Abstract

Signals measured with Chirped Laser Dispersion Spectroscopy (CLaDS) setup implemented with an intensity modulator are analyzed. We investigate the signal amplitude dependence on the modulator bias voltage and the signal generator output power. Potential strategies for signal retrieval are discussed. We demonstrate that choosing a bias voltage, an RF generator output power and a demodulation frequency is critical for CLaDS and strongly affects its performance.

© 2015 Optical Society of America

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References

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  1. G. Wysocki and D. Weidmann, “Molecular dispersion spectroscopy for chemical sensing using chirped mid-infrared quantum cascade laser,” Opt. Express 18(25), 26123–26140 (2010).
    [Crossref] [PubMed]
  2. J. B. McManus, M. S. Zahniser, J. D. D. Nelson, J. H. Shorter, S. Herndon, E. Wood, and R. Wehr, “Application of quantum cascade lasers to high-precision atmospheric trace gas measurements,” Opt. Eng. 49(11), 111124 (2010).
    [Crossref]
  3. G. B. Rieker, J. B. Jeffries, and R. K. Hanson, “Calibration-free wavelength-modulation spectroscopy for measurements of gas temperature and concentration in harsh environments,” Appl. Opt. 48(29), 5546–5560 (2009).
    [Crossref] [PubMed]
  4. A. A. Kosterev, Y. A. Bakhirkin, and F. K. Tittel, “Ultrasensitive gas detection by quartz-enhanced photoacoustic spectroscopy in the fundamental molecular absorption bands region,” Appl. Phys. B 80(1), 133–138 (2005).
    [Crossref]
  5. G. Berden, and R. Engeln, “Cavity Ring-Down Spectroscopy: Techniques and Applications,” Wiley-Blackwell (2009).
  6. M. R. McCurdy, Y. A. Bakhirkin, and F. K. Tittel, “Quantum cascade laser-based integrated cavity output spectroscopy of exhaled nitric oxide,” Appl. Phys. B 85(2-3), 445–452 (2006).
    [Crossref]
  7. M. Nikodem, D. Weidmann, and G. Wysocki, “Chirped Laser Dispersion Spectroscopy with harmonic detection of molecular spectra,” Appl. Phys. B 109(3), 477–483 (2012).
    [Crossref]
  8. M. Nikodem, G. Plant, D. Sonnenfroh, and G. Wysocki, “Open-path sensor for atmospheric methane based on chirped laser dispersion spectroscopy,” Appl. Phys. B 14, 5938 (2014).
    [Crossref]
  9. M. Nikodem and G. Wysocki, “Chirped Laser Dispersion Spectroscopy for Remote Open-Path Trace-Gas Sensing,” Sensors (Basel) 12(12), 16466–16481 (2012).
    [Crossref] [PubMed]
  10. N. S. Daghestani, R. Brownsword, and D. Weidmann, “Analysis and demonstration of atmospheric methane monitoring by mid-infrared open-path chirped laser dispersion spectroscopy,” Opt. Express 22(S7Suppl 7), A1731–A1743 (2014).
    [Crossref] [PubMed]
  11. P. Martín-Mateos, B. Jerez, and P. Acedo, “Heterodyne architecture for tunable laser chirped dispersion spectroscopy using optical processing,” Opt. Lett. 39(9), 2611–2613 (2014).
    [Crossref] [PubMed]
  12. M. Nikodem, G. Plant, Z. Wang, P. Prucnal, and G. Wysocki, “Chirped lasers dispersion spectroscopy implemented with single- and dual-sideband electro-optical modulators,” Opt. Express 21(12), 14649–14655 (2013).
    [Crossref] [PubMed]
  13. A. Hangauer, G. Spinner, M. Nikodem, and G. Wysocki, “Chirped laser dispersion spectroscopy using a directly modulated quantum cascade laser,” Appl. Phys. Lett. 103(19), 191107 (2013).
    [Crossref]
  14. W. C. Swann and S. L. Gilbert, “Line centers, pressure shift, and pressure broadening of 1530-1560 nm hydrogen cyanide wavelength calibration lines,” J. Opt. Soc. Am. B 22(8), 1749–1756 (2005).
    [Crossref]
  15. M. Nikodem, K. Krzempek, and K. Abramski, “Chirped laser dispersion spectroscopy in dual side-band frequency-shifted-carrier arrangement,” in Imaging and Applied Optics 2014(Optical Society of America, Seattle, Washington, 2014), p. LW4D.2.
  16. M. Nikodem, D. Weidmann, C. Smith, and G. Wysocki, “Signal-to-noise ratio in chirped laser dispersion spectroscopy,” Opt. Express 20(1), 644–653 (2012).
    [Crossref] [PubMed]
  17. H. Nagata, K. Kiuchi, S. Shimotsu, J. Ogiwara, and J. Minowa, “Estimation of direct current bias and drift of Ti:LiNbO3 optical modulators,” J. Appl. Phys. 76(3), 1405–1408 (1994).
    [Crossref]
  18. H. Nagata, N. Papasavvas, and D. R. Maack, “Bias stability of OC48 x-cut lithium-niobate optical modulators: four years of biased aging test results,” IEEE Photon. Technol. Lett. 15(1), 42–44 (2003).
    [Crossref]
  19. J. Svarny, “Analysis of quadrature bias-point drift of Mach-Zehnder electro-optic modulator,” in Electronics Conference (BEC), 2010 12th Biennial Baltic(2010), pp. 231–234.
    [Crossref]

2014 (3)

2013 (2)

M. Nikodem, G. Plant, Z. Wang, P. Prucnal, and G. Wysocki, “Chirped lasers dispersion spectroscopy implemented with single- and dual-sideband electro-optical modulators,” Opt. Express 21(12), 14649–14655 (2013).
[Crossref] [PubMed]

A. Hangauer, G. Spinner, M. Nikodem, and G. Wysocki, “Chirped laser dispersion spectroscopy using a directly modulated quantum cascade laser,” Appl. Phys. Lett. 103(19), 191107 (2013).
[Crossref]

2012 (3)

M. Nikodem, D. Weidmann, C. Smith, and G. Wysocki, “Signal-to-noise ratio in chirped laser dispersion spectroscopy,” Opt. Express 20(1), 644–653 (2012).
[Crossref] [PubMed]

M. Nikodem and G. Wysocki, “Chirped Laser Dispersion Spectroscopy for Remote Open-Path Trace-Gas Sensing,” Sensors (Basel) 12(12), 16466–16481 (2012).
[Crossref] [PubMed]

M. Nikodem, D. Weidmann, and G. Wysocki, “Chirped Laser Dispersion Spectroscopy with harmonic detection of molecular spectra,” Appl. Phys. B 109(3), 477–483 (2012).
[Crossref]

2010 (2)

G. Wysocki and D. Weidmann, “Molecular dispersion spectroscopy for chemical sensing using chirped mid-infrared quantum cascade laser,” Opt. Express 18(25), 26123–26140 (2010).
[Crossref] [PubMed]

J. B. McManus, M. S. Zahniser, J. D. D. Nelson, J. H. Shorter, S. Herndon, E. Wood, and R. Wehr, “Application of quantum cascade lasers to high-precision atmospheric trace gas measurements,” Opt. Eng. 49(11), 111124 (2010).
[Crossref]

2009 (1)

2006 (1)

M. R. McCurdy, Y. A. Bakhirkin, and F. K. Tittel, “Quantum cascade laser-based integrated cavity output spectroscopy of exhaled nitric oxide,” Appl. Phys. B 85(2-3), 445–452 (2006).
[Crossref]

2005 (2)

A. A. Kosterev, Y. A. Bakhirkin, and F. K. Tittel, “Ultrasensitive gas detection by quartz-enhanced photoacoustic spectroscopy in the fundamental molecular absorption bands region,” Appl. Phys. B 80(1), 133–138 (2005).
[Crossref]

W. C. Swann and S. L. Gilbert, “Line centers, pressure shift, and pressure broadening of 1530-1560 nm hydrogen cyanide wavelength calibration lines,” J. Opt. Soc. Am. B 22(8), 1749–1756 (2005).
[Crossref]

2003 (1)

H. Nagata, N. Papasavvas, and D. R. Maack, “Bias stability of OC48 x-cut lithium-niobate optical modulators: four years of biased aging test results,” IEEE Photon. Technol. Lett. 15(1), 42–44 (2003).
[Crossref]

1994 (1)

H. Nagata, K. Kiuchi, S. Shimotsu, J. Ogiwara, and J. Minowa, “Estimation of direct current bias and drift of Ti:LiNbO3 optical modulators,” J. Appl. Phys. 76(3), 1405–1408 (1994).
[Crossref]

Acedo, P.

Bakhirkin, Y. A.

M. R. McCurdy, Y. A. Bakhirkin, and F. K. Tittel, “Quantum cascade laser-based integrated cavity output spectroscopy of exhaled nitric oxide,” Appl. Phys. B 85(2-3), 445–452 (2006).
[Crossref]

A. A. Kosterev, Y. A. Bakhirkin, and F. K. Tittel, “Ultrasensitive gas detection by quartz-enhanced photoacoustic spectroscopy in the fundamental molecular absorption bands region,” Appl. Phys. B 80(1), 133–138 (2005).
[Crossref]

Brownsword, R.

Daghestani, N. S.

Gilbert, S. L.

Hangauer, A.

A. Hangauer, G. Spinner, M. Nikodem, and G. Wysocki, “Chirped laser dispersion spectroscopy using a directly modulated quantum cascade laser,” Appl. Phys. Lett. 103(19), 191107 (2013).
[Crossref]

Hanson, R. K.

Herndon, S.

J. B. McManus, M. S. Zahniser, J. D. D. Nelson, J. H. Shorter, S. Herndon, E. Wood, and R. Wehr, “Application of quantum cascade lasers to high-precision atmospheric trace gas measurements,” Opt. Eng. 49(11), 111124 (2010).
[Crossref]

Jeffries, J. B.

Jerez, B.

Kiuchi, K.

H. Nagata, K. Kiuchi, S. Shimotsu, J. Ogiwara, and J. Minowa, “Estimation of direct current bias and drift of Ti:LiNbO3 optical modulators,” J. Appl. Phys. 76(3), 1405–1408 (1994).
[Crossref]

Kosterev, A. A.

A. A. Kosterev, Y. A. Bakhirkin, and F. K. Tittel, “Ultrasensitive gas detection by quartz-enhanced photoacoustic spectroscopy in the fundamental molecular absorption bands region,” Appl. Phys. B 80(1), 133–138 (2005).
[Crossref]

Maack, D. R.

H. Nagata, N. Papasavvas, and D. R. Maack, “Bias stability of OC48 x-cut lithium-niobate optical modulators: four years of biased aging test results,” IEEE Photon. Technol. Lett. 15(1), 42–44 (2003).
[Crossref]

Martín-Mateos, P.

McCurdy, M. R.

M. R. McCurdy, Y. A. Bakhirkin, and F. K. Tittel, “Quantum cascade laser-based integrated cavity output spectroscopy of exhaled nitric oxide,” Appl. Phys. B 85(2-3), 445–452 (2006).
[Crossref]

McManus, J. B.

J. B. McManus, M. S. Zahniser, J. D. D. Nelson, J. H. Shorter, S. Herndon, E. Wood, and R. Wehr, “Application of quantum cascade lasers to high-precision atmospheric trace gas measurements,” Opt. Eng. 49(11), 111124 (2010).
[Crossref]

Minowa, J.

H. Nagata, K. Kiuchi, S. Shimotsu, J. Ogiwara, and J. Minowa, “Estimation of direct current bias and drift of Ti:LiNbO3 optical modulators,” J. Appl. Phys. 76(3), 1405–1408 (1994).
[Crossref]

Nagata, H.

H. Nagata, N. Papasavvas, and D. R. Maack, “Bias stability of OC48 x-cut lithium-niobate optical modulators: four years of biased aging test results,” IEEE Photon. Technol. Lett. 15(1), 42–44 (2003).
[Crossref]

H. Nagata, K. Kiuchi, S. Shimotsu, J. Ogiwara, and J. Minowa, “Estimation of direct current bias and drift of Ti:LiNbO3 optical modulators,” J. Appl. Phys. 76(3), 1405–1408 (1994).
[Crossref]

Nelson, J. D. D.

J. B. McManus, M. S. Zahniser, J. D. D. Nelson, J. H. Shorter, S. Herndon, E. Wood, and R. Wehr, “Application of quantum cascade lasers to high-precision atmospheric trace gas measurements,” Opt. Eng. 49(11), 111124 (2010).
[Crossref]

Nikodem, M.

M. Nikodem, G. Plant, D. Sonnenfroh, and G. Wysocki, “Open-path sensor for atmospheric methane based on chirped laser dispersion spectroscopy,” Appl. Phys. B 14, 5938 (2014).
[Crossref]

A. Hangauer, G. Spinner, M. Nikodem, and G. Wysocki, “Chirped laser dispersion spectroscopy using a directly modulated quantum cascade laser,” Appl. Phys. Lett. 103(19), 191107 (2013).
[Crossref]

M. Nikodem, G. Plant, Z. Wang, P. Prucnal, and G. Wysocki, “Chirped lasers dispersion spectroscopy implemented with single- and dual-sideband electro-optical modulators,” Opt. Express 21(12), 14649–14655 (2013).
[Crossref] [PubMed]

M. Nikodem, D. Weidmann, C. Smith, and G. Wysocki, “Signal-to-noise ratio in chirped laser dispersion spectroscopy,” Opt. Express 20(1), 644–653 (2012).
[Crossref] [PubMed]

M. Nikodem and G. Wysocki, “Chirped Laser Dispersion Spectroscopy for Remote Open-Path Trace-Gas Sensing,” Sensors (Basel) 12(12), 16466–16481 (2012).
[Crossref] [PubMed]

M. Nikodem, D. Weidmann, and G. Wysocki, “Chirped Laser Dispersion Spectroscopy with harmonic detection of molecular spectra,” Appl. Phys. B 109(3), 477–483 (2012).
[Crossref]

Ogiwara, J.

H. Nagata, K. Kiuchi, S. Shimotsu, J. Ogiwara, and J. Minowa, “Estimation of direct current bias and drift of Ti:LiNbO3 optical modulators,” J. Appl. Phys. 76(3), 1405–1408 (1994).
[Crossref]

Papasavvas, N.

H. Nagata, N. Papasavvas, and D. R. Maack, “Bias stability of OC48 x-cut lithium-niobate optical modulators: four years of biased aging test results,” IEEE Photon. Technol. Lett. 15(1), 42–44 (2003).
[Crossref]

Plant, G.

M. Nikodem, G. Plant, D. Sonnenfroh, and G. Wysocki, “Open-path sensor for atmospheric methane based on chirped laser dispersion spectroscopy,” Appl. Phys. B 14, 5938 (2014).
[Crossref]

M. Nikodem, G. Plant, Z. Wang, P. Prucnal, and G. Wysocki, “Chirped lasers dispersion spectroscopy implemented with single- and dual-sideband electro-optical modulators,” Opt. Express 21(12), 14649–14655 (2013).
[Crossref] [PubMed]

Prucnal, P.

Rieker, G. B.

Shimotsu, S.

H. Nagata, K. Kiuchi, S. Shimotsu, J. Ogiwara, and J. Minowa, “Estimation of direct current bias and drift of Ti:LiNbO3 optical modulators,” J. Appl. Phys. 76(3), 1405–1408 (1994).
[Crossref]

Shorter, J. H.

J. B. McManus, M. S. Zahniser, J. D. D. Nelson, J. H. Shorter, S. Herndon, E. Wood, and R. Wehr, “Application of quantum cascade lasers to high-precision atmospheric trace gas measurements,” Opt. Eng. 49(11), 111124 (2010).
[Crossref]

Smith, C.

Sonnenfroh, D.

M. Nikodem, G. Plant, D. Sonnenfroh, and G. Wysocki, “Open-path sensor for atmospheric methane based on chirped laser dispersion spectroscopy,” Appl. Phys. B 14, 5938 (2014).
[Crossref]

Spinner, G.

A. Hangauer, G. Spinner, M. Nikodem, and G. Wysocki, “Chirped laser dispersion spectroscopy using a directly modulated quantum cascade laser,” Appl. Phys. Lett. 103(19), 191107 (2013).
[Crossref]

Swann, W. C.

Tittel, F. K.

M. R. McCurdy, Y. A. Bakhirkin, and F. K. Tittel, “Quantum cascade laser-based integrated cavity output spectroscopy of exhaled nitric oxide,” Appl. Phys. B 85(2-3), 445–452 (2006).
[Crossref]

A. A. Kosterev, Y. A. Bakhirkin, and F. K. Tittel, “Ultrasensitive gas detection by quartz-enhanced photoacoustic spectroscopy in the fundamental molecular absorption bands region,” Appl. Phys. B 80(1), 133–138 (2005).
[Crossref]

Wang, Z.

Wehr, R.

J. B. McManus, M. S. Zahniser, J. D. D. Nelson, J. H. Shorter, S. Herndon, E. Wood, and R. Wehr, “Application of quantum cascade lasers to high-precision atmospheric trace gas measurements,” Opt. Eng. 49(11), 111124 (2010).
[Crossref]

Weidmann, D.

Wood, E.

J. B. McManus, M. S. Zahniser, J. D. D. Nelson, J. H. Shorter, S. Herndon, E. Wood, and R. Wehr, “Application of quantum cascade lasers to high-precision atmospheric trace gas measurements,” Opt. Eng. 49(11), 111124 (2010).
[Crossref]

Wysocki, G.

M. Nikodem, G. Plant, D. Sonnenfroh, and G. Wysocki, “Open-path sensor for atmospheric methane based on chirped laser dispersion spectroscopy,” Appl. Phys. B 14, 5938 (2014).
[Crossref]

A. Hangauer, G. Spinner, M. Nikodem, and G. Wysocki, “Chirped laser dispersion spectroscopy using a directly modulated quantum cascade laser,” Appl. Phys. Lett. 103(19), 191107 (2013).
[Crossref]

M. Nikodem, G. Plant, Z. Wang, P. Prucnal, and G. Wysocki, “Chirped lasers dispersion spectroscopy implemented with single- and dual-sideband electro-optical modulators,” Opt. Express 21(12), 14649–14655 (2013).
[Crossref] [PubMed]

M. Nikodem, D. Weidmann, C. Smith, and G. Wysocki, “Signal-to-noise ratio in chirped laser dispersion spectroscopy,” Opt. Express 20(1), 644–653 (2012).
[Crossref] [PubMed]

M. Nikodem and G. Wysocki, “Chirped Laser Dispersion Spectroscopy for Remote Open-Path Trace-Gas Sensing,” Sensors (Basel) 12(12), 16466–16481 (2012).
[Crossref] [PubMed]

M. Nikodem, D. Weidmann, and G. Wysocki, “Chirped Laser Dispersion Spectroscopy with harmonic detection of molecular spectra,” Appl. Phys. B 109(3), 477–483 (2012).
[Crossref]

G. Wysocki and D. Weidmann, “Molecular dispersion spectroscopy for chemical sensing using chirped mid-infrared quantum cascade laser,” Opt. Express 18(25), 26123–26140 (2010).
[Crossref] [PubMed]

Zahniser, M. S.

J. B. McManus, M. S. Zahniser, J. D. D. Nelson, J. H. Shorter, S. Herndon, E. Wood, and R. Wehr, “Application of quantum cascade lasers to high-precision atmospheric trace gas measurements,” Opt. Eng. 49(11), 111124 (2010).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (4)

A. A. Kosterev, Y. A. Bakhirkin, and F. K. Tittel, “Ultrasensitive gas detection by quartz-enhanced photoacoustic spectroscopy in the fundamental molecular absorption bands region,” Appl. Phys. B 80(1), 133–138 (2005).
[Crossref]

M. R. McCurdy, Y. A. Bakhirkin, and F. K. Tittel, “Quantum cascade laser-based integrated cavity output spectroscopy of exhaled nitric oxide,” Appl. Phys. B 85(2-3), 445–452 (2006).
[Crossref]

M. Nikodem, D. Weidmann, and G. Wysocki, “Chirped Laser Dispersion Spectroscopy with harmonic detection of molecular spectra,” Appl. Phys. B 109(3), 477–483 (2012).
[Crossref]

M. Nikodem, G. Plant, D. Sonnenfroh, and G. Wysocki, “Open-path sensor for atmospheric methane based on chirped laser dispersion spectroscopy,” Appl. Phys. B 14, 5938 (2014).
[Crossref]

Appl. Phys. Lett. (1)

A. Hangauer, G. Spinner, M. Nikodem, and G. Wysocki, “Chirped laser dispersion spectroscopy using a directly modulated quantum cascade laser,” Appl. Phys. Lett. 103(19), 191107 (2013).
[Crossref]

IEEE Photon. Technol. Lett. (1)

H. Nagata, N. Papasavvas, and D. R. Maack, “Bias stability of OC48 x-cut lithium-niobate optical modulators: four years of biased aging test results,” IEEE Photon. Technol. Lett. 15(1), 42–44 (2003).
[Crossref]

J. Appl. Phys. (1)

H. Nagata, K. Kiuchi, S. Shimotsu, J. Ogiwara, and J. Minowa, “Estimation of direct current bias and drift of Ti:LiNbO3 optical modulators,” J. Appl. Phys. 76(3), 1405–1408 (1994).
[Crossref]

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

Opt. Eng. (1)

J. B. McManus, M. S. Zahniser, J. D. D. Nelson, J. H. Shorter, S. Herndon, E. Wood, and R. Wehr, “Application of quantum cascade lasers to high-precision atmospheric trace gas measurements,” Opt. Eng. 49(11), 111124 (2010).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Sensors (Basel) (1)

M. Nikodem and G. Wysocki, “Chirped Laser Dispersion Spectroscopy for Remote Open-Path Trace-Gas Sensing,” Sensors (Basel) 12(12), 16466–16481 (2012).
[Crossref] [PubMed]

Other (3)

G. Berden, and R. Engeln, “Cavity Ring-Down Spectroscopy: Techniques and Applications,” Wiley-Blackwell (2009).

M. Nikodem, K. Krzempek, and K. Abramski, “Chirped laser dispersion spectroscopy in dual side-band frequency-shifted-carrier arrangement,” in Imaging and Applied Optics 2014(Optical Society of America, Seattle, Washington, 2014), p. LW4D.2.

J. Svarny, “Analysis of quadrature bias-point drift of Mach-Zehnder electro-optic modulator,” in Electronics Conference (BEC), 2010 12th Biennial Baltic(2010), pp. 231–234.
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 A schematic diagram of the experimental setup (DFB LD – distributed feed-back laser diode, MZM – Mach-Zehnder intensity modulator, PD – photodiode). Function generator was used to provide a current ramp for chirping the laser wavelength across the target molecular transition. (A).
Fig. 2
Fig. 2 A schematic diagram of the model proposed in this study: a bias voltage and an RF power are the input parameters which are used to obtain the optical field after the modulator. It is used to calculate CLaDS signals talking into account nine components of the optical field (carrier and sidebands M × Ω, where M = ± 1, ± 2, ± 3, and ± 4).
Fig. 3
Fig. 3 CLaDS dispersion signals retrieved through FM demodulation at 1 × Ω (inset shows absorption signals after AM demodulation) for different bias voltages and RF generator output powers (PRF). Frequency axis is centered at the transition center and the scale is shown in figure (a). Magenta dots – measured data, black line – numerical model (bias in the model was changed according to the bias used in the experiment).
Fig. 4
Fig. 4 The CLaDS amplitude vs. bias voltage measure for two different RF generator output powers (10dBm – magenta circles, 25dBm – black squares). Gray color indicates bias voltages for which RF beatnote at 1 × Ω drops and the CLaDS measurement is unreliable, whereas arrows show the modulator quadrature positions. Schematic drawings in the right are presented to show the origin of the additional beatnote signal which is responsible for the signal amplitude increase.
Fig. 5
Fig. 5 CLaDS dispersion signals retrieved through FM demodulation at 2 × Ω (inset shows absorption signals after AM demodulation) for different bias voltages and RF generator output powers (PRF). Frequency axis is centered at the transition center and the scale is shown in figures (f) and (i). Red dots – measured data, black line – numerical model (bias in the model was changed according to the bias used in the experiment). Please note: for viewing purposes spectra (both measured and modelled) in figures (a) and (f) where multiplied by the factor of 2, and spectra in figures (e) and (j) where multiplied by the factor of 1/3.
Fig. 6
Fig. 6 CLaDS amplitude in 2 × Ω demodulation mode vs. bias voltage measure for two different RF generator output powers (10dBm – red circles, 25dBm – black squares). Gray color indicates bias voltages for which RF beatnote at 2 × Ω drops and CLaDS measurement is unreliable. On the right-hand side an optical field at the output of the modulator is schematically presented. These diagrams explain the origin of different CLaDS amplitudes when modulator is biased at the minimum (top diagram) and maximum (bottom) of its transmission curve.

Equations (1)

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P= M=4 4k E M * E M+k H( ω+MΩ )H ( ω+( M+k )Ω ) * ,

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