Non-iterative characterization offew-cycle laser pulses using flat-top gates

Romedi Selm,1 Gunther Krauss,2 Alfred Leitenstorfer,2

and Andreas Zumbusch1,*

1 Department of Chemisty, University of Konstanz, D-78457 Konstanz, Germany2 Department of Phyics, University of Konstanz, D-78457 Konstanz, Germany

*andreas.zumbusch@uni-konstanz.de

Abstract: We demonstrate a method for broadband laser pulse character-ization based on a spectrally resolved cross-correlation with a narrowbandflat-top gate pulse. Excellent phase-matching by collinear excitation in amicroscope focus is exploited by degenerate four-wave mixing in a micro-scope slide. Direct group delay extraction of an octave spanning spectrumwhich is generated in a highly nonlinear fiber allows for spectral phaseretrieval. The validity of the technique is supported by the comparisonwith an independent second-harmonic fringe-resolved autocorrelationmeasurement for an 11 fs laser pulse.

© 2012 Optical Society of America

OCIS codes: (320.7100) Ultrafast measurements; (190.0190) Nonlinear optics; (180.4315)Nonlinear microscopy.

References and links1. J. A. Armstrong, “Measurement of picosecond laser pulse width,” Appl. Phys. Lett. 10, 16–18 (1967).2. J. C. Diels, J. J. Fontaine, I. C. McMichael, and F. Simoni, “Control and measurement of ultrashort pulse shapes

(in amplitude and phase) with femtosecond accuracy,”, Appl. Opt. 24, 1270–1282 (1985).3. E. B. Treacy, “Measurement and interpretation of dynamic spectrograms of picosecond light pulses,” J. Appl.

Phys. 42, 3848–3858 (1971).4. J. L. A. Chilla and O. E. Martinez,“Direct determination of the amplitude and the phase of femtosecond light

pulses,” Opt. Lett. 16, 39–41 (1991).5. D. J. Kane and R. Trebino,“Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse

by using frequency-resolved optical gating,” Opt. Lett. 18, 823–825 (1993).6. I. Amat-Roldn, I. G. Cormack, P. Loza-Alvarez, and D. Artigas, “Measurement of electric field by interferometric

spectral trace observation,” Opt. Lett. 30,, 1063–1065, (2005).7. C. X. Yu, M. Margalit, E. P. Ippen, and H. A. Haus,“Direct measurement of self-phase shift due to fiber nonlin-

earity” Opt. Lett. 23, 679–681, (1998).8. R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer, 2000).9. S. Linden, H. Giessen, and J. Kuhl, “XFROG - a new method for amplitude and phase characterization of weak

ultrashort pulses” Phys. Status Solidi B 206, 119–124 (1998).10. X. Gu, L. Xu, M. Kimmel, E. Zeek, P. OShea, A. P. Shreenath, and R. Trebino, “Frequency-resolved optical

gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum,” Opt. Lett.27, 1174–1176 (2002).

11. P. Xi, Y. Andegeko, D. Pestov, V. V. Lovozoy, and M. Dantus, “Chemical imaging by single pulse interferometriccoherent anti-stokes Raman scattering microscopy,” J. Biomed. Opt. 14, 014002 (2009).

12. S. H. Lim, A. G. Caster, O. Nicolet, and S. R. Leone, “Chemical imaging by single pulse interferometric coherentanti-stokes Raman scattering microscopy,” J. Phys. Chem. B, 110, 5196–5204, (2009).

13. R. Selm, M. Winterhalder, A. Zumbusch, G. Krauss, T. Hanke, A. Sell, and A. Leitenstorfer, “Ultrabroadbandbackground-free coherent anti-Stokes Raman scattering microscopy based on a compact Er:fiber laser system,”Opt. Lett. 35, 3282–3284 (2010).

14. W. Min, S. Lu, M. Rueckel, G. R. Holtom, and X. S. Xie, “Near-degenerate four-wave-mixing microscopy,”Nano Lett. 9, 2423–2426, (2009).

#160477 - $15.00 USD Received 22 Dec 2011; revised 3 Feb 2012; accepted 10 Feb 2012; published 27 Feb 2012(C) 2012 OSA 12 March 2012 / Vol. 20, No. 6 / OPTICS EXPRESS 5955

15. A. Sell, G. Krauss, R. Scheu, R. Huber, Rupert, and A. Leitenstorfer, “8-fs pulses from a compact Er:fiber system:quantitative modeling and experimental implementation.” Opt. Express 17, 1070–1077 (2009).

16. F. Adler, A. Sell, F. Sotier, R. Huber, and A. Leiternstorfer, “Attosecond relative timing jitter and 13 fs tunablepulses from a two-branch Er:fiber laser,” Opt. Lett. 32, 3504–3506 (2007).

17. G. Imeshev, M. A. Arbore, M. M. Fejer, A. Galvanauskas, M. Fermann, and D. Harter, “Ultrashort-pulse sec-ondharmonic generation with longitudinally non-uniform quasi-phase-matching gratings: pulse compression andshaping,” J. Opt. Soc. Am. B 17, 304–318 (2000).

18. G. Krauss, S. Lohss, T. Hanke, A. Sell, S. Eggert, R. Huber, und A. Leitenstorfer, “Synthesis of a single cycle oflight with compact erbium-doped fibre technology,” Nature Photon. 4, 33–36, (2010).

1. Introduction

Pulsed lasers have become an important tool for nonlinear optical experiments and thereforemultiple characterization techniques evolved. The duration of picosecond pulses has firstbeen demonstrated by intensity autocorrelation using a nonlinear medium [1]. The retrievalof phase information is increasingly important with shorter pulse durations. Fringe-resolvedautocorrelation (FRAC) measurements which are readily applicable to a microsope setup aresensitive to the pulse phase although with ambiguities [2]. The intensity autocorrelation andFRAC techniques work in the time-domain only. Extension to the time-frequency domainwas first demonstrated by Treacy in 1971 [3, 4]. Such spectrograms are still used in e.g.frequency-resolved optical gating (FROG) where the electric field is retrieved [5, 6]. Anothermethod is spectral phase interferometry for direct electric-field reconstruction (SPIDER) [7].A multitude of different FROG derivatives are described in [8]. Cross-correlation FROG(XFROG) is demonstrated by second-order nonlinear interaction with a well characterizedreference pulse [9]. Such schemes are used to characterize complex pulses which are generatedin microstructure-fibers [10]. XFROG spectrograms are more intuitively analyzed than FROGspectrograms but require a synchronized reference pulse which is well known. This prerequisiteoften limits the applicability.

c

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c(t,) FWM(t,,)

g(t-,)

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tgd()

Fig. 1. (a) Frequency conversion diagram of the degenerate FWM process, (b) Schematicspectrograms of the continuum pulse Ic(t,ω), the gate pulse Ig(t,ω) and the FWM sig-nal IFWM(t,τ,ω), (c) Schematic spectrogram IXFROG(τ,ω) of the cross-correlation withindicated tgd(ω) curve.

The use of ultrashort laser pulses becomes increasingly important for nonlinear optical mi-croscopy (e.g. multiphoton microscopy [11] and coherent anti-Stokes Raman scattering mi-croscopy [12, 13]). The choice of method is often determined by the geometry in which anultrashort experiment is implemented. In the field of nonlinear microscopy, typically a collineargeometry is established for high resolution imaging by exploiting the full numerical apertureof the focusing objective. In this paper we present a new method which is compatible to theexcitation geometry in typical multiphoton microscopes. It is based on degenerate four-wave

#160477 - $15.00 USD Received 22 Dec 2011; revised 3 Feb 2012; accepted 10 Feb 2012; published 27 Feb 2012(C) 2012 OSA 12 March 2012 / Vol. 20, No. 6 / OPTICS EXPRESS 5956

mixing (FWM) XFROG between an unknown ultrashort laser pulse and a bandwidth-limitednarrowband gate pulse with a flat-top profile of the temporal envelope. Despite the long dura-tion of the gate pulse its shape allows for a high temporal resolution due to the steep leading andtrailing edges and a well reproducible structure of the gating pulse between measurements. Ex-cellent phase-matching is realized in a tight microscope focus by degenerate FWM [14]. Weakpulses can sensitively be characterized due to their linear contribution to the FWM signal (seeFig. 1(a)). The sensitivity can be increased by using an intense gate pulse which contributes tothe FWM signal with the square of its intensity. Enabled by the flat-top shape of the gate pulse,the spectral phase and the intensity can be extracted in a non-iterative manner from the XFROGspectrogram to reconstruct its temporal envelope.

2. Theory

For an instantaneously responding medium, the degenerate FWM field EFWM is expressed interms of the unknown continuum field Ec(t) and the time τ delayed gate field Eg(t − τ)

EFWM(t,τ) = ε0χ(3)E∗c (t) ·E2

g (t − τ) (1)

in scalar notation for parallel electric fields. Spectral detection of the cross-correlation signalFourier transforms the above formula such that the measured spectrogram IXFROG is describedby

IXFROG(τ,ω) ∝∣∣∣∣

∫ ∞

−∞E∗

c (t) ·E2g (t − τ)e−iωtdt

∣∣∣∣

2

. (2)

The FWM signal is blueshifted and therefore free of interference with the excitation light(see Fig. 1(b)). Direct access to the group delay of the short pulse is possible by analyzingthe spectrogram IXFROG(τ,ω) (indicated by the temporal distortion versus frequency in thespectrogram, see Fig. 1(c)). The expression for the group delay tgd = dφ/dω unveils the spectralphase

φ(ω) = φ(ω0)+∫ ω

ω0

tgd(ω)dω (3)

with an arbitrary frequency ω0 and the corresponding constant φ(ω0) which is irrelevant forreconstruction of the pulse envelope. The relative spectral intensities of the broadband laserpulse Ic(ω) are directly extracted from the spectrogram IXFROG due to the linear intensity con-tribution of Ic in the FWM process (see Fig. 1(c)). In the frequency domain, this procedureyields |Ec(ω)|e−iωt+φ(ω) and a Fourier transform gives access to the electric field envelope inthe time domain.

3. Experiment and analysis

Our light source is based on a two-branch Er:fiber laser at a wavelength of 1550 nm and a repe-tition rate of 40 MHz [13, 15]. In the first branch the octave spanning continuum (from 900 nmto 1800 nm) is generated in a highly nonlinear fiber whose characterization is demonstrated inthis paper. A NSF10 prism compressor is used for chirp control. The second branch deliversthe flat-top gate pulse at a wavelength of 775 nm by second-harmonic generation of the funda-mental light at a wavelength of 1550 nm (see Fig. 2(a) and 2(b)). The pulse shape is measuredby cross-correlation with the ultrashort continuum pulse using sum-frequency generation in athin LiNbO3 crystal. A narrow bandwidth of 0.6 nm allows for a good spectral resolution in thespectrogram. The pulse duration of 3 ps yields a time-bandwidth product of 0.9 which corre-sponds to a bandwidth limited flat-top pulse. The two branches have a low mutual timing jitter

#160477 - $15.00 USD Received 22 Dec 2011; revised 3 Feb 2012; accepted 10 Feb 2012; published 27 Feb 2012(C) 2012 OSA 12 March 2012 / Vol. 20, No. 6 / OPTICS EXPRESS 5957

of less than 50 as (integrated from 1 Hz to the Nyquist frequency) [16].Although the demonstrated FWM-XFROG pulse characterization method is conveniently per-formed with a multi-branch Er:fiber laser it is not restricted to this type of light source. Anultrashort laser pulse which needs to be characterized can simply be split into two branches.Flat-top pulses can easily be generated in one branch by second-harmonic generation of the ul-trashort laser pulse in a long periodically-poled lithium niobate crystal [17]. The flat-top pulsecan subsequently be used as a gate for the characterization of the unknown ultrashort laser pulsein the other branch.

774 776 7780

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= 0.6 nm

c(t)g(t-)

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2(t-)

C(c) D

T

P

O1 O2C

F

Fig. 2. (a) Spectrum of gate pulse with a bandwidth of 0.6 nm, (b) Temporal shape of gatepulse intensity envelope with a duration of 3 ps, measured by cross-correlation with theultrashort continuum pulse using sum-frequency generation in a thin LiNbO3 crystal, thetime-bandwidth product amounts to 0.9 and indicates a bandwidth-limited flat-top pulse,(c) Experimental setup: D; delay-line, C; beam combiner, T; reflective telescope, O1/O2;Focussing and collecting objective, χ(3); susceptibility of microscope slide, F; filter, P;UVFS equilateral prism, C; CCD camera.

The XFROG setup is shown in Fig. 2(c). A mechanical delay line is used for scanning thetime-delay τ between the two laser pulses. The two branches are combined by a dichroic mir-ror, expanded by a reflective telescope and coupled into a home-built microscope. The two laserbeams are collinearly focused by a near-infrared corrected water immersion objective (NA 0.8532×, Carl Zeiss AG, Jena, Germany) into a microscope slide (SuperFrost®). The FWM signalis collected in forward direction by a long working distance objective (NA 0.6, 20×, EdmundOptics, Karlsruhe, Germany) and detected by a spectrometer based on a UVFS prism and aCCD camera (iXonEM+897 back illuminated, Andor Technology plc., Belfast, Northern Ire-land). The XFROG spectrogram is recorded by spectral acquisition of the FWM signal as afunction of the time-delay of the gate pulse (see Fig. 3(a)). In order to suppress a backgroundproportional to Ec(t)E∗

c (t)Eg(t−τ) which originates from FWM of frequency component pairsin the spectral wings of the broadband continuum pulse Ec(t) and the narrowband gate pulseEg(t) two consecutive spectrograms are recorded. Therefore the long wavelength components

#160477 - $15.00 USD Received 22 Dec 2011; revised 3 Feb 2012; accepted 10 Feb 2012; published 27 Feb 2012(C) 2012 OSA 12 March 2012 / Vol. 20, No. 6 / OPTICS EXPRESS 5958

(> 1160 nm, in the Fourier plane of the prism-compressor) of the continuum are blocked torecord a background-free IFWM which corresponds to the short wavelength part of the contin-uum (< 1160 nm). For the second measurement the short wavelength components (< 1060 nm)of the broadband continuum pulse are blocked to record the FWM signal which correspondsto the long wavelength part of the continuum (> 1060 nm). In this way the interaction be-tween the wings of the continuum is inhibited. Combination of the two measurements yields thebackground-free XFROG trace (see Fig. 3). The acquired spectrogram contains the informationabout the laser pulse relative spectral intensity Ic(t) and group-delay tgd . With the narrowbandgate pulse at 776.7 nm the FWM signal reproduces the laser spectrum. Integrating along thetime-axis τ delivers the relative spectral intensity ∝

∫ ∞−∞ IXFROG(τ,ω)dτ from which the laser

spectrum Ec(ω) is determined by wavelength conversion (see Fig. 3(c)).

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Fig. 3. (a) Measured XFROG spectrogram with a CCD camera exposure time of 1 ms andtime delay steps of 2 fs, (b) Reference cross-correlation, section at 574 nm indicated byvertical line in (a) (corresponds to 1200 nm in the continuum), (c) Retrieved laser spectrumEc(ω) by averaging over time delay τ , (d) Retrieved group delay tgd with a zoomed insetwhich indicates a temporal error of 2 fs.

The group delay versus wavelength is directly observable in the contour of the spectrogram(see Fig. 3(a)). For group delay extraction a reference gate in the spectrogram at an arbitrarywavelength (here λFWM =574 nm, which corresponds to 1200 nm in the continuum) is chosen(see vertical line in Fig. 3(a)). The section is shown in Fig. 3(b) and corresponds to the squaredintensity envelope of the gate pulse (compare Fig. 2). This temporal profile is reproduced atall wavelengths throughout the spectrogram but with a temporal shift which corresponds tothe group delay of the continuum pulse. Tracking this reference shape along all wavelengthpositions of the FWM-XFROG spectrogram unveils the corresponding group delay. This result

#160477 - $15.00 USD Received 22 Dec 2011; revised 3 Feb 2012; accepted 10 Feb 2012; published 27 Feb 2012(C) 2012 OSA 12 March 2012 / Vol. 20, No. 6 / OPTICS EXPRESS 5959

is achieved by calculating the cross-correlation between the reference gate at 574 nm and thesections through the spectrogram along all wavelengths. Since the respective profiles have anoverall rectangular shape, the cross-correlations are triangular and therefore their maximumis precisely defined. The temporal position of the maximum of the cross-correlations directlyyields the group delay tgd . Due to the steep slopes at the leading and trailing edge of the gatepulse, a good temporal resolution is obtained. In the inset of Fig. 3(d) a zoomed graph is shownwhich indicates a temporal error of 2 fs. One should note that a small error in the determinationof tgd has a relatively small effect on the determination of the pulse duration. Plugging tgd in Eq.(3) leads to the spectral phase φ(ω). In this way the electric field can be completely determined,except for a constant phase offset which is not relevant for the determination of the envelope.This finding shows that the characterization of complicated laser pulses is possible with ourtechnique.

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Fig. 4. (a) Retrieved intensity and phase spectra as well as the intensity spectrum measuredby a linear spectrometer, (b) The retrieved temporal intensity envelope and phase show apulse duration of 11.2 fs.

An analysis of the short wavelength part of the continuum is demonstrated by blocking thewavelength components above 1500 nm of the supercontinuum in the Fourier plane of the prismcompressor (see Fig. 4(a)). Characterization of the compressed spectrum unveils a pulse dura-tion of τFWHM=11.2 fs (bandwidth limit: 8.4 fs) in the focus of a microscope objective as wellas the spectral phase information. Any linear phase function can be subtracted from the exper-imentally determined trace which affects the absolute time delay of the pulse envelope but notits shape. Therefore a linear phase is subtracted from the experimental phase for best visualiza-tion of the phase curvature (see Fig. 4(a)). Fourier transform yields the pulse intensity envelopeas well at the phase in the time domain (see Fig. 4(b)). The validity of the XFROG schemeis verified by comparison of a calculated second-harmonic FRAC trace based on the XFROGretrieved electric field with an independent second-harmonic FRAC measurement. Althoughthe FRAC technique shows some phase ambiguities it is never the less a frequently used pulsecharacterization technique and therefore we think suitable for our validation. A good agreementbetween the two traces is observable in Fig. 5. This result demonstrates the applicability of thetechnique for ultrashort laser pulses in the few cycle regime.

4. Conclusion

The presented method allows for direct extraction of the group delay as a function of frequencyof an octave spanning supercontinuum output of the highly nonlinear fiber enabled by the broadphase-matching bandwidth of the FWM process in the microscope focus. High temporal andspectral resolution is exploited by the flat-top shape of the gate pulse. Direct reconstruction

#160477 - $15.00 USD Received 22 Dec 2011; revised 3 Feb 2012; accepted 10 Feb 2012; published 27 Feb 2012(C) 2012 OSA 12 March 2012 / Vol. 20, No. 6 / OPTICS EXPRESS 5960

0 20 400

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Time [fs]

Inte

nsity

[arb

. uni

t]

SimulationMeasurement

Fig. 5. Line: Calculated second-harmonic fringe-resolved autocorrelation based on theXFROG retrieved spectrum and phase, dots: Measured second-harmonic fringe-resolvedautocorrelation.

of the electric field envelope is demonstrated by analyzing the XFROG spectrogram withoutrelying on iterative calculations. A broad range of shapes can be analyzed from highly chirpedpulses to short transients close to the bandwidth limit. The collinear excitation geometry is wellsuited for pulse analysis in multiphoton microscopes which are applied to biomedical imaging.The method may also find application in the characterization of single-cycle laser pulses [18].The need for a gate pulse seems to be a drawback at first sight but pulse replicas from ultrashortlaser sources which are typically present in multiphoton microscope laboratories can be usedfor its generation.

Acknowledgments

Financial support from the Baden-Wurttemberg Stiftung is gratefully acknowledged.

#160477 - $15.00 USD Received 22 Dec 2011; revised 3 Feb 2012; accepted 10 Feb 2012; published 27 Feb 2012(C) 2012 OSA 12 March 2012 / Vol. 20, No. 6 / OPTICS EXPRESS 5961