Dual-Beam THz Spectrometer with Low-Aberration Optics and Off-Axis Multipixel Photoconductive Emitters for Reduced Systematic Errors
Open accessAbstract
A dual-beam THz spectrometer is reported that substantially reduces the influence of systematic errors in THz time-domain spectroscopy such as those caused by variations in femtosecond laser power or the environmental temperature and humidity. Dual THz beams with single-cycle waveforms were generated simultaneously using a dual-pixel interdigitated photoconductive antenna, allowing the simultaneous acquisition of sample and reference data in the spectrometer using the same optical components. A low-aberration optical geometry ensured diffraction-limited spatial profiles for both beams despite their off-axis propagation and was validated experimentally by measuring frequency-dependent beam profiles and theoretically via physical optics calculations. Although the experimental amplitudes and absolute phase spectra of both beams were very similar, we further provided a correction procedure to eliminate these small differences. The robustness of the dual-beam spectrometer design was evaluated by measuring the complex transmission of a thin plastic sheet after intentionally introducing a change in the relative humidity of the THz beam path. The dual-beam THz spectrometer was effective at removing systematic errors in the amplitude and phase by simultaneously measuring the two THz beams under the same conditions.
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Written from the paper’s full text.
TL;DR
A dual-beam THz time-domain spectrometer is demonstrated using a dual-pixel photoconductive emitter and low-aberration off-axis parabolic mirror optics to acquire sample and reference beams simultaneously through the same optical path. It suppresses systematic errors from laser-power, temperature, or humidity drift, as shown by correcting single-beam artifacts caused by a controlled humidity change.
Key findings
- The dual-pixel emitter had pixel centers spaced by Δx = 3 mm, each with a 500 × 500 μm active area, positioned at x = ±1.5 mm from the optical axis; the measured focused beams were separated by Δx = 2.8 mm, close to the 3 mm design.
- The low-aberration (a,a)(a,a) OAPM geometry produced similar diffraction-limited profiles for both beams: at 0.3 THz, Gaussian fits gave σ1 = 0.60 mm and σ2 = 0.64 mm; at 3.0 THz, σ1 = σ2 = 0.15 mm. Spectral coverage reached 100 GHz to 6.5 THz, and |R(ω)| = |E2/E1| was within 10% of unity up to 5.5 THz.
- With a 23 μm Mylar sheet and an intentional humidity change to 6% RH, single-beam transmission showed erroneous minima near water-vapor absorption lines (1.7, 2.2, 2.7 THz, etc.) and the relative THz amplitude dropped to around 50% at 3.0 THz for the 610 mm path length. The dual-beam transmission TdualH matched the purged “true” transmission in modulus and phase.
- A correction procedure was provided to eliminate small amplitude and phase differences between the two beams, and the dual-beam formula removes systematic errors when both beams experience the same perturbation.
Methods
- Experimental setup: a Ti:sapphire oscillator (100 fs, 80 MHz, 800 nm) was split into pump and probe; a transmissive DOE and 100 mm focal-length plano-convex lens produced two pump beams mainly in m = ±1 orders, giving 300 mW per beam and 3 mm spacing at the emitters. Backward-emitted THz radiation was collected, reflected by an FTO mirror, and guided by two pairs of 76.2 mm focal-length, 50.8 mm diameter OAPMs in an (a,a)(a,a) configuration. Detection used a 200 μm GaP crystal, Wollaston prism, balanced photodiodes, and lock-in amplifiers; emitters were modulated at 100 kHz with Vpp = 20 V, with emitter 2 phase-shifted by 90°.
- Design validation used Ansys Zemax physical optics with Fresnel propagation, starting from Gaussian beams with waists w0 = 0.4 mm centered at x = ±1.5 mm. Experiments used knife-edge scans in 50 μm steps, frequency-resolved beam profiles, and a phase- and amplitude-accurate discrete Fourier transform routine.
- Spectroscopy test: a 23 μm polyethylene terephthalate (Mylar) sheet was measured with a frequency-independent complex refractive index ñ = 1.78 + 0.03i, first under dry nitrogen purge (RH = 0%) and then after changing the THz beam path to RH = 6%.
Limitations
- Stated: the work is a proof-of-concept free-space THz transmission setup based around a Ti:sapphire laser, though the authors state the approach can be extended to fiber-coupled systems or reflection geometry. The authors also note a small spatial overlap of the two beams at lower frequencies, which was circumvented experimentally by a modulation scheme.
- Stated: sample positioning along z requires care because the Rayleigh range is zR = 0.77 mm at 0.3 THz and zR = 1.4 mm at 3 THz. Water-vapor line widths were limited by the 20 ps scan window.
- Evident from the text: the robustness demonstration uses one thin plastic sample and a controlled humidity perturbation, so broader material, frequency, and environmental validation is not shown.
Model-written summary. Check it against the paper before relying on it.
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Claims the paper makes
0 of 20 cited sources checked · 0 supported · 0 flagged
- Findingown data
The dual-beam THz spectrometer was effective at removing systematic errors in the amplitude and phase by simultaneously measuring the two THz beams under the same conditions.
“The dual-beam THz spectrometer was effective at removing systematic errors in the amplitude and phase by simultaneously measuring the two THz beams under the same conditions.”
Quote in the paperSubstantial claim - Findingown data
The experimental amplitudes and absolute phase spectra of both beams were very similar.
“the experimental amplitudes and absolute phase spectra of both beams were very similar”
Quote in the paperNot a substantial claim - Findingown data
A low-aberration optical geometry ensured diffraction-limited spatial profiles for both beams despite their off-axis propagation.
“A low-aberration optical geometry ensured diffraction-limited spatial profiles for both beams despite their off-axis propagation”
Quote in the paperSubstantial claim - Findingreasoning
The imaging system guides the two beams in free space, ensuring a diffraction-limited spot size at both the sample and detector planes.
“These mirrors guide the two beams in free space, ensuring a diffraction-limited spot size at both the sample and the detector planes.”
Quote in the paperSubstantial claim - Findingown data
With the plastic sample in beam 2, |Tsingle,2| reduces in amplitude to 0.86 at 2 THz before increasing.
“With the plastic sample placed in beam 2, |Tsingle,2| (orange line) can be seen to reduce in amplitude to 0.86 at 2 THz, before increasing.”
Quote in the paperNot a substantial claim
- Findingreasoning
The dual-beam transmission Tdual is similar to Tsingle,2.
“Hence, the dual-beam transmission Tdual (blue lines) is similar to Tsingle,2 (orange lines).”
Quote in the paperSubstantial claim - Findingown data
The calculated transmission of the sample, made without assuming the thin-film limit and assuming a frequency-independent complex refractive index ñ = 1.78 + 0.03i, is in excellent agreement with the amplitude and phase of the single-beam sample transmission.
“The calculated transmission of the sample, made without assuming the thin-film limit,1 and assuming a frequency-independent complex refractive index ñ = 1.78 + 0.03i, is reported by the black dashed lines. This is in excellent agreement with the amplitude and phase of the single-beam sample transmission.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [1] source
Not checked in the free run.
- The authors state this as an assumption: The sample's complex refractive index is frequency-independent with ñ = 1.78 + 0.03i.
- Findingown data
The values and z dependence of the 1/e widths are similar for both beams.
“The values and z dependence of the 1/e widths can be seen to be similar for both beams.”
Quote in the paperSubstantial claim - Findingown data
Identical beam profiles were obtained for both beams.
“Identical beam profiles were obtained for both beams.”
Quote in the paperSubstantial claim - Findingown data
Both pulses have similar frequency-dependent phases.
“The absolute phase spectra, ϕn*(ω), are reported in Figure 4e, revealing that both pulses have similar frequency-dependent phases.”
Quote in the paperSubstantial claim - Findingown data
The two pulses have similar time-domain shapes.
“Performing the inverse DFT recovered the time-overlapped En*(t), as shown in Figure 4d, where the similarity of the two pulses in the time domain is evident.”
Quote in the paperSubstantial claim - Findingreasoning
The beams are well-separated by the designed spacing of 3 mm as a result of the 1:1 magnification of the optics.
“The beams are well-separated by the designed spacing of 3 mm as a result of the 1:1 magnification of the optics (equal focal length OAPMs).”
Quote in the paperSubstantial claim - Findingown data
The beams were tightly focused within 1 mm of the focus, where they had the highest amplitude.
“The beams were tightly focused within 1 mm of the focus, where they had the highest amplitude (dark-red areas).”
Quote in the paperNot a substantial claim - Findingown data
At 0.3 THz, the THz beams are larger than at higher frequency: the diffraction-limited spot size is bigger for longer wavelengths (σ = 0.56 mm at 0.3 THz) than at shorter wavelengths (σ = 0.24 mm at 1.0 THz).
“At 0.3 THz, in Figure 2a,d, the THz beams are larger than at higher frequency: the diffraction-limited spot size is bigger for longer wavelengths (σ = 0.56 mm at 0.3 THz) than at shorter wavelengths (σ = 0.24 mm at 1.0 THz).”
Quote in the paperSubstantial claim - Findingown data
A 6% RH drift lowers the relative THz amplitude to around 50% at 3.0 THz for this spectrometer's 610 mm path length.
“Even this small drift in RH lowers the relative THz amplitude to around 50% at 3.0 THz for this spectrometer’s 610 mm path length.”
Quote in the paperSubstantial claim - Findingown data
The beam profiles were studied using theoretical and experimental methods, identifying a small spatial overlap of the beams at lower frequencies.
“The beam profiles were studied using theoretical and experimental methods, in particular, identifying a small spatial overlap of the beams at lower frequencies.”
Quote in the paperSubstantial claim - Findingown data
After the change in humidity, the dual-beam transmission TdualH is very similar in modulus and phase to the true transmission of the sample measured under purged conditions.
“Considering now the dual-beam method: after the change in humidity, the dual-beam transmission TdualH from eq 1 is shown by the green lines in Figure 5c,d and is very similar in modulus and phase to the “true” transmission of the sample as measured under purged conditions (dark blue).”
Quote in the paperSubstantial claim - Findingown data
The OAPM geometry has good spatial resolution over a broad frequency range.
“On the optics side, while our OAPM geometry has good spatial resolution over a broad frequency range, the dual-beam concept is also applicable for lens-based THz optical systems, which are more straightforward to align but have lower signal-to-noise ratios at higher frequencies as a result of absorption in the lens material.”
Quote in the paperSubstantial claim - Findingown data
The amplitude and phase of sequential single-beam transmission Tsingle,2H deviate from the true transmission Tdual at frequencies close to water vapor absorption lines (1.7, 2.2, 2.7 THz, etc.).
“The amplitude and phase of the sequential, single-beam transmission Tsingle,2H can be seen to deviate from the true transmission, Tdual (obtained with full purge), at frequencies close to the water vapor absorption lines (1.7 THz, 2.2 THz, 2.7 THz, etc.).”
Quote in the paperSubstantial claim - Interpretationown data
A correction procedure was provided to eliminate small differences between the amplitudes and absolute phase spectra of the two beams.
“we further provided a correction procedure to eliminate these small differences.”
Quote in the paperSubstantial claim - Interpretationown data
A dual-beam THz spectrometer substantially reduces the influence of systematic errors in THz time-domain spectroscopy, such as those caused by variations in femtosecond laser power or environmental temperature and humidity.
“A dual-beam THz spectrometer is reported that substantially reduces the influence of systematic errors in THz time-domain spectroscopy such as those caused by variations in femtosecond laser power or the environmental temperature and humidity.”
Quote in the paperSubstantial claim- Rests on an assumption: Fewer studies have tackled systematic errors in THz-TDS than random noise.
- Rests on an assumption: Dual-beam spectroscopy has not been widely adopted or explored in the THz range by academic and industrial users.
- Study design and conductown data
The robustness of the dual-beam spectrometer design was evaluated by measuring the complex transmission of a thin plastic sheet after intentionally introducing a change in the relative humidity of the THz beam path.
“The robustness of the dual-beam spectrometer design was evaluated by measuring the complex transmission of a thin plastic sheet after intentionally introducing a change in the relative humidity of the THz beam path.”
Quote in the paperSubstantial claim - Interpretationown data
The dual-beam spectrometer approach produces well-separated THz beams, suitable for sample and reference measurements.
“This demonstrates that the dual-beam spectrometer approach produces well-separated THz beams, suitable for sample and reference measurements.”
Quote in the paperSubstantial claim - Study design and conductreasoning
The voltage applied to emitter 2 was phase-shifted by 90° relative to emitter 1 to prevent optical cross-talk at the detection side.
“The voltage applied to emitter 2 was phase-shifted by 90° relative to emitter 1, to prevent optical cross-talk at the detection side”
Quote in the paperSubstantial claim - Interpretationreasoning
Beam 1 can be regarded as a reference beam that tracks variations in the amplitude or phase of the THz beam incident on the sample.
“Alternatively, one can regard beam 1 as a reference beam that tracks variations in the amplitude or phase of the THz beam incident on the sample, with Tsingle,1 = E1(ω)/E1,b(ω) = η1(ω) and hence2where the last step was made assuming that η2(ω) = η1(ω).”
Quote in the paperSubstantial claim- The authors state this as an assumption: The systematic error alters both THz beams in the same way (η2(ω) = η1(ω)).
- Interpretationnone given
If both THz beams are identical in amplitude and phase, the ratio E2/E1 corresponds to the transmission of the sample.
“First, the ratio E2(ω)/E1(ω) corresponds to the transmission of the sample if both THz beams are identical in amplitude and phase.”
Quote in the paperSubstantial claim - Interpretationreasoning
THz spectroscopy can be performed where one beam acts as a reference while a sample is placed in the other beam.
“Therefore, THz spectroscopy can be performed where one beam acts as a reference, while a sample is placed in the other beam.”
Quote in the paperSubstantial claim - Interpretationown data
The reduction in |Tsingle,2| is not due to physical absorption but to interference of multiple reflections within the plastic.
“This is not a consequence of any physical absorption in the sample: rather it is a consequence of the interference of multiple reflections within the plastic.”
Quote in the paperSubstantial claim - Interpretationreasoning
The extra phase of pulse 1 relative to pulse 2 in the raw data has no impact on Tdual because the ratio E1/E1,b cancels out this extra phase.
“Further, the extra phase of pulse 1 relative to pulse 2 in the raw data (Figure 4a) has no impact on Tdual as it contains the ratio E1/E1,b, which cancels out this extra phase.”
Quote in the paperSubstantial claim - Premisecitation
Collecting and using THz radiation emitted backward in reflection geometry avoids dispersion and absorption in the GaAs substrate at higher frequencies.
“The THz radiation emitted backward (reflection geometry) was collected and used, to avoid dispersion and absorption in the GaAs substrate at higher frequencies.18”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [18] source
Not checked in the free run.
- Interpretationreasoning
If the amplitude or phase of the THz pulse produced by the spectrometer has altered between acquiring the two spectra, the pulse incident on the sample is not the same as when measured previously.
“However, this is not the case if the amplitude or phase of the THz pulse produced by the spectrometer has altered in the time between acquiring the two spectra, such that the pulse incident on the sample, Ein, is not the same as when measured previously, Eb.”
Quote in the paperSubstantial claim - Interpretationreasoning
Dividing by the ratio E2,b/E1,b corrects for differences between the two beams.
“Dividing by the ratio E2,b/E1,b corrects for the differences between the two beams.”
Quote in the paperSubstantial claim - Interpretationown data
The dual-beam approach can be used to perform spectroscopy at frequencies of 0.3 THz and higher, such that a sample placed in one beam does not attenuate too much of the reference beam.
“Therefore, the dual-beam approach can be used to perform spectroscopy at frequencies of 0.3 THz and higher, such that a sample placed in one beam (covering x ≥ 0) does not attenuate too much of the reference beam (x < 0).”
Quote in the paperSubstantial claim - Interpretationown data
Having similar spectral performances for the two beams allows the reference beam to be used effectively over the same frequency range as the sample beam in dual-beam spectroscopy.
“Having similar spectral performances for the two beams allows the reference beam to be used effectively over the same frequency range as the sample beam in dual-beam spectroscopy.”
Quote in the paperSubstantial claim - Interpretationreasoning
Assuming η = 1 in single-beam spectroscopy can lead to systematic errors in the optical properties deduced from Tsingle.
“As η is assumed to be unity in single-beam spectroscopy, this can lead to systematic errors in the optical properties of the sample deduced from Tsingle (shown later in the manuscript).”
Quote in the paperSubstantial claim - Premisereasoning
For small samples, the sample and reference are located only at the correct positions for a fraction of the experiment, making for a relatively low-duty cycle of time spent usefully acquiring data.
“For small samples, the sample and reference are also located only at the correct positions for a fraction of the experiment, making for a relatively low-duty cycle of time spent usefully acquiring data.”
Quote in the paperSubstantial claim - Interpretationcitation
The sawtooth shape of the phase of beam 1 arises from the finite arrival time of the pulse at t1 = 2.3 ps, which introduces a linear phase term via the Fourier shift theorem.
“The sawtooth shape of the phase of beam 1, ϕ1(ω), arises from the finite arrival time of the pulse at t1 = 2.3 ps, which introduces a linear phase term in the frequency domain via the Fourier shift theorem.20”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [20] Lloyd-Hughes J., 2024, arXiv
Not checked in the free run.
- Study design and conductown data
The broadband design of the THz optical system was validated theoretically using the physical optics module in Ansys Zemax to propagate the wavefront of both THz beams throughout the optical setup.
“To validate the broadband design of the THz optical system theoretically, we used the physical optics module in the optics simulation software Ansys Zemax to propagate the wavefront of both THz beams throughout the optical setup.”
Quote in the paperSubstantial claim - Premisereasoning
Double-modulation terahertz spectroscopy is not compatible with modern fast-scan THz data acquisition methods that acquire THz waveforms at rates faster than a few Hz.
“This technique is thus not compatible with modern fast-scan THz data acquisition methods that acquire THz waveforms at rates of faster than a few Hz (e.g., rapid delay lines; asynchronous optical sampling).”
Quote in the paperSubstantial claim - Interpretationcitation
The excellent beam quality even for off-axis beam points is a feature of the (a,a) orientation adopted for each OAPM pair, which has minimal aberrations.
“The excellent beam quality even for off-axis beam points is a feature of the (a,a) orientation adopted for each OAPM pair,17 which has minimal aberrations.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [17] source
Not checked in the free run.
- Interpretationreasoning
The systematic error alters both THz beams in the same way for variations in laser power or atmospheric THz absorption caused by temperature, pressure, or humidity, since both beams traverse the same optical path.
“This is the case when the systematic error alters both THz beams in the same way, such as a variation in laser power or a change in atmospheric THz absorption caused by a variation in temperature, pressure, or humidity (since both THz beams traverse the same optical path).”
Quote in the paperSubstantial claim - Study design and conductcitation
The system was designed to have minimal wavefront distortion and aberration by staying within the tolerance limits for beams originating from off-axis points in the emitter plane.
“The system was designed to have minimal wavefront distortion and aberration, by staying within the tolerance limits for beams originating from off-axis points in the emitter plane.17”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [17] source
Not checked in the free run.
- Interpretationnone given
A Fourier time-shifting algorithm can synchronize the measurement time window for both beams to allow for differences in path length of the two probe beams.
“To allow for differences in path length of the two probe beams, we report how a Fourier time-shifting algorithm can synchronize the measurement time window for both beams.”
Quote in the paperSubstantial claim - Interpretationown data
Dual-beam spectroscopy can effectively eliminate systematic errors by using a reference beam that tracks a change in experimental conditions.
“Therefore, dual-beam spectroscopy can effectively eliminate systematic errors by using a reference beam that tracks a change in experimental conditions.”
Quote in the paperSubstantial claim - Interpretationreasoning
The dual-beam THz spectrometer substantially reduced the systematic errors that can lead to reproducibility issues in standard single-beam THz time-domain spectroscopy.
“We demonstrated an advanced dual-beam THz spectrometer that substantially reduced the systematic errors that can lead to reproducibility issues in standard single-beam THz time-domain spectroscopy.”
Quote in the paperSubstantial claim - Interpretationown data
The systematic error arose because the sequential single-beam measurement assumed the same humidity when sample and baseline data were acquired, whereas E2,b had RH = 0% and E2 was taken with RH = 6%.
“The systematic error has arisen because the sequential, single-beam spectroscopy measurement assumed the same humidity when the sample and baseline (reference) data were acquired, whereas in fact, E2,b had RH = 0% and E2 was taken with RH = 6%.”
Quote in the paperSubstantial claim - Premisecitation
Working under standard atmospheric conditions presents challenges for THz spectroscopy, imaging, and communications because of the rotational modes of water vapor.
“Working under standard atmospheric conditions presents challenges for THz spectroscopy, imaging, and communications because of the rotational modes of water vapor.23,24”
Quote in the paperSubstantial claim0 of 2 sources checked - Study design and conductown data
A modulation scheme allowed the two beams to be individually resolved.
“This challenge was circumvented experimentally via a modulation scheme that allowed the two beams to be individually resolved.”
Quote in the paperSubstantial claim - Premisecitation
Variations in atmospheric temperature, pressure, or humidity cause the attenuation and dispersion of THz radiation to change at frequencies close to absorption lines.
“Variations in atmospheric temperature, pressure, or humidity cause the attenuation and dispersion of THz radiation to change at frequencies close to the numerous absorption lines in this frequency band.”
Quote in the paperSubstantial claim0 of 2 sources checked - Interpretationreasoning
The effective correction for dual-beam spectroscopy was achieved because the measurement of the reference beam Tsingle,1H contained the amplitude and phase changes created by extra water vapor.
“The effective correction for dual-beam spectroscopy was achieved because the measurement of the reference beam, Tsingle,1H, contained the amplitude and phase changes created by extra water vapor in the spectrometer.”
Quote in the paperSubstantial claim
- May combine two claims. 33
- Classified as probably not a substantial claim. 5
May combine two claims.
Findingown dataDual THz beams with single-cycle waveforms were generated simultaneously using a dual-pixel interdigitated photoconductive antenna, allowing simultaneous acquisition of sample and reference data in the spectrometer using the same optical components.
“Dual THz beams with single-cycle waveforms were generated simultaneously using a dual-pixel interdigitated photoconductive antenna, allowing the simultaneous acquisition of sample and reference data in the spectrometer using the same optical components.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThe two beams had similar frequency-dependent sizes, with σ1 ≃ σ2.
“The similarity between the profiles can be further seen in Figure 3d, where it is evident that σ1 ≃ σ2, and both beams had similar frequency-dependent sizes.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataSingle-cycle THz pulses were obtained for both beams, with beam 1 arriving 2.3 ps later than beam 2 due to differing optical path lengths of probe beams 1 and 2.
“Single-cycle THz pulses were obtained for both THz beams 1 and 2, with pulses in beam 1 arriving 2.3 ps later than beam 2, as a result of the differing optical path lengths of probe beams 1 and 2.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataThe two beams were tightly focused in the sample focal plane (z = 0) and were separated by a distance Δx = 2.8 mm, close to the device's designed separation of 3 mm.
“As shown in Figure 3a, the two beams were tightly focused in the sample focal plane (z = 0) and were separated by a distance Δx = 2.8 mm, close to the device’s designed separation of 3 mm.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataAt all frequencies, the two beams are circular, and beam cross sections are close to Gaussian in shape.
“At all frequencies, the two beams are circular, and beam cross sections are close to Gaussian in shape”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataAt f = 0.3 THz, the two beams had similar amplitude profiles, consistent with Gaussian beams with σ1 = 0.60 mm and σ2 = 0.64 mm.
“As reported in Figure 3b, the beams had similar amplitude profiles at f = 0.3 THz (points), which were consistent with error function fits (black lines) corresponding to Gaussian beams with σ1 = 0.60 mm and σ2 = 0.64 mm (shaded areas).”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThe two THz beams had similar spatial profiles but were well-separated by the design distance in an intermediate focal plane.
“we first demonstrate that the two THz beams had similar spatial profiles but were well-separated by the design distance in an intermediate focal plane.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThe traditional single-beam approach was very sensitive to variations in atmospheric humidity levels, while the dual-beam method reliably reproduced the correct complex transmission.
“While the traditional single-beam approach was very sensitive to variations in atmospheric humidity levels, our dual-beam method reliably reproduced the correct complex transmission.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataAmplitude spectra show good spectral coverage from 100 GHz to 6.5 THz, with very similar spectral amplitudes for both beams (|E1| ≃ |E2|).
“Amplitude spectra in Figure 4b show good spectral coverage from 100 GHz to 6.5 THz, with very similar spectral amplitudes for both beams, |E1(ω)| ≃ |E2(ω)|.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThe amplitude ratio |R(ω)| is within 10% of 1 over the range to 5.5 THz, with a small phase difference.
“The amplitude |R(ω)| is within 10% of the ideal value |R| = 1 over the range to 5.5 THz, with a small phase difference ∠R(ω), as shown in Figure 4f.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThe intensity does not completely drop to zero between the beams on the optical axis for 0.3 THz, suggesting that at lower frequencies there may be some spatial overlap of the two beams.
“The intensity does not completely drop to zero between the beams on the optical axis (x = 0, y = 0) for 0.3 THz, suggesting that at lower frequencies, there may be some spatial overlap of the two beams.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataAt higher frequencies (1 THz and 3 THz), the two beams are more clearly distinct, with a higher peak intensity and smaller spot size.
“At higher frequencies (1 THz and 3 THz frequencies), the two beams are more clearly distinct, with a higher peak intensity and smaller spot size”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThe beam profiles were sharper at higher frequencies; at f = 3.0 THz, σ1 = σ2 = 0.15 mm.
“The beam profiles were sharper at higher frequencies, for instance, with σ1 = σ2 = 0.15 mm at f = 3.0 THz, evident in Figure 3c.”
Quote in the paperNot a substantial claimMay combine two claims.
FindingreasoningAt 0.3 THz with σ = 0.64 mm, the Rayleigh range is zR = 0.77 mm; at 3 THz with σ = 0.15 mm, zR = 1.4 mm.
“For example, using σ = 0.64 mm at 0.3 THz (Figure 3d), the Rayleigh range is zR = 0.77 mm, or at 3 THz with σ = 0.15 mm, it increased to zR = 1.4 mm.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataAltering the humidity level of the spectrometer intentionally introduced systematic errors in amplitude and phase, both of which produce significant systematic errors in conventional single-beam systems.
“To evaluate the performance of our spectrometer, we intentionally introduced systematic errors in the amplitude and phase by altering the humidity level of the spectrometer, both of which produce significant systematic errors in conventional single-beam systems.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThe low-aberration OAPM geometry achieved a diffraction-limited spot size, allowing independent sample and reference beams in the intermediate focal plane even with relatively small beam separations (3 mm here).
“Crucially, the low-aberration (a,a)(a,a) OAPM geometry achieved a diffraction-limited spot size, allowing independent sample and reference beams in the intermediate focal plane even with relatively small beam separations (3 mm here).”
Quote in the paperSubstantial claimClassified as probably not a substantial claim. May combine two claims.
PremisecitationRandom noise controls the precision of results, while systematic errors influence the accuracy of material properties derived from the experiment.
“Errors directly impact the efficacy of the parameter extraction process:3 random noise controls the precision of results, while systematic errors influence the accuracy of material properties derived from the experiment.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [3] source
Not checked in the free run.
May combine two claims.
Study design and conductown dataThe low-aberration optical geometry was validated experimentally by measuring frequency-dependent beam profiles and theoretically via physical optics calculations.
“was validated experimentally by measuring frequency-dependent beam profiles and theoretically via physical optics calculations.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationnone givenUsing two THz beams propagating along the same optical path mitigates against long-term drifts that cause systematic errors while reducing system complexity and cost.
“By using two THz beams propagating along the same optical path, this approach mitigates against long-term drifts that cause systematic errors while reducing the system complexity and cost.”
Quote in the paperSubstantial claim- Rests on an assumption: Fewer studies have tackled systematic errors in THz-TDS than random noise.
- Rests on an assumption: Dual-beam spectroscopy has not been widely adopted or explored in the THz range by academic and industrial users.
May combine two claims.
Interpretationown dataThe spatial, temporal, and spectral properties of the two THz beams are very similar, and above 300 GHz the two beams are spatially separated.
“The results above show that the spatial, temporal, and spectral properties of the two THz beams are very similar and that at higher frequencies (above 300 GHz), the two beams are spatially separated.”
Quote in the paperSubstantial claimMay combine two claims.
PremisecitationThe generalized THz ellipsometry system had roughly double the components compared to a standard THz time-domain spectrometer, adding to the system's cost and complexity.
“While an important step forward, compared to a standard THz time-domain spectrometer, the system had roughly double the components,10 adding to the system’s cost and complexity.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [10] source
Not checked in the free run.
May combine two claims.
InterpretationreasoningIf η = 1, the experimental transmission matches the actual transmission; if η ≠ 1, a systematic error has occurred.
“If η = 1, then the experimental transmission matches the actual transmission function of the sample, Tsingle = T, while η ≠ 1 implies that a systematic error has occurred in the time between measurements.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
PremisecitationGeneralized THz ellipsometry used two photoconductive antennas to generate two orthogonally polarized THz beams, which were combined, reflected, split into orthogonal polarizations, and detected by two photoconductive detectors.
“In generalized THz ellipsometry,10 two photoconductive antennas were used to generate two orthogonally polarized THz beams, which were then combined with a THz polarizer, reflected from a sample, split into orthogonal polarizations, and detected by two photoconductive detectors.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [10] source
Not checked in the free run.
May combine two claims.
PremisecitationA standard silicon lens with the dual emitters was avoided because spherical lenses only work well for on-axis point sources.
“The use of a standard silicon lens with the dual emitters was avoided, as spherical lenses only work well for on-axis point sources.19”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [19] source
Not checked in the free run.
May combine two claims.
InterpretationcitationThe second pair of OAPMs propagates the two THz beams from the sample plane to the detector plane, where diffraction-limited foci with similar optical performance are expected, including some overlap of the two beams at lower frequencies.
“The second pair of OAPMs propagates the two THz beams from the sample plane to the detector plane (Figure 1), where diffraction-limited foci with similar optical performance are expected,17 including some overlap of the two beams at lower frequencies.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [17] source
Not checked in the free run.
May combine two claims.
InterpretationcitationAt low frequencies, the near constant −π/2 phase is as expected for a single-cycle pulse; the nonlinear increase in phase with frequency can be assigned to chirp processes such as dispersion in the electro-optic crystal and the GaAs emitter.
“At low frequencies, the near constant −π/2 phase is as expected for a single-cycle pulse,20 while the nonlinear increase in phase with frequency can be assigned to processes that introduce chirp, such as dispersion in the electro-optic crystal21 and the GaAs emitter.18”
Quote in the paperNot a substantial claim0 of 3 sources checkedClassified as probably not a substantial claim. May combine two claims.
Interpretationnone givenA dual-beam transmission formula for spectroscopy allows systematic errors to be removed and corrects for any amplitude and phase differences between the two beams.
“We then define a dual-beam transmission formula for spectroscopy that allows systematic errors to be removed and which corrects for any amplitude and phase differences between the two beams.”
Quote in the paperSubstantial claimMay combine two claims.
InterpretationreasoningThe frequency dependence of the spot size is such that σn is frequency-independent at higher frequencies (σn ≃ 0.15 mm for f ≥ 1.5 THz) and σn ∝ 1/f at longer wavelengths (f < 1 THz), where the THz beam starts to overfill the first OAPM.
“σ is frequency-independent at higher frequencies, with σn(f) ≃ 0.15 mm for f ≥ 1.5 THz, while σn ∝ λ ∝ 1/f at longer wavelengths (f < 1 THz) where the THz beam starts to overfill the first OAPM.”
Quote in the paperNot a substantial claimMay combine two claims.
PremisecitationSelf-referencing methods rely on accurate knowledge of the substrate and make assumptions about sample geometry such as the absence of air gaps, which can introduce systematic errors during data postprocessing.
“However, such methods rely on accurate knowledge of the substrate and make assumptions about sample geometry such as the absence of air gaps, which can introduce systematic errors during data postprocessing.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [8] source
Not checked in the free run.
May combine two claims.
Interpretationown dataThe low-aberration design allowed good spatial separation of the two beams for frequencies of 0.3 THz and higher, enabling dual-beam spectroscopy with a sample in one beam.
“The low-aberration design of the spectrometer allowed good spatial separation of the two beams for frequencies of 0.3 THz and higher, allowing dual-beam spectroscopy measurements to be performed by placing a sample in one of the two beams.”
Quote in the paperSubstantial claimMay combine two claims.
PremisecitationDouble-modulation terahertz spectroscopy rapidly translates the sample into and out of the THz beam, resulting in a differential signal sensitive to subtle variations in absorption and phase.
“Double-modulation terahertz spectroscopy achieves this by rapidly translating the sample into and out of the THz beam,6,7 resulting in a differential signal sensitive to subtle variations in absorption and phase.”
Quote in the paperSubstantial claim0 of 2 sources checkedProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Study design and conductown dataTo prohibit cross-talk in the detection plane, the two beams can be modulated at different frequencies or with orthogonal phases, such that no cross-talk is observed between the beams.
“To prohibit cross-talk in the detection plane in the experiment (e.g., probe beam 2 sampling the edge of THz beam 1), the two beams can be modulated at different frequencies or with orthogonal phases, such that no cross-talk is observed between the beams (Supporting Information).”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductnone givenThe line widths were limited by the 20 ps scan window of the experiment.
“Here, the line widths were limited by the 20 ps scan window of the experiment.”
Quote in the paperNot a substantial claimMay combine two claims.
InterpretationreasoningThe dual-beam spectrometer suppressed these systematic errors by simultaneously measuring two THz beams that propagated along the same optical path, significantly enhancing accuracy and reliability.
“Our dual-beam spectrometer was able to suppress these systematic errors by simultaneously measuring two THz beams that propagated along the same optical path, significantly enhancing the accuracy and reliability of the measurement data.”
Quote in the paperSubstantial claim
The paper relies on this without support.
Fewer studies have tackled systematic errors in THz-TDS than random noise.
“However, fewer studies have tackled the systematic errors in THz-TDS.”
The paper relies on this without support.
Dual-beam spectroscopy has not been widely adopted or explored in the THz range by academic and industrial users.
“Dual-beam spectroscopy has not been widely adopted or explored in the THz range by the academic and industrial users of THz methods”
The authors state this as an assumption.
The systematic error alters both THz beams in the same way (η2(ω) = η1(ω)).
“where the last step was made assuming that η2(ω) = η1(ω).”
The authors state this as an assumption.
The sample's complex refractive index is frequency-independent with ñ = 1.78 + 0.03i.
“assuming a frequency-independent complex refractive index ñ = 1.78 + 0.03i”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The mean arrival time method can be calculated automatically and rapidly via numerical integration and is accurate for pulses that are not too complex, but it cannot be used for more complex waveforms such as a pulse train created by internal reflections, because the integral is pulled later in time by pulse echoes.
“The mean arrival time can be calculated automatically and rapidly via numerical integration and is accurate for pulses that are not too complex. For example, it can be used to correct for arrival time differences between two THz pulses in dual-beam THz spectroscopy [26]. However, it cannot be used for more complex waveforms: for instance, if the data set comprises a pulse train created by internal”
From A Tutorial on THz Pulse Analysis: Accurate Retrieval of Pulse Arrival Times, Spectral Energy Density and Absolute Spectral Phase (2025) · cites this paper as [26]
Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measuredThe accurate determination of the pulse arrival time may prove useful in THz time-of-flight, layer thickness, or tomography applications, and further helps to correct arrival time differences in dual-beam THz spectroscopy.
“The accurate determination of the pulse arrival time may prove useful in THz time-offlight, layer thickness, or tomography applications [38], and further helps to correct arrival time differences in dual-beam THz spectroscopy [26].”
From A Tutorial on THz Pulse Analysis: Accurate Retrieval of Pulse Arrival Times, Spectral Energy Density and Absolute Spectral Phase (2025) · cites this paper as [26]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rayleigh range at 0.3 THz conflicts with the stated formula
MinorAt 0.3 THz, the wavelength is approximately 1 mm. Applying the paper's formula with σ = 0.64 mm gives a Rayleigh range of about 2.57 mm, not 0.77 mm; the reported 3 THz example is consistent with the formula.
“For example, using σ = 0.64 mm at 0.3 THz (Figure 3d), the Rayleigh range is zR = 0.77 mm, or at 3 THz with σ = 0.15 mm, it increased to zR = 1.4 mm.”
“The radius of a Gaussian beam remains roughly constant within the Rayleigh range, a distance of zR = 2πσ2/λ from the focus.”
Cites
A Review of the Terahertz Conductivity of Bulk and Nano-Materials
Lloyd-Hughes, J., & Jeon, T.-I. (2012) · Journal of Infrared, Millimeter, and Terahertz Waves · doi:10.1007/s10762-012-9905-y · Cited by 503 · see citing works
Self-citationFundamentals of Measurement in Terahertz Time-Domain Spectroscopy
Withayachumnankul, W., & Naftaly, M. (2014) · Journal of Infrared, Millimeter, and Terahertz Waves · doi:10.1007/s10762-013-0042-z · Cited by 288 · see citing works
Gallot, G., Zhang, J., McGowan, R. W., Jeon, T.-I., & Grischkowsky, D. (1999) · Applied Physics Letters · doi:10.1063/1.124124 · Cited by 241 · see citing works
Uncertainty in terahertz time-domain spectroscopy measurement
Withayachumnankul, W., Fischer, B. M., Lin, H., & Abbott, D. (2008) · Journal of the Optical Society of America B · doi:10.1364/josab.25.001059 · Cited by 181 · see citing works
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Terahertz (THz) biophotonics technology: Instrumentation, techniques, and biomedical applications
Chen, X., Lindley-Hatcher, H., Stantchev, R. I., Wang, J., Li, K., Hernández-Serrano, A. I., Taylor, Z., Castro-Camus, E., & Pickwell‐MacPherson, E. (2022) · Chemical Physics Reviews · doi:10.1063/5.0068979 · Cited by 146 · see citing works
Dielectric constant measurement of thin films by differential time-domain spectroscopy
Jiang, Z., Li, M., & Zhang, X.-C. (2000) · Applied Physics Letters · doi:10.1063/1.126587 · Cited by 139 · see citing works
Xin, X., Altan, H., Saint, A., Matten, D., & Alfano, R. R. (2006) · Journal of Applied Physics · doi:10.1063/1.2357412 · Cited by 116 · see citing works
Improved sample characterization in terahertz reflection imaging and spectroscopy
Huang, S., Ashworth, P. C., Kan, K. W., Chen, Y., Wallace, V. P., Zhang, Y.-T., & Pickwell-MacPherson, E. (2009) · Optics Express · doi:10.1364/oe.17.003848 · Cited by 96 · see citing works
Photoconductive response correction for detectors of terahertz radiation
Castro-Camus, E., Fu, L., Lloyd‐Hughes, J., et al. (2008) · Journal of Applied Physics · doi:10.1063/1.2969035 · Cited by 67 · see citing works
Self-citationDouble modulated differential THz-TDS for thin film dielectric characterization
Mickan, S. P., Lee, K.-S., Lu, T.-M., Munch, J., Abbott, D., & Zhang, X.-C. (2002) · Microelectronics Journal · doi:10.1016/s0026-2692(02)00108-8 · Cited by 54 · see citing works
An introduction to terahertz time-domain spectroscopic ellipsometry
Chen, X., & Pickwell‐MacPherson, E. (2022) · APL Photonics · doi:10.1063/5.0094056 · Cited by 51 · see citing works
Taleb, F., Alfaro-Gomez, M., Al-Dabbagh, M. D., Ornik, J., Viana, J., Jäckel, A., Mach, C., Helminiak, J., Kleine-Ostman, T., Kürner, T., et al. (2023) · Scientific Reports · doi:10.1038/s41598-023-47586-8 · Cited by 30 · see citing works
Chopra, N., & Lloyd-Hughes, J. (2023) · Journal of Infrared, Millimeter, and Terahertz Waves · doi:10.1007/s10762-023-00949-8 · Cited by 21 · see citing works
Self-citationMosley, C. D. W., Staniforth, M. J., Serrano, A. I. H., Pickwell‐MacPherson, E., & Lloyd‐Hughes, J. (2019) · AIP Advances · doi:10.1063/1.5086428 · Cited by 17 · see citing works
Self-citationDeveikis, J., & Lloyd‐Hughes, J. (2022) · Optics Express · doi:10.1364/oe.473086 · Cited by 16 · see citing works
Self-citationDesign and evaluation of a THz time domain imaging system using standard optical design software
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Active THz beam shaping using a one-dimensional array of photoconductive emitters
Chopra, N., Deveikis, J., & Lloyd‐Hughes, J. (2023) · Applied Physics Letters · doi:10.1063/5.0132207 · Cited by 15 · see citing works
Self-citationPrecise and accurate control of the ellipticity of THz radiation using a photoconductive pixel array
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Self-citationReal-time and calibration-free generalized terahertz time-domain spectroscopic ellipsometry
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Simultaneous measurement of orthogonal terahertz fields via an emission multiplexing scheme
Ou, H., Stantchev, R. I., Chen, X., Blu, T., Semtsiv, M., Masselink, W. T., Serrano, A. H., Costa, G., Young, J., Chopra, N., et al. (2024) · Optics Express · doi:10.1364/oe.505567 · Cited by 9 · see citing works
Self-citationLloyd-Hughes, J., Chopra, N., Deveikis, J., Pandya, R., & Woolley, J. (2024) · arXiv · Cited by 6 · see citing works
Self-citation
Flagged first, then by citations
Cited by
Sorted by citations
Lloyd-Hughes, J., Chopra, N., Deveikis, J., Pandya, R., & Woolley, J. (2025) · Journal of Infrared, Millimeter, and Terahertz Waves · doi:10.1007/s10762-025-01052-w · Cited by 6 · see citing works
“The absolute phase of the electro-optic signal, reported in Fig.”
Self-citation
- Authors
- Chopra, N., & Lloyd-Hughes, J.
- Affiliations
- University of Warwick (GB)
- Department of Physics
- Corresponding author
- Chopra, Nishtha
- Venue
- ACS Photonics
- Publisher
- American Chemical Society (ACS)
- Published
- 2025-01-11
- Volume
- 12
- Issue
- 2
- Pages
- 917-924
- ISSN
- 2330-4022 (ISSN-L)
- PMC
- PMC11843712
- OpenAlex
- W4406275765
- Cited by
- 8
- References
- 22
- Citations by year
- 2026: 2 · 2025: 6
- FWCI
- 1.77
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- ACS Photonics (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Warwick Research Archive Portal (University of Warwick) (acceptedVersion)
- Funders
- Engineering and Physical Sciences Research Council (EP/V047914/1)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Terahertz technology and applications
- Physical Sciences › Chemistry › Spectroscopy › Spectroscopy and Laser Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Laser-Matter Interactions and Applications
- Keywords
- terahertz time-domain spectroscopy, systematic error reduction, photoconductive antenna, amplitude and phase correction, relative humidity effects, reference beam
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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