Abstract

In this paper, we introduce a pulse characterization technique that is free of phase-matching constraints, exploiting transient absorption in solids as an ultrafast optical switch. Based on a pump-probe setup, this technique uses pump pulses of sufficient intensity to induce the switch, while the pulses to characterize are probing the transmissivity drop of the photoexcited material. This enables the characterization of low-intensity ultra-broadband pulses at the detection limit of the spectrometer and within the transparency range of the solid. For example, by using zinc selenide (ZnSe), pulses with wavelengths from 0.5 to 20 $\mu$m can be characterized, denoting five octaves of spectral range. Using ptychography, we retrieve the temporal profiles of both the probe pulse and the switch. To demonstrate this approach, we measure ultrashort pulses from a titanium-sapphire (Ti-Sa) amplifier, which are compressed using a hollow core fiber setup, as well as infrared to mid-infrared pulses generated from an optical parametric amplifier (OPA). The characterized pulses are centered at wavelengths of 0.77, 1.53, 1.75, 4, and 10 $\mu$m, down to sub-two optical cycles duration, exceeding an octave of bandwidth, and with energy as low as a few nanojoules.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (4)

2017 (2)

2016 (6)

D. Sanchez, M. Hemmer, M. Baudisch, S. Cousin, K. Zawilski, P. Schunemann, O. Chalus, C. Simon-Boisson, and J. Biegert, “7 $\mu$μm, ultrafast, sub-millijoule-level mid-infrared optical parametric chirped pulse amplifier pumped at 2 $\mu$μm,” Optica 3(2), 147–150 (2016).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, S. I. Mitryukovsky, A. B. Fedotov, E. E. Serebryannikov, D. V. Meshchankin, V. Shumakova, S. Ališauskas, A. Pugžlys, V. Ya. Panchenko, A. Baltuška, and A. M. Zheltikov, “Subterawatt few-cycle mid-infrared pulses from a single filament,” Optica 3(3), 299–302 (2016).
[Crossref]

S. Keiber, S. Sederberg, A. Schwarz, M. Trubetskov, V. Pervak, F. Krausz, and N. Karpowicz, “Electro-optic sampling of near-infrared waveforms,” Nat. Photonics 10(3), 159–162 (2016).
[Crossref]

T. Witting, D. Greening, D. Walke, P. Matia-Hernando, T. Barillot, J. Marangos, and J. Tisch, “Time-domain ptychography of over-octave-spanning laser pulses in the single-cycle regime,” Opt. Lett. 41(18), 4218–4221 (2016).
[Crossref]

A. M. Heidt, D.-M. Spangenberg, M. Brügmann, E. G. Rohwer, and T. Feurer, “Improved retrieval of complex supercontinuum pulses from XFROG traces using a ptychographic algorithm,” Opt. Lett. 41(21), 4903–4906 (2016).
[Crossref]

P. Sidorenko, O. Lahav, Z. Avnat, and O. Cohen, “Ptychographic reconstruction algorithm for frequency-resolved optical gating: super-resolution and supreme robustness,” Optica 3(12), 1320–1330 (2016).
[Crossref]

2015 (1)

D. Spangenberg, P. Neethling, E. Rohwer, M. H. Brügmann, and T. Feurer, “Time-domain ptychography,” Phys. Rev. A 91(2), 021803 (2015).
[Crossref]

2014 (1)

2012 (1)

2011 (2)

A. Wirth, M. T. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized Light Transients,” Science 334(6053), 195–200 (2011).
[Crossref]

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kartner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5(8), 475–479 (2011).
[Crossref]

2010 (1)

F. Cilento, C. Giannetti, G. Ferrini, S. Dal Conte, T. Sala, G. Coslovich, M. Rini, A. Cavalleri, and F. Parmigiani, “Ultrafast insulator-to-metal phase transition as a switch to measure the spectrogram of a supercontinuum light pulse,” Appl. Phys. Lett. 96(2), 021102 (2010).
[Crossref]

2009 (2)

I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photonics 1(2), 308–437 (2009).
[Crossref]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref]

2008 (3)

M. Anderson, A. Monmayrant, S.-P. Gorza, P. Wasylczyk, and I. Walmsley, “SPIDER: A decade of measuring ultrashort pulses,” Laser Phys. Lett. 5(4), 259–266 (2008).
[Crossref]

H. Němec, L. Fekete, F. Kadlec, P. Kužel, M. Martin, J. Mangeney, J. Delagnes, and P. Mounaix, “Ultrafast carrier dynamics in Br+-bombarded InP studied by time-resolved terahertz spectroscopy,” Phys. Rev. B 78(23), 235206 (2008).
[Crossref]

M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92(11), 1305–1310 (2008).
[Crossref]

2007 (1)

2006 (1)

J. Salfi, U. Philipose, C. De Sousa, S. Aouba, and H. Ruda, “Electrical properties of Ohmic contacts to ZnSe nanowires and their application to nanowire-based photodetection,” Appl. Phys. Lett. 89(26), 261112 (2006).
[Crossref]

2003 (1)

2001 (1)

K. Michelmann, U. Wagner, T. Feurer, U. Teubner, E. Förster, and R. Sauerbrey, “Measurement of the Page function of an ultrashort laser pulse,” Opt. Commun. 198(1-3), 163–170 (2001).
[Crossref]

1998 (1)

1997 (1)

1994 (1)

1993 (1)

1986 (1)

1983 (1)

M. Tyagi and R. Van Overstraeten, “Minority carrier recombination in heavily-doped silicon,” Solid-State Electron. 26(6), 577–597 (1983).
[Crossref]

1982 (1)

1955 (1)

W. Dash and R. Newman, “Intrinsic optical absorption in single-crystal germanium and silicon at 77 K and 300 K,” Phys. Rev. 99(4), 1151–1155 (1955).
[Crossref]

Alahmed, Z. A.

A. Wirth, M. T. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized Light Transients,” Science 334(6053), 195–200 (2011).
[Crossref]

Ališauskas, S.

Anderson, M.

M. Anderson, A. Monmayrant, S.-P. Gorza, P. Wasylczyk, and I. Walmsley, “SPIDER: A decade of measuring ultrashort pulses,” Laser Phys. Lett. 5(4), 259–266 (2008).
[Crossref]

Aouba, S.

J. Salfi, U. Philipose, C. De Sousa, S. Aouba, and H. Ruda, “Electrical properties of Ohmic contacts to ZnSe nanowires and their application to nanowire-based photodetection,” Appl. Phys. Lett. 89(26), 261112 (2006).
[Crossref]

Arisholm, G.

M. Seidel, X. Xiao, S. A. Hussain, G. Arisholm, A. Hartung, K. T. Zawilski, P. G. Schunemann, F. Habel, M. Trubetskov, V. Pervak, O. Pronin, and F. Krausz, “Multi-watt, multi-octave, mid-infrared femtosecond source,” Sci. Adv. 4(4), eaaq1526 (2018).
[Crossref]

Avnat, Z.

Azzeer, A. M.

A. Wirth, M. T. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized Light Transients,” Science 334(6053), 195–200 (2011).
[Crossref]

Baltuška, A.

Baltuška, Andrius

Barillot, T.

Baudisch, M.

Béjot, P.

Bhardwaj, S.

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kartner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5(8), 475–479 (2011).
[Crossref]

Biegert, J.

Birge, J. R.

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kartner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5(8), 475–479 (2011).
[Crossref]

Bock, M.

Bradler, M.

Brügmann, M.

Brügmann, M. H.

D. Spangenberg, P. Neethling, E. Rohwer, M. H. Brügmann, and T. Feurer, “Time-domain ptychography,” Phys. Rev. A 91(2), 021803 (2015).
[Crossref]

Bunk, O.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref]

Canhota, M.

Cavalleri, A.

F. Cilento, C. Giannetti, G. Ferrini, S. Dal Conte, T. Sala, G. Coslovich, M. Rini, A. Cavalleri, and F. Parmigiani, “Ultrafast insulator-to-metal phase transition as a switch to measure the spectrogram of a supercontinuum light pulse,” Appl. Phys. Lett. 96(2), 021102 (2010).
[Crossref]

Cerullo, G.

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kartner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5(8), 475–479 (2011).
[Crossref]

Chalus, O.

Chen, L.-J.

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kartner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5(8), 475–479 (2011).
[Crossref]

Cho, W.

Cilento, F.

F. Cilento, C. Giannetti, G. Ferrini, S. Dal Conte, T. Sala, G. Coslovich, M. Rini, A. Cavalleri, and F. Parmigiani, “Ultrafast insulator-to-metal phase transition as a switch to measure the spectrogram of a supercontinuum light pulse,” Appl. Phys. Lett. 96(2), 021102 (2010).
[Crossref]

Cirmi, G.

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kartner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5(8), 475–479 (2011).
[Crossref]

Cohen, O.

Corkum, P. B.

Coslovich, G.

F. Cilento, C. Giannetti, G. Ferrini, S. Dal Conte, T. Sala, G. Coslovich, M. Rini, A. Cavalleri, and F. Parmigiani, “Ultrafast insulator-to-metal phase transition as a switch to measure the spectrogram of a supercontinuum light pulse,” Appl. Phys. Lett. 96(2), 021102 (2010).
[Crossref]

Cousin, S.

Crespo, H. M.

Dal Conte, S.

F. Cilento, C. Giannetti, G. Ferrini, S. Dal Conte, T. Sala, G. Coslovich, M. Rini, A. Cavalleri, and F. Parmigiani, “Ultrafast insulator-to-metal phase transition as a switch to measure the spectrogram of a supercontinuum light pulse,” Appl. Phys. Lett. 96(2), 021102 (2010).
[Crossref]

Dash, W.

W. Dash and R. Newman, “Intrinsic optical absorption in single-crystal germanium and silicon at 77 K and 300 K,” Phys. Rev. 99(4), 1151–1155 (1955).
[Crossref]

De Sousa, C.

J. Salfi, U. Philipose, C. De Sousa, S. Aouba, and H. Ruda, “Electrical properties of Ohmic contacts to ZnSe nanowires and their application to nanowire-based photodetection,” Appl. Phys. Lett. 89(26), 261112 (2006).
[Crossref]

Delagnes, J.

H. Němec, L. Fekete, F. Kadlec, P. Kužel, M. Martin, J. Mangeney, J. Delagnes, and P. Mounaix, “Ultrafast carrier dynamics in Br+-bombarded InP studied by time-resolved terahertz spectroscopy,” Phys. Rev. B 78(23), 235206 (2008).
[Crossref]

DeLong, K. W.

Dierolf, M.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref]

Dikopoltsev, A.

Dorrer, C.

I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photonics 1(2), 308–437 (2009).
[Crossref]

Eggleton, B. J.

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kartner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5(8), 475–479 (2011).
[Crossref]

Elsaesser, T.

Elser, V.

Fedotov, A. B.

Fekete, L.

H. Němec, L. Fekete, F. Kadlec, P. Kužel, M. Martin, J. Mangeney, J. Delagnes, and P. Mounaix, “Ultrafast carrier dynamics in Br+-bombarded InP studied by time-resolved terahertz spectroscopy,” Phys. Rev. B 78(23), 235206 (2008).
[Crossref]

Ferrini, G.

F. Cilento, C. Giannetti, G. Ferrini, S. Dal Conte, T. Sala, G. Coslovich, M. Rini, A. Cavalleri, and F. Parmigiani, “Ultrafast insulator-to-metal phase transition as a switch to measure the spectrogram of a supercontinuum light pulse,” Appl. Phys. Lett. 96(2), 021102 (2010).
[Crossref]

Feurer, T.

A. M. Heidt, D.-M. Spangenberg, M. Brügmann, E. G. Rohwer, and T. Feurer, “Improved retrieval of complex supercontinuum pulses from XFROG traces using a ptychographic algorithm,” Opt. Lett. 41(21), 4903–4906 (2016).
[Crossref]

D. Spangenberg, P. Neethling, E. Rohwer, M. H. Brügmann, and T. Feurer, “Time-domain ptychography,” Phys. Rev. A 91(2), 021803 (2015).
[Crossref]

K. Michelmann, U. Wagner, T. Feurer, U. Teubner, E. Förster, and R. Sauerbrey, “Measurement of the Page function of an ultrashort laser pulse,” Opt. Commun. 198(1-3), 163–170 (2001).
[Crossref]

Fienup, J. R.

Fittinghoff, D. N.

Förster, E.

K. Michelmann, U. Wagner, T. Feurer, U. Teubner, E. Förster, and R. Sauerbrey, “Measurement of the Page function of an ultrashort laser pulse,” Opt. Commun. 198(1-3), 163–170 (2001).
[Crossref]

Fuji, T.

Gagnon, J.

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Adv. Opt. Photonics (1)

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Appl. Opt. (1)

Appl. Phys. Lett. (2)

F. Cilento, C. Giannetti, G. Ferrini, S. Dal Conte, T. Sala, G. Coslovich, M. Rini, A. Cavalleri, and F. Parmigiani, “Ultrafast insulator-to-metal phase transition as a switch to measure the spectrogram of a supercontinuum light pulse,” Appl. Phys. Lett. 96(2), 021102 (2010).
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J. Salfi, U. Philipose, C. De Sousa, S. Aouba, and H. Ruda, “Electrical properties of Ohmic contacts to ZnSe nanowires and their application to nanowire-based photodetection,” Appl. Phys. Lett. 89(26), 261112 (2006).
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J. Opt. Soc. Am. A (1)

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

Laser Phys. Lett. (1)

M. Anderson, A. Monmayrant, S.-P. Gorza, P. Wasylczyk, and I. Walmsley, “SPIDER: A decade of measuring ultrashort pulses,” Laser Phys. Lett. 5(4), 259–266 (2008).
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Nat. Photonics (2)

S.-W. Huang, G. Cirmi, J. Moses, K.-H. Hong, S. Bhardwaj, J. R. Birge, L.-J. Chen, E. Li, B. J. Eggleton, G. Cerullo, and F. X. Kartner, “High-energy pulse synthesis with sub-cycle waveform control for strong-field physics,” Nat. Photonics 5(8), 475–479 (2011).
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Opt. Commun. (1)

K. Michelmann, U. Wagner, T. Feurer, U. Teubner, E. Förster, and R. Sauerbrey, “Measurement of the Page function of an ultrashort laser pulse,” Opt. Commun. 198(1-3), 163–170 (2001).
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Opt. Express (1)

Opt. Lett. (10)

M. Canhota, F. Silva, R. Weigand, and H. M. Crespo, “Inline self-diffraction dispersion-scan of over octave-spanning pulses in the single-cycle regime,” Opt. Lett. 42(15), 3048–3051 (2017).
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L. von Grafenstein, M. Bock, D. Ueberschaer, K. Zawilski, P. Schunemann, U. Griebner, and T. Elsaesser, “5 $\mu$μm few-cycle pulses with multi-gigawatt peak power at a 1 kHz repetition rate,” Opt. Lett. 42(19), 3796–3799 (2017).
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T. Fuji and T. Suzuki, “Generation of sub-two-cycle mid-infrared pulses by four-wave mixing through filamentation in air,” Opt. Lett. 32(22), 3330–3332 (2007).
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D. Kartashov, S. Ališauskas, A. Pugžlys, A. Voronin, A. Zheltikov, M. Petrarca, P. Béjot, J. Kasparian, J.-P. Wolf, and Andrius Baltuška, “White light generation over three octaves by femtosecond filament at 3.9 $\mu$μm in argon,” Opt. Lett. 37(16), 3456–3458 (2012).
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M. Bradler and E. Riedle, “Sub-20 fs $\mu$μJ-energy pulses tunable down to the near-UV from a 1 MHz Yb-fiber laser system,” Opt. Lett. 39(9), 2588–2591 (2014).
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C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23(10), 792–794 (1998).
[Crossref]

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[Crossref]

A. M. Heidt, D.-M. Spangenberg, M. Brügmann, E. G. Rohwer, and T. Feurer, “Improved retrieval of complex supercontinuum pulses from XFROG traces using a ptychographic algorithm,” Opt. Lett. 41(21), 4903–4906 (2016).
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D. Spangenberg, P. Neethling, E. Rohwer, M. H. Brügmann, and T. Feurer, “Time-domain ptychography,” Phys. Rev. A 91(2), 021803 (2015).
[Crossref]

Phys. Rev. B (1)

H. Němec, L. Fekete, F. Kadlec, P. Kužel, M. Martin, J. Mangeney, J. Delagnes, and P. Mounaix, “Ultrafast carrier dynamics in Br+-bombarded InP studied by time-resolved terahertz spectroscopy,” Phys. Rev. B 78(23), 235206 (2008).
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M. Seidel, X. Xiao, S. A. Hussain, G. Arisholm, A. Hartung, K. T. Zawilski, P. G. Schunemann, F. Habel, M. Trubetskov, V. Pervak, O. Pronin, and F. Krausz, “Multi-watt, multi-octave, mid-infrared femtosecond source,” Sci. Adv. 4(4), eaaq1526 (2018).
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Figures (16)

Fig. 1.
Fig. 1. Principle of the frequency resolved optical switching – The solid sample is photoexcited by a pump pulse $I_S(t)$ at variable pump-probe delays. Here, two different delays ($\tau _1$ and $\tau _2$) are illustrated. This acts as a transmission filter $S(t)$ for a probe pulse $P(t)$ (chirped in this the example) that changes its transmitted waveform and whose spectrum is measured.
Fig. 2.
Fig. 2. Experimental setup – (a) – To characterize short pulses at 0.77 $\mu$m, the pump pulses at 0.4 $\mu$m are obtained by frequency doubling 0.8 $\mu$m-pulses in a BBO crystal followed by two dichroic mirrors to filter the remaining 0.8 $\mu$m. – (b) – To generate mid-IR pulses by difference frequency generation (DFG) between the signal and the idler at the output of an optical parametric amplifier (OPA), a nonlinear crystal is inserted together with a long pass filter that transmits only the DFG output (4 or 10 microns). – Different dispersive media are used to validate the technique (see Fig. 5).
Fig. 3.
Fig. 3. Frequency resolved optical switching characterization of near-IR pulses – For pulses whose wavelengths are centered at (a) 0.77, (b) 1.53, and (c) 1.75 $\mu$m. Left panels, experimental spectrograms in intensity. Middle panels, reconstructed spectrograms with the reconstruction error as defined in the appendix, see Eq. (6). Right panels, in red, retrieved probe pulses $P(t)$ in intensity (solid line) and phase (dash line), in blue, retrieved switch profiles $S(t)$ in intensity, and in black, retrieved pulse profiles (intensity and phase) with SHG FROG measurements.
Fig. 4.
Fig. 4. Frequency resolved optical switching characterization of mid-IR pulses – For pulses whose wavelengths are centered at (a) 4, and (b) 10 $\mu$m. – Left panels, experimental spectrograms in intensity. – Middle panels, reconstructed spectrograms with the error factor as defined in the appendix. Right panels, in red, retrieved probe pulses $P(t)$ in intensity (solid line) and phase (dash line), and in blue, retrieved switch profiles $S(t)$ in intensity.
Fig. 5.
Fig. 5. Characterization of the dispersion of different materials – For pulses centered at 0.77 $\mu$m, panel (a), 1.53 and 1.75 $\mu$m (signal plus idler), (b), 4 $\mu$m, (c), and 10 $\mu$m, (d), the spectrum is shown at the bottom in red. – Dispersion of different materials, see legend, measured with frequency resolved optical switching, solid lines, and compared with the Sellmeier equations, dash lines. – The photoexcited material and the pump wavelength used to create the optical switch are mentioned at the top of the panels.
Fig. 6.
Fig. 6. Frequency resolved optical switching measurements of identical 0.77 $\mu$m-pulses with different pump pulse durations. – Switch parameters: ZnSe sample pumped with 0.4 $\mu$m pulses with 55fs (panels (a) and (b) and red lines on panels (e) and (f)) and 101fs duration (panels (c) and (d) and blue lines on panels (e) and (f)). – (a) to (d) – Measured and reconstructed spectrograms on the first and second columns. – (e)/(f) – Retrieved profiles, in intensity (solid lines) and phase (dashed lines), of 0.77 $\mu$m probe pulses $P(t)$, panel (e), and of the switches $S(t)$, panel (f).
Fig. 7.
Fig. 7. Frequency resolved optical switching characterization of 1.75 $\mu$m pulses using different pump energies. – (a) to (e) – Measured and reconstructed traces for 0.8 $\mu$m pump pulses with respective energy of 10, 25, 45, 65, and 100$\%$ of 600 $\mu$J, photoexciting a Si sample. – (f)/(g) – Retrieved profiles of the probe pulse and of the optical switch. – (h) – Normalized profiles of the optical switch (minimum at zero, maximum at one).
Fig. 8.
Fig. 8. Frequency resolved optical switching measurements of identical 4 $\mu$m-pulses with different switch materials. – (a)/(c) – Measured spectrograms of the 4 $\mu$m-probe pulses obtained by pumping a sample of Ge at 0.8 $\mu$m, panel (a), of Si at 0.8 $\mu$m, panel (b), and ZnSe at 0.4 $\mu$m, panel (c). – (d)/(e) – Retrieved profiles, in intensity (solid lines) and phase (dashed lines), of probe pulses $P(t)$, panel (d), and of the switches $S(t)$, panel (e). Colors: see legend in panel (e).
Fig. 9.
Fig. 9. Frequency resolved optical switching characterization with different pulses with a single setup – (a)/(b)/(c) – Measured and reconstructed spectrograms, and retrieved pulse profiles, for pulses centered at 1.75 (blue), 4.5 (green), and 9.5 $\mu$m (red). – (d) – Retrieved profiles of the optical switch (corresponding colors of the panels (a) to (c)).
Fig. 10.
Fig. 10. Frequency resolved optical switching characterization of various pulses – Retrieved profiles of the probe pulses (top panels) and of the switch (low panels) for different independent reconstructions in blue lines, and the average one in red lines. – (a) – Few-cycle pulses centered at 077 $\mu$m, duration 8.5 fs FWHM, corresponding to the measurement of Fig. 3(a) . – (b) – 40 fs-pulses centered at 1.53 $\mu$m, corresponding to the measurement of Fig. 3(b). – (c) – 50 fs-pulses centered at 4 $\mu$m, corresponding to the measurement of Fig. 4(a). – (d) – Few-cycle pulses centered at 10 $\mu$m, duration 53fs, corresponding to the measurement of Fig. 4(b).
Fig. 11.
Fig. 11. SHG FROG characterization of pulses centered at 0.77, 1.53 and 1.75 $\mu$m – Characterization of pulses centered at 0.77 $\mu$m, first row, at 1.53 $\mu$m, second row, and at 1.75 $\mu$m, third row. – SHG FROG spectrograms measured, first column, and reconstructed, second column. Retrieved pulse temporal profiles in intensity and phase, last column.
Fig. 12.
Fig. 12. SHG FROG characterization of the pump pulse centered at 0.8 $\mu$m – Measured and reconstructed SHG FROG spectrograms on panels (a) and (b) – Retrieved profile of the pump pulse intensity (solid line) and phase (dash line).
Fig. 13.
Fig. 13. TG FROG characterization of the pump pulses centered at 0.4$\mu$m – On the second row, the pulse of the first row is chirped by a 10 mm-thick fused silica window. – TG FROG spectrograms measured, first column, and reconstructed, second column. – Reconstructed pulses in intensity and phase, last column.
Fig. 14.
Fig. 14. Frequency resolved optical switching characterization of identical 4 $\mu$m-pulses with different solid samples – For a sample of Ge, column (a), Si, (b), and ZnSe, (c) : first and second rows, measured and reconstructed spectrograms; third and last rows, retrieved pulse and switch temporal profiles in intensity and phase.
Fig. 15.
Fig. 15. Transmission of the photoexcited Si sample up to 80ps pump-probe delay. – Transmission of the Si sample pumped at 0.8 $\mu$m, probed at 4 $\mu$m.
Fig. 16.
Fig. 16. Reconstruction error, defined by Eq. (11), as a function of the iteration step for ten independent reconstructions, see Fig. 10(d), of the spectrogram illustrated in the first panel of Fig. 4(b).

Equations (12)

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I ( k , r 0 ) = | r P ( r ) O ( r r 0 ) e i k r r | 2 .
I ( ω , τ ) = | t P ( t ) S ( t τ ) e i ω t t | 2 .
I ( ω , t 0 ) = | F [ Q ( t , t 0 ) ] | 2   ,
Π X P [ Q ( t , t 0 ) ] = F 1 [ F [ Q ( t , t 0 ) ] | F [ Q ( t , t 0 ) ] | I X P ( ω , t 0 ) ] .
Π p r o d [ Q ( t , t 0 ) ] = P g ( t ) S g ( t t 0 )   ,
ϵ = t , t 0 | Q ( t , t 0 ) P g ( t ) S g ( t t 0 ) | 2 .
P g ( t ) = Q ( t , t 0 ) S g ( t t 0 ) d t 0 | S g ( t 0 ) | 2 d t 0   ,
S g ( t ) = Q ( t + t 0 , t 0 ) P g ( t + t 0 ) d t 0 | P g ( t + t 0 ) | 2 d t 0   .
Q ( n + 1 ) E R = Π X P [ Π p r o d [ Q ( n ) ] ]   ,
Q ( n + 1 ) H I O = Q ( n ) + Π X P [ 2 Π p r o d [ Q ( n ) ] Q ( n ) ] Π p r o d [ Q ( n ) ]   .
E r r = 1 | F [ Q ( t , t 0 ) ] I X P ( ω , t 0 ) d ω d t 0 | 2 | F [ Q ( t , t 0 ) ] | 2 d ω d t 0 | I X P ( ω , t 0 ) | 2 d ω d t 0   .
Q ( 0 ) ( t , t 0 ) = P r a n d ( t ) S r a n d ( t t 0 )   .

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