Abstract

Precise delay control is of paramount importance in optical pump-probe measurements. Here, we report on a high-precision delay tracking technique for mechanical scanning measurements in a Mach-Zehnder interferometer configuration. The setup employs a 1.55-µm continuous-wave laser beam propagating along the interferometer arms. Sinusoidal phase modulation at 30 MHz, and demodulation of the interference signal at the fundamental frequency and its second harmonic, enables delay tracking with sampling rates of up to 10 MHz. At an interferometer arm length of 1 m, root-mean-square error values of the relative delay tracking below 10 attoseconds for both stationary and mechanically scanned (0.2 mm/s) operation are demonstrated. By averaging several scans, a precision of the delay determination better than 1 as is reached. We demonstrate this performance with a mechanical chopper periodically interrupting one of the interferometer arms, which opens the door to the combination of high-sensitivity lock-in detection with (sub-)attosecond-precision relative delay determination.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

J. Xu, B. Globisch, C. Hofer, N. Lilienfein, T. Butler, N. Karpowicz, and I. Pupeza, “Three-octave terahertz pulses from optical rectification of 20 fs, 1 µm 78 MHz pulses in GaP,” J. Phys. At. Mol. Opt. Phys. 51, 154002 (2018).

2017 (3)

2016 (1)

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the influence of delay line uncertainty in thz time-domain spectroscopy,” J. Infrared Millim. Terahertz Waves 37(6), 605–613 (2016).
[Crossref]

2015 (3)

C. Li, G.-Q. Liao, and Y.-T. Li, “Non-scanning systems for far-infrared radiation detection from laser-induced plasmas,” High Power Laser Sci. Eng. 3(May), 15 (2015).
[Crossref]

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

J. Réhault, F. Crisafi, V. Kumar, G. Ciardi, M. Marangoni, G. Cerullo, and D. Polli, “Broadband stimulated Raman scattering with Fourier-transform detection,” Opt. Express 23(19), 25235–25246 (2015).
[Crossref] [PubMed]

2013 (1)

2012 (1)

2011 (1)

2010 (2)

R. Gebs, G. Klatt, C. Janke, T. Dekorsy, and A. Bartels, “High-speed asynchronous optical sampling with sub-50fs time resolution,” Opt. Express 18(6), 5974–5983 (2010).
[Crossref] [PubMed]

A. Yabushita, Y. H. Lee, and T. Kobayashi, “Development of a multiplex fast-scan system for ultrafast time-resolved spectroscopy,” Rev. Sci. Instrum. 81(6), 063110 (2010).
[Crossref] [PubMed]

2009 (1)

2007 (2)

W. Withayachumnankul, H. Lin, S. P. Mickan, B. M. Fischer, and D. Abbott, “Analysis of measurement uncertainty in THz-TDS,” Proc. SPIE 6593, 659326 (2007).
[Crossref]

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3(6), 381–387 (2007).
[Crossref]

2003 (1)

J. Xu, T. Yuan, S. Mickan, and X. C. Zhang, “Limit of spectral resolution in terahertz time-domain spectroscopy,” Chin. Phys. Lett. 20(8), 1266–1268 (2003).
[Crossref]

2001 (1)

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[Crossref] [PubMed]

1995 (1)

1986 (1)

Abbott, D.

W. Withayachumnankul, H. Lin, S. P. Mickan, B. M. Fischer, and D. Abbott, “Analysis of measurement uncertainty in THz-TDS,” Proc. SPIE 6593, 659326 (2007).
[Crossref]

Balzer, J. C.

A. Rehn, D. Jahn, J. C. Balzer, and M. Koch, “Periodic sampling errors in terahertz time-domain measurements,” Opt. Express 25(6), 6712–6724 (2017).
[Crossref] [PubMed]

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the influence of delay line uncertainty in thz time-domain spectroscopy,” J. Infrared Millim. Terahertz Waves 37(6), 605–613 (2016).
[Crossref]

Bartels, A.

Baumert, T.

Bayer, T.

Bisi, M.

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the influence of delay line uncertainty in thz time-domain spectroscopy,” J. Infrared Millim. Terahertz Waves 37(6), 605–613 (2016).
[Crossref]

Bosse, H.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Brabec, T.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[Crossref] [PubMed]

Brida, D.

Butler, T.

J. Xu, B. Globisch, C. Hofer, N. Lilienfein, T. Butler, N. Karpowicz, and I. Pupeza, “Three-octave terahertz pulses from optical rectification of 20 fs, 1 µm 78 MHz pulses in GaP,” J. Phys. At. Mol. Opt. Phys. 51, 154002 (2018).

Cerullo, G.

Chang, Z.

Chen, S.

Chen, Y. L.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Chini, M.

Ciardi, G.

Corkum, P.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[Crossref] [PubMed]

Corkum, P. B.

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3(6), 381–387 (2007).
[Crossref]

Crisafi, F.

Crozatier, V.

Dekorsy, T.

Ding, S.

Drescher, M.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[Crossref] [PubMed]

Eisele, M.

Ellrich, F.

Estler, W. T.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Feldstein, M. J.

Fischer, B. M.

W. Withayachumnankul, H. Lin, S. P. Mickan, B. M. Fischer, and D. Abbott, “Analysis of measurement uncertainty in THz-TDS,” Proc. SPIE 6593, 659326 (2007).
[Crossref]

Forget, N.

Gao, W.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Gebs, R.

Gilbertson, S.

Globisch, B.

J. Xu, B. Globisch, C. Hofer, N. Lilienfein, T. Butler, N. Karpowicz, and I. Pupeza, “Three-octave terahertz pulses from optical rectification of 20 fs, 1 µm 78 MHz pulses in GaP,” J. Phys. At. Mol. Opt. Phys. 51, 154002 (2018).

Haitjema, H.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Heinzmann, U.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[Crossref] [PubMed]

Hentschel, M.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[Crossref] [PubMed]

Hofer, C.

J. Xu, B. Globisch, C. Hofer, N. Lilienfein, T. Butler, N. Karpowicz, and I. Pupeza, “Three-octave terahertz pulses from optical rectification of 20 fs, 1 µm 78 MHz pulses in GaP,” J. Phys. At. Mol. Opt. Phys. 51, 154002 (2018).

Hu, C.

Hu, J.

Huber, R.

Jahn, D.

A. Rehn, D. Jahn, J. C. Balzer, and M. Koch, “Periodic sampling errors in terahertz time-domain measurements,” Opt. Express 25(6), 6712–6724 (2017).
[Crossref] [PubMed]

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the influence of delay line uncertainty in thz time-domain spectroscopy,” J. Infrared Millim. Terahertz Waves 37(6), 605–613 (2016).
[Crossref]

Janke, C.

Jonuscheit, J.

Kaplan, D.

Karpowicz, N.

J. Xu, B. Globisch, C. Hofer, N. Lilienfein, T. Butler, N. Karpowicz, and I. Pupeza, “Three-octave terahertz pulses from optical rectification of 20 fs, 1 µm 78 MHz pulses in GaP,” J. Phys. At. Mol. Opt. Phys. 51, 154002 (2018).

Kienberger, R.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[Crossref] [PubMed]

Kim, S. W.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Klatt, G.

Knapp, W.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Kobayashi, T.

A. Yabushita, Y. H. Lee, and T. Kobayashi, “Development of a multiplex fast-scan system for ultrafast time-resolved spectroscopy,” Rev. Sci. Instrum. 81(6), 063110 (2010).
[Crossref] [PubMed]

Koch, M.

A. Rehn, D. Jahn, J. C. Balzer, and M. Koch, “Periodic sampling errors in terahertz time-domain measurements,” Opt. Express 25(6), 6712–6724 (2017).
[Crossref] [PubMed]

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the influence of delay line uncertainty in thz time-domain spectroscopy,” J. Infrared Millim. Terahertz Waves 37(6), 605–613 (2016).
[Crossref]

Köhler, J.

Krausz, F.

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3(6), 381–387 (2007).
[Crossref]

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[Crossref] [PubMed]

Kumar, V.

Kunzmann, H.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Lee, Y. H.

A. Yabushita, Y. H. Lee, and T. Kobayashi, “Development of a multiplex fast-scan system for ultrafast time-resolved spectroscopy,” Rev. Sci. Instrum. 81(6), 063110 (2010).
[Crossref] [PubMed]

Li, C.

C. Li, G.-Q. Liao, and Y.-T. Li, “Non-scanning systems for far-infrared radiation detection from laser-induced plasmas,” High Power Laser Sci. Eng. 3(May), 15 (2015).
[Crossref]

Li, Y.-T.

C. Li, G.-Q. Liao, and Y.-T. Li, “Non-scanning systems for far-infrared radiation detection from laser-induced plasmas,” High Power Laser Sci. Eng. 3(May), 15 (2015).
[Crossref]

Liao, G.-Q.

C. Li, G.-Q. Liao, and Y.-T. Li, “Non-scanning systems for far-infrared radiation detection from laser-induced plasmas,” High Power Laser Sci. Eng. 3(May), 15 (2015).
[Crossref]

Lilienfein, N.

J. Xu, B. Globisch, C. Hofer, N. Lilienfein, T. Butler, N. Karpowicz, and I. Pupeza, “Three-octave terahertz pulses from optical rectification of 20 fs, 1 µm 78 MHz pulses in GaP,” J. Phys. At. Mol. Opt. Phys. 51, 154002 (2018).

Lin, H.

W. Withayachumnankul, H. Lin, S. P. Mickan, B. M. Fischer, and D. Abbott, “Analysis of measurement uncertainty in THz-TDS,” Proc. SPIE 6593, 659326 (2007).
[Crossref]

Lippert, S.

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the influence of delay line uncertainty in thz time-domain spectroscopy,” J. Infrared Millim. Terahertz Waves 37(6), 605–613 (2016).
[Crossref]

Lu, X. D.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Manzoni, C.

Marangoni, M.

Mashiko, H.

Mickan, S.

J. Xu, T. Yuan, S. Mickan, and X. C. Zhang, “Limit of spectral resolution in terahertz time-domain spectroscopy,” Chin. Phys. Lett. 20(8), 1266–1268 (2003).
[Crossref]

Mickan, S. P.

W. Withayachumnankul, H. Lin, S. P. Mickan, B. M. Fischer, and D. Abbott, “Analysis of measurement uncertainty in THz-TDS,” Proc. SPIE 6593, 659326 (2007).
[Crossref]

Milosevic, N.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[Crossref] [PubMed]

Molter, D.

Ni, C.

Oberto, L.

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the influence of delay line uncertainty in thz time-domain spectroscopy,” J. Infrared Millim. Terahertz Waves 37(6), 605–613 (2016).
[Crossref]

Okazaki, H.

Polli, D.

Pupeza, I.

J. Xu, B. Globisch, C. Hofer, N. Lilienfein, T. Butler, N. Karpowicz, and I. Pupeza, “Three-octave terahertz pulses from optical rectification of 20 fs, 1 µm 78 MHz pulses in GaP,” J. Phys. At. Mol. Opt. Phys. 51, 154002 (2018).

Réhault, J.

Rehn, A.

Reider, G. A.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[Crossref] [PubMed]

Sarpe, C.

Sasaki, O.

Scherer, N. F.

Schubert, O.

Scott, S.

Spielmann, C.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[Crossref] [PubMed]

Trierweiler, M.

Vöhringer, P.

Von Freymann, G.

Wang, H.

Wang, L.

Weckenmann, A.

W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” Manuf. Technol. 64(2), 773–796 (2015).
[Crossref]

Withayachumnankul, W.

W. Withayachumnankul, H. Lin, S. P. Mickan, B. M. Fischer, and D. Abbott, “Analysis of measurement uncertainty in THz-TDS,” Proc. SPIE 6593, 659326 (2007).
[Crossref]

Wollenhaupt, M.

Xu, J.

J. Xu, B. Globisch, C. Hofer, N. Lilienfein, T. Butler, N. Karpowicz, and I. Pupeza, “Three-octave terahertz pulses from optical rectification of 20 fs, 1 µm 78 MHz pulses in GaP,” J. Phys. At. Mol. Opt. Phys. 51, 154002 (2018).

J. Xu, T. Yuan, S. Mickan, and X. C. Zhang, “Limit of spectral resolution in terahertz time-domain spectroscopy,” Chin. Phys. Lett. 20(8), 1266–1268 (2003).
[Crossref]

Yabushita, A.

A. Yabushita, Y. H. Lee, and T. Kobayashi, “Development of a multiplex fast-scan system for ultrafast time-resolved spectroscopy,” Rev. Sci. Instrum. 81(6), 063110 (2010).
[Crossref] [PubMed]

Yuan, T.

J. Xu, T. Yuan, S. Mickan, and X. C. Zhang, “Limit of spectral resolution in terahertz time-domain spectroscopy,” Chin. Phys. Lett. 20(8), 1266–1268 (2003).
[Crossref]

Yun, C.

Zhang, M.

Zhang, X. C.

J. Xu, T. Yuan, S. Mickan, and X. C. Zhang, “Limit of spectral resolution in terahertz time-domain spectroscopy,” Chin. Phys. Lett. 20(8), 1266–1268 (2003).
[Crossref]

Zhu, Y.

Appl. Opt. (2)

Chin. Phys. Lett. (1)

J. Xu, T. Yuan, S. Mickan, and X. C. Zhang, “Limit of spectral resolution in terahertz time-domain spectroscopy,” Chin. Phys. Lett. 20(8), 1266–1268 (2003).
[Crossref]

High Power Laser Sci. Eng. (1)

C. Li, G.-Q. Liao, and Y.-T. Li, “Non-scanning systems for far-infrared radiation detection from laser-induced plasmas,” High Power Laser Sci. Eng. 3(May), 15 (2015).
[Crossref]

J. Infrared Millim. Terahertz Waves (1)

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the influence of delay line uncertainty in thz time-domain spectroscopy,” J. Infrared Millim. Terahertz Waves 37(6), 605–613 (2016).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Test setup: A modified, Mach-Zehnder type position tracking interferometer (channel 1, CH1) is operated in parallel to a commercial Michelson-type sensor head (channel 2, CH2), which monitors the position of a mirror mounted into the delay stage. In CH1, a CW pilot laser output of 140 µW at 1.55 µm is amplified by a semiconductor optical amplifier (Thorlabs, EDFA100S) then split and combined by 50/50 beamsplitters (BS). One part of the interference signal is coupled into a fiber and sent back to the commercial position readout unit. A 3-port fiber circulator is used to separate the input and output beams. From the other side of the BS the signal is coupled directly onto an InGaAs photodiode (DET), which acts as a placeholder for any delay dependent setup. A chopper wheel for lock-in detection can be implemented in the focus of a one-to-one telescope and an attenuator to reduce the power in one arm.
Fig. 2
Fig. 2 The measured position (red) by the interferometer and the position calculated from the photodiode signal (black) using a linear approximation. The subtraction of the two curves gives the absolute error (blue), which can be converted to phase error using the 1.55 µm carrier wavelength. In a) a 20 seconds window is plotted and in b) a zoom to 80 ms shows the faster fluctuations. The RMS is reduced from 17.4 as (red) to 4.5 as (blue).
Fig. 3
Fig. 3 Power spectral density (PSD) and integrated noise (right axes) of the position fluctuations at a zero-crossing. The correction reduces the integrated RMS delay noise from 5.25 to 1.36 nm.
Fig. 4
Fig. 4 Comparison of the position reproducibility of the MZI and the reference setup in a) and only for the MZI with and without attenuating one arm in b). In each case 1 cm long delay scans were performed with chopped and not chopped interferometer arm.
Fig. 5
Fig. 5 The temporal stability/reproducibility of the position measurement is evaluated and plotted in an Allan deviation-like manner.

Equations (1)

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ν λf 2n