Abstract

Using an Nd:YVO4 microchip laser with a relaxation frequency in the megahertz range, we have experimentally compared a heterodyne interferometer based on a Michelson configuration with an autodyne interferometer based on the laser optical feedback imaging (LOFI) method regarding their signal-to-noise ratios. In the heterodyne configuration, the beating between the reference beam and the signal beam is realized outside the laser cavity, while in the autodyne configuration, the wave beating takes place inside the laser cavity, and the relaxation oscillations of the laser intensity then play an important part. For a given laser output power, object under investigation, and detection noise level, we have determined the amplification gain of the LOFI interferometer compared to the heterodyne interferometer. LOFI interferometry is demonstrated to show higher performance than heterodyne interferometry for a wide range of laser powers and detection levels of noise. The experimental results are in good agreement with the theoretical predictions.

© 2011 Optical Society of America

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    [CrossRef]
  4. K. Otsuka, “Highly sensitive measurement of Doppler-shift with a microchip solid-state laser,” Jpn. J. Appl. Phys. 31, L1546–L1548 (1992).
    [CrossRef]
  5. S. Okamoto, H. Takeda, and F. Kannari, “Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser,” Rev. Sci. Instrum. 66, 3116–3120 (1995).
    [CrossRef]
  6. R. Kawai, Y. Asakawa, and K. Otsuka, “Ultrahigh-sensitivity self-mixing laser Doppler velocimetry with laser-diode-pumped microchip LiNdP4O12 lasers,” IEEE Photon. Technol. Lett. 11, 706–708 (1999).
    [CrossRef]
  7. S. Suddo, T. Ohtomo, Y. Takahascvhi, T. Oishi, and K. Otsuka, “Determination of velocity of self-mobile phytoplankton using a self thin-slice solid-state laser,” Appl. Opt. 48, 4049–4055(2009).
    [CrossRef]
  8. K. Otsuka, K. Abe, J. Y. Ko, and T. S. Lim, “Real-time nanometer vibration measurement with self-mixing microchip solid-state laser,” Opt. Lett. 27, 1339–1341 (2002).
    [CrossRef]
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    [CrossRef]
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  15. O. Hugon, I. A. Paun, C. Ricard, B. van der Sanden, E. Lacot, O. Jacquin, and A. Witomski, “Cell imaging by coherent backscattering microscopy using frequency shifted optical feedback in a microchip laser,” Ultramicroscopy 108, 523–528 (2008).
    [CrossRef]
  16. E. Lacot, R. Day, and F. Stoeckel, “Coherent laser detection by frequency-shifted optical feedback,” Phys. Rev. A 64, 043815(2001).
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    [CrossRef]
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    [CrossRef]
  27. J.-Y. Ko, T. Ohtomo, K. Abe, and K. Otsuka, “Nonlinear dynamics and application of laser-diode pumped microchip solid-state lasers with optical feedback,” Int. J. Mod. Phys. B 15, 3369–3395(2001).
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2011 (1)

K. Otsuka, “Self-mixing thin-slice solid-state laser metrology,” Sensors 11, 2195–2245 (2011).
[CrossRef]

2010 (1)

2009 (1)

2008 (4)

2006 (1)

2005 (1)

V. Muzet, E. Lacot, O. Hugon, and Y. Gaillard, “Experimental comparison of shearography and laser optical feedback imaging for crack detection in concrete structures,” Proc. SPIE 5856, 793–799 (2005).
[CrossRef]

2004 (1)

E. Lacot and O. Hugon, “Phase-sensitive laser detection by frequency-shifted optical feedback,” Phys. Rev. A 70, 053824(2004).
[CrossRef]

2002 (1)

2001 (2)

E. Lacot, R. Day, and F. Stoeckel, “Coherent laser detection by frequency-shifted optical feedback,” Phys. Rev. A 64, 043815(2001).
[CrossRef]

J.-Y. Ko, T. Ohtomo, K. Abe, and K. Otsuka, “Nonlinear dynamics and application of laser-diode pumped microchip solid-state lasers with optical feedback,” Int. J. Mod. Phys. B 15, 3369–3395(2001).
[CrossRef]

1999 (3)

A. Bramati, J. P. Hermier, V. Jost, E. Giacobino, L. Fulbert, E. Molva, and J. J. Aubert, “Effects of pump fluctuations on intensity noise of Nd:YVO4 microchip lasers,” Eur. Phys. J. D 6, 513–521 (1999).
[CrossRef]

R. Kawai, Y. Asakawa, and K. Otsuka, “Ultrahigh-sensitivity self-mixing laser Doppler velocimetry with laser-diode-pumped microchip LiNdP4O12 lasers,” IEEE Photon. Technol. Lett. 11, 706–708 (1999).
[CrossRef]

E. Lacot, R. Day, and F. Stoeckel, “Laser optical feedback tomography,” Opt. Lett. 24, 744–746 (1999).
[CrossRef]

1996 (1)

1995 (1)

S. Okamoto, H. Takeda, and F. Kannari, “Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser,” Rev. Sci. Instrum. 66, 3116–3120 (1995).
[CrossRef]

1993 (2)

M. I. Kolobov, L. Davidovich, E. Giacobino, and C. Fabre, “Role of pumping statistics and dynamics of atomic polarization in quantum fluctuations of laser sources,” Phys. Rev. A 47, 1431–1446 (1993).
[CrossRef] [PubMed]

K. Otsuka, “Transverse effects on antiphase laser dynamics,” Jpn. J. Appl. Phys. 32, L1414–L1417 (1993).
[CrossRef]

1992 (1)

K. Otsuka, “Highly sensitive measurement of Doppler-shift with a microchip solid-state laser,” Jpn. J. Appl. Phys. 31, L1546–L1548 (1992).
[CrossRef]

1989 (1)

1979 (1)

K. Otsuka, “Effects of external perturbations on LiNdP4O12 lasers,” IEEE J. Quantum Electron. 15, 655–663 (1979).
[CrossRef]

Abe, K.

K. Otsuka, K. Abe, J. Y. Ko, and T. S. Lim, “Real-time nanometer vibration measurement with self-mixing microchip solid-state laser,” Opt. Lett. 27, 1339–1341 (2002).
[CrossRef]

J.-Y. Ko, T. Ohtomo, K. Abe, and K. Otsuka, “Nonlinear dynamics and application of laser-diode pumped microchip solid-state lasers with optical feedback,” Int. J. Mod. Phys. B 15, 3369–3395(2001).
[CrossRef]

Asakawa, Y.

R. Kawai, Y. Asakawa, and K. Otsuka, “Ultrahigh-sensitivity self-mixing laser Doppler velocimetry with laser-diode-pumped microchip LiNdP4O12 lasers,” IEEE Photon. Technol. Lett. 11, 706–708 (1999).
[CrossRef]

Aubert, J. J.

A. Bramati, J. P. Hermier, V. Jost, E. Giacobino, L. Fulbert, E. Molva, and J. J. Aubert, “Effects of pump fluctuations on intensity noise of Nd:YVO4 microchip lasers,” Eur. Phys. J. D 6, 513–521 (1999).
[CrossRef]

Bartolacci, C.

Belarouci, A.

Bérenguier, B.

Blaize, S.

Bramati, A.

A. Bramati, J. P. Hermier, V. Jost, E. Giacobino, L. Fulbert, E. Molva, and J. J. Aubert, “Effects of pump fluctuations on intensity noise of Nd:YVO4 microchip lasers,” Eur. Phys. J. D 6, 513–521 (1999).
[CrossRef]

Bruyant, A.

Davidovich, L.

M. I. Kolobov, L. Davidovich, E. Giacobino, and C. Fabre, “Role of pumping statistics and dynamics of atomic polarization in quantum fluctuations of laser sources,” Phys. Rev. A 47, 1431–1446 (1993).
[CrossRef] [PubMed]

Day, R.

E. Lacot, R. Day, and F. Stoeckel, “Coherent laser detection by frequency-shifted optical feedback,” Phys. Rev. A 64, 043815(2001).
[CrossRef]

E. Lacot, R. Day, and F. Stoeckel, “Laser optical feedback tomography,” Opt. Lett. 24, 744–746 (1999).
[CrossRef]

de Chatellus, H. Guillet

Fabre, C.

M. I. Kolobov, L. Davidovich, E. Giacobino, and C. Fabre, “Role of pumping statistics and dynamics of atomic polarization in quantum fluctuations of laser sources,” Phys. Rev. A 47, 1431–1446 (1993).
[CrossRef] [PubMed]

Fulbert, L.

A. Bramati, J. P. Hermier, V. Jost, E. Giacobino, L. Fulbert, E. Molva, and J. J. Aubert, “Effects of pump fluctuations on intensity noise of Nd:YVO4 microchip lasers,” Eur. Phys. J. D 6, 513–521 (1999).
[CrossRef]

Gaillard, Y.

V. Muzet, E. Lacot, O. Hugon, and Y. Gaillard, “Experimental comparison of shearography and laser optical feedback imaging for crack detection in concrete structures,” Proc. SPIE 5856, 793–799 (2005).
[CrossRef]

Giacobino, E.

A. Bramati, J. P. Hermier, V. Jost, E. Giacobino, L. Fulbert, E. Molva, and J. J. Aubert, “Effects of pump fluctuations on intensity noise of Nd:YVO4 microchip lasers,” Eur. Phys. J. D 6, 513–521 (1999).
[CrossRef]

M. I. Kolobov, L. Davidovich, E. Giacobino, and C. Fabre, “Role of pumping statistics and dynamics of atomic polarization in quantum fluctuations of laser sources,” Phys. Rev. A 47, 1431–1446 (1993).
[CrossRef] [PubMed]

Gilles, H.

Girard, S.

Hermier, J. P.

A. Bramati, J. P. Hermier, V. Jost, E. Giacobino, L. Fulbert, E. Molva, and J. J. Aubert, “Effects of pump fluctuations on intensity noise of Nd:YVO4 microchip lasers,” Eur. Phys. J. D 6, 513–521 (1999).
[CrossRef]

Hugon, O.

E. Lacot, O. Jacquin, G. Roussely, O. Hugon, and H. Guillet de Chatellus, “Comparative study of autodyne and heterodyne laser interferometry for imaging,” J. Opt. Soc. Am. A 27, 2450–2458(2010).
[CrossRef]

S. Blaize, B. Bérenguier, I. Stéfanon, A. Bruyant, G. Lerondel, P. Royer, O. Hugon, O. Jacquin, and E. Lacot, “Phase sensitive optical near-field mapping using frequency-shifted laser optical feedback interferometry,” Opt. Express 16, 11718–11726 (2008).
[CrossRef] [PubMed]

O. Hugon, I. A. Paun, C. Ricard, B. van der Sanden, E. Lacot, O. Jacquin, and A. Witomski, “Cell imaging by coherent backscattering microscopy using frequency shifted optical feedback in a microchip laser,” Ultramicroscopy 108, 523–528 (2008).
[CrossRef]

A. Witomski, E. Lacot, O. Hugon, and O. Jacquin, “Synthetic aperture laser optical feedback imaging using galvanometric scanning,” Opt. Lett. 31, 3031–3033 (2006).
[CrossRef] [PubMed]

V. Muzet, E. Lacot, O. Hugon, and Y. Gaillard, “Experimental comparison of shearography and laser optical feedback imaging for crack detection in concrete structures,” Proc. SPIE 5856, 793–799 (2005).
[CrossRef]

E. Lacot and O. Hugon, “Phase-sensitive laser detection by frequency-shifted optical feedback,” Phys. Rev. A 70, 053824(2004).
[CrossRef]

Jacquin, O.

Jost, V.

A. Bramati, J. P. Hermier, V. Jost, E. Giacobino, L. Fulbert, E. Molva, and J. J. Aubert, “Effects of pump fluctuations on intensity noise of Nd:YVO4 microchip lasers,” Eur. Phys. J. D 6, 513–521 (1999).
[CrossRef]

V. Jost, “Réduction du bruit dans les lasers: Application aux lasers à semi-conducteur et aux minilasers solides,” http://tel.archives-ouvertes.fr/docs/00/06/08/22/PDF/1997JOST.pdf, p. 54.

Kaminskii, A.

A. Kaminskii, Laser Crystals, 2nd ed. (Springer Verlag, 1981).

Kannari, F.

S. Okamoto, H. Takeda, and F. Kannari, “Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser,” Rev. Sci. Instrum. 66, 3116–3120 (1995).
[CrossRef]

Kawai, R.

R. Kawai, Y. Asakawa, and K. Otsuka, “Ultrahigh-sensitivity self-mixing laser Doppler velocimetry with laser-diode-pumped microchip LiNdP4O12 lasers,” IEEE Photon. Technol. Lett. 11, 706–708 (1999).
[CrossRef]

Khanin, Y. I.

Y. I. Khanin, Principles of Laser Dynamics (Elsevier, 1995).

Ko, J. Y.

Ko, J.-Y.

J.-Y. Ko, T. Ohtomo, K. Abe, and K. Otsuka, “Nonlinear dynamics and application of laser-diode pumped microchip solid-state lasers with optical feedback,” Int. J. Mod. Phys. B 15, 3369–3395(2001).
[CrossRef]

Koechner, W.

W. Koechner, Solid State Laser Engineering, 2nd ed. (Springer Verlag, 1988).

Kolobov, M. I.

M. I. Kolobov, L. Davidovich, E. Giacobino, and C. Fabre, “Role of pumping statistics and dynamics of atomic polarization in quantum fluctuations of laser sources,” Phys. Rev. A 47, 1431–1446 (1993).
[CrossRef] [PubMed]

Lacot, E.

E. Lacot, O. Jacquin, G. Roussely, O. Hugon, and H. Guillet de Chatellus, “Comparative study of autodyne and heterodyne laser interferometry for imaging,” J. Opt. Soc. Am. A 27, 2450–2458(2010).
[CrossRef]

S. Blaize, B. Bérenguier, I. Stéfanon, A. Bruyant, G. Lerondel, P. Royer, O. Hugon, O. Jacquin, and E. Lacot, “Phase sensitive optical near-field mapping using frequency-shifted laser optical feedback interferometry,” Opt. Express 16, 11718–11726 (2008).
[CrossRef] [PubMed]

O. Hugon, I. A. Paun, C. Ricard, B. van der Sanden, E. Lacot, O. Jacquin, and A. Witomski, “Cell imaging by coherent backscattering microscopy using frequency shifted optical feedback in a microchip laser,” Ultramicroscopy 108, 523–528 (2008).
[CrossRef]

A. Witomski, E. Lacot, O. Hugon, and O. Jacquin, “Synthetic aperture laser optical feedback imaging using galvanometric scanning,” Opt. Lett. 31, 3031–3033 (2006).
[CrossRef] [PubMed]

V. Muzet, E. Lacot, O. Hugon, and Y. Gaillard, “Experimental comparison of shearography and laser optical feedback imaging for crack detection in concrete structures,” Proc. SPIE 5856, 793–799 (2005).
[CrossRef]

E. Lacot and O. Hugon, “Phase-sensitive laser detection by frequency-shifted optical feedback,” Phys. Rev. A 70, 053824(2004).
[CrossRef]

E. Lacot, R. Day, and F. Stoeckel, “Coherent laser detection by frequency-shifted optical feedback,” Phys. Rev. A 64, 043815(2001).
[CrossRef]

E. Lacot, R. Day, and F. Stoeckel, “Laser optical feedback tomography,” Opt. Lett. 24, 744–746 (1999).
[CrossRef]

E. Lacot and F. Stoeckel, “Nonlinear mode coupling in a microchip laser,” J. Opt. Soc. Am. B 13, 2034–2040 (1996).
[CrossRef]

Laroche, M.

Lerondel, G.

Lesueur, G.

Lim, T. S.

Molva, E.

A. Bramati, J. P. Hermier, V. Jost, E. Giacobino, L. Fulbert, E. Molva, and J. J. Aubert, “Effects of pump fluctuations on intensity noise of Nd:YVO4 microchip lasers,” Eur. Phys. J. D 6, 513–521 (1999).
[CrossRef]

Mooradian, A.

Muzet, V.

V. Muzet, E. Lacot, O. Hugon, and Y. Gaillard, “Experimental comparison of shearography and laser optical feedback imaging for crack detection in concrete structures,” Proc. SPIE 5856, 793–799 (2005).
[CrossRef]

Ohtomo, T.

S. Suddo, T. Ohtomo, Y. Takahascvhi, T. Oishi, and K. Otsuka, “Determination of velocity of self-mobile phytoplankton using a self thin-slice solid-state laser,” Appl. Opt. 48, 4049–4055(2009).
[CrossRef]

J.-Y. Ko, T. Ohtomo, K. Abe, and K. Otsuka, “Nonlinear dynamics and application of laser-diode pumped microchip solid-state lasers with optical feedback,” Int. J. Mod. Phys. B 15, 3369–3395(2001).
[CrossRef]

Oishi, T.

Okamoto, S.

S. Okamoto, H. Takeda, and F. Kannari, “Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser,” Rev. Sci. Instrum. 66, 3116–3120 (1995).
[CrossRef]

Otsuka, K.

K. Otsuka, “Self-mixing thin-slice solid-state laser metrology,” Sensors 11, 2195–2245 (2011).
[CrossRef]

S. Suddo, T. Ohtomo, Y. Takahascvhi, T. Oishi, and K. Otsuka, “Determination of velocity of self-mobile phytoplankton using a self thin-slice solid-state laser,” Appl. Opt. 48, 4049–4055(2009).
[CrossRef]

K. Otsuka, K. Abe, J. Y. Ko, and T. S. Lim, “Real-time nanometer vibration measurement with self-mixing microchip solid-state laser,” Opt. Lett. 27, 1339–1341 (2002).
[CrossRef]

J.-Y. Ko, T. Ohtomo, K. Abe, and K. Otsuka, “Nonlinear dynamics and application of laser-diode pumped microchip solid-state lasers with optical feedback,” Int. J. Mod. Phys. B 15, 3369–3395(2001).
[CrossRef]

R. Kawai, Y. Asakawa, and K. Otsuka, “Ultrahigh-sensitivity self-mixing laser Doppler velocimetry with laser-diode-pumped microchip LiNdP4O12 lasers,” IEEE Photon. Technol. Lett. 11, 706–708 (1999).
[CrossRef]

K. Otsuka, “Transverse effects on antiphase laser dynamics,” Jpn. J. Appl. Phys. 32, L1414–L1417 (1993).
[CrossRef]

K. Otsuka, “Highly sensitive measurement of Doppler-shift with a microchip solid-state laser,” Jpn. J. Appl. Phys. 31, L1546–L1548 (1992).
[CrossRef]

K. Otsuka, “Effects of external perturbations on LiNdP4O12 lasers,” IEEE J. Quantum Electron. 15, 655–663 (1979).
[CrossRef]

Paun, I. A.

O. Hugon, I. A. Paun, C. Ricard, B. van der Sanden, E. Lacot, O. Jacquin, and A. Witomski, “Cell imaging by coherent backscattering microscopy using frequency shifted optical feedback in a microchip laser,” Ultramicroscopy 108, 523–528 (2008).
[CrossRef]

Ricard, C.

O. Hugon, I. A. Paun, C. Ricard, B. van der Sanden, E. Lacot, O. Jacquin, and A. Witomski, “Cell imaging by coherent backscattering microscopy using frequency shifted optical feedback in a microchip laser,” Ultramicroscopy 108, 523–528 (2008).
[CrossRef]

Roussely, G.

Royer, P.

Stéfanon, I.

Stoeckel, F.

Suddo, S.

Takahascvhi, Y.

Takeda, H.

S. Okamoto, H. Takeda, and F. Kannari, “Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser,” Rev. Sci. Instrum. 66, 3116–3120 (1995).
[CrossRef]

van der Sanden, B.

O. Hugon, I. A. Paun, C. Ricard, B. van der Sanden, E. Lacot, O. Jacquin, and A. Witomski, “Cell imaging by coherent backscattering microscopy using frequency shifted optical feedback in a microchip laser,” Ultramicroscopy 108, 523–528 (2008).
[CrossRef]

Witomski, A.

O. Hugon, I. A. Paun, C. Ricard, B. van der Sanden, E. Lacot, O. Jacquin, and A. Witomski, “Cell imaging by coherent backscattering microscopy using frequency shifted optical feedback in a microchip laser,” Ultramicroscopy 108, 523–528 (2008).
[CrossRef]

A. Witomski, E. Lacot, O. Hugon, and O. Jacquin, “Synthetic aperture laser optical feedback imaging using galvanometric scanning,” Opt. Lett. 31, 3031–3033 (2006).
[CrossRef] [PubMed]

Zaykowski, J. J.

Appl. Opt. (1)

Eur. Phys. J. D (1)

A. Bramati, J. P. Hermier, V. Jost, E. Giacobino, L. Fulbert, E. Molva, and J. J. Aubert, “Effects of pump fluctuations on intensity noise of Nd:YVO4 microchip lasers,” Eur. Phys. J. D 6, 513–521 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Otsuka, “Effects of external perturbations on LiNdP4O12 lasers,” IEEE J. Quantum Electron. 15, 655–663 (1979).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

R. Kawai, Y. Asakawa, and K. Otsuka, “Ultrahigh-sensitivity self-mixing laser Doppler velocimetry with laser-diode-pumped microchip LiNdP4O12 lasers,” IEEE Photon. Technol. Lett. 11, 706–708 (1999).
[CrossRef]

Int. J. Mod. Phys. B (1)

J.-Y. Ko, T. Ohtomo, K. Abe, and K. Otsuka, “Nonlinear dynamics and application of laser-diode pumped microchip solid-state lasers with optical feedback,” Int. J. Mod. Phys. B 15, 3369–3395(2001).
[CrossRef]

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

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

Jpn. J. Appl. Phys. (2)

K. Otsuka, “Transverse effects on antiphase laser dynamics,” Jpn. J. Appl. Phys. 32, L1414–L1417 (1993).
[CrossRef]

K. Otsuka, “Highly sensitive measurement of Doppler-shift with a microchip solid-state laser,” Jpn. J. Appl. Phys. 31, L1546–L1548 (1992).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. A (3)

E. Lacot, R. Day, and F. Stoeckel, “Coherent laser detection by frequency-shifted optical feedback,” Phys. Rev. A 64, 043815(2001).
[CrossRef]

E. Lacot and O. Hugon, “Phase-sensitive laser detection by frequency-shifted optical feedback,” Phys. Rev. A 70, 053824(2004).
[CrossRef]

M. I. Kolobov, L. Davidovich, E. Giacobino, and C. Fabre, “Role of pumping statistics and dynamics of atomic polarization in quantum fluctuations of laser sources,” Phys. Rev. A 47, 1431–1446 (1993).
[CrossRef] [PubMed]

Proc. SPIE (1)

V. Muzet, E. Lacot, O. Hugon, and Y. Gaillard, “Experimental comparison of shearography and laser optical feedback imaging for crack detection in concrete structures,” Proc. SPIE 5856, 793–799 (2005).
[CrossRef]

Rev. Sci. Instrum. (1)

S. Okamoto, H. Takeda, and F. Kannari, “Ultrahighly sensitive laser-Doppler velocity meter with a diode-pumped Nd:YVO4 microchip laser,” Rev. Sci. Instrum. 66, 3116–3120 (1995).
[CrossRef]

Sensors (1)

K. Otsuka, “Self-mixing thin-slice solid-state laser metrology,” Sensors 11, 2195–2245 (2011).
[CrossRef]

Ultramicroscopy (1)

O. Hugon, I. A. Paun, C. Ricard, B. van der Sanden, E. Lacot, O. Jacquin, and A. Witomski, “Cell imaging by coherent backscattering microscopy using frequency shifted optical feedback in a microchip laser,” Ultramicroscopy 108, 523–528 (2008).
[CrossRef]

Other (5)

T.Yoshizawa, ed., Handbook of Optical Metrology: Principles and Applications (CRC Press, 2009).
[CrossRef]

Y. I. Khanin, Principles of Laser Dynamics (Elsevier, 1995).

V. Jost, “Réduction du bruit dans les lasers: Application aux lasers à semi-conducteur et aux minilasers solides,” http://tel.archives-ouvertes.fr/docs/00/06/08/22/PDF/1997JOST.pdf, p. 54.

W. Koechner, Solid State Laser Engineering, 2nd ed. (Springer Verlag, 1988).

A. Kaminskii, Laser Crystals, 2nd ed. (Springer Verlag, 1981).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagrams of the (a) autodyne interferometer setup and (b) heterodyne interferometer setup for scanning microscopy: L 1 , L 2 , and L 3 , lenses; OI, optical isolator; BS, beam splitter with power reflectivity of R bs ; GS, galvanometric scanner; RM, reference mirror with unitary power reflectivity of R rm = 1 ; FS, frequency shifter with round trip frequency shift of F e ; PD, photodiode with a white-noise spectrum. The lock-in amplifier is characterized by a bandwidth of Δ F around the reference frequency F e . The laser output power is characterized by p out (photons/s), and the target is characterized by its effective reflectivity R e 1 .

Fig. 2
Fig. 2

Calculated normalized noise power spectra of the laser output power for two different values of the dimensionless parameter: b = γ b / κ . The other laser dynamical parameters correspond to a conventional Nd 3 + : YVO 4 microchip laser: a = 2 × 10 6 , a = 2 × 10 7 , η = 1 / 2 , r = 5 [19]. The 0 dB level corresponds to the shot noise level.

Fig. 3
Fig. 3

Laser relaxation frequency ( F R = Ω R / 2 π ) versus the normalized pumping parameter (r). Laser dynamical parameters: γ a = 3.3 × 10 4 s 1 , γ a = 3.3 × 10 3 s 1 , and κ = 2.1 × 10 9 s 1 .

Fig. 4
Fig. 4

Experimental (solid curve) and theoretical (dashed curve) power spectra of the laser output power of a Nd : YVO 4 microchip laser with p out = 2.14 × 10 17 / photons / s ( P out = 40 mW at λ = 1064 nm ), r = 2.6 , κ = 2.1 × 10 9 s 1 , η = 0.3 , γ a = 3.3 × 10 4 s 1 , γ a = 3.3 × 10 3 s 1 , γ b = 3.3 × 10 9 s 1 . The experimental conditions are Δ F = 500 Hz , R bs = 1 / 10 , R load = 50 Ω . The horizontal dotted line is the detection noise level.

Fig. 5
Fig. 5

Autodyne signal (dashed lines) and heterodyne signal (solid lines) versus laser power sent on the target ( p target ) for different values of the shift frequency: (▪), F e = 2.9 × 10 6 Hz ; (▴), F e = 4.9 × 10 6 Hz ; ( █ ), F e = 8.9 × 10 6 Hz ; (▾), F e = 18.9 × 10 6 Hz .

Tables (2)

Tables Icon

Table 1 Experimental ( S LOFI / S Heterodyne ) and Predicted [ G ( F e ) × η ] Values of the LOFI Signal Gain a

Tables Icon

Table 2 Experimental ( S LOFI / N Laser / S Heterodyne / N Detection ) and Predicted [ G ( F + ) × η ] Values of the LOFI SNR Gain a

Equations (16)

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V out , B ( Ω ˜ ) = 1 + η 2 b ( a + a ) b a 1 D B ( Ω ˜ ) ( [ b 2 + Ω ˜ 2 ] [ ( a + a ) 2 + Ω ˜ 2 ] [ n a + a ] + 2 w B 2 { [ ( b a ) 2 + Ω ˜ 2 ] n [ ( b a ) ( a + a ) + Ω ˜ 2 ] [ r a + 2 a a + a n ] + [ ( a + a ) 2 + Ω ˜ 2 ] [ a a + a ] } ) ,
D B ( Ω ˜ ) = | i Ω ˜ ( b i Ω ˜ ) ( a + a i Ω ˜ ) + 2 w B 2 ( a + b i 2 Ω ˜ ) ( 1 i Ω ˜ ) | 2 ,
n = r a + b + a ( r 1 ) a + b ,
w B 2 = ( a + a ) b 2 ( a + b ) ( r 1 ) .
G ( Ω ˜ ) = V out , B ( Ω ˜ ) 1 η .
G ( Ω ) κ ( γ a + γ a ) 2 r + Ω 2 ( Ω R 2 Ω 2 ) 2 + Δ Ω R 2 Ω 2 ,
Ω R = κ ( γ a + γ a ) ( r 1 ) .
G ( F R ) × η = 7.5 × 10 3 ,
G ( F + ) × η = 21.
η 2 R bs 1.25 × 10 9 W Hz 1 / h c λ p out = 21 ,
S LOFI ( p target , F e ) S Heterodyne ( p target ) = G ( F e ) × η .
S LOFI ( P target , F e ) N Laser ( F e , Δ F ) = R bs η 2 Δ F R e ( 1 R bs ) ρ p out = R bs η 2 Δ F p target R e p out ,
p out = κ out γ b γ b + γ a γ a + γ a σ c V ( r 1 ) ,
S Heterodyne ( p target ) N Detection ( Δ F ) = R bs R e p target ( 1.25 × 10 9 W / Hz h c / λ ) Δ F .
S LOFI ( p target , F e ) N Laser ( F e , Δ F ) / S Heterodyne ( p target ) N Detection ( Δ F ) = η 2 R bs [ ( 1.25 × 10 9 W / Hz ) h c / λ ] p out = G ( F + ) × η .
( S LOFI ( p target , F e ) N Laser ( F e , Δ F ) / S Heterodyne ( p target ) N Detector ( Δ F ) )

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