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Draft:Terahertz frequency-domain spectroscopy

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Terahertz Frequency-Domain Spectroscopy (THz-FDS) is a spectroscopic technique that uses continuous-wave terahertz radiation to probe the optical and dielectric properties of materials. Unlike time-domain terahertz spectroscopy (THz-TDS), which measures pulsed signals in the time domain, THz-FDS analyzes the steady-state response of a sample as the frequency of terahertz radiation is swept. This allows high spectral resolution and coherent detection of amplitude and phase.

Principles

Fig. 1: A schematic diagram showing the principle of photomixing. Two continuous-wave lasers with a small frequency offset illuminate a LTG-GaAs photomixer, generating carriers whose conductivity oscillates at the difference frequency and drives an antenna that radiates terahertz waves.
Fig. 2: Schematic of a THz-FDS detector. A photomixer illuminated by two lasers mixes the incoming terahertz field with the optical beat, producing a photocurrent that preserves amplitude and phase.
Fig. 3: Full system diagram of a THz-FDS that illustrates the dual lasers, photomixing emitter, beam optics, sample chamber, and photomixing receiver.
Fig. 4: Conceptual schematic illustrating how mismatched optical and terahertz path lengths act like an interferometer, producing unwanted periodic fringes in frequency-domain spectra.
Fig. 5: The THz spectrum illustrating both a fringe pattern as well as the spectral content of DHO and H2O water vapor.

THz-FDS relies on the generation of continuous-wave terahertz signals by photomixing, a process in which two near-infrared lasers with a small frequency offset illuminate a photomixer (Fig. 1). The optical beat frequency modulates the carrier density in a semiconductor, producing an oscillating photocurrent that drives a terahertz antenna.[1] Generally, the photomixer bias is modulated to allow the use of lock-in detection techniques.[citation needed]

Historically, photomixers have most often been fabricated from low-temperature-grown gallium arsenide (LTG-GaAs), due to its ultrafast carrier recombination characteristics, which enables effective generation and detection of continuous-wave THz radiation. LTG-GaAs devices typically feature interdigitated electrodes or coplanar antennas lithographically defined on the material substrate. Early devices showed significantly increased output near 3 THz compared to earlier designs, and were used as tunable local oscillators and broadband THz sweep sources in spectroscopy applications.[2][3]

Coherent detection is often performed using a second photomixer illuminated by the same pair of lasers (Fig 2). The incident terahertz signal and optical beat note interfere at the detector, producing a measurable photocurrent that preserves both amplitude and phase information. This coherent, homodyne, detection scheme allows operation at room temperature without the need for cryogenic cooling, unlike traditional thermal detectors such as bolometers or Golay cells.[4] [5]

In spectroscopy applications, the terahertz beam is directed through or reflected from a sample before reaching the detector (Fig. 3).[citation needed]

Variations in amplitude and phase reveal absorption lines, refractive index, and other material properties. Lock-in amplification and modulation techniques are commonly employed to enhance signal-to-noise ratios.[6] Subsequent implementations achieved 60 dB SNR at 1 THz,[7] [8]

In practice it is not quite as simple as this. The primary challenge of using a coherent THz-FDS for spectroscopy is balancing the lengths of the optical and THz paths of what is principally an interferometer with two different length arms (Fig 4). The path length difference between A and B will result in an interference pattern with frequency periodicity proportional to the delay. With a fiber-based system this may be achieved by increasing the length of the detector PCS fiber relative to the length of the source PCS fiber and thereby balance the arms of the interferometer.[citation needed]

The periodicity of the fringe pattern is determined by the imbalance between the optical path and the terahertz path. Adjusting the relative distances of the source and detector arms can shift or reduce the fringe pattern but perfect cancellation is generally not possible across the entire bandwidth because of dispersion effects in the antennas and optical components.[9]

As an example, Fig. 5 is the spectra of the vapor from a mixture of 10% DHO in H2O ,[10]. Both the spectral features as well as the fringe pattern are present. While some of the absorptions due to the DHO are present, others are hidden by the null of a fringe.[citation needed]

Generally speaking, the fringe pattern detracts from the utility of the spectrometer because weak absorptions of interest may not be measured where a fringe exists. On the other hand, the fringes are not entirely unwanted. Besides the weak DHO absorptions, Fig. 5 also displays a very strong and saturated H2O vapor absorption line at 1410 GHz. Note how the fringe spacing decreases in the frequencies around this absorption. This is indicative of how the index of refraction changes near absorption features.

What is desirable is a THZ-FDS instrument that can separate the fringe pattern from the spectrum. Fortunately, it is possible to do this through phase modulation and 2nd harmonic detection.[11]

Phase modulation

Figure 6 illustrates a THz-FDS that includes an optical phase modulator. In this technique, an optical phase modulation replaces a modulated photomixer bias to the source photomixer.[citation needed]

The optical phase modulation is then transferred from the optical domain to the THz domain. As the phase of the source THz beam is shifted, the fringe pattern effectively converts the phase modulation into an amplitude modulation on the detector. Depending on the location of the instrument frequency on the fringe pattern, when the conversion from phase modulation to amplitude modulation occurs, it will result in an amplitude modulation at the same frequency as the phase modulation (1st harmonic) or at twice the frequency of the phase modulation (2nd harmonic). This is illustrated in Figure 7. When both the 1st and 2nd harmonics are plotted it is clear that the 2nd harmonic is shifted 90 degrees of phase relative to the 1st harmonic and that abortions hidden by a null with one of the fringes will be displayed in the other harmonic.[citation needed]

The summation of the 1st and 2nd harmonics then produces a spectrum which removes the fringes and leaves the spectral features of the sample.[citation needed]

  • Fig. 6: A block diagram of a THz-FDS that employs optical phase modulation on the source photomixer.
    Fig. 6: A block diagram of a THz-FDS that employs optical phase modulation on the source photomixer.
  • Fig. 7: An illustration of how a phase modulation results in the production of the 1st harmonic and second harmonic on the detector depending on the position of the fringe frequency.
    Fig. 7: An illustration of how a phase modulation results in the production of the 1st harmonic and second harmonic on the detector depending on the position of the fringe frequency.
  • Fig. 8: Measured detector output in a phase-modulated THz-FDS system, illustrating the 1st harmonic and 2nd harmonic 90 degree offset.
    Fig. 8: Measured detector output in a phase-modulated THz-FDS system, illustrating the 1st harmonic and 2nd harmonic 90 degree offset.
  • Fig.9: Processed terahertz spectrum obtained by summing harmonic detection channels in a phase-modulated THz-FDS. Fringes are removed and water-vapor absorption lines become visible.
    Fig.9: Processed terahertz spectrum obtained by summing harmonic detection channels in a phase-modulated THz-FDS. Fringes are removed and water-vapor absorption lines become visible.

Applications

THz-FDS has been applied in a range of scientific and industrial fields: performing real-time airborne gas analysis from a consumer drone,[12] examining electronic and magnetic materials at low temperatures,[13] reducing Fabry–Perot interference and system dispersion in continuous-wave THz coherence measurements,[14] testing silicon gradient refractive index lenses for millimeter-wave radiometers,[15] testing tunable graphene-based metamaterial THz modulators,[16], Developing modulation-capable silicon waveguides for on-wafer THz interconnects,[17] fabricating affordable THz components via 3D printing,[18] advancing broadband impedance matching to two-dimensional materials,[19]

History

The development of THz-FDS followed advances in Photomixing and coherent detection in the late 20th century. In the early 1990s, researchers demonstrated that low-temperature-grown gallium arsenide (LTG-GaAs) photomixers could efficiently generate and detect continuous-wave THz radiation by optical heterodyning of two lasers.[citation needed]

This innovation established photomixers as practical continuous-wave THz sources. By the 2000s, THz-FDS instruments were developed for laboratory spectroscopy, and subsequent commercialization made them available for industrial and applied research. Later advances introduced phase modulation and harmonic detection techniques, which improved measurement fidelity by reducing interference artifacts.[citation needed]

Commercial THz-FDS systems are rare compared to THz-TDS systems and as of 2025, only two companies are known to manufacture and sell THz-FDS systems: Bakman Technologies and TOPTICA Photonics.[citation needed]

References

  1. ^ Brown, E.R.; McIntosh, K.A.; Nicholas, G.M.; DiNatale, W.F.; Dennis, K.L. (1995). "Photomixing up to 3.8 THz in low-temperature-grown GaAs." Applied Physics Letters. 66 (3): 285–287. doi:10.1063/1.114006.
  2. ^ Brown, E. R.; Verghese, S.; McIntosh, K. A. (1997). "Terahertz photomixing in low-temperature-grown GaAs". Conference Proceedings – Lasers and Electro-Optics Society Annual Meeting, 1997, 363–365.
  3. ^ Verghese, S.; McIntosh, K. A.; Brown, E. R. (1997). "Highly tunable fibre-coupled photomixers with coherent terahertz output power". IEEE Transactions on Microwave Theory and Techniques, 45, 1301–1309.
  4. ^ Siegel, P. H. (2004). "Terahertz technology". IEEE Transactions on Microwave Theory and Techniques, 52(10), 2438–2447.
  5. ^ Zhang, X.-C. & Xu, J. (2010). Introduction to THz Wave Photonics. Springer. doi:10.1007/978-1-4419-0978-7.
  6. ^ Demers, J.R.; Logan, R.T. Jr.; Brown, E.R.; Bergeron, N.J. "A high signal-to-noise ratio, coherent, frequency-domain THz spectrometer employed to characterize explosive compounds," in Proceedings of the IEEE 33rd International Conference on Infrared, Millimeter and Terahertz Waves, Pasadena, CA, 15–19 Sept. 2008. IEEE.
  7. ^ Demers, J.R.; Logan, R.T. Jr.; Brown, E.R.; Bergeron, N.J. "A coherent frequency-domain THz spectrometer with a signal-to-noise ratio of 60 dB at 1 THz," in Defense and Security Symposium, Orlando, FL, March 2008. SPIE.
  8. ^ Demers, J.R.; Logan, R.T.; Brown, E.R. "An optically integrated coherent frequency-domain THz spectrometer with signal-to-noise ratio up to 80 dB," in Proceedings of the 2007 IEEE International Topical Meeting on Microwave Photonics, Victoria, BC, October 2007. IEEE.
  9. ^ Roggenbuck, A., et al. (2010). Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples. New Journal of Physics, 12(4), 043017.
  10. ^ Demers, J.R.; Dale, E. (2019). "Determining DHO detection limits for a frequency domain THz spectrometer coupled to a light-weight multi-pass sample cell". 2019 44th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz). pp. 1–1. doi:10.1109/IRMMW-THz.2019.8874469.
  11. ^ US 9429473, Joseph R. Demers; Bryon Kasper, "Terahertz spectrometer and method for reducing photomixing interference pattern" ; US 9239264, Joseph R. Demers, "Transceiver method and apparatus having phase modulation and common mode phase drift rejection" ; US 9103715, Joseph R. Demers; Bryon L. Kasper, "Terahertz spectrometer phase modulator control using second harmonic nulling" ; US 9086374, Joseph R. Demers; Bryon L. Kasper, "Terahertz spectrometer with phase modulation and method" 
  12. ^ Demers, J.R.; Garet, F.; Coutaz, J.-L. (2018). "A UAV-mounted THz spectrometer for real-time gas analysis". Proc. SPIE 10531, Terahertz, RF, Millimeter, and Submillimeter-Wave Technology and Applications XI. pp. 105310K. doi:10.1117/12.2290765.
  13. ^ Daughton, D.R.; Higgins, R.; Yano, S.; Demers, J.R. (2012). "Coherent THz spectroscopy with photomixers in cryogenic environments". Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), 2012 37th International Conference. pp. 1–2.
  14. ^ Lin, Qi; Lin, Zhongxi; Li, Yong; Su, Hui; Ma, Fusheng (2020). "Reduce the effects of Fabry–Perot interference and system dispersion in continuous wave terahertz coherence measurements with two optical-path differences". Optics and Lasers in Engineering. 134: 106234. doi:10.1016/j.optlaseng.2020.106234. ISSN 0143-8166.{{cite journal}}: CS1 maint: article number as page number (link)
  15. ^ Pursula, P.; Lamminen, A.; Mannila, R.; Tappura, K.; Saarilahti, J. (2019). "Silicon Gradient Refractive Index Lens for Millimeter Wave Radiometers". 2019 44th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz). Paris, France. pp. 1–3. doi:10.1109/IRMMW-THz.2019.8874541.
  16. ^ Yan, R. (2013). "Tunable graphene-based metamaterial terahertz modulators". CLEO: 2013. San Jose, CA, USA. pp. 1–2.
  17. ^ Myers, J.C.; Kaur, A.; Byford, J.A.; Chahal, P. (2015). "Investigation of modulation-capable silicon waveguides for efficient on-wafer terahertz interconnects". 2015 IEEE 65th Electronic Components and Technology Conference (ECTC). San Diego, CA, USA. pp. 1010–1016. doi:10.1109/ECTC.2015.7159719.
  18. ^ Kaur, A.; Myers, J.C.; Ghazali, M.I.M.; Byford, J.; Chahal, P. (2015). "Affordable terahertz components using 3D printing". 2015 IEEE 65th Electronic Components and Technology Conference (ECTC). San Diego, CA, USA. pp. 2071–2076. doi:10.1109/ECTC.2015.7159888.
  19. ^ Pham, P.H.Q.; Zhang, W.; Quach, N.V. (2017). "Broadband impedance match to two-dimensional materials in the terahertz domain". Nature Communications. 8: 2233. doi:10.1038/s41467-017-02336-z.
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