Abstract

In a continuous-wave terahertz system based on photomixing, the measured amplitude of the terahertz signal shows a variability due to drifts of the responsivities of the photomixers and of the optical power illuminating the photomixers. We report a simple method to substantially reduce this variability. By normalizing the amplitude to the DC photocurrents in both the transmitter and receiver photomixers, we achieve a significant increase in stability. If, e.g., the optical power of one laser is reduced by 10%, the normalized signal is expected to change by only 0.3%, i.e., less than the typical uncertainty due to short-term fluctuations. This stabilization can be particularly valuable for terahertz applications in nonideal environmental conditions outside of a temperature-stabilized laboratory.

© 2013 Optical Society of America

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  1. K. A. McIntosh, E. R. Brown, K. B. Nichols, O. B. McMahon, W. F. DiNatale, and T. M. Lyszczarz, “Terahertz photomixing with diode lasers in low-temperature-grown GaAs,” Appl. Phys. Lett. 67, 3844–3846 (1995).
    [CrossRef]
  2. S. Verghese, K. A. McIntosh, S. Calawa, W. F. Dinatale, E. K. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Appl. Phys. Lett. 73, 3824–3826 (1998).
    [CrossRef]
  3. A. J. Deninger, T. Göbel, D. Schönherr, T. Kinder, A. Roggenbuck, M. Köberle, F. Lison, T. Müller-Wirts, and P. Meissner, “Precisely tunable continuous-wave terahertz source with interferometric frequency control,” Rev. Sci. Instrum. 79, 044702 (2008).
    [CrossRef]
  4. A. Roggenbuck, H. Schmitz, A. Deninger, I. Cámara Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New J. Phys. 12, 043017 (2010).
    [CrossRef]
  5. S. Matsuura and H. Ito, “Generation of cw terahertz radiation with photomixing,” in Terahertz Optoelectronics, K. Sakai, ed. (Springer-Verlag, 2005), pp. 157–202.
  6. D. Saeedkia and S. Safavi-Naeini, “Terahertz photonics: optoelectronic techniques for generation and detection of terahertz waves,” J. Lightwave Technol. 26, 2409–2423(2008).
    [CrossRef]
  7. S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys. 109, 61301–61356 (2011).
    [CrossRef]
  8. J. E. Bjarnason and E. R. Brown, “Sensitivity measurement and analysis of an ErAs:GaAs coherent photomixing transceiver,” Appl. Phys. Lett. 87, 134105 (2005).
    [CrossRef]
  9. A. Roggenbuck, K. Thirunavukkuarasu, H. Schmitz, J. Marx, A. Deninger, I. Cámara Mayorga, R. Güsten, J. Hemberger, and M. Grüninger, “Using a fiber stretcher as a fast phase modulator in a continuous wave terahertz spectrometer,” J. Opt. Soc. Am. B 29, 614–620 (2012).
    [CrossRef]
  10. The responsivities STx and SRx depend on the respective bias voltages (or electric fields). At the receiver, we may safely write SRx∝ETHz,Rx·dSRx/dV (see Fig. 1) in order to separate the terahertz electric field. At the transmitter with its large bias voltage, it is not necessary to assume a linear current-voltage characteristic. This explains the apparent asymmetry of Eq. (3) with respect to STx and dSRx/dV.
  11. I. Cámara Mayorga, E. A. Michael, A. Schmitz, P. van der Wal, R. Güsten, K. Maier, and A. Dewald, “Terahertz photomixing in high energy oxygen- and nitrogen-ion-implanted GaAs,” Appl. Phys. Lett. 91, 031107 (2007).
    [CrossRef]
  12. Biased uni-travelling-carrier photodiodes have been employed as receivers; see T. Nagatsuma, A. Kaino, S. Hisatake, K. Ajito, H.-J. Song, A. Wakatsuki, Y. Muramoto, N. Kukutsu, and Y. Kado, “Continuous-wave terahertz spectroscopy system based on photodiodes,” PIERS Online 6, 390–394 (2010) (but there the purpose of biasing is not related to normalization).
  13. E. R. Brown, K. A. McIntosh, F. W. Smith, K. B. Nichols, M. J. Manfra, C. L. Dennis, and J. P. Mattia, “Milliwatt output levels and superquadratic bias dependence in a low-temperature-grown GaAs photomixer,” Appl. Phys. Lett. 64, 3311–3313 (1994).
    [CrossRef]

2012 (1)

2011 (1)

S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys. 109, 61301–61356 (2011).
[CrossRef]

2010 (2)

A. Roggenbuck, H. Schmitz, A. Deninger, I. Cámara Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New J. Phys. 12, 043017 (2010).
[CrossRef]

Biased uni-travelling-carrier photodiodes have been employed as receivers; see T. Nagatsuma, A. Kaino, S. Hisatake, K. Ajito, H.-J. Song, A. Wakatsuki, Y. Muramoto, N. Kukutsu, and Y. Kado, “Continuous-wave terahertz spectroscopy system based on photodiodes,” PIERS Online 6, 390–394 (2010) (but there the purpose of biasing is not related to normalization).

2008 (2)

A. J. Deninger, T. Göbel, D. Schönherr, T. Kinder, A. Roggenbuck, M. Köberle, F. Lison, T. Müller-Wirts, and P. Meissner, “Precisely tunable continuous-wave terahertz source with interferometric frequency control,” Rev. Sci. Instrum. 79, 044702 (2008).
[CrossRef]

D. Saeedkia and S. Safavi-Naeini, “Terahertz photonics: optoelectronic techniques for generation and detection of terahertz waves,” J. Lightwave Technol. 26, 2409–2423(2008).
[CrossRef]

2007 (1)

I. Cámara Mayorga, E. A. Michael, A. Schmitz, P. van der Wal, R. Güsten, K. Maier, and A. Dewald, “Terahertz photomixing in high energy oxygen- and nitrogen-ion-implanted GaAs,” Appl. Phys. Lett. 91, 031107 (2007).
[CrossRef]

2005 (1)

J. E. Bjarnason and E. R. Brown, “Sensitivity measurement and analysis of an ErAs:GaAs coherent photomixing transceiver,” Appl. Phys. Lett. 87, 134105 (2005).
[CrossRef]

1998 (1)

S. Verghese, K. A. McIntosh, S. Calawa, W. F. Dinatale, E. K. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Appl. Phys. Lett. 73, 3824–3826 (1998).
[CrossRef]

1995 (1)

K. A. McIntosh, E. R. Brown, K. B. Nichols, O. B. McMahon, W. F. DiNatale, and T. M. Lyszczarz, “Terahertz photomixing with diode lasers in low-temperature-grown GaAs,” Appl. Phys. Lett. 67, 3844–3846 (1995).
[CrossRef]

1994 (1)

E. R. Brown, K. A. McIntosh, F. W. Smith, K. B. Nichols, M. J. Manfra, C. L. Dennis, and J. P. Mattia, “Milliwatt output levels and superquadratic bias dependence in a low-temperature-grown GaAs photomixer,” Appl. Phys. Lett. 64, 3311–3313 (1994).
[CrossRef]

Ajito, K.

Biased uni-travelling-carrier photodiodes have been employed as receivers; see T. Nagatsuma, A. Kaino, S. Hisatake, K. Ajito, H.-J. Song, A. Wakatsuki, Y. Muramoto, N. Kukutsu, and Y. Kado, “Continuous-wave terahertz spectroscopy system based on photodiodes,” PIERS Online 6, 390–394 (2010) (but there the purpose of biasing is not related to normalization).

Bjarnason, J. E.

J. E. Bjarnason and E. R. Brown, “Sensitivity measurement and analysis of an ErAs:GaAs coherent photomixing transceiver,” Appl. Phys. Lett. 87, 134105 (2005).
[CrossRef]

Brown, E. R.

J. E. Bjarnason and E. R. Brown, “Sensitivity measurement and analysis of an ErAs:GaAs coherent photomixing transceiver,” Appl. Phys. Lett. 87, 134105 (2005).
[CrossRef]

K. A. McIntosh, E. R. Brown, K. B. Nichols, O. B. McMahon, W. F. DiNatale, and T. M. Lyszczarz, “Terahertz photomixing with diode lasers in low-temperature-grown GaAs,” Appl. Phys. Lett. 67, 3844–3846 (1995).
[CrossRef]

E. R. Brown, K. A. McIntosh, F. W. Smith, K. B. Nichols, M. J. Manfra, C. L. Dennis, and J. P. Mattia, “Milliwatt output levels and superquadratic bias dependence in a low-temperature-grown GaAs photomixer,” Appl. Phys. Lett. 64, 3311–3313 (1994).
[CrossRef]

Calawa, S.

S. Verghese, K. A. McIntosh, S. Calawa, W. F. Dinatale, E. K. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Appl. Phys. Lett. 73, 3824–3826 (1998).
[CrossRef]

Cámara Mayorga, I.

A. Roggenbuck, K. Thirunavukkuarasu, H. Schmitz, J. Marx, A. Deninger, I. Cámara Mayorga, R. Güsten, J. Hemberger, and M. Grüninger, “Using a fiber stretcher as a fast phase modulator in a continuous wave terahertz spectrometer,” J. Opt. Soc. Am. B 29, 614–620 (2012).
[CrossRef]

A. Roggenbuck, H. Schmitz, A. Deninger, I. Cámara Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New J. Phys. 12, 043017 (2010).
[CrossRef]

I. Cámara Mayorga, E. A. Michael, A. Schmitz, P. van der Wal, R. Güsten, K. Maier, and A. Dewald, “Terahertz photomixing in high energy oxygen- and nitrogen-ion-implanted GaAs,” Appl. Phys. Lett. 91, 031107 (2007).
[CrossRef]

Deninger, A.

A. Roggenbuck, K. Thirunavukkuarasu, H. Schmitz, J. Marx, A. Deninger, I. Cámara Mayorga, R. Güsten, J. Hemberger, and M. Grüninger, “Using a fiber stretcher as a fast phase modulator in a continuous wave terahertz spectrometer,” J. Opt. Soc. Am. B 29, 614–620 (2012).
[CrossRef]

A. Roggenbuck, H. Schmitz, A. Deninger, I. Cámara Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New J. Phys. 12, 043017 (2010).
[CrossRef]

Deninger, A. J.

A. J. Deninger, T. Göbel, D. Schönherr, T. Kinder, A. Roggenbuck, M. Köberle, F. Lison, T. Müller-Wirts, and P. Meissner, “Precisely tunable continuous-wave terahertz source with interferometric frequency control,” Rev. Sci. Instrum. 79, 044702 (2008).
[CrossRef]

Dennis, C. L.

E. R. Brown, K. A. McIntosh, F. W. Smith, K. B. Nichols, M. J. Manfra, C. L. Dennis, and J. P. Mattia, “Milliwatt output levels and superquadratic bias dependence in a low-temperature-grown GaAs photomixer,” Appl. Phys. Lett. 64, 3311–3313 (1994).
[CrossRef]

Dewald, A.

I. Cámara Mayorga, E. A. Michael, A. Schmitz, P. van der Wal, R. Güsten, K. Maier, and A. Dewald, “Terahertz photomixing in high energy oxygen- and nitrogen-ion-implanted GaAs,” Appl. Phys. Lett. 91, 031107 (2007).
[CrossRef]

Dinatale, W. F.

S. Verghese, K. A. McIntosh, S. Calawa, W. F. Dinatale, E. K. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Appl. Phys. Lett. 73, 3824–3826 (1998).
[CrossRef]

K. A. McIntosh, E. R. Brown, K. B. Nichols, O. B. McMahon, W. F. DiNatale, and T. M. Lyszczarz, “Terahertz photomixing with diode lasers in low-temperature-grown GaAs,” Appl. Phys. Lett. 67, 3844–3846 (1995).
[CrossRef]

Döhler, G. H.

S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys. 109, 61301–61356 (2011).
[CrossRef]

Duerr, E. K.

S. Verghese, K. A. McIntosh, S. Calawa, W. F. Dinatale, E. K. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Appl. Phys. Lett. 73, 3824–3826 (1998).
[CrossRef]

Göbel, T.

A. J. Deninger, T. Göbel, D. Schönherr, T. Kinder, A. Roggenbuck, M. Köberle, F. Lison, T. Müller-Wirts, and P. Meissner, “Precisely tunable continuous-wave terahertz source with interferometric frequency control,” Rev. Sci. Instrum. 79, 044702 (2008).
[CrossRef]

Gossard, A. C.

S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys. 109, 61301–61356 (2011).
[CrossRef]

Grüninger, M.

A. Roggenbuck, K. Thirunavukkuarasu, H. Schmitz, J. Marx, A. Deninger, I. Cámara Mayorga, R. Güsten, J. Hemberger, and M. Grüninger, “Using a fiber stretcher as a fast phase modulator in a continuous wave terahertz spectrometer,” J. Opt. Soc. Am. B 29, 614–620 (2012).
[CrossRef]

A. Roggenbuck, H. Schmitz, A. Deninger, I. Cámara Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New J. Phys. 12, 043017 (2010).
[CrossRef]

Güsten, R.

A. Roggenbuck, K. Thirunavukkuarasu, H. Schmitz, J. Marx, A. Deninger, I. Cámara Mayorga, R. Güsten, J. Hemberger, and M. Grüninger, “Using a fiber stretcher as a fast phase modulator in a continuous wave terahertz spectrometer,” J. Opt. Soc. Am. B 29, 614–620 (2012).
[CrossRef]

A. Roggenbuck, H. Schmitz, A. Deninger, I. Cámara Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New J. Phys. 12, 043017 (2010).
[CrossRef]

I. Cámara Mayorga, E. A. Michael, A. Schmitz, P. van der Wal, R. Güsten, K. Maier, and A. Dewald, “Terahertz photomixing in high energy oxygen- and nitrogen-ion-implanted GaAs,” Appl. Phys. Lett. 91, 031107 (2007).
[CrossRef]

Hemberger, J.

A. Roggenbuck, K. Thirunavukkuarasu, H. Schmitz, J. Marx, A. Deninger, I. Cámara Mayorga, R. Güsten, J. Hemberger, and M. Grüninger, “Using a fiber stretcher as a fast phase modulator in a continuous wave terahertz spectrometer,” J. Opt. Soc. Am. B 29, 614–620 (2012).
[CrossRef]

A. Roggenbuck, H. Schmitz, A. Deninger, I. Cámara Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New J. Phys. 12, 043017 (2010).
[CrossRef]

Hisatake, S.

Biased uni-travelling-carrier photodiodes have been employed as receivers; see T. Nagatsuma, A. Kaino, S. Hisatake, K. Ajito, H.-J. Song, A. Wakatsuki, Y. Muramoto, N. Kukutsu, and Y. Kado, “Continuous-wave terahertz spectroscopy system based on photodiodes,” PIERS Online 6, 390–394 (2010) (but there the purpose of biasing is not related to normalization).

Ito, H.

S. Matsuura and H. Ito, “Generation of cw terahertz radiation with photomixing,” in Terahertz Optoelectronics, K. Sakai, ed. (Springer-Verlag, 2005), pp. 157–202.

Kado, Y.

Biased uni-travelling-carrier photodiodes have been employed as receivers; see T. Nagatsuma, A. Kaino, S. Hisatake, K. Ajito, H.-J. Song, A. Wakatsuki, Y. Muramoto, N. Kukutsu, and Y. Kado, “Continuous-wave terahertz spectroscopy system based on photodiodes,” PIERS Online 6, 390–394 (2010) (but there the purpose of biasing is not related to normalization).

Kaino, A.

Biased uni-travelling-carrier photodiodes have been employed as receivers; see T. Nagatsuma, A. Kaino, S. Hisatake, K. Ajito, H.-J. Song, A. Wakatsuki, Y. Muramoto, N. Kukutsu, and Y. Kado, “Continuous-wave terahertz spectroscopy system based on photodiodes,” PIERS Online 6, 390–394 (2010) (but there the purpose of biasing is not related to normalization).

Kinder, T.

A. J. Deninger, T. Göbel, D. Schönherr, T. Kinder, A. Roggenbuck, M. Köberle, F. Lison, T. Müller-Wirts, and P. Meissner, “Precisely tunable continuous-wave terahertz source with interferometric frequency control,” Rev. Sci. Instrum. 79, 044702 (2008).
[CrossRef]

Köberle, M.

A. J. Deninger, T. Göbel, D. Schönherr, T. Kinder, A. Roggenbuck, M. Köberle, F. Lison, T. Müller-Wirts, and P. Meissner, “Precisely tunable continuous-wave terahertz source with interferometric frequency control,” Rev. Sci. Instrum. 79, 044702 (2008).
[CrossRef]

Kukutsu, N.

Biased uni-travelling-carrier photodiodes have been employed as receivers; see T. Nagatsuma, A. Kaino, S. Hisatake, K. Ajito, H.-J. Song, A. Wakatsuki, Y. Muramoto, N. Kukutsu, and Y. Kado, “Continuous-wave terahertz spectroscopy system based on photodiodes,” PIERS Online 6, 390–394 (2010) (but there the purpose of biasing is not related to normalization).

Lison, F.

A. J. Deninger, T. Göbel, D. Schönherr, T. Kinder, A. Roggenbuck, M. Köberle, F. Lison, T. Müller-Wirts, and P. Meissner, “Precisely tunable continuous-wave terahertz source with interferometric frequency control,” Rev. Sci. Instrum. 79, 044702 (2008).
[CrossRef]

Lyszczarz, T. M.

K. A. McIntosh, E. R. Brown, K. B. Nichols, O. B. McMahon, W. F. DiNatale, and T. M. Lyszczarz, “Terahertz photomixing with diode lasers in low-temperature-grown GaAs,” Appl. Phys. Lett. 67, 3844–3846 (1995).
[CrossRef]

Maier, K.

I. Cámara Mayorga, E. A. Michael, A. Schmitz, P. van der Wal, R. Güsten, K. Maier, and A. Dewald, “Terahertz photomixing in high energy oxygen- and nitrogen-ion-implanted GaAs,” Appl. Phys. Lett. 91, 031107 (2007).
[CrossRef]

Malzer, S.

S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys. 109, 61301–61356 (2011).
[CrossRef]

Manfra, M. J.

E. R. Brown, K. A. McIntosh, F. W. Smith, K. B. Nichols, M. J. Manfra, C. L. Dennis, and J. P. Mattia, “Milliwatt output levels and superquadratic bias dependence in a low-temperature-grown GaAs photomixer,” Appl. Phys. Lett. 64, 3311–3313 (1994).
[CrossRef]

Marx, J.

Matsuura, S.

S. Matsuura and H. Ito, “Generation of cw terahertz radiation with photomixing,” in Terahertz Optoelectronics, K. Sakai, ed. (Springer-Verlag, 2005), pp. 157–202.

Mattia, J. P.

E. R. Brown, K. A. McIntosh, F. W. Smith, K. B. Nichols, M. J. Manfra, C. L. Dennis, and J. P. Mattia, “Milliwatt output levels and superquadratic bias dependence in a low-temperature-grown GaAs photomixer,” Appl. Phys. Lett. 64, 3311–3313 (1994).
[CrossRef]

McIntosh, K. A.

S. Verghese, K. A. McIntosh, S. Calawa, W. F. Dinatale, E. K. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Appl. Phys. Lett. 73, 3824–3826 (1998).
[CrossRef]

K. A. McIntosh, E. R. Brown, K. B. Nichols, O. B. McMahon, W. F. DiNatale, and T. M. Lyszczarz, “Terahertz photomixing with diode lasers in low-temperature-grown GaAs,” Appl. Phys. Lett. 67, 3844–3846 (1995).
[CrossRef]

E. R. Brown, K. A. McIntosh, F. W. Smith, K. B. Nichols, M. J. Manfra, C. L. Dennis, and J. P. Mattia, “Milliwatt output levels and superquadratic bias dependence in a low-temperature-grown GaAs photomixer,” Appl. Phys. Lett. 64, 3311–3313 (1994).
[CrossRef]

McMahon, O. B.

K. A. McIntosh, E. R. Brown, K. B. Nichols, O. B. McMahon, W. F. DiNatale, and T. M. Lyszczarz, “Terahertz photomixing with diode lasers in low-temperature-grown GaAs,” Appl. Phys. Lett. 67, 3844–3846 (1995).
[CrossRef]

Meissner, P.

A. J. Deninger, T. Göbel, D. Schönherr, T. Kinder, A. Roggenbuck, M. Köberle, F. Lison, T. Müller-Wirts, and P. Meissner, “Precisely tunable continuous-wave terahertz source with interferometric frequency control,” Rev. Sci. Instrum. 79, 044702 (2008).
[CrossRef]

Michael, E. A.

I. Cámara Mayorga, E. A. Michael, A. Schmitz, P. van der Wal, R. Güsten, K. Maier, and A. Dewald, “Terahertz photomixing in high energy oxygen- and nitrogen-ion-implanted GaAs,” Appl. Phys. Lett. 91, 031107 (2007).
[CrossRef]

Molvar, K. A.

S. Verghese, K. A. McIntosh, S. Calawa, W. F. Dinatale, E. K. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Appl. Phys. Lett. 73, 3824–3826 (1998).
[CrossRef]

Müller-Wirts, T.

A. J. Deninger, T. Göbel, D. Schönherr, T. Kinder, A. Roggenbuck, M. Köberle, F. Lison, T. Müller-Wirts, and P. Meissner, “Precisely tunable continuous-wave terahertz source with interferometric frequency control,” Rev. Sci. Instrum. 79, 044702 (2008).
[CrossRef]

Muramoto, Y.

Biased uni-travelling-carrier photodiodes have been employed as receivers; see T. Nagatsuma, A. Kaino, S. Hisatake, K. Ajito, H.-J. Song, A. Wakatsuki, Y. Muramoto, N. Kukutsu, and Y. Kado, “Continuous-wave terahertz spectroscopy system based on photodiodes,” PIERS Online 6, 390–394 (2010) (but there the purpose of biasing is not related to normalization).

Nagatsuma, T.

Biased uni-travelling-carrier photodiodes have been employed as receivers; see T. Nagatsuma, A. Kaino, S. Hisatake, K. Ajito, H.-J. Song, A. Wakatsuki, Y. Muramoto, N. Kukutsu, and Y. Kado, “Continuous-wave terahertz spectroscopy system based on photodiodes,” PIERS Online 6, 390–394 (2010) (but there the purpose of biasing is not related to normalization).

Nichols, K. B.

K. A. McIntosh, E. R. Brown, K. B. Nichols, O. B. McMahon, W. F. DiNatale, and T. M. Lyszczarz, “Terahertz photomixing with diode lasers in low-temperature-grown GaAs,” Appl. Phys. Lett. 67, 3844–3846 (1995).
[CrossRef]

E. R. Brown, K. A. McIntosh, F. W. Smith, K. B. Nichols, M. J. Manfra, C. L. Dennis, and J. P. Mattia, “Milliwatt output levels and superquadratic bias dependence in a low-temperature-grown GaAs photomixer,” Appl. Phys. Lett. 64, 3311–3313 (1994).
[CrossRef]

Preu, S.

S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys. 109, 61301–61356 (2011).
[CrossRef]

Roggenbuck, A.

A. Roggenbuck, K. Thirunavukkuarasu, H. Schmitz, J. Marx, A. Deninger, I. Cámara Mayorga, R. Güsten, J. Hemberger, and M. Grüninger, “Using a fiber stretcher as a fast phase modulator in a continuous wave terahertz spectrometer,” J. Opt. Soc. Am. B 29, 614–620 (2012).
[CrossRef]

A. Roggenbuck, H. Schmitz, A. Deninger, I. Cámara Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New J. Phys. 12, 043017 (2010).
[CrossRef]

A. J. Deninger, T. Göbel, D. Schönherr, T. Kinder, A. Roggenbuck, M. Köberle, F. Lison, T. Müller-Wirts, and P. Meissner, “Precisely tunable continuous-wave terahertz source with interferometric frequency control,” Rev. Sci. Instrum. 79, 044702 (2008).
[CrossRef]

Saeedkia, D.

Safavi-Naeini, S.

Schmitz, A.

I. Cámara Mayorga, E. A. Michael, A. Schmitz, P. van der Wal, R. Güsten, K. Maier, and A. Dewald, “Terahertz photomixing in high energy oxygen- and nitrogen-ion-implanted GaAs,” Appl. Phys. Lett. 91, 031107 (2007).
[CrossRef]

Schmitz, H.

A. Roggenbuck, K. Thirunavukkuarasu, H. Schmitz, J. Marx, A. Deninger, I. Cámara Mayorga, R. Güsten, J. Hemberger, and M. Grüninger, “Using a fiber stretcher as a fast phase modulator in a continuous wave terahertz spectrometer,” J. Opt. Soc. Am. B 29, 614–620 (2012).
[CrossRef]

A. Roggenbuck, H. Schmitz, A. Deninger, I. Cámara Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New J. Phys. 12, 043017 (2010).
[CrossRef]

Schönherr, D.

A. J. Deninger, T. Göbel, D. Schönherr, T. Kinder, A. Roggenbuck, M. Köberle, F. Lison, T. Müller-Wirts, and P. Meissner, “Precisely tunable continuous-wave terahertz source with interferometric frequency control,” Rev. Sci. Instrum. 79, 044702 (2008).
[CrossRef]

Smith, F. W.

E. R. Brown, K. A. McIntosh, F. W. Smith, K. B. Nichols, M. J. Manfra, C. L. Dennis, and J. P. Mattia, “Milliwatt output levels and superquadratic bias dependence in a low-temperature-grown GaAs photomixer,” Appl. Phys. Lett. 64, 3311–3313 (1994).
[CrossRef]

Song, H.-J.

Biased uni-travelling-carrier photodiodes have been employed as receivers; see T. Nagatsuma, A. Kaino, S. Hisatake, K. Ajito, H.-J. Song, A. Wakatsuki, Y. Muramoto, N. Kukutsu, and Y. Kado, “Continuous-wave terahertz spectroscopy system based on photodiodes,” PIERS Online 6, 390–394 (2010) (but there the purpose of biasing is not related to normalization).

Thirunavukkuarasu, K.

van der Wal, P.

I. Cámara Mayorga, E. A. Michael, A. Schmitz, P. van der Wal, R. Güsten, K. Maier, and A. Dewald, “Terahertz photomixing in high energy oxygen- and nitrogen-ion-implanted GaAs,” Appl. Phys. Lett. 91, 031107 (2007).
[CrossRef]

Verghese, S.

S. Verghese, K. A. McIntosh, S. Calawa, W. F. Dinatale, E. K. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Appl. Phys. Lett. 73, 3824–3826 (1998).
[CrossRef]

Wakatsuki, A.

Biased uni-travelling-carrier photodiodes have been employed as receivers; see T. Nagatsuma, A. Kaino, S. Hisatake, K. Ajito, H.-J. Song, A. Wakatsuki, Y. Muramoto, N. Kukutsu, and Y. Kado, “Continuous-wave terahertz spectroscopy system based on photodiodes,” PIERS Online 6, 390–394 (2010) (but there the purpose of biasing is not related to normalization).

Wang, L. J.

S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys. 109, 61301–61356 (2011).
[CrossRef]

Appl. Phys. Lett. (5)

K. A. McIntosh, E. R. Brown, K. B. Nichols, O. B. McMahon, W. F. DiNatale, and T. M. Lyszczarz, “Terahertz photomixing with diode lasers in low-temperature-grown GaAs,” Appl. Phys. Lett. 67, 3844–3846 (1995).
[CrossRef]

S. Verghese, K. A. McIntosh, S. Calawa, W. F. Dinatale, E. K. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Appl. Phys. Lett. 73, 3824–3826 (1998).
[CrossRef]

J. E. Bjarnason and E. R. Brown, “Sensitivity measurement and analysis of an ErAs:GaAs coherent photomixing transceiver,” Appl. Phys. Lett. 87, 134105 (2005).
[CrossRef]

I. Cámara Mayorga, E. A. Michael, A. Schmitz, P. van der Wal, R. Güsten, K. Maier, and A. Dewald, “Terahertz photomixing in high energy oxygen- and nitrogen-ion-implanted GaAs,” Appl. Phys. Lett. 91, 031107 (2007).
[CrossRef]

E. R. Brown, K. A. McIntosh, F. W. Smith, K. B. Nichols, M. J. Manfra, C. L. Dennis, and J. P. Mattia, “Milliwatt output levels and superquadratic bias dependence in a low-temperature-grown GaAs photomixer,” Appl. Phys. Lett. 64, 3311–3313 (1994).
[CrossRef]

J. Appl. Phys. (1)

S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys. 109, 61301–61356 (2011).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (1)

New J. Phys. (1)

A. Roggenbuck, H. Schmitz, A. Deninger, I. Cámara Mayorga, J. Hemberger, R. Güsten, and M. Grüninger, “Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples,” New J. Phys. 12, 043017 (2010).
[CrossRef]

PIERS (1)

Biased uni-travelling-carrier photodiodes have been employed as receivers; see T. Nagatsuma, A. Kaino, S. Hisatake, K. Ajito, H.-J. Song, A. Wakatsuki, Y. Muramoto, N. Kukutsu, and Y. Kado, “Continuous-wave terahertz spectroscopy system based on photodiodes,” PIERS Online 6, 390–394 (2010) (but there the purpose of biasing is not related to normalization).

Rev. Sci. Instrum. (1)

A. J. Deninger, T. Göbel, D. Schönherr, T. Kinder, A. Roggenbuck, M. Köberle, F. Lison, T. Müller-Wirts, and P. Meissner, “Precisely tunable continuous-wave terahertz source with interferometric frequency control,” Rev. Sci. Instrum. 79, 044702 (2008).
[CrossRef]

Other (2)

S. Matsuura and H. Ito, “Generation of cw terahertz radiation with photomixing,” in Terahertz Optoelectronics, K. Sakai, ed. (Springer-Verlag, 2005), pp. 157–202.

The responsivities STx and SRx depend on the respective bias voltages (or electric fields). At the receiver, we may safely write SRx∝ETHz,Rx·dSRx/dV (see Fig. 1) in order to separate the terahertz electric field. At the transmitter with its large bias voltage, it is not necessary to assume a linear current-voltage characteristic. This explains the apparent asymmetry of Eq. (3) with respect to STx and dSRx/dV.

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Figures (6)

Fig. 1.
Fig. 1.

Current–voltage characteristic of an illuminated photomixer. At low voltages, the photocurrent is proportional to the voltage (black points, data; red line, linear fit). Consequently, the photomixer converts a terahertz electric field linearly into a photocurrent [see Eq. (2)] and can be used as a detector. Inset: photocurrent–voltage characteristic for larger voltages (see also [13]).

Fig. 2.
Fig. 2.

Setup of the continuous wave terahertz spectrometer (from [9]). Red-colored parts: for the normalization described in this paper, the receiver is biased with a small DC voltage and additional photocurrents I Tx and I Rx are measured in the transmitter and receiver, respectively.

Fig. 3.
Fig. 3.

Drift of the measured terahertz photocurrent I THz (black) and of the normalized photocurrent I THz , norm (red) upon reduction of the power P 1 of one of the two lasers. Δ P 1 = 0 corresponds to equal laser powers, i.e., r = 0.5 or P 1 = P 2 . Solid lines: predictions according to Eqs. (3) and (9). Full symbols: measured data. Crosses are obtained by subtracting the deviation between the black symbols and the black line from the red symbols.

Fig. 4.
Fig. 4.

Normalized terahertz photocurrent I THz , norm versus splitting ratio of the two laser powers, r = P 1 / ( P 1 + P 2 ) , for a constant total power P 1 + P 2 = const . The solid line depicts our expectation I THz , norm r ( 1 r ) ; see Eq. (9). I THz , norm is scaled such that I THz , norm ( r = 0.5 ) = 1 .

Fig. 5.
Fig. 5.

Effect of a periodic variation of the laboratory temperature by ± 1 K (top panel) on the stability of the measured terahertz signal I THz (black line, bottom panel). The drift is strongly suppressed in the normalized photocurrent I THz , norm (red line, bottom panel). Second and third panels: DC photocurrents I Tx and I Rx at the transmitter and receiver, respectively. Fourth panel: normalized photocurrent if only I Tx (green) or only I Rx (blue) is used for the normalization, e.g., I THz , norm , Tx = I THz ( I Tx , 0 / I Tx ) 2 .

Fig. 6.
Fig. 6.

A 100% line, i.e., the ratio of the terahertz signals of two consecutive runs, measured directly after power up of the system. The data have been smoothed by averaging over five points.

Equations (10)

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I Tx = S Tx ( V bias ) · ( P 1 , Tx + P 2 , Tx ) ,
I 0 , THz P THz , Rx 1 / 2 d S Rx d V ( P 1 , Rx P 2 , Rx ) 1 / 2 ,
I 0 , THz T sample 1 / 2 · S Tx ( V bias ) · d S Rx d V · ( P 1 , Tx P 2 , Tx P 1 , Rx P 2 , Rx ) 1 / 2 .
I Rx = V bias , Rx d S Rx d V ( P 1 , Rx + P 2 , Rx ) .
I THz , norm = I THz I Tx , 0 I Tx I Rx , 0 I Rx T sample 1 / 2 ( P 1 , Tx P 2 , Tx P 1 , Rx P 2 , Rx ) 1 / 2 ( P 1 , Tx + P 2 , Tx ) ( P 1 , Rx + P 2 , Rx ) ,
I THz P 1 , Tx = 1 2 I THz P 1 , Tx and I THz P 2 , Tx = 1 2 I THz P 2 , Tx ,
( I THz , norm ) P 1 , Tx = 1 2 I THz , norm P 1 , Tx ( P 1 , Tx P 2 , Tx ) P 1 , Tx + P 2 , Tx , ( I THz , norm ) P 2 , Tx = 1 2 I THz , norm P 2 , Tx ( P 1 , Tx P 2 , Tx ) P 1 , Tx + P 2 , Tx .
| P 1 , Tx P 2 , Tx P 1 , Tx + P 2 , Tx | .
I THz , norm T sample 1 / 2 [ r Tx ( 1 r Tx ) ] 1 / 2 [ r Rx ( 1 r Rx ) ] 1 / 2 .
I THz , norm T sample 1 / 2 r ( 1 r ) .

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