Abstract

We present a method using spectral interferometry (SI) to characterize a pulse in the presence of an incoherent background such as amplified spontaneous emission (ASE). The output of a regenerative amplifier is interfered with a copy of the pulse that has been converted using third-order cross-polarized wave generation (XPW). The ASE shows as a pedestal background in the interference pattern. The energy contrast between the short-pulse component and the ASE is retrieved. The spectra of the interacting beams are obtained through an improvement to the self-referenced spectral interferometry (SRSI) analysis.

© 2014 Optical Society of America

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2013

A. Ricci, A. Jullien, J.-P. Rousseau, Y. Liu, A. Houard, P. Ramirez, D. Papadopoulos, A. Pellegrina, P. Georges, F. Druon, N. Forget, and R. Lopez-Martens, “Energy-scalable temporal cleaning device for femtosecond laser pulses based on cross-polarized wave generation,” Rev. Sci. Instrum. 84, 043106 (2013).
[CrossRef] [PubMed]

H. J. Liu, Q. B. Sun, J. W. N. Huang, and Z. L. Wang, “Highly efficient pulse cleaner via nonlinear ellipse rotation in liquid CS2 for ultrashort pulses,” Opt. Lett. 38, 1838–1840 (2013).
[CrossRef] [PubMed]

2012

2010

D. Adams, T. Planchon, J. Squier, and C. G. Durfee, “Spatio-temporal dynamics of cross-polarized wave generation,” Opt. Lett. 35, 1115–1117 (2010).
[CrossRef] [PubMed]

M. K. Yetzbacher, T. L. Courtney, W. K. Peters, K. A. Kitney, E. R. Smith, and D. M. Jonas, “Spectral restoration for femtosecond spectral interferometry with attosecond accuracy,” J. Opt. Soc. Am. B 27, 1104–1117 (2010).
[CrossRef]

A. Jullien, X. Chen, A. Ricci, J. P. Rousseau, R. Lopez-Martens, L.P. Ramirez, D. Papadopoulos, A. Pellegrina, F. Druon, and P. Georges, “High-fidelity front-end for high-power, high temporal quality few-cycle lasers,” Appl. Phys. B 102, 769–774 (2010).
[CrossRef]

T. Oksenhendler, S. Coudreau, N. Forget, V. Crozatier, S. Grabielle, R. Herzog, O. Gobert, and D. Kaplan, “Self-referenced spectral interferometry,” Appl. Phys. B 99, 7–12 (2010).
[CrossRef]

2009

2007

2006

2005

2002

2000

1999

A. W. Albrecht, J. D. Hybl, S. M. G. Faeder, and D. M. Jonas, “Experimental distinction between phase shifts and time delays: Implications for femtosecond spectroscopy and coherent control of chemical reactions,” J. Chem. Phys. 111, 10934–10956 (1999).
[CrossRef]

1996

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749 (1996).
[CrossRef]

1993

S. Luan, M. Hutchinson, R. A. Smith, and F. Zhou, “High dynamic range third-order correlation measurement of picosecond laser pulse shapes,” Meas. Sci. Tech. 4, 1426–1429 (1993).
[CrossRef]

1992

1991

1989

M. Pessot, J. Squier, and G. Mourou, “Chirped-pulse amplification of 100-fs pulses,” Opt. Lett. 14, 797–799 (1989).
[CrossRef] [PubMed]

M. M. Murnane, H. C. Kapteyn, and R. W. Falcone, “High-density plasmas produced by ultrafast laser pulses,” Phys. Rev. Lett. 62, 155–158 (1989).
[CrossRef] [PubMed]

1985

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 55, 447–449 (1985).
[CrossRef]

Adams, D.

Adams, D. E.

Albert, O.

Albrecht, A. W.

A. W. Albrecht, J. D. Hybl, S. M. G. Faeder, and D. M. Jonas, “Experimental distinction between phase shifts and time delays: Implications for femtosecond spectroscopy and coherent control of chemical reactions,” J. Chem. Phys. 111, 10934–10956 (1999).
[CrossRef]

Bartels, R.

Beaudoin, Y.

Begishev, I. A.

Behmke, M.

C. Rödel, M. Heyer, M. Behmke, M. Kübel, O. Jäckel, W. Ziegler, D. Ehrt, M. Kaluza, and G. Paulus, “High repetition rate plasma mirror for temporal contrast enhancement of terawatt femtosecond laser pulses by three orders of magnitude,” Appl. Phys. B (2010).

Belabas, N.

Chen, X.

A. Jullien, X. Chen, A. Ricci, J. P. Rousseau, R. Lopez-Martens, L.P. Ramirez, D. Papadopoulos, A. Pellegrina, F. Druon, and P. Georges, “High-fidelity front-end for high-power, high temporal quality few-cycle lasers,” Appl. Phys. B 102, 769–774 (2010).
[CrossRef]

Chériaux, G.

Chien, C. Y.

Chvykov, V.

Coe, J. S.

Coudreau, S.

T. Oksenhendler, S. Coudreau, N. Forget, V. Crozatier, S. Grabielle, R. Herzog, O. Gobert, and D. Kaplan, “Self-referenced spectral interferometry,” Appl. Phys. B 99, 7–12 (2010).
[CrossRef]

Courtney, T. L.

Crozatier, V.

T. Oksenhendler, S. Coudreau, N. Forget, V. Crozatier, S. Grabielle, R. Herzog, O. Gobert, and D. Kaplan, “Self-referenced spectral interferometry,” Appl. Phys. B 99, 7–12 (2010).
[CrossRef]

Dorrer, C.

Druon, F.

A. Ricci, A. Jullien, J.-P. Rousseau, Y. Liu, A. Houard, P. Ramirez, D. Papadopoulos, A. Pellegrina, P. Georges, F. Druon, N. Forget, and R. Lopez-Martens, “Energy-scalable temporal cleaning device for femtosecond laser pulses based on cross-polarized wave generation,” Rev. Sci. Instrum. 84, 043106 (2013).
[CrossRef] [PubMed]

A. Jullien, X. Chen, A. Ricci, J. P. Rousseau, R. Lopez-Martens, L.P. Ramirez, D. Papadopoulos, A. Pellegrina, F. Druon, and P. Georges, “High-fidelity front-end for high-power, high temporal quality few-cycle lasers,” Appl. Phys. B 102, 769–774 (2010).
[CrossRef]

Durfee, C. G.

Ehrt, D.

C. Rödel, M. Heyer, M. Behmke, M. Kübel, O. Jäckel, W. Ziegler, D. Ehrt, M. Kaluza, and G. Paulus, “High repetition rate plasma mirror for temporal contrast enhancement of terawatt femtosecond laser pulses by three orders of magnitude,” Appl. Phys. B (2010).

Etchepare, J.

Faeder, S. M. G.

A. W. Albrecht, J. D. Hybl, S. M. G. Faeder, and D. M. Jonas, “Experimental distinction between phase shifts and time delays: Implications for femtosecond spectroscopy and coherent control of chemical reactions,” J. Chem. Phys. 111, 10934–10956 (1999).
[CrossRef]

Falcone, R. W.

M. M. Murnane, H. C. Kapteyn, and R. W. Falcone, “High-density plasmas produced by ultrafast laser pulses,” Phys. Rev. Lett. 62, 155–158 (1989).
[CrossRef] [PubMed]

Feit, M. D.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749 (1996).
[CrossRef]

Forget, N.

A. Ricci, A. Jullien, J.-P. Rousseau, Y. Liu, A. Houard, P. Ramirez, D. Papadopoulos, A. Pellegrina, P. Georges, F. Druon, N. Forget, and R. Lopez-Martens, “Energy-scalable temporal cleaning device for femtosecond laser pulses based on cross-polarized wave generation,” Rev. Sci. Instrum. 84, 043106 (2013).
[CrossRef] [PubMed]

T. Oksenhendler, S. Coudreau, N. Forget, V. Crozatier, S. Grabielle, R. Herzog, O. Gobert, and D. Kaplan, “Self-referenced spectral interferometry,” Appl. Phys. B 99, 7–12 (2010).
[CrossRef]

Gaeta, A. L.

Georges, P.

A. Ricci, A. Jullien, J.-P. Rousseau, Y. Liu, A. Houard, P. Ramirez, D. Papadopoulos, A. Pellegrina, P. Georges, F. Druon, N. Forget, and R. Lopez-Martens, “Energy-scalable temporal cleaning device for femtosecond laser pulses based on cross-polarized wave generation,” Rev. Sci. Instrum. 84, 043106 (2013).
[CrossRef] [PubMed]

A. Jullien, X. Chen, A. Ricci, J. P. Rousseau, R. Lopez-Martens, L.P. Ramirez, D. Papadopoulos, A. Pellegrina, F. Druon, and P. Georges, “High-fidelity front-end for high-power, high temporal quality few-cycle lasers,” Appl. Phys. B 102, 769–774 (2010).
[CrossRef]

Gobert, O.

T. Oksenhendler, S. Coudreau, N. Forget, V. Crozatier, S. Grabielle, R. Herzog, O. Gobert, and D. Kaplan, “Self-referenced spectral interferometry,” Appl. Phys. B 99, 7–12 (2010).
[CrossRef]

Grabielle, S.

T. Oksenhendler, S. Coudreau, N. Forget, V. Crozatier, S. Grabielle, R. Herzog, O. Gobert, and D. Kaplan, “Self-referenced spectral interferometry,” Appl. Phys. B 99, 7–12 (2010).
[CrossRef]

Herman, S.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749 (1996).
[CrossRef]

Herzog, R.

T. Oksenhendler, S. Coudreau, N. Forget, V. Crozatier, S. Grabielle, R. Herzog, O. Gobert, and D. Kaplan, “Self-referenced spectral interferometry,” Appl. Phys. B 99, 7–12 (2010).
[CrossRef]

Heyer, M.

C. Rödel, M. Heyer, M. Behmke, M. Kübel, O. Jäckel, W. Ziegler, D. Ehrt, M. Kaluza, and G. Paulus, “High repetition rate plasma mirror for temporal contrast enhancement of terawatt femtosecond laser pulses by three orders of magnitude,” Appl. Phys. B (2010).

Homoelle, D.

Houard, A.

A. Ricci, A. Jullien, J.-P. Rousseau, Y. Liu, A. Houard, P. Ramirez, D. Papadopoulos, A. Pellegrina, P. Georges, F. Druon, N. Forget, and R. Lopez-Martens, “Energy-scalable temporal cleaning device for femtosecond laser pulses based on cross-polarized wave generation,” Rev. Sci. Instrum. 84, 043106 (2013).
[CrossRef] [PubMed]

Hrin, A.

Huang, J. W. N.

Hutchinson, M.

S. Luan, M. Hutchinson, R. A. Smith, and F. Zhou, “High dynamic range third-order correlation measurement of picosecond laser pulse shapes,” Meas. Sci. Tech. 4, 1426–1429 (1993).
[CrossRef]

Hybl, J. D.

A. W. Albrecht, J. D. Hybl, S. M. G. Faeder, and D. M. Jonas, “Experimental distinction between phase shifts and time delays: Implications for femtosecond spectroscopy and coherent control of chemical reactions,” J. Chem. Phys. 111, 10934–10956 (1999).
[CrossRef]

Jäckel, O.

C. Rödel, M. Heyer, M. Behmke, M. Kübel, O. Jäckel, W. Ziegler, D. Ehrt, M. Kaluza, and G. Paulus, “High repetition rate plasma mirror for temporal contrast enhancement of terawatt femtosecond laser pulses by three orders of magnitude,” Appl. Phys. B (2010).

Joffre, M.

Jonas, D. M.

M. K. Yetzbacher, T. L. Courtney, W. K. Peters, K. A. Kitney, E. R. Smith, and D. M. Jonas, “Spectral restoration for femtosecond spectral interferometry with attosecond accuracy,” J. Opt. Soc. Am. B 27, 1104–1117 (2010).
[CrossRef]

A. W. Albrecht, J. D. Hybl, S. M. G. Faeder, and D. M. Jonas, “Experimental distinction between phase shifts and time delays: Implications for femtosecond spectroscopy and coherent control of chemical reactions,” J. Chem. Phys. 111, 10934–10956 (1999).
[CrossRef]

Jullien, A.

A. Ricci, A. Jullien, J.-P. Rousseau, Y. Liu, A. Houard, P. Ramirez, D. Papadopoulos, A. Pellegrina, P. Georges, F. Druon, N. Forget, and R. Lopez-Martens, “Energy-scalable temporal cleaning device for femtosecond laser pulses based on cross-polarized wave generation,” Rev. Sci. Instrum. 84, 043106 (2013).
[CrossRef] [PubMed]

A. Jullien, X. Chen, A. Ricci, J. P. Rousseau, R. Lopez-Martens, L.P. Ramirez, D. Papadopoulos, A. Pellegrina, F. Druon, and P. Georges, “High-fidelity front-end for high-power, high temporal quality few-cycle lasers,” Appl. Phys. B 102, 769–774 (2010).
[CrossRef]

A. Jullien, O. Albert, G. Chériaux, J. Etchepare, S. Kourtev, N. Minkovski, and S. Saltiel, “Nonlinear polarization rotation of elliptical light in cubic crystals, with application to cross-polarized wave generation,” J. Opt. Soc. Am. B 22, 2635–2641 (2005).
[CrossRef]

Kalinchenko, G.

Kaluza, M.

C. Rödel, M. Heyer, M. Behmke, M. Kübel, O. Jäckel, W. Ziegler, D. Ehrt, M. Kaluza, and G. Paulus, “High repetition rate plasma mirror for temporal contrast enhancement of terawatt femtosecond laser pulses by three orders of magnitude,” Appl. Phys. B (2010).

Kaplan, D.

T. Oksenhendler, S. Coudreau, N. Forget, V. Crozatier, S. Grabielle, R. Herzog, O. Gobert, and D. Kaplan, “Self-referenced spectral interferometry,” Appl. Phys. B 99, 7–12 (2010).
[CrossRef]

Kapteyn, H. C.

M. M. Murnane, H. C. Kapteyn, and R. W. Falcone, “High-density plasmas produced by ultrafast laser pulses,” Phys. Rev. Lett. 62, 155–158 (1989).
[CrossRef] [PubMed]

Kitney, K. A.

Kourtev, S.

Kübel, M.

C. Rödel, M. Heyer, M. Behmke, M. Kübel, O. Jäckel, W. Ziegler, D. Ehrt, M. Kaluza, and G. Paulus, “High repetition rate plasma mirror for temporal contrast enhancement of terawatt femtosecond laser pulses by three orders of magnitude,” Appl. Phys. B (2010).

Likforman, J.-P.

Liu, H. J.

Liu, Y.

A. Ricci, A. Jullien, J.-P. Rousseau, Y. Liu, A. Houard, P. Ramirez, D. Papadopoulos, A. Pellegrina, P. Georges, F. Druon, N. Forget, and R. Lopez-Martens, “Energy-scalable temporal cleaning device for femtosecond laser pulses based on cross-polarized wave generation,” Rev. Sci. Instrum. 84, 043106 (2013).
[CrossRef] [PubMed]

Lopez-Martens, R.

A. Ricci, A. Jullien, J.-P. Rousseau, Y. Liu, A. Houard, P. Ramirez, D. Papadopoulos, A. Pellegrina, P. Georges, F. Druon, N. Forget, and R. Lopez-Martens, “Energy-scalable temporal cleaning device for femtosecond laser pulses based on cross-polarized wave generation,” Rev. Sci. Instrum. 84, 043106 (2013).
[CrossRef] [PubMed]

A. Jullien, X. Chen, A. Ricci, J. P. Rousseau, R. Lopez-Martens, L.P. Ramirez, D. Papadopoulos, A. Pellegrina, F. Druon, and P. Georges, “High-fidelity front-end for high-power, high temporal quality few-cycle lasers,” Appl. Phys. B 102, 769–774 (2010).
[CrossRef]

Luan, S.

S. Luan, M. Hutchinson, R. A. Smith, and F. Zhou, “High dynamic range third-order correlation measurement of picosecond laser pulse shapes,” Meas. Sci. Tech. 4, 1426–1429 (1993).
[CrossRef]

Minkovski, N.

Mourou, G.

Murnane, M. M.

M. M. Murnane, H. C. Kapteyn, and R. W. Falcone, “High-density plasmas produced by ultrafast laser pulses,” Phys. Rev. Lett. 62, 155–158 (1989).
[CrossRef] [PubMed]

Okishev, A. V.

Oksenhendler, T.

T. Oksenhendler, S. Coudreau, N. Forget, V. Crozatier, S. Grabielle, R. Herzog, O. Gobert, and D. Kaplan, “Self-referenced spectral interferometry,” Appl. Phys. B 99, 7–12 (2010).
[CrossRef]

Papadopoulos, D.

A. Ricci, A. Jullien, J.-P. Rousseau, Y. Liu, A. Houard, P. Ramirez, D. Papadopoulos, A. Pellegrina, P. Georges, F. Druon, N. Forget, and R. Lopez-Martens, “Energy-scalable temporal cleaning device for femtosecond laser pulses based on cross-polarized wave generation,” Rev. Sci. Instrum. 84, 043106 (2013).
[CrossRef] [PubMed]

A. Jullien, X. Chen, A. Ricci, J. P. Rousseau, R. Lopez-Martens, L.P. Ramirez, D. Papadopoulos, A. Pellegrina, F. Druon, and P. Georges, “High-fidelity front-end for high-power, high temporal quality few-cycle lasers,” Appl. Phys. B 102, 769–774 (2010).
[CrossRef]

Paulus, G.

C. Rödel, M. Heyer, M. Behmke, M. Kübel, O. Jäckel, W. Ziegler, D. Ehrt, M. Kaluza, and G. Paulus, “High repetition rate plasma mirror for temporal contrast enhancement of terawatt femtosecond laser pulses by three orders of magnitude,” Appl. Phys. B (2010).

Pellegrina, A.

A. Ricci, A. Jullien, J.-P. Rousseau, Y. Liu, A. Houard, P. Ramirez, D. Papadopoulos, A. Pellegrina, P. Georges, F. Druon, N. Forget, and R. Lopez-Martens, “Energy-scalable temporal cleaning device for femtosecond laser pulses based on cross-polarized wave generation,” Rev. Sci. Instrum. 84, 043106 (2013).
[CrossRef] [PubMed]

A. Jullien, X. Chen, A. Ricci, J. P. Rousseau, R. Lopez-Martens, L.P. Ramirez, D. Papadopoulos, A. Pellegrina, F. Druon, and P. Georges, “High-fidelity front-end for high-power, high temporal quality few-cycle lasers,” Appl. Phys. B 102, 769–774 (2010).
[CrossRef]

Perry, M. D.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749 (1996).
[CrossRef]

Pessot, M.

Peters, W. K.

Planchon, T.

Planchon, T. A.

Ramirez, L.P.

A. Jullien, X. Chen, A. Ricci, J. P. Rousseau, R. Lopez-Martens, L.P. Ramirez, D. Papadopoulos, A. Pellegrina, F. Druon, and P. Georges, “High-fidelity front-end for high-power, high temporal quality few-cycle lasers,” Appl. Phys. B 102, 769–774 (2010).
[CrossRef]

Ramirez, P.

A. Ricci, A. Jullien, J.-P. Rousseau, Y. Liu, A. Houard, P. Ramirez, D. Papadopoulos, A. Pellegrina, P. Georges, F. Druon, N. Forget, and R. Lopez-Martens, “Energy-scalable temporal cleaning device for femtosecond laser pulses based on cross-polarized wave generation,” Rev. Sci. Instrum. 84, 043106 (2013).
[CrossRef] [PubMed]

Ratner, J.

Reed, S.

Ricci, A.

A. Ricci, A. Jullien, J.-P. Rousseau, Y. Liu, A. Houard, P. Ramirez, D. Papadopoulos, A. Pellegrina, P. Georges, F. Druon, N. Forget, and R. Lopez-Martens, “Energy-scalable temporal cleaning device for femtosecond laser pulses based on cross-polarized wave generation,” Rev. Sci. Instrum. 84, 043106 (2013).
[CrossRef] [PubMed]

A. Jullien, X. Chen, A. Ricci, J. P. Rousseau, R. Lopez-Martens, L.P. Ramirez, D. Papadopoulos, A. Pellegrina, F. Druon, and P. Georges, “High-fidelity front-end for high-power, high temporal quality few-cycle lasers,” Appl. Phys. B 102, 769–774 (2010).
[CrossRef]

Rödel, C.

C. Rödel, M. Heyer, M. Behmke, M. Kübel, O. Jäckel, W. Ziegler, D. Ehrt, M. Kaluza, and G. Paulus, “High repetition rate plasma mirror for temporal contrast enhancement of terawatt femtosecond laser pulses by three orders of magnitude,” Appl. Phys. B (2010).

Rousseau, J. P.

A. Jullien, X. Chen, A. Ricci, J. P. Rousseau, R. Lopez-Martens, L.P. Ramirez, D. Papadopoulos, A. Pellegrina, F. Druon, and P. Georges, “High-fidelity front-end for high-power, high temporal quality few-cycle lasers,” Appl. Phys. B 102, 769–774 (2010).
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C. Rödel, M. Heyer, M. Behmke, M. Kübel, O. Jäckel, W. Ziegler, D. Ehrt, M. Kaluza, and G. Paulus, “High repetition rate plasma mirror for temporal contrast enhancement of terawatt femtosecond laser pulses by three orders of magnitude,” Appl. Phys. B (2010).

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A. Jullien, X. Chen, A. Ricci, J. P. Rousseau, R. Lopez-Martens, L.P. Ramirez, D. Papadopoulos, A. Pellegrina, F. Druon, and P. Georges, “High-fidelity front-end for high-power, high temporal quality few-cycle lasers,” Appl. Phys. B 102, 769–774 (2010).
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A. Ricci, A. Jullien, J.-P. Rousseau, Y. Liu, A. Houard, P. Ramirez, D. Papadopoulos, A. Pellegrina, P. Georges, F. Druon, N. Forget, and R. Lopez-Martens, “Energy-scalable temporal cleaning device for femtosecond laser pulses based on cross-polarized wave generation,” Rev. Sci. Instrum. 84, 043106 (2013).
[CrossRef] [PubMed]

Other

C. Rödel, M. Heyer, M. Behmke, M. Kübel, O. Jäckel, W. Ziegler, D. Ehrt, M. Kaluza, and G. Paulus, “High repetition rate plasma mirror for temporal contrast enhancement of terawatt femtosecond laser pulses by three orders of magnitude,” Appl. Phys. B (2010).

L. Veisz, “Contrast improvement of relativistic few-cycle light pulses,” in “Coherence and Ultrashort Pulse Laser Emission,”, F. J. Duarte, ed. (Coherence and Ultrashort Pulse Laser Emission, 2010), pp. 305–330.

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Figures (4)

Fig. 1
Fig. 1

In-line interferometer layout. Polarizer P1 cleans up the input polarization and the calcite plate CP creates two copies of the input signal with relative delay and opposite polarization. A 4-f imaging system relays the output of the calcite birefringent plate (CP) to the spectrometer, with XPW conversion of one of the two puIses in the barium fluoride crystal (BaF2). Analyzing polarizer P2 selects this XPW signal and also passes the lower energy second pulse. The graphs illustrate the different signals in a simulated data run for a case where the energy content of the ASE is 25% of that of the fundamental wave and the ASE central wavelength is slightly lower. IF (λ), IA(λ) and IX (λ) represent the spectral intensities of the fundamental wave, ASE and the XPW signals, respectively. IFA(λ) represents the combined spectrum of the FW and ASE that would be measured by the time-integrating spectrometer. The calculated interferogram IINT (λ) shows a pedestal background that results from the presence of the incoherent ASE signal.

Fig. 2
Fig. 2

Proposed SRSI algorithm flowchart. The components of the phase and amplitude retrieval loops are outlined in blue and red, respectively. A brief description of each step is displayed at the top of each box in bold. ϕ refers to phase, I to intensity, A to real amplitude, E to a complex electro-magnetic field. The superscripts (M) and (R) refer to measured and retrieved data, respectively. Subscripts F, A, X, FA correspond to FW, ASE, XPW, and FW+ASE respectively. The function XPW[...] returns the XPW field from the time-domain FW field. The ε terms represent the root-mean-square (RMS) error, and the subscript i denotes the iteration index.

Fig. 3
Fig. 3

XPW spectra: measured (solid line), retrieved without spectral loop (green), retrieved with spectral loop (red). (a) Analysis of experimental data. (b) Example with model using conditions from Fig. 1.

Fig. 4
Fig. 4

(a) Low ASE content (7.5%) interferogram. (b) Transform space representation of the interferogram (red) along with measured spectrometer transfer function (dashed). The black line results from division by the transfer function. (c) Retrieved FW spectrum (black), low ASE spectrum (solid-red) and high ASE spectrum (dashed-red).

Equations (4)

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I INT = I F + I A + I X + A F A X exp [ i ( ω τ + Δ ϕ AC ) ] + A F A X exp [ i ( ω τ + Δ ϕ AC ) ]
I DC ( M ) ( ω ) = c FA * I FA ( M ) ( ω ) + c X * I X ( M ) ( ω ) ,
I measured ( ω ) = I actual ( ω ) h ( ω , ω ) ,
I actual ( ω ) = { I ˜ measured ( t ) H ˜ ( t , ω ) } ,

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