Abstract

The accuracy of high-resolution spectroscopy depends critically on the stability, frequency control, and traceability available from laser sources. In this work, we report exact tunable frequency synthesis and phase control of a terahertz laser. The terahertz laser is locked by a terahertz injection phase lock loop for the first time, with the terahertz signal generated by heterodyning selected lines from an all-fiber infrared frequency comb generator in an ultrafast photodetector. The comb line frequency separation is exactly determined by a Global Positioning System-locked microwave frequency synthesizer, providing traceability of the terahertz laser frequency to primary standards. The locking technique reduced the heterodyne linewidth of the terahertz laser to a measurement instrument-limited linewidth of ${\lt}1\;{\rm Hz}$, robust against short- and long-term environmental fluctuations. The terahertz laser frequency can be tuned in increments determined only by the microwave synthesizer resolution, and the phase of the laser, relative to the reference, is independently and precisely controlled within a range $\pm{0.3}\pi$. These findings are expected to enable applications in phase-resolved high-precision terahertz gas spectroscopy and radiometry.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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2020 (1)

I. Kundu, J. R. Freeman, P. Dean, L. Li, E. H. Linfield, and A. G. Davies, “Wideband electrically controlled vernier frequency tunable terahertz quantum cascade laser,” ACS Photon. 7, 765–773 (2020).
[Crossref]

2018 (3)

X. Dong, J. S. Fu, K. Huang, N. H. Lin, S. H. Wang, and C. E. Yang, “Analysis of the co-existence of long-range transport biomass burning and dust in the subtropical West Pacific Region,” Sci. Rep. 8, 1–10 (2018).
[Crossref]

C. Solaro, S. Meyer, K. Fisher, M. V. Depalatis, and M. Drewsen, “Direct frequency-comb-driven raman transitions in the terahertz range,” Phys. Rev. Lett. 120, 253601 (2018).
[Crossref]

L. Ponnampalam, M. Fice, H. Shams, C. Renaud, and A. Seeds, “Optical comb for generation of a continuously tunable coherent THz signal from 122.5  GHz to 27  THz,” Opt. Lett. 43, 2507–2510 (2018).
[Crossref]

2017 (3)

L. H. Li, L. Chen, J. R. Freeman, M. Salih, P. Dean, A. G. Davies, and E. H. Linfield, “Multi-watt high-power THz frequency quantum cascade lasers,” Electron. Lett. 53, 799–800 (2017).
[Crossref]

K. V. Pokazeev, A. S. Zapevalov, and K. E. Lebedev, “Measurements of sea surface slopes by laser sensing from a space vehicle,” Moscow Univ. Phys. Bull. 72(4), 410–414 (2017).
[Crossref]

J. R. Freeman, L. Ponnampalam, H. Shams, R. A. Mohandas, C. C. Renaud, P. Dean, L. Li, A. Giles Davies, A. J. Seeds, and E. H. Linfield, “Injection locking of a terahertz quantum cascade laser to a telecommunications wavelength frequency comb,” Optica 4, 1059–1064 (2017).
[Crossref]

2016 (4)

B. P. Abbott, “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 61102–61116 (2016).
[Crossref]

S. Albert, F. Arn, I. Bolotova, Z. Chen, C. Fábri, G. Grassi, P. Lerch, M. Quack, G. Seyfang, A. Wokaun, and D. Zindel, “Synchrotron-based highest resolution terahertz spectroscopy of the ν24 band system of 1,2-dithiine (C4H4S2): a candidate for measuring the parity violating energy difference between enantiomers of chiral molecules,” J. Phys. Chem. Lett. 7, 3847–3853 (2016).
[Crossref]

N. Balakrishnan, “Perspective: ultracold molecules and the dawn of cold controlled chemistry,” J. Chem. Phys. 145, 150901 (2016).
[Crossref]

C. Risacher, R. Güsten, J. Stutzki, H.-W. Hübers, A. Bell, C. Buchbender, D. Büchel, T. Csengeri, U. U. Graf, S. Heyminck, R. D. Higgins, C. E. Honingh, K. Jacobs, B. Klein, Y. Okada, A. Parikka, P. Pütz, N. Reyes, O. Ricken, D. Riquelme, R. Simon, and H. Wiesemeyer, “The upGREAT 1.9  THz multi-pixel high resolution spectrometer for the SOFIA observatory,” Astron. Astrophys. 595, A34 (2016).
[Crossref]

2015 (2)

H. Richter, M. Wienold, L. Schrottke, K. Biermann, H. T. Grahn, and H. W. Hubers, “4.7-THz local oscillator for the GREAT heterodyne spectrometer on SOFIA,” IEEE Trans. Terahertz Sci. Technol. 5, 539–545 (2015).
[Crossref]

D. Fehrenbacher, P. Sulzer, A. Liehl, T. Kälberer, C. Riek, D. V. Seletskiy, and A. Leitenstorfer, “Free-running performance and full control of a passively phase-stable Er:fiber frequency comb,” Optica 2, 917–923 (2015).
[Crossref]

2014 (3)

S. Bartalini, L. Consolino, P. Cancio, P. De Natale, P. Bartolini, A. Taschin, M. De Pas, H. Beere, D. Ritchie, M. S. Vitiello, and R. Torre, “Frequency-comb-assisted terahertz quantum cascade laser spectroscopy,” Phys. Rev. X 4, 21006 (2014).
[Crossref]

D. Burghoff, T.-Y. Kao, N. Han, C. Wang, I. Chan, X. Cai, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8, 462–467 (2014).
[Crossref]

P. Jansen, H. L. Bethlem, and W. Ubachs, “Minimization of ion micromotion in a Paul trap,” J. Chem. Phys. 140, 10901 (2014).
[Crossref]

2013 (1)

J. L. Kloosterman, D. J. Hayton, Y. Ren, T. Y. Kao, J. N. Hovenier, J. R. Gao, T. M. Klapwijk, Q. Hu, C. K. Walker, and J. L. Reno, “Hot electron bolometer heterodyne receiver with a 4.7-THz quantum cascade laser as a local oscillator,” Appl. Phys. Lett. 102, 011123 (2013).
[Crossref]

2012 (4)

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
[Crossref]

M. S. Vitiello, L. Consolino, S. Bartalini, A. Taschin, A. Tredicucci, M. Inguscio, and P. De Natale, “Quantum-limited frequency fluctuations in a terahertz laser,” Nat. Photonics 6, 525–528 (2012).
[Crossref]

M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20, 25654–25661 (2012).
[Crossref]

L. Consolino, A. Taschin, P. Bartolini, S. Bartalini, P. Cancio, A. Tredicucci, H. E. Beere, D. A. Ritchie, R. Torre, M. S. Vitiello, and P. De Natale, “Phase-locking to a free-space terahertz comb for metrological-grade terahertz lasers,” Nat. Commun. 3, 1040–1045 (2012).
[Crossref]

2010 (4)

S. Barbieri, P. Gellie, G. Santarelli, L. Ding, W. Maineult, C. Sirtori, R. Colombelli, H. Beere, and D. Ritchie, “Phase-locking of a 2.7-THz quantum cascade laser to a mode-locked erbium-doped fibre laser,” Nat. Photonics 4, 636–640 (2010).
[Crossref]

H. Richter, S. G. Pavlov, A. D. Semenov, L. Mahler, A. Tredicucci, H. E. Beere, D. A. Ritchie, and H.-W. Hübers, “Submegahertz frequency stabilization of a terahertz quantum cascade laser to a molecular absorption line,” Appl. Phys. Lett. 96, 71112 (2010).
[Crossref]

Y. Ren, J. N. Hovenier, R. Higgins, J. R. Gao, T. M. Klapwijk, S. C. Shi, A. Bell, B. Klein, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Terahertz heterodyne spectrometer using a quantum cascade laser,” Appl. Phys. Lett. 97, 161103 (2010).
[Crossref]

W. Zeller, L. Naehle, P. Fuchs, F. Gerschuetz, L. Hildebrandt, J. Koeth, W. Zeller, L. Naehle, P. Fuchs, F. Gerschuetz, L. Hildebrandt, and J. Koeth, “DFB lasers between 760  nm and 16  µm for sensing applications,” Sensors 10, 2492–2510 (2010).
[Crossref]

2009 (2)

2008 (1)

H. W. Hübers, “Terahertz heterodyne receivers,” IEEE J. Sel. Top. Quantum Electron. 14, 378–391 (2008).
[Crossref]

2007 (1)

C. Walther, M. Fischer, G. Scalari, R. Terazzi, N. Hoyler, and J. Faist, “Quantum cascade lasers operating from 1.2  THz to 1.6  THz,” Appl. Phys. Lett. 91, 131122 (2007).
[Crossref]

2006 (3)

A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Real-time terahertz imaging over a standoff distance (>25  meters),” Appl. Phys. Lett. 89, 141125 (2006).
[Crossref]

J. G. Henning and P. J. Radtke, “Ground-based laser imaging for assessing three-dimensional forest canopy structure,” Photogramm. Eng. Remote Sens. 72, 1349–1358 (2006).
[Crossref]

E. R. Hudson, H. J. Lewandowski, B. C. Sawyer, and J. Ye, “Cold molecule spectroscopy for constraining the evolution of the fine structure constant,” Phys. Rev. Lett. 96, 143004 (2006).
[Crossref]

2005 (1)

I. S. Gregory, C. Baker, W. R. Tribe, I. V. Bradley, M. J. Evans, E. H. Linfield, G. Davies, and M. Missous, “Optimization of photomixers and antennas for continuous-wave terahertz emission,” IEEE J. Quantum Electron. 41, 717–728 (2005).
[Crossref]

2004 (1)

2003 (1)

X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol. 21, 803–806 (2003).
[Crossref]

2002 (1)

R. Kohler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
[Crossref]

1994 (2)

G. Santarelli, A. Clairon, S. N. Lea, and G. M. Tino, “Heterodyne optical phase-locking of extended-cavity semiconductor lasers at 9  GHz,” Opt. Commun. 104, 339–344 (1994).
[Crossref]

R. T. Ramos, P. Gallion, D. Erasme, A. J. Seeds, and A. Bordonalli, “Optical injection locking and phase-lock loop combined systems,” Opt. Lett. 19, 4–6 (1994).
[Crossref]

1992 (1)

1960 (1)

T. H. Maiman, “Stimulated optical radiation in ruby,” Nature 187, 493–494 (1960).
[Crossref]

1946 (1)

R. Adler, “A study of locking phenomena in oscillators,” Proc. IRE 34, 351–357 (1946).
[Crossref]

Abbott, B. P.

B. P. Abbott, “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 61102–61116 (2016).
[Crossref]

Adler, R.

R. Adler, “A study of locking phenomena in oscillators,” Proc. IRE 34, 351–357 (1946).
[Crossref]

Ajili, L.

Albert, S.

S. Albert, F. Arn, I. Bolotova, Z. Chen, C. Fábri, G. Grassi, P. Lerch, M. Quack, G. Seyfang, A. Wokaun, and D. Zindel, “Synchrotron-based highest resolution terahertz spectroscopy of the ν24 band system of 1,2-dithiine (C4H4S2): a candidate for measuring the parity violating energy difference between enantiomers of chiral molecules,” J. Phys. Chem. Lett. 7, 3847–3853 (2016).
[Crossref]

Arn, F.

S. Albert, F. Arn, I. Bolotova, Z. Chen, C. Fábri, G. Grassi, P. Lerch, M. Quack, G. Seyfang, A. Wokaun, and D. Zindel, “Synchrotron-based highest resolution terahertz spectroscopy of the ν24 band system of 1,2-dithiine (C4H4S2): a candidate for measuring the parity violating energy difference between enantiomers of chiral molecules,” J. Phys. Chem. Lett. 7, 3847–3853 (2016).
[Crossref]

Averitt, R. D.

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3, 148–151 (2009).
[Crossref]

Azad, A. K.

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3, 148–151 (2009).
[Crossref]

Baker, C.

I. S. Gregory, C. Baker, W. R. Tribe, I. V. Bradley, M. J. Evans, E. H. Linfield, G. Davies, and M. Missous, “Optimization of photomixers and antennas for continuous-wave terahertz emission,” IEEE J. Quantum Electron. 41, 717–728 (2005).
[Crossref]

Balakrishnan, N.

N. Balakrishnan, “Perspective: ultracold molecules and the dawn of cold controlled chemistry,” J. Chem. Phys. 145, 150901 (2016).
[Crossref]

Barbieri, S.

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Supplementary Material (1)

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Figures (6)

Fig. 1.
Fig. 1. Schematic diagram of the experimental arrangement. EDFA, erbium doped fibre amplifier; Tx, photomixer emitter; Rx1 and Rx2, photomixer receivers; PLL, phase lock loop; ${\Delta \varphi}$, variable delay line. Electrical connections are shown in black, optical fiber and IR connections in red, and terahertz connections in green.
Fig. 2.
Fig. 2. (a) Terahertz electric field of the locked QCL at ${\sim}{2}\;{\rm THz}$ for $|{f_{{\rm ref}}} - {f_{{\rm QCL}}}|\approx {0}$, as a function of delay. The node (red) and antinode (blue) positions are marked (b) calculated waveform shapes at the Rx2 for the node and antinode positions of the receiver and (c) terahertz amplitude from the Rx2 by modulating the QCL DC source at the node (red curve) and antinode (blue curve) positions of the Rx2 delay line. Frequency scale is the difference between the QCL frequency (tuned by the current modulation) and the terahertz reference frequency (constant).
Fig. 3.
Fig. 3. Measured linewidth spectra for the terahertz-IL (black) and terahertz-IPLL (red) states. The resolution bandwidth (RBW) for each spectrum is indicated and the frequency is offset by 80.98 MHz for clarity. Spectra were acquired after 30 trace averages.
Fig. 4.
Fig. 4. Terahertz amplitude and phase at Rx2 measured as a function of time for the terahertz IL (hollow symbols with dotted lines) and terahertz IPLL (solid symbols with solid line). The delay line of the Rx2 was scanned for each data point for the same scan length, position, and resolution.
Fig. 5.
Fig. 5. QCL current, ${{ I }_{{\rm QCL}}}$, and QCL frequency, ${f_{{\rm QCL}}}$, as a function of terahertz reference frequency, ${f_{{\rm ref}}}$. The reference frequency is switched by 1010 kHz. The QCL frequency axis is calculated from the QCL current using measured tuning of ${-}{6.5}\;{{\rm MHz}/{\rm mA}}$.
Fig. 6.
Fig. 6. Terahertz signal amplitude (black symbols and line) and phase (red symbols and line) plotted as a function of the DC voltage offset. The inset shows the phase change in the sinusoidal signal obtained by scanning the Rx2 for ${+}{0.3}\;{\rm V}$ (blue) and ${-}{0.3}\;{\rm V}$ (brown) values of the DC voltage offset. The delay line of Rx2 was scanned for each data point for the same scan length, position, and resolution.

Equations (2)

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I R x 1 , 2 E Q C L sin [ ( f r e f f Q C L ) t + ( φ r e f φ Q C L ) ] ,
I R x 2 | E Q C L L | sin [ Δ φ + sin 1 ( f r e f f Q C L U f l o c k ) ] ,