Abstract

We propose and experimentally demonstrate an original method to analytically retrieve complete spectral phase of ultrashort pulses by measuring two modified interferometric field autocorrelation traces using thick nonlinear crystals with slightly different central phase-matching wavelengths. This new scheme requires no spectrometer, detector array, nor iterative data inversion, and is compatible with periodically poled lithium niobate (PPLN) waveguide technology offering potential for high measurement sensitivity.

© 2008 Optical Society of America

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References

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  1. N. Dudovich, D. Oron, and Y. Silberberg, "Single-pulse coherently controlled nonlinear Ramman spectroscopy and microscopy," Nature (London) 418, 512-514 (2002).
    [CrossRef]
  2. M. Yamashita, K. Yamane, and R. Morita, "Quasi-automatic phase-control technique for chirp compensation of pulse with over-one-octave bandwidth-generation of few to mono-cycle optical pulses," IEEE J. Quantum Electron. 16, 213-222 (2006).
  3. J. W. Nicholson, J. Jasapara, W. Rudolph, F. G. Omenetto, and A. J. Taylor, "Full-field characterization of femtosecond pulses by spectrum and cross-correlation measurements," Opt. Lett. 24, 1774-1776 (1999).
    [CrossRef]
  4. R. Trebino, in Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulse, (Kluwer Academic Publisher, Boston, MA, 2000).
  5. I. Amat-Roldan, I. G. Cormack, P. Loza-Alvarez, and D. Artigas, "Measurement of electric field by interferometric spectral trace observation," Opt. Lett. 30, 1063-1065 (2005).
    [CrossRef] [PubMed]
  6. C. Iaconis and I. A. Walmsley, "Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses," Opt. Lett. 23, 792-794 (1998).
    [CrossRef]
  7. A. M. Weiner, "Effect of group velocity mismatch on the measurement of ultrashort optical pulses via second harmonic generation," IEEE J. Quantum Electron. 19, 1276-1283 (1983).
    [CrossRef]
  8. P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, "Highly simplified device for ultrashort-pulse measurement," Opt. Lett. 26, 932-934 (2001).
    [CrossRef]
  9. S. -D. Yang, A. M. Weiner, K. R. Parameswaran, and M. M. Fejer,"400-photon-per-pulse ultrashort pulse autocorrelation measurement with aperiodically poled lithium niobate waveguides at 1.55 um," Opt. Lett. 29, 2070-2072 (2004).
    [CrossRef] [PubMed]
  10. S. -D. Yang, A. M. Weiner, K. R. Parameswaran, and M. M. Fejer, "Ultra-sensitive second-harmonic generation frequency-resolved optical gating by aperiodically poled LiNbO3 waveguides at 1.5 um," Opt. Lett. 30, 2164-2166 (2005).
    [CrossRef] [PubMed]
  11. H. Miao, S. -D. Yang, C. Langrock, R. V. Roussev, M. M. Fejer, and A. M. Weiner, "Ultralow-power secondharmonic generation frequency-resolved optical gating using aperiodically poled lithium niobate waveguides," J. Opt. Soc. Am. B 25, A41-A53 (2008).
    [CrossRef]
  12. S. -D. Yang, H. Miao, Z. Jiang, A. M. Weiner, K. R. Parameswaran, and M. M. Fejer, "Ultrasensitive nonlinear measurements of femtosecond pulses in the telecommunications band by aperiodically poled LiNbO3 waveguides," Appl. Opt. 46, 6759-6769 (2007).
    [CrossRef] [PubMed]
  13. A. S. Radunsky, E. M. Kosik Williams, I. A. Walmsley, P. Wasylczyk, W. Wasilewski, A. B. U’Ren, and M. E. Anderson, "Simplified spectral phase interferometry for direct electric-field reconstruction by using a thick nonlinear crystal," Opt. Lett. 31, 1008-1010 (2006).
    [CrossRef] [PubMed]
  14. S. -D. Yang, S. -L. Lin and Y. -Y. Huang, "Complete spectral phase retrieval by modified interferometric field autocorrelation traces," Proc. Conf. Lasers Elec. Opt. (2008).
    [CrossRef]
  15. A. M. Weiner, Z. Jiang, and D. E. Leaird, "Spectrally phase-coded O-CDMA," J. Opt. Netw. 6, 728-755 (2007).
    [CrossRef]
  16. I. Amat-Roldan, D. Artigas, I. G. Cormack, and P. Loza-Alvarez, "Simultaneous analytical characterization of two ultrashort laser pulses using spectrally resolved interferometric correlations," Opt. Express 14, 4538-4551 (2006).
    [CrossRef] [PubMed]
  17. D. N. Fittinghoff, K. W. DeLong, R. Trebino, and C. L. Ladera, "Noise sensitivity in frequency-resolved opticalgating measurements of ultrashort pulses," J. Opt. Soc. Am. B 12, 1955-1967 (1995).
    [CrossRef]
  18. K. W. DeLong and R. Trebino, "Improved ultrashort pulse-retrieval algorithm for frequency-resolved opticalgating," J. Opt. Soc. Am. A 11, 2429-2437 (1994).
    [CrossRef]
  19. A. M. Weiner, Ultrafast Optics (Wiley, in preparation).
  20. K. R. Parameswaran, R. K. Route, J. R. Kurz, R. V. Roussev, and M. M. Fejer, "Highly efficient second-harmonic generation in buried waveguides formed by annealed and reverse proton exchange in periodically poled lithium niobate," Opt. Lett. 27, 179-181 (2002).
    [CrossRef]
  21. J. Bethge and G. Steinmeyer, "Numerical fringe pattern demodulation strategies in interferometry," Rev. Sci. Instrum. 79, 073102 (2008).
    [CrossRef] [PubMed]

2008 (2)

2007 (2)

2006 (3)

2005 (2)

2004 (1)

2002 (2)

2001 (1)

1999 (1)

1998 (1)

1995 (1)

1994 (1)

1983 (1)

A. M. Weiner, "Effect of group velocity mismatch on the measurement of ultrashort optical pulses via second harmonic generation," IEEE J. Quantum Electron. 19, 1276-1283 (1983).
[CrossRef]

Amat-Roldan, I.

Artigas, D.

Bethge, J.

J. Bethge and G. Steinmeyer, "Numerical fringe pattern demodulation strategies in interferometry," Rev. Sci. Instrum. 79, 073102 (2008).
[CrossRef] [PubMed]

Cormack, I. G.

DeLong, K. W.

Dudovich, N.

N. Dudovich, D. Oron, and Y. Silberberg, "Single-pulse coherently controlled nonlinear Ramman spectroscopy and microscopy," Nature (London) 418, 512-514 (2002).
[CrossRef]

Fejer, M. M.

Fittinghoff, D. N.

Gu, X.

Iaconis, C.

Jasapara, J.

Jiang, Z.

Kimmel, M.

Kosik Williams, E. M.

Kurz, J. R.

Ladera, C. L.

Langrock, C.

Leaird, D. E.

Loza-Alvarez, P.

Miao, H.

Morita, R.

M. Yamashita, K. Yamane, and R. Morita, "Quasi-automatic phase-control technique for chirp compensation of pulse with over-one-octave bandwidth-generation of few to mono-cycle optical pulses," IEEE J. Quantum Electron. 16, 213-222 (2006).

Nicholson, J. W.

O’Shea, P.

Omenetto, F. G.

Oron, D.

N. Dudovich, D. Oron, and Y. Silberberg, "Single-pulse coherently controlled nonlinear Ramman spectroscopy and microscopy," Nature (London) 418, 512-514 (2002).
[CrossRef]

Parameswaran, K. R.

Radunsky, A. S.

Roussev, R. V.

Route, R. K.

Rudolph, W.

Silberberg, Y.

N. Dudovich, D. Oron, and Y. Silberberg, "Single-pulse coherently controlled nonlinear Ramman spectroscopy and microscopy," Nature (London) 418, 512-514 (2002).
[CrossRef]

Steinmeyer, G.

J. Bethge and G. Steinmeyer, "Numerical fringe pattern demodulation strategies in interferometry," Rev. Sci. Instrum. 79, 073102 (2008).
[CrossRef] [PubMed]

Taylor, A. J.

Trebino, R.

Walmsley, I. A.

Wasilewski, W.

Wasylczyk, P.

Weiner, A. M.

Yamane, K.

M. Yamashita, K. Yamane, and R. Morita, "Quasi-automatic phase-control technique for chirp compensation of pulse with over-one-octave bandwidth-generation of few to mono-cycle optical pulses," IEEE J. Quantum Electron. 16, 213-222 (2006).

Yamashita, M.

M. Yamashita, K. Yamane, and R. Morita, "Quasi-automatic phase-control technique for chirp compensation of pulse with over-one-octave bandwidth-generation of few to mono-cycle optical pulses," IEEE J. Quantum Electron. 16, 213-222 (2006).

Yang, S. -D.

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

M. Yamashita, K. Yamane, and R. Morita, "Quasi-automatic phase-control technique for chirp compensation of pulse with over-one-octave bandwidth-generation of few to mono-cycle optical pulses," IEEE J. Quantum Electron. 16, 213-222 (2006).

A. M. Weiner, "Effect of group velocity mismatch on the measurement of ultrashort optical pulses via second harmonic generation," IEEE J. Quantum Electron. 19, 1276-1283 (1983).
[CrossRef]

J. Opt. Netw. (1)

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

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

Nature (London) (1)

N. Dudovich, D. Oron, and Y. Silberberg, "Single-pulse coherently controlled nonlinear Ramman spectroscopy and microscopy," Nature (London) 418, 512-514 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (8)

C. Iaconis and I. A. Walmsley, "Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses," Opt. Lett. 23, 792-794 (1998).
[CrossRef]

J. W. Nicholson, J. Jasapara, W. Rudolph, F. G. Omenetto, and A. J. Taylor, "Full-field characterization of femtosecond pulses by spectrum and cross-correlation measurements," Opt. Lett. 24, 1774-1776 (1999).
[CrossRef]

P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, "Highly simplified device for ultrashort-pulse measurement," Opt. Lett. 26, 932-934 (2001).
[CrossRef]

K. R. Parameswaran, R. K. Route, J. R. Kurz, R. V. Roussev, and M. M. Fejer, "Highly efficient second-harmonic generation in buried waveguides formed by annealed and reverse proton exchange in periodically poled lithium niobate," Opt. Lett. 27, 179-181 (2002).
[CrossRef]

S. -D. Yang, A. M. Weiner, K. R. Parameswaran, and M. M. Fejer,"400-photon-per-pulse ultrashort pulse autocorrelation measurement with aperiodically poled lithium niobate waveguides at 1.55 um," Opt. Lett. 29, 2070-2072 (2004).
[CrossRef] [PubMed]

I. Amat-Roldan, I. G. Cormack, P. Loza-Alvarez, and D. Artigas, "Measurement of electric field by interferometric spectral trace observation," Opt. Lett. 30, 1063-1065 (2005).
[CrossRef] [PubMed]

S. -D. Yang, A. M. Weiner, K. R. Parameswaran, and M. M. Fejer, "Ultra-sensitive second-harmonic generation frequency-resolved optical gating by aperiodically poled LiNbO3 waveguides at 1.5 um," Opt. Lett. 30, 2164-2166 (2005).
[CrossRef] [PubMed]

A. S. Radunsky, E. M. Kosik Williams, I. A. Walmsley, P. Wasylczyk, W. Wasilewski, A. B. U’Ren, and M. E. Anderson, "Simplified spectral phase interferometry for direct electric-field reconstruction by using a thick nonlinear crystal," Opt. Lett. 31, 1008-1010 (2006).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

J. Bethge and G. Steinmeyer, "Numerical fringe pattern demodulation strategies in interferometry," Rev. Sci. Instrum. 79, 073102 (2008).
[CrossRef] [PubMed]

Other (3)

S. -D. Yang, S. -L. Lin and Y. -Y. Huang, "Complete spectral phase retrieval by modified interferometric field autocorrelation traces," Proc. Conf. Lasers Elec. Opt. (2008).
[CrossRef]

A. M. Weiner, Ultrafast Optics (Wiley, in preparation).

R. Trebino, in Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulse, (Kluwer Academic Publisher, Boston, MA, 2000).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic diagram of MIFA measurement. MI: Michelson interferometer.

Fig. 2.
Fig. 2.

Theoretical verification of MIFA method. (a) Assumed power spectrum (dash), assumed spectral phase (solid), retrieved spectral phase (open circles). (b-e) The corresponding MIFA traces S 1(τ), S 2(τ), and even phases ψe1(f),ψe2(f) produced in retrieving spectral phase in (a). (f) Simulation result by assuming π-phase shift. The corresponding rms errors in (a) and (f) are 8.18×10-5 rad, and 6.13×10-5 rad, respectively.

Fig. 3.
Fig. 3.

Rms error of even phase functions ψe1 (circles),ψe2 (triangles), and complete phase ψ (squares) versus normalized PM bandwidth at fixed PM spacing of 2Δ=0.5 THz. Inset shows the definition of PM power spectral pair used in the simulation.

Fig. 4.
Fig. 4.

Experimental setup of MIFA measurement. W#: WDM, C#: 3-dB coupler, PC#: polarization controller, PD1&PD2: InGaAs photodetectors, PD3: Si photodetector.

Fig. 5.
Fig. 5.

(a) Even-order spectral phase before (dash) and after (dash-dot) the insertion of 5.15-m-long SMF. (b) Complete spectral phase imposed by pulse shaper (dash) and retrieved by MIFA scheme (dash-dot).

Equations (8)

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S 1 ( τ ) 1 + 2 G ' 1 ( τ ) 2 + 4 Re [ G ' 1 ( τ ) ] cos ( 2 π f 0 τ ) + cos ( 4 π f 0 τ ) ,
G ' 1 ( τ ) a ( t ) a ( t τ ) a 2 ( t ) .
G ' ˜ 1 ( f ) A ( f ) · A ( f ) = A ( f ) · A ( f ) · exp { j [ ψ ( f ) + ψ ( f ) ] } ,
ψ e 1 ( f ) [ ψ ( f ) + ψ ( f ) ] 2 = G ' ˜ 1 ( f ) 2 .
ψ e 2 ( f ) [ ψ ( f ) + ψ ( f + 2 Δ ) ] 2 ,
ψ ( f + 2 Δ ) ψ ( f ) = 2 [ ψ e 2 ( f + 2 Δ ) ψ e 1 ( f ) ] .
S 1 ( τ ) 1 + 4 r 1 + r 2 G ' 1 ( τ ) 2 + 2 r 1 + r 2 cos ( 4 π f 0 τ ) +
4 r 1 + r 2 { ( r + 1 ) Re [ G ' 1 ( τ ) ] · cos ( 2 π f 0 τ ) + ( r 1 ) Im [ G ' 1 ( τ ) ] · sin ( 2 π f 0 τ ) } ,

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