Abstract

We propose and experimentally demonstrate an interferometer for femtosecond pulses with spectral bandwidth about 100 nm. The scheme is based on a Michelson interferometer with a dispersion compensating module. A diffractive lens serves the purpose of equalizing the optical-path-length difference for a wide range of frequencies. In this way, it is possible to register high-contrast interference fringes with micrometric resolution over the whole area of a commercial CCD sensor for broadband femtosecond pulses.

©2009 Optical Society of America

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References

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  1. A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography-principles and applications,” Rep. Prog. Phys. 66(2), 239–303 ( 2003).
    [Crossref]
  2. L. Vabre, A. Dubois, and A. C. Boccara, “Thermal-light full-field optical coherence tomography,” Opt. Lett. 27(7), 530–532 ( 2002).
    [Crossref] [PubMed]
  3. E. Cuche, P. Poscio, and C. Depeursinge, “Optical tomography by means of a numerical low-coherence holographic technique,” J. Opt. 28(6), 260–264 ( 1997).
    [Crossref]
  4. L. Martínez-León, G. Pedrini, and W. Osten, “Applications of short-coherence digital holography in microscopy,” Appl. Opt. 44(19), 3977–3984 ( 2005).
    [Crossref] [PubMed]
  5. P. Massatsch, F. Charrière, E. Cuche, P. Marquet, and C. D. Depeursinge, “Time-domain optical coherence tomography with digital holographic microscopy,” Appl. Opt. 44(10), 1806–1812 ( 2005).
    [Crossref] [PubMed]
  6. A. A. Maznev, T. F. Crimmins, and K. A. Nelson, “How to make femtosecond pulses overlap,” Opt. Lett. 23(17), 1378–1380 ( 1998).
    [Crossref] [PubMed]
  7. Z. Ansari, Y. Gu, M. Tziraki, R. Jones, P. M. W. French, D. D. Nolte, and M. R. Melloch, “Elimination of beam walk-off in low-coherence off-axis photorefractive holography,” Opt. Lett. 26(6), 334–336 ( 2001).
    [Crossref] [PubMed]
  8. B. E. A. Saleh, and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley, 2007), Chap. 11.
  9. E. N. Leith and G. J. Swanson, “Achromatic interferometers for white-light optical processing and holography,” Appl. Opt. 19, 638–644 ( 1980).
    [Crossref] [PubMed]
  10. J. Hebling, I. Z. Kozma, and J. Kuhl, “Compact high-aperture optical setup for excitation of dynamic gratings by ultrashort light pulses,” J. Opt. Soc. Am. B 17(10), 1803–1805 ( 2000).
    [Crossref]
  11. T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78(17), 3282–3285 ( 1997).
    [Crossref]
  12. H. Xiao and K. E. Oughstun, “Failure of the group-velocity description for ultrawideband pulse propagation in causally dispersive, absorptive dielectric,” J. Opt. Soc. Am. B 16(10), 1773–1785 ( 1999).
    [Crossref]
  13. P. Andrés, J. Lancis, E. E. Sicre, and E. Bonet, “Achromatic Fresnel diffraction patterns,” Opt. Commun. 104(1-3), 39–45 ( 1993).
    [Crossref]
  14. J. Lancis, E. E. Sicre, A. Pons, and G. Saavedra, “Achromatic white-light self-imaging phenomenon-an approach using the Wigner distribution function,” J. Mod. Opt. 42(2), 425–434 ( 1995).
    [Crossref]
  15. G. Mínguez-Vega, O. Mendoza-Yero, M. Fernández-Alonso, P. Andrés, V. Climent, and J. Lancis, “Experimental generation of high-contrast Talbot images with an ultrashort laser pulse,” Opt. Commun. 281, 374–379 ( 2008).

2008 (1)

G. Mínguez-Vega, O. Mendoza-Yero, M. Fernández-Alonso, P. Andrés, V. Climent, and J. Lancis, “Experimental generation of high-contrast Talbot images with an ultrashort laser pulse,” Opt. Commun. 281, 374–379 ( 2008).

2005 (2)

2003 (1)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography-principles and applications,” Rep. Prog. Phys. 66(2), 239–303 ( 2003).
[Crossref]

2002 (1)

2001 (1)

2000 (1)

1999 (1)

1998 (1)

1997 (2)

E. Cuche, P. Poscio, and C. Depeursinge, “Optical tomography by means of a numerical low-coherence holographic technique,” J. Opt. 28(6), 260–264 ( 1997).
[Crossref]

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78(17), 3282–3285 ( 1997).
[Crossref]

1995 (1)

J. Lancis, E. E. Sicre, A. Pons, and G. Saavedra, “Achromatic white-light self-imaging phenomenon-an approach using the Wigner distribution function,” J. Mod. Opt. 42(2), 425–434 ( 1995).
[Crossref]

1993 (1)

P. Andrés, J. Lancis, E. E. Sicre, and E. Bonet, “Achromatic Fresnel diffraction patterns,” Opt. Commun. 104(1-3), 39–45 ( 1993).
[Crossref]

1980 (1)

Andrés, P.

G. Mínguez-Vega, O. Mendoza-Yero, M. Fernández-Alonso, P. Andrés, V. Climent, and J. Lancis, “Experimental generation of high-contrast Talbot images with an ultrashort laser pulse,” Opt. Commun. 281, 374–379 ( 2008).

P. Andrés, J. Lancis, E. E. Sicre, and E. Bonet, “Achromatic Fresnel diffraction patterns,” Opt. Commun. 104(1-3), 39–45 ( 1993).
[Crossref]

Ansari, Z.

Boccara, A. C.

Bonet, E.

P. Andrés, J. Lancis, E. E. Sicre, and E. Bonet, “Achromatic Fresnel diffraction patterns,” Opt. Commun. 104(1-3), 39–45 ( 1993).
[Crossref]

Brabec, T.

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78(17), 3282–3285 ( 1997).
[Crossref]

Charrière, F.

Climent, V.

G. Mínguez-Vega, O. Mendoza-Yero, M. Fernández-Alonso, P. Andrés, V. Climent, and J. Lancis, “Experimental generation of high-contrast Talbot images with an ultrashort laser pulse,” Opt. Commun. 281, 374–379 ( 2008).

Crimmins, T. F.

Cuche, E.

P. Massatsch, F. Charrière, E. Cuche, P. Marquet, and C. D. Depeursinge, “Time-domain optical coherence tomography with digital holographic microscopy,” Appl. Opt. 44(10), 1806–1812 ( 2005).
[Crossref] [PubMed]

E. Cuche, P. Poscio, and C. Depeursinge, “Optical tomography by means of a numerical low-coherence holographic technique,” J. Opt. 28(6), 260–264 ( 1997).
[Crossref]

Depeursinge, C.

E. Cuche, P. Poscio, and C. Depeursinge, “Optical tomography by means of a numerical low-coherence holographic technique,” J. Opt. 28(6), 260–264 ( 1997).
[Crossref]

Depeursinge, C. D.

Drexler, W.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography-principles and applications,” Rep. Prog. Phys. 66(2), 239–303 ( 2003).
[Crossref]

Dubois, A.

Fercher, A. F.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography-principles and applications,” Rep. Prog. Phys. 66(2), 239–303 ( 2003).
[Crossref]

Fernández-Alonso, M.

G. Mínguez-Vega, O. Mendoza-Yero, M. Fernández-Alonso, P. Andrés, V. Climent, and J. Lancis, “Experimental generation of high-contrast Talbot images with an ultrashort laser pulse,” Opt. Commun. 281, 374–379 ( 2008).

French, P. M. W.

Gu, Y.

Hebling, J.

Hitzenberger, C. K.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography-principles and applications,” Rep. Prog. Phys. 66(2), 239–303 ( 2003).
[Crossref]

Jones, R.

Kozma, I. Z.

Krausz, F.

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78(17), 3282–3285 ( 1997).
[Crossref]

Kuhl, J.

Lancis, J.

G. Mínguez-Vega, O. Mendoza-Yero, M. Fernández-Alonso, P. Andrés, V. Climent, and J. Lancis, “Experimental generation of high-contrast Talbot images with an ultrashort laser pulse,” Opt. Commun. 281, 374–379 ( 2008).

J. Lancis, E. E. Sicre, A. Pons, and G. Saavedra, “Achromatic white-light self-imaging phenomenon-an approach using the Wigner distribution function,” J. Mod. Opt. 42(2), 425–434 ( 1995).
[Crossref]

P. Andrés, J. Lancis, E. E. Sicre, and E. Bonet, “Achromatic Fresnel diffraction patterns,” Opt. Commun. 104(1-3), 39–45 ( 1993).
[Crossref]

Lasser, T.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography-principles and applications,” Rep. Prog. Phys. 66(2), 239–303 ( 2003).
[Crossref]

Leith, E. N.

Marquet, P.

Martínez-León, L.

Massatsch, P.

Maznev, A. A.

Melloch, M. R.

Mendoza-Yero, O.

G. Mínguez-Vega, O. Mendoza-Yero, M. Fernández-Alonso, P. Andrés, V. Climent, and J. Lancis, “Experimental generation of high-contrast Talbot images with an ultrashort laser pulse,” Opt. Commun. 281, 374–379 ( 2008).

Mínguez-Vega, G.

G. Mínguez-Vega, O. Mendoza-Yero, M. Fernández-Alonso, P. Andrés, V. Climent, and J. Lancis, “Experimental generation of high-contrast Talbot images with an ultrashort laser pulse,” Opt. Commun. 281, 374–379 ( 2008).

Nelson, K. A.

Nolte, D. D.

Osten, W.

Oughstun, K. E.

Pedrini, G.

Pons, A.

J. Lancis, E. E. Sicre, A. Pons, and G. Saavedra, “Achromatic white-light self-imaging phenomenon-an approach using the Wigner distribution function,” J. Mod. Opt. 42(2), 425–434 ( 1995).
[Crossref]

Poscio, P.

E. Cuche, P. Poscio, and C. Depeursinge, “Optical tomography by means of a numerical low-coherence holographic technique,” J. Opt. 28(6), 260–264 ( 1997).
[Crossref]

Saavedra, G.

J. Lancis, E. E. Sicre, A. Pons, and G. Saavedra, “Achromatic white-light self-imaging phenomenon-an approach using the Wigner distribution function,” J. Mod. Opt. 42(2), 425–434 ( 1995).
[Crossref]

Sicre, E. E.

J. Lancis, E. E. Sicre, A. Pons, and G. Saavedra, “Achromatic white-light self-imaging phenomenon-an approach using the Wigner distribution function,” J. Mod. Opt. 42(2), 425–434 ( 1995).
[Crossref]

P. Andrés, J. Lancis, E. E. Sicre, and E. Bonet, “Achromatic Fresnel diffraction patterns,” Opt. Commun. 104(1-3), 39–45 ( 1993).
[Crossref]

Swanson, G. J.

Tziraki, M.

Vabre, L.

Xiao, H.

Appl. Opt. (3)

J. Mod. Opt. (1)

J. Lancis, E. E. Sicre, A. Pons, and G. Saavedra, “Achromatic white-light self-imaging phenomenon-an approach using the Wigner distribution function,” J. Mod. Opt. 42(2), 425–434 ( 1995).
[Crossref]

J. Opt. (1)

E. Cuche, P. Poscio, and C. Depeursinge, “Optical tomography by means of a numerical low-coherence holographic technique,” J. Opt. 28(6), 260–264 ( 1997).
[Crossref]

J. Opt. Soc. Am. B (2)

Opt. Commun. (2)

P. Andrés, J. Lancis, E. E. Sicre, and E. Bonet, “Achromatic Fresnel diffraction patterns,” Opt. Commun. 104(1-3), 39–45 ( 1993).
[Crossref]

G. Mínguez-Vega, O. Mendoza-Yero, M. Fernández-Alonso, P. Andrés, V. Climent, and J. Lancis, “Experimental generation of high-contrast Talbot images with an ultrashort laser pulse,” Opt. Commun. 281, 374–379 ( 2008).

Opt. Lett. (3)

Phys. Rev. Lett. (1)

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78(17), 3282–3285 ( 1997).
[Crossref]

Rep. Prog. Phys. (1)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography-principles and applications,” Rep. Prog. Phys. 66(2), 239–303 ( 2003).
[Crossref]

Other (1)

B. E. A. Saleh, and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley, 2007), Chap. 11.

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Figures (5)

Fig. 1
Fig. 1 Sketch of a conventional Michelson interferometer with tilted mirrors for spatial recording of interference fringes. The length mistmatch between the interferometer arms is Δ e ≡ C B S C M , 1 - C B S C M , 2 . The carrier frequency and the spectral width of the source fix the number of recordable fringes.

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Fig. 2
Fig. 2 Interferometer for femtosecond pulses with extended visibility. The arms of the interferometer are of identical length and a diffractive lens is inserted at the image focal plane of the achromatic lens.

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Fig. 3
Fig. 3 Plot of the visibility of the interference fringes as a function of the normalized transverse coordinate at the sensor plane for the optical setup in Fig. 1 (solid line) and the optical setup in Fig. 2. For the former, both the quadratic approximation (long-dashed line) and the full dependence with the frequency of the phase difference between the object and the reference wave (short-dashed line) are plotted.

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Fig. 4
Fig. 4 a) Picture of the interferometer with the DCM for femtosecond pulses. b) Spectral energy distribution of the Ti:sapphire femtosecond source (solid line) and its Gaussian fit (dashed line).

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Fig. 5
Fig. 5 Interference fringes and corresponding line scans recorded at the sensor plane of: (a) the optical setup in Fig. 1; and (b) the optical setup in Fig. 2.

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Equations (8)

Equations on this page are rendered with MathJax. Learn more.

S ( ω ) = | a ˜ ( ω ) | 2 = | ∫ − ∞ ∞ a ( t )   e − i ω t   d t | 2 ,
I = I o + ℜ e { ∫ - ∞ ∞ S ( ω ) e i   Δ Φ ( ω + ω o ) d ω   } ,
Δ Φ ( ω + ω o ) ≃ Δ Φ o + τ   ω + 1 2 τ ′   ω 2 ,
I ( τ , τ ′ ) = I o { 1 + V ( τ , τ ′ ) cos [ Δ Φ o + φ ( τ , τ ′ ) ] } ,
γ g ( τ , τ ′ ) = 1 I o ∫ - ∞ ∞ S ( ω ) e i τ ω   e i ( τ ′ / 2 ) ω 2   d ω .
Δ Φ ( ω ) =   ω   Δ L ( ω ) c ,
Δ L ( ω ) = f 2 B [ A f ( θ 2 2 - θ 1 2 ) − 2 x S ( θ 2 - θ 1 ) ] .
∂ ∂ ω ( ω B ) | ω o = 0   ,   ∂ ∂ ω ( A ω B ) | ω o = 0.  

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