Abstract

We report new approaches for signal generation in Chirped Laser Dispersion Spectroscopy (CLaDS). Two optical arrangements based on electro-optical modulators significantly reduce CLaDS system complexity and enable optimum performance when applied to detection of GHz-wide molecular transitions. Proof-of-principle experiments in the near-infrared spectral range are presented and potential strategies for application in the mid-infrared are discussed.

© 2013 OSA

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  1. A. A. Kosterev and F. K. Tittel, “Chemical sensors based on quantum cascade lasers,” IEEE J. Quantum Electron.38(6), 582–591 (2002).
    [CrossRef]
  2. M. R. McCurdy, Y. Bakhirkin, G. Wysocki, R. Lewicki, and F. K. Tittel, “Recent advances of laser-spectroscopy-based techniques for applications in breath analysis,” J Breath Res1(1), 014001 (2007).
    [CrossRef] [PubMed]
  3. E. Kerstel and L. Gianfrani, “Advances in laser-based isotope ratio measurements: selected applications,” Appl. Phys. B92(3), 439–449 (2008).
    [CrossRef]
  4. R. Lewicki, J. H. Doty, R. F. Curl, F. K. Tittel, and G. Wysocki, “Ultrasensitive detection of nitric oxide at 5.33 microm by using external cavity quantum cascade laser-based Faraday rotation spectroscopy,” Proc. Natl. Acad. Sci. U.S.A.106(31), 12587–12592 (2009).
    [CrossRef] [PubMed]
  5. 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]
  6. R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
    [CrossRef]
  7. S. Lundqvist, P. Kluczynski, R. Weih, M. von Edlinger, L. Nähle, M. Fischer, A. Bauer, S. Höfling, and J. Koeth, “Sensing of formaldehyde using a distributed feedback interband cascade laser emitting around 3493 nm,” Appl. Opt.51(25), 6009–6013 (2012).
    [CrossRef] [PubMed]
  8. B. Brumfield, W. Sun, Y. Ju, and G. Wysocki, “Direct In Situ Quantification of HO2 from a Flow Reactor,” J. Phys. Chem. Lett.4(6), 872–876 (2013).
    [CrossRef]
  9. G. Wysocki and D. Weidmann, “Molecular dispersion spectroscopy for chemical sensing using chirped mid-infrared quantum cascade laser,” Opt. Express18(25), 26123–26140 (2010).
    [CrossRef] [PubMed]
  10. 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]
  11. M. Nikodem, D. Weidmann, C. Smith, and G. Wysocki, “Signal-to-noise ratio in chirped laser dispersion spectroscopy,” Opt. Express20(1), 644–653 (2012).
    [CrossRef] [PubMed]
  12. M. Nikodem and G. Wysocki, “Molecular dispersion spectroscopy--new capabilities in laser chemical sensing,” Ann. N. Y. Acad. Sci.1260(1), 101–111 (2012).
    [CrossRef] [PubMed]
  13. G. C. Bjorklund, “Frequency-modulation spectroscopy: a new method for measuring weak absorptions and dispersions,” Opt. Lett.5(1), 15–17 (1980).
    [CrossRef] [PubMed]
  14. G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B32(3), 145–152 (1983).
    [CrossRef]
  15. B. Hraimel, X. Zhang, Y. Pei, K. Wu, T. Liu, T. Xu, and Q. Nie, “Optical Single-Sideband Modulation With Tunable Optical Carrier to Sideband Ratio in Radio Over Fiber Systems,” J. Lightwave Technol.29(5), 775–781 (2011).
    [CrossRef]
  16. 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. B22(8), 1749–1756 (2005).
    [CrossRef]
  17. D. Richter, A. Fried, and P. Weibring, “Difference frequency generation laser based spectrometers,” Laser Photonics Rev.3(4), 343–354 (2009).
    [CrossRef]
  18. M. Nikodem, K. Krzempek, G. Plant, K. Abramski, G. Wysocki, “Methane sensing at 3.4um using Chirped Laser Dispersion Spectroscopy with DFG source,” in CLEO/Europe-IQEC 2013 Conference Digest, OSA Technical Digest (CD) (Optical Society of America, 2013), paper CH-1.3.
  19. A. Hangauer, G. Spinner, M. Nikodem, and G. Wysocki, “Chirped Laser Dispersion Spectroscopy with Directly Modulated Quantum Cascade Laser,” in CLEO: Science and Innovations 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper CW1L.5.

2013 (1)

B. Brumfield, W. Sun, Y. Ju, and G. Wysocki, “Direct In Situ Quantification of HO2 from a Flow Reactor,” J. Phys. Chem. Lett.4(6), 872–876 (2013).
[CrossRef]

2012 (4)

2011 (1)

2010 (2)

G. Wysocki and D. Weidmann, “Molecular dispersion spectroscopy for chemical sensing using chirped mid-infrared quantum cascade laser,” Opt. Express18(25), 26123–26140 (2010).
[CrossRef] [PubMed]

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
[CrossRef]

2009 (3)

D. Richter, A. Fried, and P. Weibring, “Difference frequency generation laser based spectrometers,” Laser Photonics Rev.3(4), 343–354 (2009).
[CrossRef]

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]

R. Lewicki, J. H. Doty, R. F. Curl, F. K. Tittel, and G. Wysocki, “Ultrasensitive detection of nitric oxide at 5.33 microm by using external cavity quantum cascade laser-based Faraday rotation spectroscopy,” Proc. Natl. Acad. Sci. U.S.A.106(31), 12587–12592 (2009).
[CrossRef] [PubMed]

2008 (1)

E. Kerstel and L. Gianfrani, “Advances in laser-based isotope ratio measurements: selected applications,” Appl. Phys. B92(3), 439–449 (2008).
[CrossRef]

2007 (1)

M. R. McCurdy, Y. Bakhirkin, G. Wysocki, R. Lewicki, and F. K. Tittel, “Recent advances of laser-spectroscopy-based techniques for applications in breath analysis,” J Breath Res1(1), 014001 (2007).
[CrossRef] [PubMed]

2005 (1)

2002 (1)

A. A. Kosterev and F. K. Tittel, “Chemical sensors based on quantum cascade lasers,” IEEE J. Quantum Electron.38(6), 582–591 (2002).
[CrossRef]

1983 (1)

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B32(3), 145–152 (1983).
[CrossRef]

1980 (1)

Bakhirkin, Y.

M. R. McCurdy, Y. Bakhirkin, G. Wysocki, R. Lewicki, and F. K. Tittel, “Recent advances of laser-spectroscopy-based techniques for applications in breath analysis,” J Breath Res1(1), 014001 (2007).
[CrossRef] [PubMed]

Bauer, A.

Bjorklund, G. C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B32(3), 145–152 (1983).
[CrossRef]

G. C. Bjorklund, “Frequency-modulation spectroscopy: a new method for measuring weak absorptions and dispersions,” Opt. Lett.5(1), 15–17 (1980).
[CrossRef] [PubMed]

Brumfield, B.

B. Brumfield, W. Sun, Y. Ju, and G. Wysocki, “Direct In Situ Quantification of HO2 from a Flow Reactor,” J. Phys. Chem. Lett.4(6), 872–876 (2013).
[CrossRef]

Capasso, F.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
[CrossRef]

Curl, R. F.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
[CrossRef]

R. Lewicki, J. H. Doty, R. F. Curl, F. K. Tittel, and G. Wysocki, “Ultrasensitive detection of nitric oxide at 5.33 microm by using external cavity quantum cascade laser-based Faraday rotation spectroscopy,” Proc. Natl. Acad. Sci. U.S.A.106(31), 12587–12592 (2009).
[CrossRef] [PubMed]

Doty, J. H.

R. Lewicki, J. H. Doty, R. F. Curl, F. K. Tittel, and G. Wysocki, “Ultrasensitive detection of nitric oxide at 5.33 microm by using external cavity quantum cascade laser-based Faraday rotation spectroscopy,” Proc. Natl. Acad. Sci. U.S.A.106(31), 12587–12592 (2009).
[CrossRef] [PubMed]

Fischer, M.

Fried, A.

D. Richter, A. Fried, and P. Weibring, “Difference frequency generation laser based spectrometers,” Laser Photonics Rev.3(4), 343–354 (2009).
[CrossRef]

Gianfrani, L.

E. Kerstel and L. Gianfrani, “Advances in laser-based isotope ratio measurements: selected applications,” Appl. Phys. B92(3), 439–449 (2008).
[CrossRef]

Gilbert, S. L.

Gmachl, C.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
[CrossRef]

Hanson, R. K.

Höfling, S.

Hraimel, B.

Jeffries, J. B.

Ju, Y.

B. Brumfield, W. Sun, Y. Ju, and G. Wysocki, “Direct In Situ Quantification of HO2 from a Flow Reactor,” J. Phys. Chem. Lett.4(6), 872–876 (2013).
[CrossRef]

Kerstel, E.

E. Kerstel and L. Gianfrani, “Advances in laser-based isotope ratio measurements: selected applications,” Appl. Phys. B92(3), 439–449 (2008).
[CrossRef]

Kluczynski, P.

Koeth, J.

Kosterev, A. A.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
[CrossRef]

A. A. Kosterev and F. K. Tittel, “Chemical sensors based on quantum cascade lasers,” IEEE J. Quantum Electron.38(6), 582–591 (2002).
[CrossRef]

Lenth, W.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B32(3), 145–152 (1983).
[CrossRef]

Levenson, M. D.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B32(3), 145–152 (1983).
[CrossRef]

Lewicki, R.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
[CrossRef]

R. Lewicki, J. H. Doty, R. F. Curl, F. K. Tittel, and G. Wysocki, “Ultrasensitive detection of nitric oxide at 5.33 microm by using external cavity quantum cascade laser-based Faraday rotation spectroscopy,” Proc. Natl. Acad. Sci. U.S.A.106(31), 12587–12592 (2009).
[CrossRef] [PubMed]

M. R. McCurdy, Y. Bakhirkin, G. Wysocki, R. Lewicki, and F. K. Tittel, “Recent advances of laser-spectroscopy-based techniques for applications in breath analysis,” J Breath Res1(1), 014001 (2007).
[CrossRef] [PubMed]

Liu, T.

Lundqvist, S.

McCurdy, M. R.

M. R. McCurdy, Y. Bakhirkin, G. Wysocki, R. Lewicki, and F. K. Tittel, “Recent advances of laser-spectroscopy-based techniques for applications in breath analysis,” J Breath Res1(1), 014001 (2007).
[CrossRef] [PubMed]

McManus, B.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
[CrossRef]

Nähle, L.

Nie, Q.

Nikodem, M.

M. Nikodem, D. Weidmann, C. Smith, and G. Wysocki, “Signal-to-noise ratio in chirped laser dispersion spectroscopy,” Opt. Express20(1), 644–653 (2012).
[CrossRef] [PubMed]

M. Nikodem and G. Wysocki, “Molecular dispersion spectroscopy--new capabilities in laser chemical sensing,” Ann. N. Y. Acad. Sci.1260(1), 101–111 (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]

Ortiz, C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B32(3), 145–152 (1983).
[CrossRef]

Pei, Y.

Pusharsky, M.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
[CrossRef]

Richter, D.

D. Richter, A. Fried, and P. Weibring, “Difference frequency generation laser based spectrometers,” Laser Photonics Rev.3(4), 343–354 (2009).
[CrossRef]

Rieker, G. B.

Smith, C.

Sun, W.

B. Brumfield, W. Sun, Y. Ju, and G. Wysocki, “Direct In Situ Quantification of HO2 from a Flow Reactor,” J. Phys. Chem. Lett.4(6), 872–876 (2013).
[CrossRef]

Swann, W. C.

Tittel, F. K.

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
[CrossRef]

R. Lewicki, J. H. Doty, R. F. Curl, F. K. Tittel, and G. Wysocki, “Ultrasensitive detection of nitric oxide at 5.33 microm by using external cavity quantum cascade laser-based Faraday rotation spectroscopy,” Proc. Natl. Acad. Sci. U.S.A.106(31), 12587–12592 (2009).
[CrossRef] [PubMed]

M. R. McCurdy, Y. Bakhirkin, G. Wysocki, R. Lewicki, and F. K. Tittel, “Recent advances of laser-spectroscopy-based techniques for applications in breath analysis,” J Breath Res1(1), 014001 (2007).
[CrossRef] [PubMed]

A. A. Kosterev and F. K. Tittel, “Chemical sensors based on quantum cascade lasers,” IEEE J. Quantum Electron.38(6), 582–591 (2002).
[CrossRef]

von Edlinger, M.

Weibring, P.

D. Richter, A. Fried, and P. Weibring, “Difference frequency generation laser based spectrometers,” Laser Photonics Rev.3(4), 343–354 (2009).
[CrossRef]

Weidmann, D.

Weih, R.

Wu, K.

Wysocki, G.

B. Brumfield, W. Sun, Y. Ju, and G. Wysocki, “Direct In Situ Quantification of HO2 from a Flow Reactor,” J. Phys. Chem. Lett.4(6), 872–876 (2013).
[CrossRef]

M. Nikodem, D. Weidmann, C. Smith, and G. Wysocki, “Signal-to-noise ratio in chirped laser dispersion spectroscopy,” Opt. Express20(1), 644–653 (2012).
[CrossRef] [PubMed]

M. Nikodem and G. Wysocki, “Molecular dispersion spectroscopy--new capabilities in laser chemical sensing,” Ann. N. Y. Acad. Sci.1260(1), 101–111 (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]

G. Wysocki and D. Weidmann, “Molecular dispersion spectroscopy for chemical sensing using chirped mid-infrared quantum cascade laser,” Opt. Express18(25), 26123–26140 (2010).
[CrossRef] [PubMed]

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
[CrossRef]

R. Lewicki, J. H. Doty, R. F. Curl, F. K. Tittel, and G. Wysocki, “Ultrasensitive detection of nitric oxide at 5.33 microm by using external cavity quantum cascade laser-based Faraday rotation spectroscopy,” Proc. Natl. Acad. Sci. U.S.A.106(31), 12587–12592 (2009).
[CrossRef] [PubMed]

M. R. McCurdy, Y. Bakhirkin, G. Wysocki, R. Lewicki, and F. K. Tittel, “Recent advances of laser-spectroscopy-based techniques for applications in breath analysis,” J Breath Res1(1), 014001 (2007).
[CrossRef] [PubMed]

Xu, T.

Zhang, X.

Ann. N. Y. Acad. Sci. (1)

M. Nikodem and G. Wysocki, “Molecular dispersion spectroscopy--new capabilities in laser chemical sensing,” Ann. N. Y. Acad. Sci.1260(1), 101–111 (2012).
[CrossRef] [PubMed]

Appl. Opt. (2)

Appl. Phys. B (2)

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B32(3), 145–152 (1983).
[CrossRef]

E. Kerstel and L. Gianfrani, “Advances in laser-based isotope ratio measurements: selected applications,” Appl. Phys. B92(3), 439–449 (2008).
[CrossRef]

Chem. Phys. Lett. (1)

R. F. Curl, F. Capasso, C. Gmachl, A. A. Kosterev, B. McManus, R. Lewicki, M. Pusharsky, G. Wysocki, and F. K. Tittel, “Quantum cascade lasers in chemical physics,” Chem. Phys. Lett.487(1-3), 1–18 (2010).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. A. Kosterev and F. K. Tittel, “Chemical sensors based on quantum cascade lasers,” IEEE J. Quantum Electron.38(6), 582–591 (2002).
[CrossRef]

J Breath Res (1)

M. R. McCurdy, Y. Bakhirkin, G. Wysocki, R. Lewicki, and F. K. Tittel, “Recent advances of laser-spectroscopy-based techniques for applications in breath analysis,” J Breath Res1(1), 014001 (2007).
[CrossRef] [PubMed]

J. Lightwave Technol. (1)

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

J. Phys. Chem. Lett. (1)

B. Brumfield, W. Sun, Y. Ju, and G. Wysocki, “Direct In Situ Quantification of HO2 from a Flow Reactor,” J. Phys. Chem. Lett.4(6), 872–876 (2013).
[CrossRef]

Laser Photonics Rev. (1)

D. Richter, A. Fried, and P. Weibring, “Difference frequency generation laser based spectrometers,” Laser Photonics Rev.3(4), 343–354 (2009).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Proc. Natl. Acad. Sci. U.S.A. (1)

R. Lewicki, J. H. Doty, R. F. Curl, F. K. Tittel, and G. Wysocki, “Ultrasensitive detection of nitric oxide at 5.33 microm by using external cavity quantum cascade laser-based Faraday rotation spectroscopy,” Proc. Natl. Acad. Sci. U.S.A.106(31), 12587–12592 (2009).
[CrossRef] [PubMed]

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 (2)

M. Nikodem, K. Krzempek, G. Plant, K. Abramski, G. Wysocki, “Methane sensing at 3.4um using Chirped Laser Dispersion Spectroscopy with DFG source,” in CLEO/Europe-IQEC 2013 Conference Digest, OSA Technical Digest (CD) (Optical Society of America, 2013), paper CH-1.3.

A. Hangauer, G. Spinner, M. Nikodem, and G. Wysocki, “Chirped Laser Dispersion Spectroscopy with Directly Modulated Quantum Cascade Laser,” in CLEO: Science and Innovations 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper CW1L.5.

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Figures (3)

Fig. 1
Fig. 1

a) CLaDS system with DPMZM for dual-color beam (SSB spectrum) generation. 3dB hybrid coupler is used to drive modulator with two orthogonal signals; b) CLaDS system with MZM for triple-color beam (DSB spectrum) generation (LD – laser diode, SG – signal generator, PC – polarization controller, PD – photodetector, OS – optical spectrum).

Fig. 2
Fig. 2

a) Normalized transmission spectrum of the target HCN transition and b) a quasi SSB spectrum at the output of DPMZM when driven at 1.5 GHz, both measured with high-resolution spectrum analyzer; c) CLaDS spectrum of the P15 transition of HCN recorded using SSB modulation with spacing of Ω = 1.45 GHz. Frequency axes show detuning of the laser frequency from the center of the P15 transition at 1553.755 nm (~193.86 THz). Spectrum in c) is normalized by the chirp rate to facilitate comparison with DSB-based signals recorded at different chirp rate.

Fig. 3
Fig. 3

a) Experimental CLaDS spectra recorded using setup shown in Fig. 1(b) for three different modulation frequencies (spectra are shifted vertically and horizontally for viewing purposes only) shown together with simulations calculated using Eq. (2). The changes of the CLaDS signal shape at different Ω is in good agreement with the prediction shown in Fig. 7 of Ref [9]; b) The amplitude of the CLaDS signal as a function of modulation frequencies Ω obtained with SSB modulator shown in Fig. 1(a) and DSB modulator in Fig. 1(b). Excellent agreement with the model is observed.

Equations (2)

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f DSB (ω)=Ω+ω 1 2 SL c ( dn dω | ω+Ω dn dω | ω )+(ωΩ) 1 2 SL c ( dn dω | ω dn dω | ωΩ )
f DSB (ω)=Ω+ 1 2 SLω c ( dn dω | ω+Ω dn dω | ωΩ )

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