter (for up conversion) and receiver (for down conversion) side of the setup. The hollow metallic waveguides are used for rejecting out of band noise while allowing for the integration of the planar Schottky diodes with transitions to microstrip waveguides or similar. However, they bear the main disadvantage: the bandwidth of the frequency-extended system is limited to about 50% of the center frequency due to the cutoff towards the lower frequencies and onset of the multi-modal behavior at the higher frequencies. Consequently, a broad frequency range analysis from 220 GHz to 1.5 THz requires at least 5 extenders [7], possibly more, to guarantee overlap of individual bands. This drastically increases the effort and time for wideband measurements as components have to be exchanged, aligned and calibrated multiple times. Furthermore, with each additional extender, the system becomes more and more expensive.

A potential solution to the bandwidth limitation is replacing electronic with photonic systems. Terahertz sources and receivers based on a photonic approach have enormously improved within the last decade, making them an excellent candidate for Photonic VNA (PVNA) concepts. A popular method of generating and detecting large bandwidth terahertz radiation involves systems using photoconductors, which can reach up to 6.5 THz under pulsed operation [8,9]. Commercial pulsed systems are yet frequently used for time-domain spectroscopy (TDS) to investigate the optical properties of materials over a wide frequency range [10]. A terahertz-TDS system records the amplitude and phase information of the terahertz signal transmitted through or reflected by the sample, yielding the transmission or reflection coefficient, respectively, which are analogous to $S_{21}$ and $S_{11}$ parameters. To date, several studies have reported terahertz-TDS systems capable of measuring one or two S parameters as useful tools for characterizing meta-materials [11], non-reciprocal devices [12], as well as electronic devices [13].

In this work, we present a complete two-port photonic vector network analyzer (PVNA) capable of obtaining a complete set of S-parameters simultaneously. We demonstrate that PVNAs do not require a rigorous calibration process. Also, we verify the principle of operation at several examples: we examine the S-parameters of a split ring resonator (SRR) array and a distributed Bragg reflector (DBR) and characterize two materials in terms of their dielectric properties. The results are then compared with literature (for dielectric properties) or simulation (for SRR and DBR) for validation. Within a small band of 220-330 GHz, the obtained data is also compared to commercial electronic VNA data.

2. Experimental setup

Each of the two ports of the system is composed of an ErAs:In(Al)GaAs based photoconductive slotline antenna that generates terahertz pulses and an ErAs:InGaAs based photoconductive H-dipole antenna receiver. All devices are driven with a modified Menlo C-fiber laser system operating at a center frequency of around 1560 nm with 90 fs pulse duration and a repetition rate of 100 MHz. The ErAs:In(Al)GaAs sources absorb the fs laser pulse altering its conductance at the same time scale. An applied DC bias gives rise to a photocurrent with terahertz components that is subsequently radiated. On the receiver side, the antenna receives the terahertz field, which biases the photoconductor. Similar to the source, the conductivity of the receiver is modulated by a laser pulse with a known time delay. This results in a mixing process with a DC component that is proportional to the received terahertz field strength convoluted with the optical pulse. Scanning the time delay essentially resolves the terahertz field [14]. Details about the photoconductors and their performances are discussed in [8]. Fig. 1 illustrates the setup of the PVNA. In order to drive four photoconductive devices, two fiber ports and an additional, phase-locked free-space port of the modified Menlo-C-fiber system are used. The fiber ports drive the receivers with 16 mW of power each, while the pulse emerging from the free-space port (maximum power of 350 mW) goes through a delay stage, is split in two, and then drives the sources with a power of 46 mW each. Parabolic mirrors and TPX lenses collimate the terahertz signal. In order to realize frequency-independent 3 dB couplers, two wire grid polarizers (WGP) are implemented on either side of the sample.

First, Tx1 emits vertically polarized light. WGP1 oriented at 45$^{\circ }$ (projected on the optical axis) and aligned under 45$^{\circ }$ to the optical axis turns the polarization to a diagonal state (linearly polarized at 45$^{\circ }$). WGP2 turns the polarization back to the vertical state. A part of the signal is reflected ($S_{11}$) by the DUT, back to WGP2. If the sample does not affect the polarization state, the signal goes through WGP2 without any alteration in the polarization. WGP1 then reflects 50% of the signal under 90$^{\circ }$ towards receiver Rx1 for detection. In a similar fashion, the transmitted signal ($S_{21}$) and the other S-parameters with signals emerging from Tx2 are recorded as the setup is symmetric. Due to the orientation of the wire grid polarizers, four changes in polarization (vertical to diagonal and vice versa), each corresponding to a loss of 3 dB, take place, accumulating to an overall loss of around 12 dB for each S-parameter.

 figure: Fig. 1.

Fig. 1. Experimental setup of two-port PVNA. The optical path of the free-space laser beam is shown in red, whereas blue regions portray the terahertz path. Black arrows show the path of the terahertz signal emitted by Tx1. A part of the signal is reflected from the DUT and detected by Rx1, whereas the other part is partially transmitted through DUT towards Rx2. And white arrows represent the same journey for the terahertz wave generated by Tx2. Tx = Transmitter, Rx = Receiver, WGP = Wire grid polarizer, DUT = Device under test.

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Rx1 receives two signals - one from Tx1, which is reflected from the DUT and another from Tx2, transmitted through the DUT. Similarly, Rx2 receives a signal each from Tx1 and Tx2, transmitted through and reflected from DUT, respectively. To distinguish the signals coming from different sources, their biases are modulated at different frequencies (11.17 kHz for Tx1 and 19.71 kHz for Tx2) and demodulated at those frequencies using the lock-in technique. Two lock-ins (Zurich Instruments MFLI-MD) with two demodulators each are used for this purpose. These lock-ins are synchronized to have an aligned time stamp. Both emitters are biased with 150 Volts (peak) sinusoidal signal originating from the built-in signal generators of the lock-ins followed by a high voltage amplifier. A low noise transimpedance amplifier from TEM Messtechnik (PDA-S) attached to both receivers converts the photocurrent to voltage prior to the readout. Furthermore, a graphic user interface is configured in-house to facilitate data reading and saving from four demodulators simultaneously in sync with the delay stage movement.

2.1 Calibration and performance

 figure: Fig. 2.

Fig. 2. The two-port PVNA has an available bandwidth of more than 2 THz, with maximum DNR of 51 dB at around 500 GHz. The measurements are done with an integration time of 100 $\mu$s per time step (ENBW = 937.6 Hz).

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Electronic VNA measurements require a proper definition of the calibration plane where the DUT will be mounted. The calibration ensures that the measurement result is not affected by any inductive, capacitive, or resistive contribution from the propagation path to the DUT and it further rejects any reflections inside the measurement system, such as, e.g. caused by impedance mismatches. "Short-Open-Load-Through" (SOLT) [15], "Through-Reflect-Line" (TRL) [16], "Line-Reflect-Line" (LRL) [17] are few of the standard procedures. Unlike $S_{21}$ measurements with VNAs, transmission data recorded with TDS systems only require a measurement of the empty setup as reference (corresponding to a "through" measurement) without any further calibration. The reason is that for an electronic VNA, the Smith chart must be calibrated to and corrected for the respective waveguide connecting the DUT. For a TDS system, the propagation takes place in air with a very well-known wave impedance of 376.7 $\Omega$. This technique is adapted for the PVNA. Prior to placing the DUT, calibration references for the empty setup are recorded, corresponding to a "Through" or a "Line" calibration. Subsequently, a "Reflect" calibration is performed by putting a metal surface at the DUT position. Again, a third calibration is not necessary due to the very well-known wave impedance of the propagation path.

The transfer functions and, subsequently, the S-parameters are obtained from the ratio of DUT signals to their corresponding reference signals. All four S-parameters can be recorded synchronously. The modulation frequencies are separated by approximately 8 kHz (11.17 kHz and 19.71 kHz), whereas the 3 dB bandwidth of the low pass filter used in the lock-in is around 811.5 Hz. Moreover, due to temporal separation, transmitted and reflected signals arrive at the receiver at slightly different times. As the receivers are operated far below their saturation regime, these measures ensure cross-talk free measurement of the S-parameters. Also, there is no cross-talk within the emitter structures which may be perturbed by receiving a reflected THz wave. The bias generated by receiving a reflection is at worst 7 orders of magnitude smaller than the applied DC bias. However, due to the presence of four wire grid polarizers and the sample holder in the terahertz path, some minor scattering and reflections occur despite mounting the wire grids under an angle. These are particularly visible at lower frequencies in the $S_{11}$ and $S_{22}$ parameters with a relative strength of about -30 dB at 500 GHz. $S_{12}$ and $S_{21}$ are essentially free of undesired reflections down to 300 GHz. Similar to a classical electronic VNA, these reflections are calibrated out by the reference measurements.

Fig. 2 illustrates that the available bandwidth of the system for all four paths is more than 2 THz for an integration time of 100 $\mu$s per time step with a wait time of 900 $\mu$s between subsequent points and a system spectral resolution of 7.14 GHz. The peak dynamic range around 500 GHz is approximately 51 dB. To the knowledge of the authors, there are no commercially available extenders for electronic VNAs above 1.5 THz where the PVNA can still operate. In terms of DNR, the commercial, electronic VNA is superior in the lower terahertz range, where it can reach more than 100 dB in the 26 - 750 GHz range. However, for a state-of-the-art electronic VNA with WR 0.65 extender (1.1 - 1.5 THz) of Virginia Diodes, Inc., the DNR is 40-60 dB, which is reduced to 25-45 dB for TxRx-TxRx configuration [7]. Our system is comparable, if not better, as we achieve 35 - 45 dB DNR within 1.1 - 1.5 THz range. With improved 3 dB couplers and reduced losses in the system, even much higher bandwidths are possible. The DNR is highly dependent on the integration time; by increasing the integration time, the DNR of our system can further be improved to some extent. With the same ErAs:In(Al)GaAs photoconductors, we have recently reported a dynamic range of a TDS system ($S_{21}$ measurement) of more than 100 dB at 500 GHz and 40 dB at 4 THz with an integration time of around 428 ms [18].

3. Results and discussion

Split ring resonators (SRRs) have been utilized in quite a few multidisciplinary sensing applications in the terahertz range [19,20]. A common application exploits the fact that both the resonance frequency and the quality (Q) factor of an SRR resonance change by adsorption of a substance under test. The frequency shift and quality factor degradation are a direct measure for the refractive index and the loss of the adsorbed material. A high Q resonance thus yields high sensitivity. Functionalization of the SRR surface enables specificity. We characterize an SRR array with a design similar to the one presented in [21] by exploring its S-parameters for both horizontal and vertical polarization of terahertz radiation. Fig. 3 depicts a section of the SRR array and the dimensions of a unit cell. It is patterned with gold ($d_{G}$ = 210 nm) and chromium ($d_{C}$ = 20 nm), on a low-loss quartz substrate of ($d_{Q}$ =) 212 $\mu$m thickness. Each ring has an inner radius ($r_{2}$) of 75 $\mu$m and an outer radius ($r_{1}$) of 100 $\mu$m with a periodicity ($x$) of the array at 300 $\mu$m. The ring asymmetry angle ($\theta$) is set to 10$^{\circ }$ for a gap size ($w$) of 23 $\mu$m.

 figure: Fig. 3.

Fig. 3. (a) Section of an SRR array and (b) design parameters of a unit cell. $x$ = 300 $\mu$m, $r_{1}$ = 100 $\mu$m, $r_{2}$ = 75 $\mu$m, $\theta$ = 10$^{\circ }$, $w$ = 23 $\mu$m, $d_{G}$ = 210 nm, $d_{Q}$ = 212 $\mu$m.

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The SRR array is placed in the collimated terahertz beam for recording all four S-parameters. Fig. 4 depicts the S-parameters for vertically polarized terahertz field ( Fig. 4(a)) and horizontally polarized field (Fig. 4(b)). The dashed grey lines represent the results of a simulation done using CST Microwave Studio. The main resonances are well reproduced. High Q-resonances, however, show reduced amplitude, particularly in the $S_{11}$ and $S_{22}$ data above 1 THz due to the limited resolution of the pulsed PVNA of 7.14 GHz (zero-padded resolution 3.66 GHz for better representation). Still, several double-peak structures are resolved in the $S_{11}$ and $S_{22}$ parameters.

 figure: Fig. 4.

Fig. 4. S-parameters of SRR. The measured data is depicted in blue, and grey dashed lines shows the simulated results. Two different polarization of incident terahertz wave is used to investigate the SRR, where figure (a) and figure (b) illustrate the S parameters retrieved for vertically polarized and horizontally polarized incident, respectively.

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A further example of a frequently used device is a distributed Bragg reflector (DBR) with applications in optical filters [22], surface-emitting lasers [23], photonic crystals [24], increasing efficiency of light emitting diodes [25], amongst others. It consists of alternate material layers with high refractive index contrast. The dimensions are chosen such that their thickness is $(2m-1)\lambda /(4n)$ at the design frequency, where $m$ is an integer and $\lambda$ is the design wavelength. Then, the partial reflections at each interface sum up constructively in reflection and destructively in transmission, yielding a band block filter for transmission with a pronounced stop band. Alternatively, the high index layers can be considered as resonators, weakly coupled by the low index material. From this perspective, the system represents coupled resonators with mode splitting [26] and resonances will also appear if the low index material is much shorter than $\lambda /(4n)$.

 figure: Fig. 5.

Fig. 5. The design of the investigated DBR. It comprises three Si layers with 520 $\mu$m thickness separated by air gaps of 150 $\mu$m.

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 figure: Fig. 6.

Fig. 6. S-parameters of DBR. Data measured using PVNA is shown in blue and theoretical calculation is represented by grey (dashed) line.

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This study investigates such a structure containing three Silicon wafers with a thickness of $d_{Si}=$ 520 $\mu$m, separated by an air gap of $d_{air}=$ 150 $\mu$m (corresponding to about 1/12 of the optical thickness of the HR-Si wafer) as depicted in Fig. 5. Fig. 6 illustrates the S-parameters of the Bragg reflector. The grey dashed line represents the theoretically calculated result. The PVNA data are in excellent agreement with the theoretical data in terms of the position of the stop bands and their attenuation ($S_{21}$ and $S_{12}$). From reflected signals ($S_{22}$ and $S_{11}$), it is noticeable that both simulation and experiment show multiple resonances in close proximity, as illustrated by the zoom-in. Despite the system resolution of only 7.14 GHz (3.66 GHz after zero-padding), the three resonances are clearly visible and in excellent agreement with the calculation. The origin of the substructures is the three individual silicon layers that represent coupled cavities with corresponding mode splitting [26].

3.1 Comparison with commercial electronic VNA

In order to validate the performance of the system, the obtained S-parameters are compared with the S-parameters retrieved using a commercial, electronic, frequency-extended VNA. The measurement is performed using Agilent Technologies PNA (N5222A) connected to a pair of Virginia Diodes, Inc. WR3.4 VNAX extender, which operates in the frequency range of 220 - 330 GHz. Horn antennas are used to transmit and receive the signals in free space.

The S-parameters obtained using both VNA and PVNA systems are compared in Fig. 7 and Fig. 8, where Fig. 7 shows the results for the SRR (vertical polarized incident wave) and Fig. 8 for the DBR. For both the cases, the $S_{12}$ and $S_{21}$ parameters of the PVNA and VNA measurements match perfectly. The $S_{11}$ and $S_{22}$ measurements of the SRR also show reasonably good matching. The main difference is oscillations in the electronic VNA due to standing waves combined with its high spectral resolution (11 MHz). For the DBR, the higher Q modes in $S_{11}$ and $S_{22}$ appear broadened due to the much lower spectral resolution of the PVNA (7.14 GHz system resolution; in Fig. 7 and Fig. 8 zero-padded resolution of 0.92 GHz is used for better representation). Further, these data are at the low edge of the spectrum, which may be affected by windowing of the Fourier transformation. Still, the resonances of the DBR are visible in both measurements, including the double peak structure around 255 GHz and there is a very good agreement between both measurement types. High Q resonances, compared with the simulations, show reduced amplitude and appear slightly shifted in frequency, both in the cases of PVNA and VNA measurements of SRR (Fig. 7) due to consideration of lossless material in simulation and geometrical imperfections in the produced SRR array. Still, there is a good match between the resonance modes of simulation and experiment. The measured S-parameters also exhibit excellent agreement to the theoretical calculation for the DBR (Fig. 8).

 figure: Fig. 7.

Fig. 7. S-parameters of SRR for vertically polarized incident terahertz signal, measured using PVNA (blue) and compared with the data acquired using VNA extender (black) and simulation (grey dashed).

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 figure: Fig. 8.

Fig. 8. Comparison between the S-parameters of DBR attained using PVNA (blue) and VNA (black). Theoretically calculated S-parameters are depicted by grey dashed lines.

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4. Permittivity extraction from PVNA measurements

Free space VNAs have been traditionally used to calculate material permittivity below 300 GHz [27]. Now with the availability of the frequency extenders, this method can also be used to extract parameters up to 1.5 THz [28,29]. Besides S-parameter measurements of THz devices, the PVNA data also allow for material’s parameter extraction by recording the S-parameters from a plane-plane cut dielectric. These are reciprocal in nature, implying $S_{12}$ = $S_{21}$ and $S_{22}$ = $S_{11}$. To determine the complex dielectric permittivity (or, alternatively, the complex refractive index) and DUT thickness simultaneously, we modified the algorithms reported by Taschin et al. [30] and Scheller [31], to use it for transmission and reflection data in conjunction.

As the first step, a preliminary thickness ($d_{p}$) is calculated from the position of the peaks in the time domain using the time of flight method. The time domain data show several peaks that are used for time of flight extraction of $d_{p}$. The distance between the reference transmission peak and the main DUT transmission peak is $\Delta t=(\bar {n}-n_{0})d_p/c_0$, where $\bar {n}$ is the mean refractive index of DUT, $n_{0}$ is the refractive index of air and $c_0$ is the speed of light. From the DUT recordings, there are several peaks visible, both in reflection and transmission, which are spaced by $\Delta t=2\bar {n}d_p/c_0$. These are due to round trips in the sample. For low-loss DUTs, such as HR-Si, $d_{p}$ and $\bar {n}$ estimated from these two equations are already very close to the real values. For materials with frequency-dependent loss, like PVC, or dispersive samples, the second reflected or even the first transmitted peaks feature a different shape as compared to the reference measurement due to a loss or a temporal shift of spectral components, respectively. Further, some of the peaks might not be visible anymore due to excessive attenuation after round trips in the DUT. In ref. [32], we have already demonstrated that a measurement of both reflection and transmission with a 1.5 port PVNA is superior to a simple TDS transmission measurement.

Subsequently, we convert the time domain signal to frequency domain using Fast Fourier Transform and calculate the field transmission and reflection functions $t(\omega )$ and $r(\omega )$ from the ratio of the measured sample signal and their respective reference signal.

$$S_{21}(\omega) = t(\omega) = \frac{E^{DUT}_{T}(\omega)}{E^{ref}_{T}(\omega)}, \;\;\;\;\;\;\;\; S_{11}(\omega)=r(\omega) = \frac{E^{DUT}_{R}(\omega)}{E^{ref}_{R}(\omega)}$$

The phase shift induced by the sample for reflection is smaller than the transmission case, as the latter depends on the sample thickness. So the transmission data is used for increased accuracy to calculate the preliminary values of real ($n_{p}(\omega )$) and imaginary ($\kappa _{p}(\omega )$) part of the refractive index applying the following equations [33]:

$$n_{p}(\omega) = n_{0} - \frac{c_{0}}{\omega d_{p}}\angle{t}(\omega)$$
$$\kappa_{p}(\omega) = \frac{{c_{0}}}{\omega d_{p}}\left\{\ln \frac{4n_{0}n_{p}(\omega)}{(n_{0}+n_{p}(\omega))^2} - \ln\mid{t(\omega)}\mid\right\}$$
where, $\mid {t(\omega )}\mid$ and $\angle {t(\omega )}$ are the magnitude and phase of the measured transmission function. An adapted phase unwrapping scheme is used to avoid false unwrapping [33].

A subsequent iterative process calculates the frequency-dependent complex refractive index and the correct sample thickness. The value for the complex refractive index $\tilde {n}_{p}(\omega )= n_{p}(\omega , d_{p})-j\kappa _{p}(\omega , d_{p})$ is numerically optimized to minimize the global error function,

$$EF = \sum_\omega\left[(|t(\omega)|-|t_{calc}(\omega)|)^2 +(|r(\omega)|-|r_{calc}(\omega)|)^2\right]$$
and the local error function at each frequency step, $\omega _{x}$,
$$EF(\omega_{x}) =\left[(|t(\omega_{x})|-|t_{calc}(\omega_{x})|)^2 +(|r(\omega_{x})|-|r_{calc}(\omega_{x})|)^2\right]$$

The theoretical values of $t_{calc}$ and $r_{calc}$ are given by

$$t_{calc} (\omega)= \tau\tau'\exp\left[{-}j(\tilde{n}_{p}(\omega)-n_{0})\frac{\omega d_{p}}{c_{0}}\right] FP (\omega)$$
$$r_{calc} (\omega)= \rho + \tau\tau'\rho'\exp\left[{-}2j\tilde{n}_{p}(\omega)\frac{\omega d_{p}}{c_{0}}\right] FP (\omega)$$
where the Fabry-Pérot (FP) term is given by
$$FP (\omega)= \left\{1-\rho'^2\exp\left[{-}2j\tilde{n}_{p}(\omega)\frac{\omega d_{p}}{c_{0}}\right]\right\}^{{-}1}$$
and the field transmission and reflection coefficients are
$$\tau = \frac{2n_{0}}{n_{0} + \tilde{n}_{p}(\omega)};\;\; \tau' = \frac{2\tilde{n}_{p}(\omega)}{n_{0} + \tilde{n}_{p}(\omega)};\;\; \rho = \frac{\tilde{n}_{p}(\omega)-n_{0}}{n_{0} + \tilde{n}_{p}(\omega)};\;\; \rho' = \frac{n_{0} - \tilde{n}_{p}(\omega)}{n_{0} + \tilde{n}_{p}(\omega)}\;\;$$

Fig. 9 summarizes the numerical procedure for obtaining the correct frequency-dependent complex refractive index and the physical thickness. For the first step of the optimization, the value of $d_{p}$ is varied within a range of $\pm$ 0.1 mm with an (arbitrarily chosen) step size of 0.001 mm which is of the order of the expected system resolution. For each value of $d_{p}$, the values for $n_{p}(\omega ,d_{p})$ and $\kappa _{p}(\omega , d_{p})$ are calculated [Eq. (2) and Eq. (3)], filtered (with polynomial fit to remove FP oscillations) and optimized to minimize the global error function, $EF$ [Eq. (4)] using a two-dimensional Nelder-Mead simplex algorithm (NMSA). From this step, a thickness value of $d_{s}$ is acquired, for which $EF$ is minimum and subsequently the values of $n_{s}(\omega , d_{s})$ and $\kappa _{s}(\omega ,d_{s})$ are also acquired. In the next step, these parameters are refined, this time with three-dimensional NMSA. This yields the thickness of the material $d_{t}$, as well as corresponding real ($n_{t}(\omega )$) and imaginary part ($\kappa _{t}(\omega )$) of the refractive index. Now, for the final step we optimize $n_{t}(\omega )$ and $\kappa _{t}(\omega )$ for each frequency step $\omega _{x}$ and minimize the function $EF(\omega _{x})$ [Eq. (5)] with thickness fixed at $d_{t}$. This step recovers any features of the parameters that might have been affected by the filtering process. The optimized parameters of this final step ($d_{t}$, $n_{f}(\omega )$ and $\kappa _{f}(\omega )$) are then used as the input for a new optimization cycle. The three-step optimization cycle is then repeated several times until the minimum value of $EF$ is achieved.

 figure: Fig. 9.

Fig. 9. Schematic of the optimization process.

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The complex dielectric permittivity is then given by

$$\epsilon'(\omega) = n_{f}^2(\omega)-\kappa_{f}^2(\omega)$$
$$\epsilon^{\prime\prime}(\omega) = 2n_{f}(\omega)\kappa_{f}(\omega) ;$$
and the loss tangent by
$$\tan\delta(\omega)=\frac{\epsilon^{\prime\prime}(\omega)}{\epsilon'(\omega)}= \frac{2n_{f}(\omega)\kappa_{f}(\omega)}{n_{f}^2(\omega)-\kappa_{f}^2(\omega)}$$

Fig. 10 depicts the real part of the dielectric permittivity of a high resistive Silicon (HR-Si) (> 10,000 $\Omega$cm) wafer as an example of a low-loss dielectric. The dielectric permittivity is constant within the measurement error with a value of 11.6410 $\pm$ 0.0588 (averaged over the whole frequency range). Compared with the literature value of 11.67 at 1 THz [34], the error is less than 0.03%. The loss tangent is close to zero and below the minimum value measurable for the available DNR, therefore $\epsilon ''\approx 0$. The HR-Si wafer thickness is calculated to be $d_t$ = 0.6544 $\pm$ 0.0050 mm, which complies with the caliper measurement of 0.65 $\pm$ 0.01 mm.

 figure: Fig. 10.

Fig. 10. Real part of dielectric permitttivity of HR-Si.

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Fig. 11 depicts the dielectric permittivity values for polyvinyl chloride (PVC) as an example for a lossy dielectric. At 1 THz, $\epsilon '$ = 2.648 and $\tan \delta$ = 0.053. The thickness is measured at 1.0179 $\pm$ 0.0100 mm, showing excellent agreement with the caliper reading of 1.01 $\pm$ 0.02 mm (the PVC sample used has an uneven surface). We note that the measurement error by the PVNA is smaller than that of the caliper in both cases.

 figure: Fig. 11.

Fig. 11. Dielectric properties of PVC.(a) Real part of dielectric permitttivity and (b) Loss tangent of PVC.

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5. Conclusion

We demonstrated a two-port photonic vector network analyzer and its capability of measuring S-parameters of devices in the terahertz band at the example of a split ring resonator array and a stop band filter. For both cases, there is an excellent agreement with simulation results within the given spectral resolution of 7.14 GHz of the system. The spectral resolution can be enhanced by using a larger scan window than applied in this study. Sub-GHz resolution seems feasible as reported for other pulsed photonic systems [35]. We further implemented a material parameter extraction algorithm employing the $S_{21}$ and $S_{11}$ parameters and compared results for low loss, high resistivity silicon and high loss polyvinyl chloride to the literature with an excellent match. The algorithm further allows extracting the sample thickness at the same time with an accuracy in the range of less than 10 $\mu$m.

PVNA measurements are more rigid compared with electronic VNA measurements as they are free from standing waves, which complicate the parameter extraction process as well as introduce errors. The free-space PVNA is not prone to errors introduced by the metal waveguides and misalignment of waveguide flanges [36,37]. Moreover, a simple calibration by reference measurements is sufficient for a PVNA, as the impedance of air is well-known. This is in stark contrast to the mandatory, rigorous calibration processes required for electronic VNA. With huge bandwidth beyond 2 THz and a DNR that is comparable or better than that of electronic VNAs beyond 1 THz, this system can well become a tool that accelerates the development of terahertz components and devices. Further frequency extension is relatively straightforward by using antenna structures optimized for higher frequencies as opposed to electronic VNAs that require individual designs for each band with severe limitations beyond 1.5 THz due to the skin effect and material losses of the commonly implemented hollow metal waveguides.

Funding

European Research Council (Pho-T-Lyze, GA 713780); Deutsche Forschungsgemeinschaft (REPHCON, PR1413/3-2).

Acknowledgments

The authors would like to thank Anuar Fernandez Olvera, Amlan kusum Mukherjee, Uttam Nandi and Alejandro Jiménez Sáez for their assistance in this research work.

Disclosures

The authors declare no conflicts of interest.

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2. Q. Sun, Y. He, K. Liu, S. Fan, E. P. J. Parrott, and E. Pickwell-MacPherson, “Recent advances in terahertz technology for biomedical applications,” Quant. Imaging Med. Surg. 7(3), 345–355 (2017). [CrossRef]  

3. G. Tzydynzhapov, P. Gusikhin, V. Muravev, A. Dremin, Y. Nefyodov, and I. Kukushkin, “New Real-Time Sub-Terahertz Security Body Scanner,” J. Infrared, Millimeter, Terahertz Waves 41(6), 632–641 (2020). [CrossRef]  

4. D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68(6), 1085–1094 (1999). [CrossRef]  

5. M. Naftaly, N. Vieweg, and A. Deninger, “Industrial Applications of Terahertz Sensing: State of Play,” Sensors 19(19), 4203 (2019). [CrossRef]  

6. P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging – Modern techniques and applications,” Laser Photonics Rev. 5(1), 124–166 (2011). [CrossRef]  

7. Virginia Diodes, Inc., “Vector Network Analyzer Extension Modules (VNAX),” [Online] (2020) [Accessed 11 Nov 2020], Available: http://www.vadiodes.com/en/products/vector-network-analyzer-extension-modules.

8. U. Nandi, J. C. Norman, A. C. Gossard, H. Lu, and S. Preu, “1550-nm Driven ErAs:In(Al)GaAs Photoconductor-Based Terahertz Time Domain System with 6.5 THz Bandwidth,” J. Infrared, Millimeter, Terahertz Waves 39(4), 340–348 (2018). [CrossRef]  

9. R. B. Kohlhaas, S. Breuer, S. Nellen, L. Liebermeister, M. Schell, M. P. Semtsiv, W. T. Masselink, and B. Globisch, “Photoconductive terahertz detectors with 105 dB peak dynamic range made of rhodium doped InGaAs,” Appl. Phys. Lett. 114(22), 221103 (2019). [CrossRef]  

10. Menlo Systems GmbH, “TERA K15 - All fiber-coupled Terahertz Spectrometer,” [Online] (2020) [Accessed 11 Nov 2020], Available: https://www.menlosystems.com/products/thz-time-domain-solutions/terak15-terahertz-spectrometer/.

11. M. Awad, M. Nagel, and H. Kurz, “Characterization of wire-pair negative index material at terahertz frequencies,” in 2007 Joint 32nd International Conference on Infrared and Millimeter Waves and the 15th International Conference on Terahertz Electronics, (2007), pp. 340–341.

12. F. R. Faridi and S. Preu, “Characterization of a Terahertz Isolator using a 1.5 Port Vector Spectrometer,” in 2019 44th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), (2019), pp. 1–2.

13. J. M. Ramer and G. Von Freymann, “A Terahertz Time-Domain Spectroscopy-Based Network Analyzer,” J. Lightwave Technol. 33(2), 403–407 (2015). [CrossRef]  

14. S. Preu, “A Unified Derivation of the Terahertz Spectra Generated by Photoconductors and Diodes,” J. Infrared, Millimeter, Terahertz Waves 35(12), 998–1010 (2014). [CrossRef]  

15. W. Kruppa and K. F. Sodomsky, “An Explicit Solution for the Scattering Parameters of a Linear Two-Port Measured with an Imperfect Test Set (Correspondence),” IEEE Trans. Microwave Theory Techn. 19(1), 122–123 (1971). [CrossRef]  

16. G. F. Engen and C. A. Hoer, “Thru-Reflect-Line: An Improved Technique for Calibrating the Dual Six-Port Automatic Network Analyzer,” IEEE Trans. Microwave Theory Techn. 27(12), 987–993 (1979). [CrossRef]  

17. C. A. Hoer and G. F. Engen, “On-line accuracy assessment for the dual six-port ANA: Extension to nonmating connectors,” IEEE Trans. Instrum. Meas. IM-36(2), 524–529 (1987). [CrossRef]  

18. U. Nandi, K. Dutzi, A. Deninger, H. Lu, J. Norman, A. C. Gossard, N. Vieweg, and S. Preu, “ErAs:In(Al)GaAs photoconductor-based time domain system with 4.5 THz single shot bandwidth and emitted terahertz power of 164 µW,” Opt. Lett. 45(10), 2812–2815 (2020). [CrossRef]  

19. C. Debus and P. H. Bolivar, “Frequency selective surfaces for high sensitivity terahertz sensing,” Appl. Phys. Lett. 91(18), 184102 (2007). [CrossRef]  

20. T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, “Tuned permeability in terahertz split-ring resonators for devices and sensors,” Appl. Phys. Lett. 91(6), 062511 (2007). [CrossRef]  

21. M. Mueh, M. Maasch, R. A. Knieß, H. U. Göringer, and C. Damm, “Detection of African trypanosomes using asymmetric double-split ring based THz sensors,” IEEE J. Electromagn. RF and Microwaves Medicine Biol. , 1(2), 66–73 (2017). [CrossRef]  

22. J. Dai, W. Gao, B. Liu, X. Cao, T. Tao, Z. Xie, H. Zhao, D. Chen, H. Ping, and R. Zhang, “Design and fabrication of UV band-pass filters based on SiO2/Si3N4 dielectric distributed bragg reflectors,” Appl. Surf. Sci. 364, 886–891 (2016). [CrossRef]  

23. B. Kogel, P. Debernardi, P. Westbergh, J. S. Gustavsson, Å. Haglund, E. Haglund, J. Bengtsson, and A. Larsson, “Integrated MEMS-Tunable VCSELs Using a Self-Aligned Reflow Process,” IEEE J. Quantum Electron. 48(2), 144–152 (2012). [CrossRef]  

24. G. Ma, J. Shen, Z. Zhang, Z. Hua, and S. H. Tang, “Ultrafast all-optical switching in one-dimensional photonic crystal with two defects,” Opt. Express 14(2), 858–865 (2006). [CrossRef]  

25. H.-Y. Lin, K.-J. Chen, S.-W. Wang, C.-C. Lin, K.-Y. Wang, J.-R. Li, P.-T. Lee, M.-H. Shih, X. Li, H.-M. Chen, and H.-C. Kuo, “Improvement of light quality by DBR structure in white LED,” Opt. Express 23(3), A27–A33 (2015). [CrossRef]  

26. S. Preu, H. G. L. Schwefel, S. Malzer, G. H. Döhler, L. J. Wang, M. Hanson, J. D. Zimmerman, and A. C. Gossard, “Coupled whispering gallery mode resonators in the Terahertz frequency range,” Opt. Express 16(10), 7336–7343 (2008). [CrossRef]  

27. T. Tosaka, K. Fujii, K. Fukunaga, and A. Kasamatsu, “Development of Complex Relative Permittivity Measurement System Based on Free-Space in 220–330 GHz Range,” IEEE Trans. THz Sci. Technol. 5, 1–8 (2014). [CrossRef]  

28. A. Kazemipour, M. Hudlička, M. Salhi, T. Kleine-Ostmann, and T. Schrader, “Free-space quasi-optical spectrometer for material characterization in the 50–500 GHz frequency range,” in 2014 44th European Microwave Conference, (2014), pp. 636–639.

29. J. Hammler, A. J. Gallant, and C. Balocco, “Free-Space Permittivity Measurement at Terahertz Frequencies With a Vector Network Analyzer,” IEEE Trans. THz Sci. Technol. 6(6), 817–823 (2016). [CrossRef]  

30. A. Taschin, P. Bartolini, J. Tasseva, and R. Torre, “THz time-domain spectroscopic investigations of thin films,” Measurement 118, 282–288 (2018). [CrossRef]  

31. M. Scheller, “Real-time terahertz material characterization by numerical three-dimensional optimization,” Opt. Express 19(11), 10647–10655 (2011). [CrossRef]  

32. F. R. Faridi, U. Nandi, and S. Preu, “1.5 Port Vector Spectrometer for Terahertz Time Domain Spectroscopy,” in 2018 43rd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), (2018), pp. 1–2.

33. W. Withayachumnankul and M. Naftaly, “Fundamentals of Measurement in Terahertz Time-Domain Spectroscopy,” J. Infrared, Millimeter, Terahertz Waves 35, 610–637 (2014). [CrossRef]  

34. P. H. Bolivar, M. Brucherseifer, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microwave Theory Techn. 51(4), 1062–1066 (2003). [CrossRef]  

35. T. Yasui, K. Kawamoto, Y.-D. Hsieh, Y. Sakaguchi, M. Jewariya, H. Inaba, K. Minoshima, F. Hindle, and T. Araki, “Enhancement of spectral resolution and accuracy in asynchronous-optical-sampling terahertz time-domain spectroscopy for low-pressure gas-phase analysis,” Opt. Express 20(14), 15071–15078 (2012). [CrossRef]  

36. H. Li, A. Arsenovic, J. L. Hesler, A. R. Kerr, and R. M. Weikle, “Repeatability and Mismatch of Waveguide Flanges in the 500–750 GHz Band,” IEEE Trans. THz Sci. Technol. 4(1), 39–48 (2014). [CrossRef]  

37. N. M. Ridler, S. Johny, M. J. Salter, X. Shang, W. Sun, and A. Wilson, “Establishing waveguide lines as primary standards for scattering parameter measurements at submillimetre wavelengths,” Metrologia 58(1), 015015 (2021). [CrossRef]  

References

  • View by:

  1. H. Song, J. Kim, K. Ajito, M. Yaita, and N. Kukutsu, “Fully Integrated ASK Receiver MMIC for Terahertz Communications at 300 GHz,” IEEE Trans. THz Sci. Technol 3(4), 445–452 (2013).
    [Crossref]
  2. Q. Sun, Y. He, K. Liu, S. Fan, E. P. J. Parrott, and E. Pickwell-MacPherson, “Recent advances in terahertz technology for biomedical applications,” Quant. Imaging Med. Surg. 7(3), 345–355 (2017).
    [Crossref]
  3. G. Tzydynzhapov, P. Gusikhin, V. Muravev, A. Dremin, Y. Nefyodov, and I. Kukushkin, “New Real-Time Sub-Terahertz Security Body Scanner,” J. Infrared, Millimeter, Terahertz Waves 41(6), 632–641 (2020).
    [Crossref]
  4. D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68(6), 1085–1094 (1999).
    [Crossref]
  5. M. Naftaly, N. Vieweg, and A. Deninger, “Industrial Applications of Terahertz Sensing: State of Play,” Sensors 19(19), 4203 (2019).
    [Crossref]
  6. P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging – Modern techniques and applications,” Laser Photonics Rev. 5(1), 124–166 (2011).
    [Crossref]
  7. Virginia Diodes, Inc., “Vector Network Analyzer Extension Modules (VNAX),” [Online] (2020) [Accessed 11 Nov 2020], Available: http://www.vadiodes.com/en/products/vector-network-analyzer-extension-modules .
  8. U. Nandi, J. C. Norman, A. C. Gossard, H. Lu, and S. Preu, “1550-nm Driven ErAs:In(Al)GaAs Photoconductor-Based Terahertz Time Domain System with 6.5 THz Bandwidth,” J. Infrared, Millimeter, Terahertz Waves 39(4), 340–348 (2018).
    [Crossref]
  9. R. B. Kohlhaas, S. Breuer, S. Nellen, L. Liebermeister, M. Schell, M. P. Semtsiv, W. T. Masselink, and B. Globisch, “Photoconductive terahertz detectors with 105 dB peak dynamic range made of rhodium doped InGaAs,” Appl. Phys. Lett. 114(22), 221103 (2019).
    [Crossref]
  10. Menlo Systems GmbH, “TERA K15 - All fiber-coupled Terahertz Spectrometer,” [Online] (2020) [Accessed 11 Nov 2020], Available: https://www.menlosystems.com/products/thz-time-domain-solutions/terak15-terahertz-spectrometer/ .
  11. M. Awad, M. Nagel, and H. Kurz, “Characterization of wire-pair negative index material at terahertz frequencies,” in 2007 Joint 32nd International Conference on Infrared and Millimeter Waves and the 15th International Conference on Terahertz Electronics, (2007), pp. 340–341.
  12. F. R. Faridi and S. Preu, “Characterization of a Terahertz Isolator using a 1.5 Port Vector Spectrometer,” in 2019 44th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), (2019), pp. 1–2.
  13. J. M. Ramer and G. Von Freymann, “A Terahertz Time-Domain Spectroscopy-Based Network Analyzer,” J. Lightwave Technol. 33(2), 403–407 (2015).
    [Crossref]
  14. S. Preu, “A Unified Derivation of the Terahertz Spectra Generated by Photoconductors and Diodes,” J. Infrared, Millimeter, Terahertz Waves 35(12), 998–1010 (2014).
    [Crossref]
  15. W. Kruppa and K. F. Sodomsky, “An Explicit Solution for the Scattering Parameters of a Linear Two-Port Measured with an Imperfect Test Set (Correspondence),” IEEE Trans. Microwave Theory Techn. 19(1), 122–123 (1971).
    [Crossref]
  16. G. F. Engen and C. A. Hoer, “Thru-Reflect-Line: An Improved Technique for Calibrating the Dual Six-Port Automatic Network Analyzer,” IEEE Trans. Microwave Theory Techn. 27(12), 987–993 (1979).
    [Crossref]
  17. C. A. Hoer and G. F. Engen, “On-line accuracy assessment for the dual six-port ANA: Extension to nonmating connectors,” IEEE Trans. Instrum. Meas. IM-36(2), 524–529 (1987).
    [Crossref]
  18. U. Nandi, K. Dutzi, A. Deninger, H. Lu, J. Norman, A. C. Gossard, N. Vieweg, and S. Preu, “ErAs:In(Al)GaAs photoconductor-based time domain system with 4.5 THz single shot bandwidth and emitted terahertz power of 164 µW,” Opt. Lett. 45(10), 2812–2815 (2020).
    [Crossref]
  19. C. Debus and P. H. Bolivar, “Frequency selective surfaces for high sensitivity terahertz sensing,” Appl. Phys. Lett. 91(18), 184102 (2007).
    [Crossref]
  20. T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, “Tuned permeability in terahertz split-ring resonators for devices and sensors,” Appl. Phys. Lett. 91(6), 062511 (2007).
    [Crossref]
  21. M. Mueh, M. Maasch, R. A. Knieß, H. U. Göringer, and C. Damm, “Detection of African trypanosomes using asymmetric double-split ring based THz sensors,” IEEE J. Electromagn. RF and Microwaves Medicine Biol., 1(2), 66–73 (2017).
    [Crossref]
  22. J. Dai, W. Gao, B. Liu, X. Cao, T. Tao, Z. Xie, H. Zhao, D. Chen, H. Ping, and R. Zhang, “Design and fabrication of UV band-pass filters based on SiO2/Si3N4 dielectric distributed bragg reflectors,” Appl. Surf. Sci. 364, 886–891 (2016).
    [Crossref]
  23. B. Kogel, P. Debernardi, P. Westbergh, J. S. Gustavsson, Å. Haglund, E. Haglund, J. Bengtsson, and A. Larsson, “Integrated MEMS-Tunable VCSELs Using a Self-Aligned Reflow Process,” IEEE J. Quantum Electron. 48(2), 144–152 (2012).
    [Crossref]
  24. G. Ma, J. Shen, Z. Zhang, Z. Hua, and S. H. Tang, “Ultrafast all-optical switching in one-dimensional photonic crystal with two defects,” Opt. Express 14(2), 858–865 (2006).
    [Crossref]
  25. H.-Y. Lin, K.-J. Chen, S.-W. Wang, C.-C. Lin, K.-Y. Wang, J.-R. Li, P.-T. Lee, M.-H. Shih, X. Li, H.-M. Chen, and H.-C. Kuo, “Improvement of light quality by DBR structure in white LED,” Opt. Express 23(3), A27–A33 (2015).
    [Crossref]
  26. S. Preu, H. G. L. Schwefel, S. Malzer, G. H. Döhler, L. J. Wang, M. Hanson, J. D. Zimmerman, and A. C. Gossard, “Coupled whispering gallery mode resonators in the Terahertz frequency range,” Opt. Express 16(10), 7336–7343 (2008).
    [Crossref]
  27. T. Tosaka, K. Fujii, K. Fukunaga, and A. Kasamatsu, “Development of Complex Relative Permittivity Measurement System Based on Free-Space in 220–330 GHz Range,” IEEE Trans. THz Sci. Technol. 5, 1–8 (2014).
    [Crossref]
  28. A. Kazemipour, M. Hudlička, M. Salhi, T. Kleine-Ostmann, and T. Schrader, “Free-space quasi-optical spectrometer for material characterization in the 50–500 GHz frequency range,” in 2014 44th European Microwave Conference, (2014), pp. 636–639.
  29. J. Hammler, A. J. Gallant, and C. Balocco, “Free-Space Permittivity Measurement at Terahertz Frequencies With a Vector Network Analyzer,” IEEE Trans. THz Sci. Technol. 6(6), 817–823 (2016).
    [Crossref]
  30. A. Taschin, P. Bartolini, J. Tasseva, and R. Torre, “THz time-domain spectroscopic investigations of thin films,” Measurement 118, 282–288 (2018).
    [Crossref]
  31. M. Scheller, “Real-time terahertz material characterization by numerical three-dimensional optimization,” Opt. Express 19(11), 10647–10655 (2011).
    [Crossref]
  32. F. R. Faridi, U. Nandi, and S. Preu, “1.5 Port Vector Spectrometer for Terahertz Time Domain Spectroscopy,” in 2018 43rd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), (2018), pp. 1–2.
  33. W. Withayachumnankul and M. Naftaly, “Fundamentals of Measurement in Terahertz Time-Domain Spectroscopy,” J. Infrared, Millimeter, Terahertz Waves 35, 610–637 (2014).
    [Crossref]
  34. P. H. Bolivar, M. Brucherseifer, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microwave Theory Techn. 51(4), 1062–1066 (2003).
    [Crossref]
  35. T. Yasui, K. Kawamoto, Y.-D. Hsieh, Y. Sakaguchi, M. Jewariya, H. Inaba, K. Minoshima, F. Hindle, and T. Araki, “Enhancement of spectral resolution and accuracy in asynchronous-optical-sampling terahertz time-domain spectroscopy for low-pressure gas-phase analysis,” Opt. Express 20(14), 15071–15078 (2012).
    [Crossref]
  36. H. Li, A. Arsenovic, J. L. Hesler, A. R. Kerr, and R. M. Weikle, “Repeatability and Mismatch of Waveguide Flanges in the 500–750 GHz Band,” IEEE Trans. THz Sci. Technol. 4(1), 39–48 (2014).
    [Crossref]
  37. N. M. Ridler, S. Johny, M. J. Salter, X. Shang, W. Sun, and A. Wilson, “Establishing waveguide lines as primary standards for scattering parameter measurements at submillimetre wavelengths,” Metrologia 58(1), 015015 (2021).
    [Crossref]

2021 (1)

N. M. Ridler, S. Johny, M. J. Salter, X. Shang, W. Sun, and A. Wilson, “Establishing waveguide lines as primary standards for scattering parameter measurements at submillimetre wavelengths,” Metrologia 58(1), 015015 (2021).
[Crossref]

2020 (2)

U. Nandi, K. Dutzi, A. Deninger, H. Lu, J. Norman, A. C. Gossard, N. Vieweg, and S. Preu, “ErAs:In(Al)GaAs photoconductor-based time domain system with 4.5 THz single shot bandwidth and emitted terahertz power of 164 µW,” Opt. Lett. 45(10), 2812–2815 (2020).
[Crossref]

G. Tzydynzhapov, P. Gusikhin, V. Muravev, A. Dremin, Y. Nefyodov, and I. Kukushkin, “New Real-Time Sub-Terahertz Security Body Scanner,” J. Infrared, Millimeter, Terahertz Waves 41(6), 632–641 (2020).
[Crossref]

2019 (2)

R. B. Kohlhaas, S. Breuer, S. Nellen, L. Liebermeister, M. Schell, M. P. Semtsiv, W. T. Masselink, and B. Globisch, “Photoconductive terahertz detectors with 105 dB peak dynamic range made of rhodium doped InGaAs,” Appl. Phys. Lett. 114(22), 221103 (2019).
[Crossref]

M. Naftaly, N. Vieweg, and A. Deninger, “Industrial Applications of Terahertz Sensing: State of Play,” Sensors 19(19), 4203 (2019).
[Crossref]

2018 (2)

U. Nandi, J. C. Norman, A. C. Gossard, H. Lu, and S. Preu, “1550-nm Driven ErAs:In(Al)GaAs Photoconductor-Based Terahertz Time Domain System with 6.5 THz Bandwidth,” J. Infrared, Millimeter, Terahertz Waves 39(4), 340–348 (2018).
[Crossref]

A. Taschin, P. Bartolini, J. Tasseva, and R. Torre, “THz time-domain spectroscopic investigations of thin films,” Measurement 118, 282–288 (2018).
[Crossref]

2017 (2)

M. Mueh, M. Maasch, R. A. Knieß, H. U. Göringer, and C. Damm, “Detection of African trypanosomes using asymmetric double-split ring based THz sensors,” IEEE J. Electromagn. RF and Microwaves Medicine Biol., 1(2), 66–73 (2017).
[Crossref]

Q. Sun, Y. He, K. Liu, S. Fan, E. P. J. Parrott, and E. Pickwell-MacPherson, “Recent advances in terahertz technology for biomedical applications,” Quant. Imaging Med. Surg. 7(3), 345–355 (2017).
[Crossref]

2016 (2)

J. Dai, W. Gao, B. Liu, X. Cao, T. Tao, Z. Xie, H. Zhao, D. Chen, H. Ping, and R. Zhang, “Design and fabrication of UV band-pass filters based on SiO2/Si3N4 dielectric distributed bragg reflectors,” Appl. Surf. Sci. 364, 886–891 (2016).
[Crossref]

J. Hammler, A. J. Gallant, and C. Balocco, “Free-Space Permittivity Measurement at Terahertz Frequencies With a Vector Network Analyzer,” IEEE Trans. THz Sci. Technol. 6(6), 817–823 (2016).
[Crossref]

2015 (2)

2014 (4)

S. Preu, “A Unified Derivation of the Terahertz Spectra Generated by Photoconductors and Diodes,” J. Infrared, Millimeter, Terahertz Waves 35(12), 998–1010 (2014).
[Crossref]

T. Tosaka, K. Fujii, K. Fukunaga, and A. Kasamatsu, “Development of Complex Relative Permittivity Measurement System Based on Free-Space in 220–330 GHz Range,” IEEE Trans. THz Sci. Technol. 5, 1–8 (2014).
[Crossref]

W. Withayachumnankul and M. Naftaly, “Fundamentals of Measurement in Terahertz Time-Domain Spectroscopy,” J. Infrared, Millimeter, Terahertz Waves 35, 610–637 (2014).
[Crossref]

H. Li, A. Arsenovic, J. L. Hesler, A. R. Kerr, and R. M. Weikle, “Repeatability and Mismatch of Waveguide Flanges in the 500–750 GHz Band,” IEEE Trans. THz Sci. Technol. 4(1), 39–48 (2014).
[Crossref]

2013 (1)

H. Song, J. Kim, K. Ajito, M. Yaita, and N. Kukutsu, “Fully Integrated ASK Receiver MMIC for Terahertz Communications at 300 GHz,” IEEE Trans. THz Sci. Technol 3(4), 445–452 (2013).
[Crossref]

2012 (2)

B. Kogel, P. Debernardi, P. Westbergh, J. S. Gustavsson, Å. Haglund, E. Haglund, J. Bengtsson, and A. Larsson, “Integrated MEMS-Tunable VCSELs Using a Self-Aligned Reflow Process,” IEEE J. Quantum Electron. 48(2), 144–152 (2012).
[Crossref]

T. Yasui, K. Kawamoto, Y.-D. Hsieh, Y. Sakaguchi, M. Jewariya, H. Inaba, K. Minoshima, F. Hindle, and T. Araki, “Enhancement of spectral resolution and accuracy in asynchronous-optical-sampling terahertz time-domain spectroscopy for low-pressure gas-phase analysis,” Opt. Express 20(14), 15071–15078 (2012).
[Crossref]

2011 (2)

M. Scheller, “Real-time terahertz material characterization by numerical three-dimensional optimization,” Opt. Express 19(11), 10647–10655 (2011).
[Crossref]

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging – Modern techniques and applications,” Laser Photonics Rev. 5(1), 124–166 (2011).
[Crossref]

2008 (1)

2007 (2)

C. Debus and P. H. Bolivar, “Frequency selective surfaces for high sensitivity terahertz sensing,” Appl. Phys. Lett. 91(18), 184102 (2007).
[Crossref]

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, “Tuned permeability in terahertz split-ring resonators for devices and sensors,” Appl. Phys. Lett. 91(6), 062511 (2007).
[Crossref]

2006 (1)

2003 (1)

P. H. Bolivar, M. Brucherseifer, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microwave Theory Techn. 51(4), 1062–1066 (2003).
[Crossref]

1999 (1)

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68(6), 1085–1094 (1999).
[Crossref]

1987 (1)

C. A. Hoer and G. F. Engen, “On-line accuracy assessment for the dual six-port ANA: Extension to nonmating connectors,” IEEE Trans. Instrum. Meas. IM-36(2), 524–529 (1987).
[Crossref]

1979 (1)

G. F. Engen and C. A. Hoer, “Thru-Reflect-Line: An Improved Technique for Calibrating the Dual Six-Port Automatic Network Analyzer,” IEEE Trans. Microwave Theory Techn. 27(12), 987–993 (1979).
[Crossref]

1971 (1)

W. Kruppa and K. F. Sodomsky, “An Explicit Solution for the Scattering Parameters of a Linear Two-Port Measured with an Imperfect Test Set (Correspondence),” IEEE Trans. Microwave Theory Techn. 19(1), 122–123 (1971).
[Crossref]

Ajito, K.

H. Song, J. Kim, K. Ajito, M. Yaita, and N. Kukutsu, “Fully Integrated ASK Receiver MMIC for Terahertz Communications at 300 GHz,” IEEE Trans. THz Sci. Technol 3(4), 445–452 (2013).
[Crossref]

Andreev, G. O.

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, “Tuned permeability in terahertz split-ring resonators for devices and sensors,” Appl. Phys. Lett. 91(6), 062511 (2007).
[Crossref]

Araki, T.

Arsenovic, A.

H. Li, A. Arsenovic, J. L. Hesler, A. R. Kerr, and R. M. Weikle, “Repeatability and Mismatch of Waveguide Flanges in the 500–750 GHz Band,” IEEE Trans. THz Sci. Technol. 4(1), 39–48 (2014).
[Crossref]

Awad, M.

M. Awad, M. Nagel, and H. Kurz, “Characterization of wire-pair negative index material at terahertz frequencies,” in 2007 Joint 32nd International Conference on Infrared and Millimeter Waves and the 15th International Conference on Terahertz Electronics, (2007), pp. 340–341.

Balocco, C.

J. Hammler, A. J. Gallant, and C. Balocco, “Free-Space Permittivity Measurement at Terahertz Frequencies With a Vector Network Analyzer,” IEEE Trans. THz Sci. Technol. 6(6), 817–823 (2016).
[Crossref]

Baraniuk, R. G.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68(6), 1085–1094 (1999).
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A. Taschin, P. Bartolini, J. Tasseva, and R. Torre, “THz time-domain spectroscopic investigations of thin films,” Measurement 118, 282–288 (2018).
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T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, “Tuned permeability in terahertz split-ring resonators for devices and sensors,” Appl. Phys. Lett. 91(6), 062511 (2007).
[Crossref]

Bengtsson, J.

B. Kogel, P. Debernardi, P. Westbergh, J. S. Gustavsson, Å. Haglund, E. Haglund, J. Bengtsson, and A. Larsson, “Integrated MEMS-Tunable VCSELs Using a Self-Aligned Reflow Process,” IEEE J. Quantum Electron. 48(2), 144–152 (2012).
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Bolivar, P. H.

C. Debus and P. H. Bolivar, “Frequency selective surfaces for high sensitivity terahertz sensing,” Appl. Phys. Lett. 91(18), 184102 (2007).
[Crossref]

P. H. Bolivar, M. Brucherseifer, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microwave Theory Techn. 51(4), 1062–1066 (2003).
[Crossref]

Breuer, S.

R. B. Kohlhaas, S. Breuer, S. Nellen, L. Liebermeister, M. Schell, M. P. Semtsiv, W. T. Masselink, and B. Globisch, “Photoconductive terahertz detectors with 105 dB peak dynamic range made of rhodium doped InGaAs,” Appl. Phys. Lett. 114(22), 221103 (2019).
[Crossref]

Brucherseifer, M.

P. H. Bolivar, M. Brucherseifer, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microwave Theory Techn. 51(4), 1062–1066 (2003).
[Crossref]

Cao, X.

J. Dai, W. Gao, B. Liu, X. Cao, T. Tao, Z. Xie, H. Zhao, D. Chen, H. Ping, and R. Zhang, “Design and fabrication of UV band-pass filters based on SiO2/Si3N4 dielectric distributed bragg reflectors,” Appl. Surf. Sci. 364, 886–891 (2016).
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Chen, D.

J. Dai, W. Gao, B. Liu, X. Cao, T. Tao, Z. Xie, H. Zhao, D. Chen, H. Ping, and R. Zhang, “Design and fabrication of UV band-pass filters based on SiO2/Si3N4 dielectric distributed bragg reflectors,” Appl. Surf. Sci. 364, 886–891 (2016).
[Crossref]

Chen, H.-M.

Chen, K.-J.

Cho, S. Y.

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, “Tuned permeability in terahertz split-ring resonators for devices and sensors,” Appl. Phys. Lett. 91(6), 062511 (2007).
[Crossref]

Cooke, D. G.

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging – Modern techniques and applications,” Laser Photonics Rev. 5(1), 124–166 (2011).
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Dai, J.

J. Dai, W. Gao, B. Liu, X. Cao, T. Tao, Z. Xie, H. Zhao, D. Chen, H. Ping, and R. Zhang, “Design and fabrication of UV band-pass filters based on SiO2/Si3N4 dielectric distributed bragg reflectors,” Appl. Surf. Sci. 364, 886–891 (2016).
[Crossref]

Damm, C.

M. Mueh, M. Maasch, R. A. Knieß, H. U. Göringer, and C. Damm, “Detection of African trypanosomes using asymmetric double-split ring based THz sensors,” IEEE J. Electromagn. RF and Microwaves Medicine Biol., 1(2), 66–73 (2017).
[Crossref]

de Maagt, P.

P. H. Bolivar, M. Brucherseifer, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microwave Theory Techn. 51(4), 1062–1066 (2003).
[Crossref]

Debernardi, P.

B. Kogel, P. Debernardi, P. Westbergh, J. S. Gustavsson, Å. Haglund, E. Haglund, J. Bengtsson, and A. Larsson, “Integrated MEMS-Tunable VCSELs Using a Self-Aligned Reflow Process,” IEEE J. Quantum Electron. 48(2), 144–152 (2012).
[Crossref]

Debus, C.

C. Debus and P. H. Bolivar, “Frequency selective surfaces for high sensitivity terahertz sensing,” Appl. Phys. Lett. 91(18), 184102 (2007).
[Crossref]

Deninger, A.

Döhler, G. H.

Dremin, A.

G. Tzydynzhapov, P. Gusikhin, V. Muravev, A. Dremin, Y. Nefyodov, and I. Kukushkin, “New Real-Time Sub-Terahertz Security Body Scanner,” J. Infrared, Millimeter, Terahertz Waves 41(6), 632–641 (2020).
[Crossref]

Driscoll, T.

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, “Tuned permeability in terahertz split-ring resonators for devices and sensors,” Appl. Phys. Lett. 91(6), 062511 (2007).
[Crossref]

Dutzi, K.

Ederra, I.

P. H. Bolivar, M. Brucherseifer, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microwave Theory Techn. 51(4), 1062–1066 (2003).
[Crossref]

Engen, G. F.

C. A. Hoer and G. F. Engen, “On-line accuracy assessment for the dual six-port ANA: Extension to nonmating connectors,” IEEE Trans. Instrum. Meas. IM-36(2), 524–529 (1987).
[Crossref]

G. F. Engen and C. A. Hoer, “Thru-Reflect-Line: An Improved Technique for Calibrating the Dual Six-Port Automatic Network Analyzer,” IEEE Trans. Microwave Theory Techn. 27(12), 987–993 (1979).
[Crossref]

Fan, S.

Q. Sun, Y. He, K. Liu, S. Fan, E. P. J. Parrott, and E. Pickwell-MacPherson, “Recent advances in terahertz technology for biomedical applications,” Quant. Imaging Med. Surg. 7(3), 345–355 (2017).
[Crossref]

Faridi, F. R.

F. R. Faridi and S. Preu, “Characterization of a Terahertz Isolator using a 1.5 Port Vector Spectrometer,” in 2019 44th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), (2019), pp. 1–2.

F. R. Faridi, U. Nandi, and S. Preu, “1.5 Port Vector Spectrometer for Terahertz Time Domain Spectroscopy,” in 2018 43rd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), (2018), pp. 1–2.

Fujii, K.

T. Tosaka, K. Fujii, K. Fukunaga, and A. Kasamatsu, “Development of Complex Relative Permittivity Measurement System Based on Free-Space in 220–330 GHz Range,” IEEE Trans. THz Sci. Technol. 5, 1–8 (2014).
[Crossref]

Fukunaga, K.

T. Tosaka, K. Fujii, K. Fukunaga, and A. Kasamatsu, “Development of Complex Relative Permittivity Measurement System Based on Free-Space in 220–330 GHz Range,” IEEE Trans. THz Sci. Technol. 5, 1–8 (2014).
[Crossref]

Gallant, A. J.

J. Hammler, A. J. Gallant, and C. Balocco, “Free-Space Permittivity Measurement at Terahertz Frequencies With a Vector Network Analyzer,” IEEE Trans. THz Sci. Technol. 6(6), 817–823 (2016).
[Crossref]

Gao, W.

J. Dai, W. Gao, B. Liu, X. Cao, T. Tao, Z. Xie, H. Zhao, D. Chen, H. Ping, and R. Zhang, “Design and fabrication of UV band-pass filters based on SiO2/Si3N4 dielectric distributed bragg reflectors,” Appl. Surf. Sci. 364, 886–891 (2016).
[Crossref]

Globisch, B.

R. B. Kohlhaas, S. Breuer, S. Nellen, L. Liebermeister, M. Schell, M. P. Semtsiv, W. T. Masselink, and B. Globisch, “Photoconductive terahertz detectors with 105 dB peak dynamic range made of rhodium doped InGaAs,” Appl. Phys. Lett. 114(22), 221103 (2019).
[Crossref]

Gonzalo, R.

P. H. Bolivar, M. Brucherseifer, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microwave Theory Techn. 51(4), 1062–1066 (2003).
[Crossref]

Göringer, H. U.

M. Mueh, M. Maasch, R. A. Knieß, H. U. Göringer, and C. Damm, “Detection of African trypanosomes using asymmetric double-split ring based THz sensors,” IEEE J. Electromagn. RF and Microwaves Medicine Biol., 1(2), 66–73 (2017).
[Crossref]

Gossard, A. C.

Gupta, M.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68(6), 1085–1094 (1999).
[Crossref]

Gusikhin, P.

G. Tzydynzhapov, P. Gusikhin, V. Muravev, A. Dremin, Y. Nefyodov, and I. Kukushkin, “New Real-Time Sub-Terahertz Security Body Scanner,” J. Infrared, Millimeter, Terahertz Waves 41(6), 632–641 (2020).
[Crossref]

Gustavsson, J. S.

B. Kogel, P. Debernardi, P. Westbergh, J. S. Gustavsson, Å. Haglund, E. Haglund, J. Bengtsson, and A. Larsson, “Integrated MEMS-Tunable VCSELs Using a Self-Aligned Reflow Process,” IEEE J. Quantum Electron. 48(2), 144–152 (2012).
[Crossref]

Haglund, Å.

B. Kogel, P. Debernardi, P. Westbergh, J. S. Gustavsson, Å. Haglund, E. Haglund, J. Bengtsson, and A. Larsson, “Integrated MEMS-Tunable VCSELs Using a Self-Aligned Reflow Process,” IEEE J. Quantum Electron. 48(2), 144–152 (2012).
[Crossref]

Haglund, E.

B. Kogel, P. Debernardi, P. Westbergh, J. S. Gustavsson, Å. Haglund, E. Haglund, J. Bengtsson, and A. Larsson, “Integrated MEMS-Tunable VCSELs Using a Self-Aligned Reflow Process,” IEEE J. Quantum Electron. 48(2), 144–152 (2012).
[Crossref]

Hammler, J.

J. Hammler, A. J. Gallant, and C. Balocco, “Free-Space Permittivity Measurement at Terahertz Frequencies With a Vector Network Analyzer,” IEEE Trans. THz Sci. Technol. 6(6), 817–823 (2016).
[Crossref]

Hanson, M.

He, Y.

Q. Sun, Y. He, K. Liu, S. Fan, E. P. J. Parrott, and E. Pickwell-MacPherson, “Recent advances in terahertz technology for biomedical applications,” Quant. Imaging Med. Surg. 7(3), 345–355 (2017).
[Crossref]

Hesler, J. L.

H. Li, A. Arsenovic, J. L. Hesler, A. R. Kerr, and R. M. Weikle, “Repeatability and Mismatch of Waveguide Flanges in the 500–750 GHz Band,” IEEE Trans. THz Sci. Technol. 4(1), 39–48 (2014).
[Crossref]

Hindle, F.

Hoer, C. A.

C. A. Hoer and G. F. Engen, “On-line accuracy assessment for the dual six-port ANA: Extension to nonmating connectors,” IEEE Trans. Instrum. Meas. IM-36(2), 524–529 (1987).
[Crossref]

G. F. Engen and C. A. Hoer, “Thru-Reflect-Line: An Improved Technique for Calibrating the Dual Six-Port Automatic Network Analyzer,” IEEE Trans. Microwave Theory Techn. 27(12), 987–993 (1979).
[Crossref]

Holker, M.

P. H. Bolivar, M. Brucherseifer, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microwave Theory Techn. 51(4), 1062–1066 (2003).
[Crossref]

Hsieh, Y.-D.

Hua, Z.

Hudlicka, M.

A. Kazemipour, M. Hudlička, M. Salhi, T. Kleine-Ostmann, and T. Schrader, “Free-space quasi-optical spectrometer for material characterization in the 50–500 GHz frequency range,” in 2014 44th European Microwave Conference, (2014), pp. 636–639.

Inaba, H.

Jepsen, P. U.

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging – Modern techniques and applications,” Laser Photonics Rev. 5(1), 124–166 (2011).
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Jewariya, M.

Johny, S.

N. M. Ridler, S. Johny, M. J. Salter, X. Shang, W. Sun, and A. Wilson, “Establishing waveguide lines as primary standards for scattering parameter measurements at submillimetre wavelengths,” Metrologia 58(1), 015015 (2021).
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Jokerst, N. M.

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, “Tuned permeability in terahertz split-ring resonators for devices and sensors,” Appl. Phys. Lett. 91(6), 062511 (2007).
[Crossref]

Kasamatsu, A.

T. Tosaka, K. Fujii, K. Fukunaga, and A. Kasamatsu, “Development of Complex Relative Permittivity Measurement System Based on Free-Space in 220–330 GHz Range,” IEEE Trans. THz Sci. Technol. 5, 1–8 (2014).
[Crossref]

Kawamoto, K.

Kazemipour, A.

A. Kazemipour, M. Hudlička, M. Salhi, T. Kleine-Ostmann, and T. Schrader, “Free-space quasi-optical spectrometer for material characterization in the 50–500 GHz frequency range,” in 2014 44th European Microwave Conference, (2014), pp. 636–639.

Kerr, A. R.

H. Li, A. Arsenovic, J. L. Hesler, A. R. Kerr, and R. M. Weikle, “Repeatability and Mismatch of Waveguide Flanges in the 500–750 GHz Band,” IEEE Trans. THz Sci. Technol. 4(1), 39–48 (2014).
[Crossref]

Kim, J.

H. Song, J. Kim, K. Ajito, M. Yaita, and N. Kukutsu, “Fully Integrated ASK Receiver MMIC for Terahertz Communications at 300 GHz,” IEEE Trans. THz Sci. Technol 3(4), 445–452 (2013).
[Crossref]

Kleine-Ostmann, T.

A. Kazemipour, M. Hudlička, M. Salhi, T. Kleine-Ostmann, and T. Schrader, “Free-space quasi-optical spectrometer for material characterization in the 50–500 GHz frequency range,” in 2014 44th European Microwave Conference, (2014), pp. 636–639.

Knieß, R. A.

M. Mueh, M. Maasch, R. A. Knieß, H. U. Göringer, and C. Damm, “Detection of African trypanosomes using asymmetric double-split ring based THz sensors,” IEEE J. Electromagn. RF and Microwaves Medicine Biol., 1(2), 66–73 (2017).
[Crossref]

Koch, M.

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging – Modern techniques and applications,” Laser Photonics Rev. 5(1), 124–166 (2011).
[Crossref]

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68(6), 1085–1094 (1999).
[Crossref]

Kogel, B.

B. Kogel, P. Debernardi, P. Westbergh, J. S. Gustavsson, Å. Haglund, E. Haglund, J. Bengtsson, and A. Larsson, “Integrated MEMS-Tunable VCSELs Using a Self-Aligned Reflow Process,” IEEE J. Quantum Electron. 48(2), 144–152 (2012).
[Crossref]

Kohlhaas, R. B.

R. B. Kohlhaas, S. Breuer, S. Nellen, L. Liebermeister, M. Schell, M. P. Semtsiv, W. T. Masselink, and B. Globisch, “Photoconductive terahertz detectors with 105 dB peak dynamic range made of rhodium doped InGaAs,” Appl. Phys. Lett. 114(22), 221103 (2019).
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Kruppa, W.

W. Kruppa and K. F. Sodomsky, “An Explicit Solution for the Scattering Parameters of a Linear Two-Port Measured with an Imperfect Test Set (Correspondence),” IEEE Trans. Microwave Theory Techn. 19(1), 122–123 (1971).
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Kukushkin, I.

G. Tzydynzhapov, P. Gusikhin, V. Muravev, A. Dremin, Y. Nefyodov, and I. Kukushkin, “New Real-Time Sub-Terahertz Security Body Scanner,” J. Infrared, Millimeter, Terahertz Waves 41(6), 632–641 (2020).
[Crossref]

Kukutsu, N.

H. Song, J. Kim, K. Ajito, M. Yaita, and N. Kukutsu, “Fully Integrated ASK Receiver MMIC for Terahertz Communications at 300 GHz,” IEEE Trans. THz Sci. Technol 3(4), 445–452 (2013).
[Crossref]

Kuo, H.-C.

Kurz, H.

M. Awad, M. Nagel, and H. Kurz, “Characterization of wire-pair negative index material at terahertz frequencies,” in 2007 Joint 32nd International Conference on Infrared and Millimeter Waves and the 15th International Conference on Terahertz Electronics, (2007), pp. 340–341.

Larsson, A.

B. Kogel, P. Debernardi, P. Westbergh, J. S. Gustavsson, Å. Haglund, E. Haglund, J. Bengtsson, and A. Larsson, “Integrated MEMS-Tunable VCSELs Using a Self-Aligned Reflow Process,” IEEE J. Quantum Electron. 48(2), 144–152 (2012).
[Crossref]

Lee, P.-T.

Li, H.

H. Li, A. Arsenovic, J. L. Hesler, A. R. Kerr, and R. M. Weikle, “Repeatability and Mismatch of Waveguide Flanges in the 500–750 GHz Band,” IEEE Trans. THz Sci. Technol. 4(1), 39–48 (2014).
[Crossref]

Li, J.-R.

Li, X.

Liebermeister, L.

R. B. Kohlhaas, S. Breuer, S. Nellen, L. Liebermeister, M. Schell, M. P. Semtsiv, W. T. Masselink, and B. Globisch, “Photoconductive terahertz detectors with 105 dB peak dynamic range made of rhodium doped InGaAs,” Appl. Phys. Lett. 114(22), 221103 (2019).
[Crossref]

Lin, C.-C.

Lin, H.-Y.

Liu, B.

J. Dai, W. Gao, B. Liu, X. Cao, T. Tao, Z. Xie, H. Zhao, D. Chen, H. Ping, and R. Zhang, “Design and fabrication of UV band-pass filters based on SiO2/Si3N4 dielectric distributed bragg reflectors,” Appl. Surf. Sci. 364, 886–891 (2016).
[Crossref]

Liu, K.

Q. Sun, Y. He, K. Liu, S. Fan, E. P. J. Parrott, and E. Pickwell-MacPherson, “Recent advances in terahertz technology for biomedical applications,” Quant. Imaging Med. Surg. 7(3), 345–355 (2017).
[Crossref]

Lu, H.

U. Nandi, K. Dutzi, A. Deninger, H. Lu, J. Norman, A. C. Gossard, N. Vieweg, and S. Preu, “ErAs:In(Al)GaAs photoconductor-based time domain system with 4.5 THz single shot bandwidth and emitted terahertz power of 164 µW,” Opt. Lett. 45(10), 2812–2815 (2020).
[Crossref]

U. Nandi, J. C. Norman, A. C. Gossard, H. Lu, and S. Preu, “1550-nm Driven ErAs:In(Al)GaAs Photoconductor-Based Terahertz Time Domain System with 6.5 THz Bandwidth,” J. Infrared, Millimeter, Terahertz Waves 39(4), 340–348 (2018).
[Crossref]

Ma, G.

Maasch, M.

M. Mueh, M. Maasch, R. A. Knieß, H. U. Göringer, and C. Damm, “Detection of African trypanosomes using asymmetric double-split ring based THz sensors,” IEEE J. Electromagn. RF and Microwaves Medicine Biol., 1(2), 66–73 (2017).
[Crossref]

Malzer, S.

Masselink, W. T.

R. B. Kohlhaas, S. Breuer, S. Nellen, L. Liebermeister, M. Schell, M. P. Semtsiv, W. T. Masselink, and B. Globisch, “Photoconductive terahertz detectors with 105 dB peak dynamic range made of rhodium doped InGaAs,” Appl. Phys. Lett. 114(22), 221103 (2019).
[Crossref]

Minoshima, K.

Mittleman, D. M.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68(6), 1085–1094 (1999).
[Crossref]

Mueh, M.

M. Mueh, M. Maasch, R. A. Knieß, H. U. Göringer, and C. Damm, “Detection of African trypanosomes using asymmetric double-split ring based THz sensors,” IEEE J. Electromagn. RF and Microwaves Medicine Biol., 1(2), 66–73 (2017).
[Crossref]

Muravev, V.

G. Tzydynzhapov, P. Gusikhin, V. Muravev, A. Dremin, Y. Nefyodov, and I. Kukushkin, “New Real-Time Sub-Terahertz Security Body Scanner,” J. Infrared, Millimeter, Terahertz Waves 41(6), 632–641 (2020).
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Naftaly, M.

M. Naftaly, N. Vieweg, and A. Deninger, “Industrial Applications of Terahertz Sensing: State of Play,” Sensors 19(19), 4203 (2019).
[Crossref]

W. Withayachumnankul and M. Naftaly, “Fundamentals of Measurement in Terahertz Time-Domain Spectroscopy,” J. Infrared, Millimeter, Terahertz Waves 35, 610–637 (2014).
[Crossref]

Nagel, M.

M. Awad, M. Nagel, and H. Kurz, “Characterization of wire-pair negative index material at terahertz frequencies,” in 2007 Joint 32nd International Conference on Infrared and Millimeter Waves and the 15th International Conference on Terahertz Electronics, (2007), pp. 340–341.

Nandi, U.

U. Nandi, K. Dutzi, A. Deninger, H. Lu, J. Norman, A. C. Gossard, N. Vieweg, and S. Preu, “ErAs:In(Al)GaAs photoconductor-based time domain system with 4.5 THz single shot bandwidth and emitted terahertz power of 164 µW,” Opt. Lett. 45(10), 2812–2815 (2020).
[Crossref]

U. Nandi, J. C. Norman, A. C. Gossard, H. Lu, and S. Preu, “1550-nm Driven ErAs:In(Al)GaAs Photoconductor-Based Terahertz Time Domain System with 6.5 THz Bandwidth,” J. Infrared, Millimeter, Terahertz Waves 39(4), 340–348 (2018).
[Crossref]

F. R. Faridi, U. Nandi, and S. Preu, “1.5 Port Vector Spectrometer for Terahertz Time Domain Spectroscopy,” in 2018 43rd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), (2018), pp. 1–2.

Neelamani, R.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68(6), 1085–1094 (1999).
[Crossref]

Nefyodov, Y.

G. Tzydynzhapov, P. Gusikhin, V. Muravev, A. Dremin, Y. Nefyodov, and I. Kukushkin, “New Real-Time Sub-Terahertz Security Body Scanner,” J. Infrared, Millimeter, Terahertz Waves 41(6), 632–641 (2020).
[Crossref]

Nellen, S.

R. B. Kohlhaas, S. Breuer, S. Nellen, L. Liebermeister, M. Schell, M. P. Semtsiv, W. T. Masselink, and B. Globisch, “Photoconductive terahertz detectors with 105 dB peak dynamic range made of rhodium doped InGaAs,” Appl. Phys. Lett. 114(22), 221103 (2019).
[Crossref]

Norman, J.

Norman, J. C.

U. Nandi, J. C. Norman, A. C. Gossard, H. Lu, and S. Preu, “1550-nm Driven ErAs:In(Al)GaAs Photoconductor-Based Terahertz Time Domain System with 6.5 THz Bandwidth,” J. Infrared, Millimeter, Terahertz Waves 39(4), 340–348 (2018).
[Crossref]

Palit, S.

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, “Tuned permeability in terahertz split-ring resonators for devices and sensors,” Appl. Phys. Lett. 91(6), 062511 (2007).
[Crossref]

Parrott, E. P. J.

Q. Sun, Y. He, K. Liu, S. Fan, E. P. J. Parrott, and E. Pickwell-MacPherson, “Recent advances in terahertz technology for biomedical applications,” Quant. Imaging Med. Surg. 7(3), 345–355 (2017).
[Crossref]

Pickwell-MacPherson, E.

Q. Sun, Y. He, K. Liu, S. Fan, E. P. J. Parrott, and E. Pickwell-MacPherson, “Recent advances in terahertz technology for biomedical applications,” Quant. Imaging Med. Surg. 7(3), 345–355 (2017).
[Crossref]

Ping, H.

J. Dai, W. Gao, B. Liu, X. Cao, T. Tao, Z. Xie, H. Zhao, D. Chen, H. Ping, and R. Zhang, “Design and fabrication of UV band-pass filters based on SiO2/Si3N4 dielectric distributed bragg reflectors,” Appl. Surf. Sci. 364, 886–891 (2016).
[Crossref]

Preu, S.

U. Nandi, K. Dutzi, A. Deninger, H. Lu, J. Norman, A. C. Gossard, N. Vieweg, and S. Preu, “ErAs:In(Al)GaAs photoconductor-based time domain system with 4.5 THz single shot bandwidth and emitted terahertz power of 164 µW,” Opt. Lett. 45(10), 2812–2815 (2020).
[Crossref]

U. Nandi, J. C. Norman, A. C. Gossard, H. Lu, and S. Preu, “1550-nm Driven ErAs:In(Al)GaAs Photoconductor-Based Terahertz Time Domain System with 6.5 THz Bandwidth,” J. Infrared, Millimeter, Terahertz Waves 39(4), 340–348 (2018).
[Crossref]

S. Preu, “A Unified Derivation of the Terahertz Spectra Generated by Photoconductors and Diodes,” J. Infrared, Millimeter, Terahertz Waves 35(12), 998–1010 (2014).
[Crossref]

S. Preu, H. G. L. Schwefel, S. Malzer, G. H. Döhler, L. J. Wang, M. Hanson, J. D. Zimmerman, and A. C. Gossard, “Coupled whispering gallery mode resonators in the Terahertz frequency range,” Opt. Express 16(10), 7336–7343 (2008).
[Crossref]

F. R. Faridi, U. Nandi, and S. Preu, “1.5 Port Vector Spectrometer for Terahertz Time Domain Spectroscopy,” in 2018 43rd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), (2018), pp. 1–2.

F. R. Faridi and S. Preu, “Characterization of a Terahertz Isolator using a 1.5 Port Vector Spectrometer,” in 2019 44th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), (2019), pp. 1–2.

Ramer, J. M.

Reynolds, A. L.

P. H. Bolivar, M. Brucherseifer, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microwave Theory Techn. 51(4), 1062–1066 (2003).
[Crossref]

Ridler, N. M.

N. M. Ridler, S. Johny, M. J. Salter, X. Shang, W. Sun, and A. Wilson, “Establishing waveguide lines as primary standards for scattering parameter measurements at submillimetre wavelengths,” Metrologia 58(1), 015015 (2021).
[Crossref]

Rivas, J. G.

P. H. Bolivar, M. Brucherseifer, J. G. Rivas, R. Gonzalo, I. Ederra, A. L. Reynolds, M. Holker, and P. de Maagt, “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Trans. Microwave Theory Techn. 51(4), 1062–1066 (2003).
[Crossref]

Rudd, J. V.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68(6), 1085–1094 (1999).
[Crossref]

Sakaguchi, Y.

Salhi, M.

A. Kazemipour, M. Hudlička, M. Salhi, T. Kleine-Ostmann, and T. Schrader, “Free-space quasi-optical spectrometer for material characterization in the 50–500 GHz frequency range,” in 2014 44th European Microwave Conference, (2014), pp. 636–639.

Salter, M. J.

N. M. Ridler, S. Johny, M. J. Salter, X. Shang, W. Sun, and A. Wilson, “Establishing waveguide lines as primary standards for scattering parameter measurements at submillimetre wavelengths,” Metrologia 58(1), 015015 (2021).
[Crossref]

Schell, M.

R. B. Kohlhaas, S. Breuer, S. Nellen, L. Liebermeister, M. Schell, M. P. Semtsiv, W. T. Masselink, and B. Globisch, “Photoconductive terahertz detectors with 105 dB peak dynamic range made of rhodium doped InGaAs,” Appl. Phys. Lett. 114(22), 221103 (2019).
[Crossref]

Scheller, M.

Schrader, T.

A. Kazemipour, M. Hudlička, M. Salhi, T. Kleine-Ostmann, and T. Schrader, “Free-space quasi-optical spectrometer for material characterization in the 50–500 GHz frequency range,” in 2014 44th European Microwave Conference, (2014), pp. 636–639.

Schwefel, H. G. L.

Semtsiv, M. P.

R. B. Kohlhaas, S. Breuer, S. Nellen, L. Liebermeister, M. Schell, M. P. Semtsiv, W. T. Masselink, and B. Globisch, “Photoconductive terahertz detectors with 105 dB peak dynamic range made of rhodium doped InGaAs,” Appl. Phys. Lett. 114(22), 221103 (2019).
[Crossref]

Shang, X.

N. M. Ridler, S. Johny, M. J. Salter, X. Shang, W. Sun, and A. Wilson, “Establishing waveguide lines as primary standards for scattering parameter measurements at submillimetre wavelengths,” Metrologia 58(1), 015015 (2021).
[Crossref]

Shen, J.

Shih, M.-H.

Smith, D. R.

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, “Tuned permeability in terahertz split-ring resonators for devices and sensors,” Appl. Phys. Lett. 91(6), 062511 (2007).
[Crossref]

Sodomsky, K. F.

W. Kruppa and K. F. Sodomsky, “An Explicit Solution for the Scattering Parameters of a Linear Two-Port Measured with an Imperfect Test Set (Correspondence),” IEEE Trans. Microwave Theory Techn. 19(1), 122–123 (1971).
[Crossref]

Song, H.

H. Song, J. Kim, K. Ajito, M. Yaita, and N. Kukutsu, “Fully Integrated ASK Receiver MMIC for Terahertz Communications at 300 GHz,” IEEE Trans. THz Sci. Technol 3(4), 445–452 (2013).
[Crossref]

Sun, Q.

Q. Sun, Y. He, K. Liu, S. Fan, E. P. J. Parrott, and E. Pickwell-MacPherson, “Recent advances in terahertz technology for biomedical applications,” Quant. Imaging Med. Surg. 7(3), 345–355 (2017).
[Crossref]

Sun, W.

N. M. Ridler, S. Johny, M. J. Salter, X. Shang, W. Sun, and A. Wilson, “Establishing waveguide lines as primary standards for scattering parameter measurements at submillimetre wavelengths,” Metrologia 58(1), 015015 (2021).
[Crossref]

Tang, S. H.

Tao, T.

J. Dai, W. Gao, B. Liu, X. Cao, T. Tao, Z. Xie, H. Zhao, D. Chen, H. Ping, and R. Zhang, “Design and fabrication of UV band-pass filters based on SiO2/Si3N4 dielectric distributed bragg reflectors,” Appl. Surf. Sci. 364, 886–891 (2016).
[Crossref]

Taschin, A.

A. Taschin, P. Bartolini, J. Tasseva, and R. Torre, “THz time-domain spectroscopic investigations of thin films,” Measurement 118, 282–288 (2018).
[Crossref]

Tasseva, J.

A. Taschin, P. Bartolini, J. Tasseva, and R. Torre, “THz time-domain spectroscopic investigations of thin films,” Measurement 118, 282–288 (2018).
[Crossref]

Torre, R.

A. Taschin, P. Bartolini, J. Tasseva, and R. Torre, “THz time-domain spectroscopic investigations of thin films,” Measurement 118, 282–288 (2018).
[Crossref]

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T. Tosaka, K. Fujii, K. Fukunaga, and A. Kasamatsu, “Development of Complex Relative Permittivity Measurement System Based on Free-Space in 220–330 GHz Range,” IEEE Trans. THz Sci. Technol. 5, 1–8 (2014).
[Crossref]

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G. Tzydynzhapov, P. Gusikhin, V. Muravev, A. Dremin, Y. Nefyodov, and I. Kukushkin, “New Real-Time Sub-Terahertz Security Body Scanner,” J. Infrared, Millimeter, Terahertz Waves 41(6), 632–641 (2020).
[Crossref]

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H. Li, A. Arsenovic, J. L. Hesler, A. R. Kerr, and R. M. Weikle, “Repeatability and Mismatch of Waveguide Flanges in the 500–750 GHz Band,” IEEE Trans. THz Sci. Technol. 4(1), 39–48 (2014).
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B. Kogel, P. Debernardi, P. Westbergh, J. S. Gustavsson, Å. Haglund, E. Haglund, J. Bengtsson, and A. Larsson, “Integrated MEMS-Tunable VCSELs Using a Self-Aligned Reflow Process,” IEEE J. Quantum Electron. 48(2), 144–152 (2012).
[Crossref]

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N. M. Ridler, S. Johny, M. J. Salter, X. Shang, W. Sun, and A. Wilson, “Establishing waveguide lines as primary standards for scattering parameter measurements at submillimetre wavelengths,” Metrologia 58(1), 015015 (2021).
[Crossref]

Withayachumnankul, W.

W. Withayachumnankul and M. Naftaly, “Fundamentals of Measurement in Terahertz Time-Domain Spectroscopy,” J. Infrared, Millimeter, Terahertz Waves 35, 610–637 (2014).
[Crossref]

Xie, Z.

J. Dai, W. Gao, B. Liu, X. Cao, T. Tao, Z. Xie, H. Zhao, D. Chen, H. Ping, and R. Zhang, “Design and fabrication of UV band-pass filters based on SiO2/Si3N4 dielectric distributed bragg reflectors,” Appl. Surf. Sci. 364, 886–891 (2016).
[Crossref]

Yaita, M.

H. Song, J. Kim, K. Ajito, M. Yaita, and N. Kukutsu, “Fully Integrated ASK Receiver MMIC for Terahertz Communications at 300 GHz,” IEEE Trans. THz Sci. Technol 3(4), 445–452 (2013).
[Crossref]

Yasui, T.

Zhang, R.

J. Dai, W. Gao, B. Liu, X. Cao, T. Tao, Z. Xie, H. Zhao, D. Chen, H. Ping, and R. Zhang, “Design and fabrication of UV band-pass filters based on SiO2/Si3N4 dielectric distributed bragg reflectors,” Appl. Surf. Sci. 364, 886–891 (2016).
[Crossref]

Zhang, Z.

Zhao, H.

J. Dai, W. Gao, B. Liu, X. Cao, T. Tao, Z. Xie, H. Zhao, D. Chen, H. Ping, and R. Zhang, “Design and fabrication of UV band-pass filters based on SiO2/Si3N4 dielectric distributed bragg reflectors,” Appl. Surf. Sci. 364, 886–891 (2016).
[Crossref]

Zimmerman, J. D.

Appl. Phys. B (1)

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68(6), 1085–1094 (1999).
[Crossref]

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R. B. Kohlhaas, S. Breuer, S. Nellen, L. Liebermeister, M. Schell, M. P. Semtsiv, W. T. Masselink, and B. Globisch, “Photoconductive terahertz detectors with 105 dB peak dynamic range made of rhodium doped InGaAs,” Appl. Phys. Lett. 114(22), 221103 (2019).
[Crossref]

C. Debus and P. H. Bolivar, “Frequency selective surfaces for high sensitivity terahertz sensing,” Appl. Phys. Lett. 91(18), 184102 (2007).
[Crossref]

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, “Tuned permeability in terahertz split-ring resonators for devices and sensors,” Appl. Phys. Lett. 91(6), 062511 (2007).
[Crossref]

Appl. Surf. Sci. (1)

J. Dai, W. Gao, B. Liu, X. Cao, T. Tao, Z. Xie, H. Zhao, D. Chen, H. Ping, and R. Zhang, “Design and fabrication of UV band-pass filters based on SiO2/Si3N4 dielectric distributed bragg reflectors,” Appl. Surf. Sci. 364, 886–891 (2016).
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IEEE J. Quantum Electron. (1)

B. Kogel, P. Debernardi, P. Westbergh, J. S. Gustavsson, Å. Haglund, E. Haglund, J. Bengtsson, and A. Larsson, “Integrated MEMS-Tunable VCSELs Using a Self-Aligned Reflow Process,” IEEE J. Quantum Electron. 48(2), 144–152 (2012).
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[Crossref]

W. Kruppa and K. F. Sodomsky, “An Explicit Solution for the Scattering Parameters of a Linear Two-Port Measured with an Imperfect Test Set (Correspondence),” IEEE Trans. Microwave Theory Techn. 19(1), 122–123 (1971).
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IEEE Trans. THz Sci. Technol (1)

H. Song, J. Kim, K. Ajito, M. Yaita, and N. Kukutsu, “Fully Integrated ASK Receiver MMIC for Terahertz Communications at 300 GHz,” IEEE Trans. THz Sci. Technol 3(4), 445–452 (2013).
[Crossref]

IEEE Trans. THz Sci. Technol. (3)

T. Tosaka, K. Fujii, K. Fukunaga, and A. Kasamatsu, “Development of Complex Relative Permittivity Measurement System Based on Free-Space in 220–330 GHz Range,” IEEE Trans. THz Sci. Technol. 5, 1–8 (2014).
[Crossref]

J. Hammler, A. J. Gallant, and C. Balocco, “Free-Space Permittivity Measurement at Terahertz Frequencies With a Vector Network Analyzer,” IEEE Trans. THz Sci. Technol. 6(6), 817–823 (2016).
[Crossref]

H. Li, A. Arsenovic, J. L. Hesler, A. R. Kerr, and R. M. Weikle, “Repeatability and Mismatch of Waveguide Flanges in the 500–750 GHz Band,” IEEE Trans. THz Sci. Technol. 4(1), 39–48 (2014).
[Crossref]

J. Infrared, Millimeter, Terahertz Waves (4)

W. Withayachumnankul and M. Naftaly, “Fundamentals of Measurement in Terahertz Time-Domain Spectroscopy,” J. Infrared, Millimeter, Terahertz Waves 35, 610–637 (2014).
[Crossref]

G. Tzydynzhapov, P. Gusikhin, V. Muravev, A. Dremin, Y. Nefyodov, and I. Kukushkin, “New Real-Time Sub-Terahertz Security Body Scanner,” J. Infrared, Millimeter, Terahertz Waves 41(6), 632–641 (2020).
[Crossref]

U. Nandi, J. C. Norman, A. C. Gossard, H. Lu, and S. Preu, “1550-nm Driven ErAs:In(Al)GaAs Photoconductor-Based Terahertz Time Domain System with 6.5 THz Bandwidth,” J. Infrared, Millimeter, Terahertz Waves 39(4), 340–348 (2018).
[Crossref]

S. Preu, “A Unified Derivation of the Terahertz Spectra Generated by Photoconductors and Diodes,” J. Infrared, Millimeter, Terahertz Waves 35(12), 998–1010 (2014).
[Crossref]

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Measurement (1)

A. Taschin, P. Bartolini, J. Tasseva, and R. Torre, “THz time-domain spectroscopic investigations of thin films,” Measurement 118, 282–288 (2018).
[Crossref]

Metrologia (1)

N. M. Ridler, S. Johny, M. J. Salter, X. Shang, W. Sun, and A. Wilson, “Establishing waveguide lines as primary standards for scattering parameter measurements at submillimetre wavelengths,” Metrologia 58(1), 015015 (2021).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Quant. Imaging Med. Surg. (1)

Q. Sun, Y. He, K. Liu, S. Fan, E. P. J. Parrott, and E. Pickwell-MacPherson, “Recent advances in terahertz technology for biomedical applications,” Quant. Imaging Med. Surg. 7(3), 345–355 (2017).
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F. R. Faridi and S. Preu, “Characterization of a Terahertz Isolator using a 1.5 Port Vector Spectrometer,” in 2019 44th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), (2019), pp. 1–2.

A. Kazemipour, M. Hudlička, M. Salhi, T. Kleine-Ostmann, and T. Schrader, “Free-space quasi-optical spectrometer for material characterization in the 50–500 GHz frequency range,” in 2014 44th European Microwave Conference, (2014), pp. 636–639.

F. R. Faridi, U. Nandi, and S. Preu, “1.5 Port Vector Spectrometer for Terahertz Time Domain Spectroscopy,” in 2018 43rd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), (2018), pp. 1–2.

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Figures (11)

Fig. 1.
Fig. 1. Experimental setup of two-port PVNA. The optical path of the free-space laser beam is shown in red, whereas blue regions portray the terahertz path. Black arrows show the path of the terahertz signal emitted by Tx1. A part of the signal is reflected from the DUT and detected by Rx1, whereas the other part is partially transmitted through DUT towards Rx2. And white arrows represent the same journey for the terahertz wave generated by Tx2. Tx = Transmitter, Rx = Receiver, WGP = Wire grid polarizer, DUT = Device under test.
Fig. 2.
Fig. 2. The two-port PVNA has an available bandwidth of more than 2 THz, with maximum DNR of 51 dB at around 500 GHz. The measurements are done with an integration time of 100 $\mu$s per time step (ENBW = 937.6 Hz).
Fig. 3.
Fig. 3. (a) Section of an SRR array and (b) design parameters of a unit cell. $x$ = 300 $\mu$m, $r_{1}$ = 100 $\mu$m, $r_{2}$ = 75 $\mu$m, $\theta$ = 10$^{\circ }$, $w$ = 23 $\mu$m, $d_{G}$ = 210 nm, $d_{Q}$ = 212 $\mu$m.
Fig. 4.
Fig. 4. S-parameters of SRR. The measured data is depicted in blue, and grey dashed lines shows the simulated results. Two different polarization of incident terahertz wave is used to investigate the SRR, where figure (a) and figure (b) illustrate the S parameters retrieved for vertically polarized and horizontally polarized incident, respectively.
Fig. 5.
Fig. 5. The design of the investigated DBR. It comprises three Si layers with 520 $\mu$m thickness separated by air gaps of 150 $\mu$m.
Fig. 6.
Fig. 6. S-parameters of DBR. Data measured using PVNA is shown in blue and theoretical calculation is represented by grey (dashed) line.
Fig. 7.
Fig. 7. S-parameters of SRR for vertically polarized incident terahertz signal, measured using PVNA (blue) and compared with the data acquired using VNA extender (black) and simulation (grey dashed).
Fig. 8.
Fig. 8. Comparison between the S-parameters of DBR attained using PVNA (blue) and VNA (black). Theoretically calculated S-parameters are depicted by grey dashed lines.
Fig. 9.
Fig. 9. Schematic of the optimization process.
Fig. 10.
Fig. 10. Real part of dielectric permitttivity of HR-Si.
Fig. 11.
Fig. 11. Dielectric properties of PVC.(a) Real part of dielectric permitttivity and (b) Loss tangent of PVC.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

S 21 ( ω ) = t ( ω ) = E T D U T ( ω ) E T r e f ( ω ) , S 11 ( ω ) = r ( ω ) = E R D U T ( ω ) E R r e f ( ω )
n p ( ω ) = n 0 c 0 ω d p t ( ω )
κ p ( ω ) = c 0 ω d p { ln 4 n 0 n p ( ω ) ( n 0 + n p ( ω ) ) 2 ln t ( ω ) }
E F = ω [ ( | t ( ω ) | | t c a l c ( ω ) | ) 2 + ( | r ( ω ) | | r c a l c ( ω ) | ) 2 ]
E F ( ω x ) = [ ( | t ( ω x ) | | t c a l c ( ω x ) | ) 2 + ( | r ( ω x ) | | r c a l c ( ω x ) | ) 2 ]
t c a l c ( ω ) = τ τ exp [ j ( n ~ p ( ω ) n 0 ) ω d p c 0 ] F P ( ω )
r c a l c ( ω ) = ρ + τ τ ρ exp [ 2 j n ~ p ( ω ) ω d p c 0 ] F P ( ω )
F P ( ω ) = { 1 ρ 2 exp [ 2 j n ~ p ( ω ) ω d p c 0 ] } 1
τ = 2 n 0 n 0 + n ~ p ( ω ) ; τ = 2 n ~ p ( ω ) n 0 + n ~ p ( ω ) ; ρ = n ~ p ( ω ) n 0 n 0 + n ~ p ( ω ) ; ρ = n 0 n ~ p ( ω ) n 0 + n ~ p ( ω )
ϵ ( ω ) = n f 2 ( ω ) κ f 2 ( ω )
ϵ ( ω ) = 2 n f ( ω ) κ f ( ω ) ;
tan δ ( ω ) = ϵ ( ω ) ϵ ( ω ) = 2 n f ( ω ) κ f ( ω ) n f 2 ( ω ) κ f 2 ( ω )

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