## Unobtrusive interferometer tracking by path length oscillation for multidimensional spectroscopy

Optics Express, Vol. 17, Issue 15, pp. 12379-12384 (2009)

http://dx.doi.org/10.1364/OE.17.012379

Acrobat PDF (409 KB)

### Abstract

We track the path difference between interferometer arms with few-nanometer accuracy without adding optics to the beam path. We measure the interference of a helium-neon beam that copropagates through the interferometer with midinfrared pulses used for multidimensional spectroscopy. This can indicate motion, but not direction. By oscillating the path length of one arm with a mirror on a piezoelectric stack and monitoring the oscillations of the recombined helium-neon beam, the direction can be calculated, and the path delay can be continuously tracked.

© 2009 Optical Society of America

## 1. Introduction

2. B. Abbott*et al.* (LIGO Scientific Collaboration), “Search for Gravitational-Wave Bursts from Soft Gamma Repeaters,” Phys. Rev. Lett. **101**, 211102 (2008).
[CrossRef] [PubMed]

4. L. P. DeFlores, R. A. Nicodemus, and A. Tokmakoff, “Two-dimensional Fourier transform spectroscopy in the pump-probe geometry,” Opt. Lett. **32**, 2966–2968 (2007).
[CrossRef] [PubMed]

5. M. M. Salour and C. Cohen-Tannoudji, “Observation of Ramsey’s Interference Fringes in the Profile of Doppler-Free Two-Photon Resonances,” Phys. Rev. Lett. **38**, 757–760 (1977).
[CrossRef]

6. N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, “Fluorescence-detected wave packet interferometry: Time resolved molecular spectroscopy with sequences of femtosecond phase-locked pulses,” J. Chem. Phys. **95**, 1487–1511 (1991).
[CrossRef]

7. T. Zhang, C. Borca, X. Li, and S. Cundiff, “Optical two-dimensional Fourier transform spectroscopy with active interferometric stabilization,” Opt. Express **13**, 7432–7441 (2005).
[CrossRef] [PubMed]

8. C. J. Buchenauer and A. R. Jacobson, “Quadrature interferometer for plasma density measurements,” Rev. Sci. Instrum. **48**, 769–774 (1977).
[CrossRef]

11. N. Belabas and M. Joffre, “Visible-infrared two-dimensional Fourier-transform spectroscopy,” Opt. Lett. **27**, 2043–2045 (2002).
[CrossRef]

12. M. Winter, M. Wollenhaupt, and T. Baumert, “Coherent matter waves for ultrafast laser pulse characterization,” Opt. Commun. **264**, 285–292 (2006).
[CrossRef]

13. E. H. G. Backus, S. Garrett-Roe, and P. Hamm, “Phasing problem of heterodyne-detected two-dimensional infrared spectroscopy,” Opt. Lett. **33**, 2665–2667 (2008).
[CrossRef] [PubMed]

14. A. D. Bristow, D. Karaiskaj, X. Dai, and S. T. Cundiff, “All-optical retrieval of the global phase for two-dimensional Fourier-transform spectroscopy,” Opt. Express **16**, 18017–18027 (2008).
[CrossRef] [PubMed]

15. A. L. Besse and J. G. Kelley, “Interferometer for Shock Tube,” Rev. Sci. Instrum. **37**, 1497–1499 (1966).
[CrossRef]

16. V. Volkov, R. Shanz, and P. Hamm, “Active phase stabilization in Fourier-transform two-dimensional infrared spectroscopy,” Opt. Lett. **30**, 2010–2012 (2005).
[CrossRef] [PubMed]

17. G. D. Goodno, G. Dadusc, and R. J. D. Miller, “Ultrafast heterodyne-detected transient-grating spectroscopy using diffractive optics,” J. Opt. Soc. Am. B **15**, 1791–1794 (1998).
[CrossRef]

18. A. A. Maznev, K. A. Nelson, and J. Rogers, “Optical heterodyne detection of laser-induced gratings,” Opt. Lett. **23**, 1319–1321 (1998).
[CrossRef]

19. S.-H. Shim, D. B. Strasfeld, Y. L. Ling, and M. T. Zanni, “Automated 2D IR spectroscopy using a mid-IR pulse shaper and application of this technology to the human islet amyloid polypeptide,” Proc. Natl. Acad. Sci. USA **104**, 14197–14202 (2007).
[CrossRef] [PubMed]

20. K. Gundogdu, K. W. Stone, D. B. Turner, and K. A. Nelson, “Multidimensional coherent spectroscopy made easy,” Chem. Phys. **341**, 89–94 (2007).
[CrossRef]

21. U. Selig, F. Langhojer, F. Dimler, T. Löhrig, C. Schwarz, B. Gieseking, and T. Brixner, “Inherently phase-stable coherent two-dimensional spectroscopy using only conventional optics,” Opt. Lett. **33**, 2851–2853 (2008).
[CrossRef] [PubMed]

## 2. Experimental

22. M. J. Nee, R. McCanne, K. J. Kubarych, and M. Joffre, “Two-dimensional infrared spectroscopy detected by chirped pulse upconversion,” Opt. Lett. **32**, 713–715 (2007).
[CrossRef] [PubMed]

## 3. Calculation

_{1}=cos(φ), and the next valley, x

_{2}=cos(φ - π/4). We extrapolate the desired quadrature y

_{1}=x

_{3}=cos(φ - π/2), using the trigonometric formula: cos(α - β)=2 cos(α) cos(β) - cos(α+β). With α=φ - π/4, and β=π/4, we get x

_{3}=2

^{1/2}x

_{2}-x

_{1}. We also average the adjacent valley and hill contributions. For consistency, we apply this same π/4 extrapolation to the hill and valley calculations, using their adjacent middle points. This reduces the time range, and thus sensitivity to fast motion.

## 4. Testing

23. L. Lepetit, G. Chériaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B **12**, 2467–2474 (1995).
[CrossRef]

24. K. F. Lee, K. J. Kubarych, A. Bonvalet, and M. Joffre, “Characterization of mid-infrared femtosecond pulses,” J. Opt. Soc. Am. B **25**, A54–A62 (2008).
[CrossRef]

_{2}O Tris-HCl buffer, while tracking with both the HeNe, and the rotary encoder on the DC motor driving the stage. The 2D spectrum is taken using the pump-probe geometry [4

4. L. P. DeFlores, R. A. Nicodemus, and A. Tokmakoff, “Two-dimensional Fourier transform spectroscopy in the pump-probe geometry,” Opt. Lett. **32**, 2966–2968 (2007).
[CrossRef] [PubMed]

19. S.-H. Shim, D. B. Strasfeld, Y. L. Ling, and M. T. Zanni, “Automated 2D IR spectroscopy using a mid-IR pulse shaper and application of this technology to the human islet amyloid polypeptide,” Proc. Natl. Acad. Sci. USA **104**, 14197–14202 (2007).
[CrossRef] [PubMed]

19. S.-H. Shim, D. B. Strasfeld, Y. L. Ling, and M. T. Zanni, “Automated 2D IR spectroscopy using a mid-IR pulse shaper and application of this technology to the human islet amyloid polypeptide,” Proc. Natl. Acad. Sci. USA **104**, 14197–14202 (2007).
[CrossRef] [PubMed]

## 5. Conclusion

## Acknowledgements

## References and links

1. | A. A. Michelson, “The relative motion of the Earth and the Luminiferous ether,” Am. J. Sci. |

2. | B. Abbott |

3. | D. M. Jonas, “Two-Dimensional Femtosecond Spectroscopy,” Annu. Rev. Phys. Chem. |

4. | L. P. DeFlores, R. A. Nicodemus, and A. Tokmakoff, “Two-dimensional Fourier transform spectroscopy in the pump-probe geometry,” Opt. Lett. |

5. | M. M. Salour and C. Cohen-Tannoudji, “Observation of Ramsey’s Interference Fringes in the Profile of Doppler-Free Two-Photon Resonances,” Phys. Rev. Lett. |

6. | N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, “Fluorescence-detected wave packet interferometry: Time resolved molecular spectroscopy with sequences of femtosecond phase-locked pulses,” J. Chem. Phys. |

7. | T. Zhang, C. Borca, X. Li, and S. Cundiff, “Optical two-dimensional Fourier transform spectroscopy with active interferometric stabilization,” Opt. Express |

8. | C. J. Buchenauer and A. R. Jacobson, “Quadrature interferometer for plasma density measurements,” Rev. Sci. Instrum. |

9. | M. U. Wehner, M. H. Ulm, and M. Wegener, “Scanning interferometer stabilized by use of Pancharatnam’s phase,” Opt. Lett. |

10. | S. Pancharatnam, “Generalized Theory of Interference and its Applications,” Proc. Indian Acad. Sci. Sect. A |

11. | N. Belabas and M. Joffre, “Visible-infrared two-dimensional Fourier-transform spectroscopy,” Opt. Lett. |

12. | M. Winter, M. Wollenhaupt, and T. Baumert, “Coherent matter waves for ultrafast laser pulse characterization,” Opt. Commun. |

13. | E. H. G. Backus, S. Garrett-Roe, and P. Hamm, “Phasing problem of heterodyne-detected two-dimensional infrared spectroscopy,” Opt. Lett. |

14. | A. D. Bristow, D. Karaiskaj, X. Dai, and S. T. Cundiff, “All-optical retrieval of the global phase for two-dimensional Fourier-transform spectroscopy,” Opt. Express |

15. | A. L. Besse and J. G. Kelley, “Interferometer for Shock Tube,” Rev. Sci. Instrum. |

16. | V. Volkov, R. Shanz, and P. Hamm, “Active phase stabilization in Fourier-transform two-dimensional infrared spectroscopy,” Opt. Lett. |

17. | G. D. Goodno, G. Dadusc, and R. J. D. Miller, “Ultrafast heterodyne-detected transient-grating spectroscopy using diffractive optics,” J. Opt. Soc. Am. B |

18. | A. A. Maznev, K. A. Nelson, and J. Rogers, “Optical heterodyne detection of laser-induced gratings,” Opt. Lett. |

19. | S.-H. Shim, D. B. Strasfeld, Y. L. Ling, and M. T. Zanni, “Automated 2D IR spectroscopy using a mid-IR pulse shaper and application of this technology to the human islet amyloid polypeptide,” Proc. Natl. Acad. Sci. USA |

20. | K. Gundogdu, K. W. Stone, D. B. Turner, and K. A. Nelson, “Multidimensional coherent spectroscopy made easy,” Chem. Phys. |

21. | U. Selig, F. Langhojer, F. Dimler, T. Löhrig, C. Schwarz, B. Gieseking, and T. Brixner, “Inherently phase-stable coherent two-dimensional spectroscopy using only conventional optics,” Opt. Lett. |

22. | M. J. Nee, R. McCanne, K. J. Kubarych, and M. Joffre, “Two-dimensional infrared spectroscopy detected by chirped pulse upconversion,” Opt. Lett. |

23. | L. Lepetit, G. Chériaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B |

24. | K. F. Lee, K. J. Kubarych, A. Bonvalet, and M. Joffre, “Characterization of mid-infrared femtosecond pulses,” J. Opt. Soc. Am. B |

**OCIS Codes**

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(120.5050) Instrumentation, measurement, and metrology : Phase measurement

(300.6240) Spectroscopy : Spectroscopy, coherent transient

(300.6300) Spectroscopy : Spectroscopy, Fourier transforms

(300.6340) Spectroscopy : Spectroscopy, infrared

(300.6420) Spectroscopy : Spectroscopy, nonlinear

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: May 26, 2009

Revised Manuscript: June 24, 2009

Manuscript Accepted: July 1, 2009

Published: July 7, 2009

**Citation**

Kevin F. Lee, Adeline Bonvalet, Patrick Nuernberger, and Manuel Joffre, "Unobtrusive interferometer tracking by path
length oscillation for multidimensional
spectroscopy," Opt. Express **17**, 12379-12384 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-12379

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### References

- A. A. Michelson, "The relative motion of the Earth and the Luminiferous ether," Am. J. Sci. 22, 120-129 (1881).
- B. Abbott et al.(LIGO Scientiﬁc Collaboration), "Search for Gravitational-Wave Bursts from Soft Gamma Repeaters," Phys. Rev. Lett. 101, 211102 (2008). [CrossRef] [PubMed]
- D. M. Jonas, "Two-Dimensional Femtosecond Spectroscopy," Annu. Rev. Phys. Chem. 54, 425-463 (2003).
- L. P. DeFlores, R. A. Nicodemus, and A. Tokmakoff, "Two-dimensional Fourier transform spectroscopy in the pump-probe geometry," Opt. Lett. 32, 2966-2968 (2007). [CrossRef] [PubMed]
- M. M. Salour and C. Cohen-Tannoudji, "Observation of Ramsey’s Interference Fringes in the Proﬁle of Doppler-Free Two-Photon Resonances," Phys. Rev. Lett. 38, 757-760 (1977). [CrossRef]
- N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, "Fluorescence-detected wave packet interferometry: Time resolved molecular spectroscopy with sequences of femtosecond phase-locked pulses," J. Chem. Phys. 95, 1487-1511 (1991). [CrossRef]
- T. Zhang, C. Borca, X. Li, and S. Cundiff, "Optical two-dimensional Fourier transform spectroscopy with active interferometric stabilization," Opt. Express 13, 7432-7441 (2005). [CrossRef] [PubMed]
- C. J. Buchenauer and A. R. Jacobson, "Quadrature interferometer for plasma density measurements," Rev. Sci. Instrum. 48, 769-774 (1977). [CrossRef]
- M. U. Wehner, M. H. Ulm, and M. Wegener, "Scanning interferometer stabilized by use of Pancharatnam’s phase," Opt. Lett. 22, 1455-1457 (1997). [CrossRef]
- Q1. S. Pancharatnam, "Generalized Theory of Interference and its Applications," Proc. Indian Acad. Sci. Sect. A 44, 247-262 (1956).
- N. Belabas and M. Joffre, "Visible-infrared two-dimensional Fourier-transform spectroscopy," Opt. Lett. 27, 2043-2045 (2002). [CrossRef]
- M. Winter, M. Wollenhaupt, and T. Baumert, "Coherent matter waves for ultrafast laser pulse characterization," Opt. Commun. 264, 285 - 292 (2006). [CrossRef]
- E. H. G. Backus, S. Garrett-Roe, and P. Hamm, "Phasing problem of heterodyne-detected two-dimensional infrared spectroscopy," Opt. Lett. 33, 2665-2667 (2008). [CrossRef] [PubMed]
- A. D. Bristow, D. Karaiskaj, X. Dai, and S. T. Cundiff, "All-optical retrieval of the global phase for two-dimensional Fourier-transform spectroscopy," Opt. Express 16, 18017-18027 (2008). [CrossRef] [PubMed]
- A. L. Besse and J. G. Kelley, "Interferometer for Shock Tube," Rev. Sci. Instrum. 37, 1497-1499 (1966). [CrossRef]
- V. Volkov, R. Shanz, and P. Hamm, "Active phase stabilization in Fourier-transform two-dimensional infrared spectroscopy," Opt. Lett. 30, 2010-2012 (2005). [CrossRef] [PubMed]
- G. D. Goodno, G. Dadusc, and R. J. D. Miller, "Ultrafast heterodyne-detected transient-grating spectroscopy using diffractive optics," J. Opt. Soc. Am. B 15, 1791-1794 (1998). [CrossRef]
- A. A. Maznev, K. A. Nelson, and J. Rogers, "Optical heterodyne detection of laser-induced gratings," Opt. Lett. 23, 1319-1321 (1998). [CrossRef]
- S.-H. Shim, D. B. Strasfeld, Y. L. Ling, and M. T. Zanni, "Automated 2D IR spectroscopy using a mid-IR pulse shaper and application of this technology to the human islet amyloid polypeptide," Proc. Natl. Acad. Sci. USA 104, 14197-14202 (2007). [CrossRef] [PubMed]
- K. Gundogdu, K. W. Stone, D. B. Turner, and K. A. Nelson, "Multidimensional coherent spectroscopy made easy," Chem. Phys. 341, 89 - 94 (2007). [CrossRef]
- U. Selig, F. Langhojer, F. Dimler, T. Löhrig, C. Schwarz, B. Gieseking, and T. Brixner, "Inherently phase-stable coherent two-dimensional spectroscopy using only conventional optics," Opt. Lett. 33, 2851-2853 (2008). [CrossRef] [PubMed]
- M. J. Nee, R. McCanne, K. J. Kubarych, and M. Joffre, "Two-dimensional infrared spectroscopy detected by chirped pulse upconversion," Opt. Lett. 32, 713-715 (2007). [CrossRef] [PubMed]
- L. Lepetit, G. Chériaux, and M. Joffre, "Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy," J. Opt. Soc. Am. B 12, 2467-2474 (1995). [CrossRef]
- K. F. Lee, K. J. Kubarych, A. Bonvalet, and M. Joffre, "Characterization of mid-infrared femtosecond pulses," J. Opt. Soc. Am. B 25, A54-A62 (2008). [CrossRef]

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