Optimum Optical Designs for Diffraction-Limited Terahertz Spectroscopy and Imaging Systems Using Off-Axis Parabolic Mirrors
Open accessAbstract
Off-axis parabolic mirrors (OAPMs) are widely used in the THz and mm-wave communities for spectroscopy and imaging applications, as a result of their broadband, low-loss operation and high numerical apertures. However, the aspherical shape of an OAPM creates significant geometric aberrations: these make achieving diffraction-limited performance a challenge, and lower the peak electric field strength in the focal plane. Here, we quantify the impact of geometric aberrations on the performance of the most widely used spectrometer designs, by using ray tracing and physical optics calculations to investigate whether diffraction-limited performance can be achieved in both the sample and the detector plane. We identify simple rules, based on marginal ray propagation, that allow spectrometers to be designed that are more robust to misalignment errors, and which have minimal aberrations for THz beams. For a given source, this allows the design of optical paths that give the smallest THz beam focal spot, with the highest THz electric field strength possible. This is desirable for improved THz imaging, for better signal-to-noise ratios in linear THz spectroscopy and optical-pump THz-probe spectroscopy, and to achieve higher electric field strengths in non-linear THz spectroscopy.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
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 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”
From Dual-Beam THz Spectrometer with Low-Aberration Optics and Off-Axis Multipixel Photoconductive Emitters for Reduced Systematic Errors (2025) · cites this paper as [17]
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.”
From Dual-Beam THz Spectrometer with Low-Aberration Optics and Off-Axis Multipixel Photoconductive Emitters for Reduced Systematic Errors (2025) · cites this paper as [17]
The 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.”
From Dual-Beam THz Spectrometer with Low-Aberration Optics and Off-Axis Multipixel Photoconductive Emitters for Reduced Systematic Errors (2025) · cites this paper as [17]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy
Ulbricht, R., Hendry, E., Shan, J., Heinz, T. F., & Bonn, M. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.543 · Cited by 1,293 · see citing works
Terahertz Spectroscopy and Imaging
(2013) · Springer Series in Optical Sciences · doi:10.1007/978-3-642-29564-5 · Cited by 323 · see citing works
Distortion of a simple Gaussian beam on reflection from off-axis ellipsoidal mirrors
Murphy, J. A. (1987) · International Journal of Infrared and Millimeter Waves · doi:10.1007/bf01010819 · Cited by 145 · see citing works
Broadband Spintronic Terahertz Source with Peak Electric Fields Exceeding 1.5 MV/cm
Rouzegar, R., Chekhov, A. L., Behovits, Y., Serrano, B. R., Syskaki, M. A., Lambert, C., Engel, D. W., Martens, U., Münzenberg, M., Wolf, M., et al. (2023) · Physical Review Applied · doi:10.1103/physrevapplied.19.034018 · Cited by 114 · see citing works
The 2021 ultrafast spectroscopic probes of condensed matter roadmap
Lloyd‐Hughes, J., Oppeneer, P. M., dos Santos, T. P., et al. (2021) · Journal of Physics Condensed Matter · doi:10.1088/1361-648x/abfe21 · Cited by 111 · see citing works
Self-citationTerahertz imaging and spectroscopy of large-area single-layer graphene.
Tomaino, J., Jameson, A., Kevek, J. W., Paul, M., van der Zande, A. M., Barton, R. A., McEuen, P., Minot, E., & Lee, Y.-S. (2011) · Optics Express · doi:10.1364/oe.19.000141 · Cited by 110 · see citing works
2D measurement and spatio-temporal coupling of few-cycle THz pulses
Jiang, Z., & Zhang, X. (1999) · Optics Express · doi:10.1364/oe.5.000243 · Cited by 84 · see citing works
Terahertz pulse propagation in the near field and the far field
Gürtler, A., Winnewisser, C., Helm, H., & Uhd Jepsen, P. (2000) · Journal of the Optical Society of America A · doi:10.1364/josaa.17.000074 · Cited by 75 · see citing works
Jones, S. P. P., Gaw, S. M., Doig, K. I., Prabhakaran, D., Wheeler, E. M., Timothy, B. A., & Lloyd‐Hughes, J. (2014) · Nature Communications · doi:10.1038/ncomms4787 · Cited by 67 · see citing works
Self-citationTerahertz spectroscopy of anisotropic materials using beams with rotatable polarization
Mosley, C. D. W., Failla, M., Prabhakaran, D., & Lloyd-Hughes, J. (2017) · Scientific Reports · doi:10.1038/s41598-017-12568-0 · Cited by 53 · see citing works
Self-citationTwo-dimensional terahertz spectroscopy of condensed-phase molecular systems
Reimann, K., Woerner, M., & Elsaesser, T. (2021) · The Journal of Chemical Physics · doi:10.1063/5.0046664 · Cited by 50 · see citing works
Optimal arrangement of 90° off-axis parabolic mirrors in THz setups
Brückner, C., Notni, G., & Tünnermann, A. (2008) · Optik · doi:10.1016/j.ijleo.2008.05.024 · Cited by 29 · see citing works
Lloyd‐Hughes, J., Scalari, G., van Kolck, A., Fischer, M., Beck, M., & Faist, J. (2009) · Optics Express · doi:10.1364/oe.17.018387 · Cited by 29 · see citing works
Self-citationSun, Q., Liu, X., Cao, J., et al. (2018) · The Journal of Physical Chemistry C · doi:10.1021/acs.jpcc.8b05695 · Cited by 27 · see citing works
Exact ray-trace beam for an off-axis paraboloid surface
Arguijo, P., & Scholl, M. S. (2003) · Applied Optics · doi:10.1364/ao.42.003284 · Cited by 20 · see citing works
Deveikis, J., & Lloyd‐Hughes, J. (2022) · Optics Express · doi:10.1364/oe.473086 · Cited by 16 · see citing works
Self-citationActive 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-citationTakai, M., Shibata, K., Uemoto, M., et al. (2016) · Applied Physics Express · doi:10.7567/apex.9.052206 · Cited by 14 · see citing works
Laurita, N. J., Cheng, B., Barkhouser, R., Neumann, V. A., & Armitage, N. P. (2016) · Journal of Infrared Millimeter and Terahertz Waves · doi:10.1007/s10762-016-0281-x · Cited by 13 · see citing works
Terahertz photoconductance dynamics of semiconductors from sub-nanosecond to millisecond timescales
Butler‐Caddle, E., Grant, N. E., Pain, S. L., et al. (2023) · Applied Physics Letters · doi:10.1063/5.0130721 · Cited by 10 · see citing works
Micro-mirrors for a multifocus terahertz imaging system
Jördens, C., Salhi, M., Hasek, T., et al. (2006) · elib (German Aerospace Center) · Cited by 6 · see citing works
Analysis and optimization of THz imaging optics with off-axis parabolic mirrors
Sung, S., Garritano, J., Bajwa, N., et al. (2014) · International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) · doi:10.1109/irmmw-thz.2014.6956302 · Cited by 4 · see citing works
Flagged first, then by citations
Research works printed but not linked: 1
- Y.-S. Lee. Principles of terahertz science and technology, volume 170. Springer Science & Business Media, 2009.
Cited by
Sorted by citations
Chopra, N., & Lloyd-Hughes, J. (2025) · ACS Photonics · doi:10.1021/acsphotonics.4c01934 · Cited by 8 · see citing works
Self-citationLloyd-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
“…even occur during propagation in free space: broadband electromagnetic pulses change spectral phase as a result of the geometric aberrations of the optical system, which alter the path length [6]; the Gouy effect causes the carrier-envelope phase to evolve as a beam propagates through a focus [7].”
Self-citation
- Authors
- Chopra, N., & Lloyd-Hughes, J.
- Affiliations
- University of Warwick (GB)
- ORCID
- Chopra, Nishtha
- Venue
- Journal of Infrared, Millimeter, and Terahertz Waves
- Published
- 2023-11-21
- Volume
- 44
- Issue
- 11-12
- Pages
- 981-997
- ISSN
- 1866-6892 (ISSN-L)
- 1866-6906
- OpenAlex
- W4388865587
- Cited by
- 21
- References
- 22
- Citations by year
- 2026: 5 · 2025: 10 · 2024: 6
- FWCI
- 1.56
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Locations
- Journal of Infrared Millimeter and Terahertz Waves (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion, cc-by)
- Figshare (submittedVersion, cc-by)
- arXiv (Cornell University) (cc-by)
- Funders
- Engineering and Physical Sciences Research Council (EP/V047914/1)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Terahertz technology and applications
- Physical Sciences › Engineering › Biomedical Engineering › Advanced optical system design
- Physical Sciences › Chemistry › Spectroscopy › Spectroscopy and Laser Applications
- Keywords
- off-axis parabolic mirror, terahertz spectroscopy, terahertz imaging, diffraction-limited performance, geometric aberrations, aspheric mirrors, misalignment robustness, focal spot size, electric field strength, spectrometer design, optical pump-THz probe spectroscopy, ray tracing
About these checks
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.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review