1780 OPTICS LETTERS / Vol. 24, No. 23 / December 1, 1999

Second-harmonic generation–frequency-resolvedoptical gating analysis of

low-intensity shaped femtosecond pulses at 1.55 mm

F. G. Omenetto, J. W. Nicholson,* and A. J. Taylor

Materials Science and Technology Division, MSK764, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

Received July 28, 1999

We illustrate observation and characterization of medium- and low-intensity shaped ultrashort pulses atl � 1.55 mm through single-shot geometry (multishot-average) second-harmonic generation–frequency-resolvedoptical gating. The pulses are shaped by amplitude filters in the Fourier plane of a compact foldedshaper. Sensitivity to pulses with energies of less than 20 pJ and high dynamic range is reported for thisconfiguration. Application of this method to the propagation of �170-fs pulses through a 50-m fiber link isalso illustrated. 1999 Optical Society of America

OCIS codes: 320.0320, 320.2250, 320.5540, 320.7100.

The field of ultrafast pulse shaping has matured con-siderably over the past few years. Arbitrary synthe-sis of pulse shapes has been performed through avariety of techniques, the majority of which rely on fil-tering the spectrally dispersed Fourier components ofthe pulse.1 This technique allows femtosecond-scaletailoring of the temporal envelope, permitting new ex-perimental approaches in which one can employ shapedpulses to provide selective excitation patterns, whichare important in many experiments.2,3 An excitingcomplement to this technique lies in the use of feedbackfrom the experiment, in which dynamic pulse shapingis dictated by the application.4 – 7 Accurate characteri-zation of the amplitude and phase of the pulse is crucialwhen one is tailoring the pulse shape on the femtosec-ond scale. A variety of techniques that recover the in-tensity and phase of the pulse have been developed inrecent years8,9 as a result of the progressively decreas-ing duration of pulses.10,11

Frequency-resolved optical gating (FROG) hasproved itself as a versatile and reliable method forultrashort-pulse analysis by virtue of its accuracyin determining phase variations and the temporalprofile of the pulse under examination. Numerousexamples are available in recent literature addressingthe performance and sensitivity of this technique.9

In this Letter we explore the possibility of employinga single-shot second-harmonic generation–frequency-resolved optical gating geometry to characterizemedium- and low-intensity shaped femtosecond pulsesat a wavelength of 1.55 mm. The single-shot geometryprovides a simple, effective diagnostic for ultrafastshaping at this wavelength. One can use the featuresdetected both by observation of the trace and byreconstruction of the phase and amplitude profiles tooptimize the pulses for phase-sensitive experiments.Accurate diagnostics at this specific wavelength,furthermore, are of particular interest for addressingpropagation issues in fibers, specifically, for defeatingfiber dispersion effects by suitable shaping of the inputpulse (i.e., prechirping).12 The pulses that are sent

0146-9592/99/231780-03$15.00/0

to the shaper have a duration t of �170 fs and aregenerated by an optical parametric oscillator (Spectra-Physics Opal) tuned to a wavelength of 1.55 mm. Thissystem furnishes pulses of energies of 3.5 nJ at a80-MHz repetition rate, with excellent pulse-to-pulsestability. The pulse-shaping arrangement consistsof an all-ref lective folded zero-dispersion stretcher.Amplitude filtering is performed by insertion of aspectrally selective element at the Fourier plane,which in our case is situated at the plane of the f latretroref lecting mirror. The folded geometry of theshaper allows for simpler alignment, at the expenseof a decreased contrast ratio (spectral selectivity) thatis due to the filter’s not being precisely located at theFourier plane. (This disadvantage will be especiallytrue when one is inserting a bulkier filtering devicesuch as a spatial light modulator: The transition ofthe spatial light modulator might require that oneadapt the geometry to keep the liquid crystals withinthe Rayleigh range centered at the focal spot on theretroref lector.)

Alternatively, this configuration is suited for othershaping devices such as piezoelectric actuated mir-rors.13,14 The resulting shaped pulses are then sentto a single-shot second-harmonic generation–FROGarrangement in which, after the pulses are split,they traverse separate paths and then are cylin-drically focused and overlapped in a 0.5-mm-thickb-barium borate crystal. The crossing angle betweenthe two beams is �12.5±, and their cylindrical focalspot size is 1 cm. The energy of the pulses enteringthe FROG apparatus is 1 nJ. Pump-depletion effectsin the crystal do not present a problem at these energylevels. Trace distortion was visible in similar mea-surements performed with an optical parametricamplif ier �Epulse � 50 mJ�, which incurred high re-construction errors when the pulse was not attenu-ated. The FROG traces are observed on a 16-bitair-cooled CCD camera (Spectrasource), and, once ac-quired, are recovered both by means of a single, novelreconstruction algorithm based on genetic algorithms15

1999 Optical Society of America

December 1, 1999 / Vol. 24, No. 23 / OPTICS LETTERS 1781

and by conventional methods.9 We take special careduring the acquisition of the experimental FROGtraces by also acquiring background traces at thesame exposure times of the corresponding FROG traceto obtain the highest dynamic range possible by sub-sequent background subtraction. The performanceof the experiment is assessed by verif ication that(a) phase information is detected satisfactorily,(b) the technique has sufficient sensitivity to work atlow energy levels, and (c) a sufficiently broad temporalrange can be covered.

We perform a series of measurements, varying theshape of the femtosecond pulses furnished by the op-tical parametric oscillator. By placing the notch fil-ter at the center of the spectrum, we approximate asclosely as this filtering permits a square spectral pro-file. This particular filtering condition is an excellentexample, since the temporal structure that is due toa square spectrum should give a sinc function for thee f ield in time, i.e., E�t� � sin�pDft���pDft�, whereDf is the frequency width of the filter. The pulseenergy entering the FROG apparatus, after this fil-tering is performed, is equal to 0.8 nJ. The signal-to-background ratio of the FROG trace covers 4 orders ofmagnitude. The FROG trace, the recovered pulse in-tensity and phase, and its filtered spectrum are shownin Fig. 1. It can be seen that the temporal profile ofthe reconstructed e-f ield intensity follows the expectedsinc function for the e f ield, with its characteristic side-lobes. Complete adherence to a sinc functional shapecannot be expected, given the rounded square shape ofthe spectrum. Fitting the recovered intensity data tothe function sin2�pDft���pDft�2, we obtain a FWHMvalue of Dl � 14 nm for the best fit �x2 � 2 3 1024�,in good agreement with the FWHM value observedfor the reconstructed spectrum. We can infer periodictemporal structures by carefully observing the pulse inthe time domain and matching it to the reconstructedphase. These structures become more apparent whenwe plot the pulses on a logarithmic scale, as shown inFig. 1(d). The recovered phase follows the functionalbehavior, showing the same periodicity and displaying�p phase jumps corresponding to the zero crossings ofthe temporal profile.

To address more-intricate pulse-structure analysiswe shape the pulse by placing three closely spaced1-mm-wide slits at the Fourier plane. The FROGtrace, the spectrum of the filtered pulse, and recon-struction results from the resultant 0.3-nJ pulse areshown in Fig. 2. The resulting pulse exhibits sizabletemporal broadening, with features that extend to thelimit of 1 ps, along with a significant temporal struc-ture, as can be expected from the nature of the filter-ing being performed (independently verified by Fouriertransformation of the detected spectrum). The signal-to-noise ratio of the FROG trace (before backgroundsubtraction), even in these circumstances, covers morethan 3 orders of magnitude, and the pulse is success-fully recovered (FROG error G , 0.003, 256 3 256grid). Note that this seems to be approaching the up-per limit of successful temporal recovery for this ar-rangement. As temporal values increase (the longestsuccessfully reconstructed FROG trace was t � 1.3 ps),

reconstruction becomes more problematic, mainly ow-ing to a concomitance of effects (geometrical consid-erations such as the need for a larger crossing angle,lower efficiency, and angular acceptance of the crys-tal). Verification of the energy sensitivity of this ar-rangement was performed by measurement of FROGtraces of an unshaped pulse, attenuated by means ofneutral-density filters. Successful reconstruction of a12.5 6 2 pJ pulse (G � 0.0021, 256 3 256 grid) was ob-tained, as shown in Fig. 3, revealing a pulse length of220 fs, owing to temporal broadening in the neutral-density filters. In this case the exposure time waslonger (70 s, as opposed to 50 ms for the 3.5-nJ case).The reconstruction time for both cases was quite short

Fig. 1. (a) FROG trace, (b) spectrum, and (c) recon-structed pulse for filtering performed in the central portionof the spectrum �G � 0.0023�. The pulse duration FWHM(i.e., in the central peak of the sinc) is 203 fs FWHM. Therecovered phase follows the functional behavior, showingthe same periodicity. This result is evidenced in (d) thelogarithmic plot of the temporal profile.

Fig. 2. (a) FROG trace, (b) recovered intensity and phase,and (c) spectrum for a filtering arrangement with three1-mm-wide slits. The three transmitted spectral featuresare more apparent on a logarithmic scale, as shown inthe inset of (c). The energy of the pulse entering thesingle-shot apparatus is 0.3 nJ, and the FROG error afterreconstruction is G � 0.0032.

1782 OPTICS LETTERS / Vol. 24, No. 23 / December 1, 1999

Fig. 3. (a) FROG trace and (b) reconstruction for anattenuated unshaped pulse. The pulse energy is 12.5 62 pJ, and the reconstructed pulse duration is t � 220 fs.

Fig. 4. FROG traces and reconstructed temporal andphase profiles detected at the output of a 50-m linkof single-mode fiber. The traces in (a) illustrate thepropagation of an unshaped pulse with energy E � 120 pJ,and those in (b) illustrate the propagation of a pulse withE � 500 pJ.

(60–90 s on a 256 3 256 grid AMD K6-II 333-MHzprocessor).

Application of this method is illustrated by propaga-tion of pulses through an optical fiber. In this casethe output pulses from the OPO are coupled in a 50-mlink of conventional Corning SMF-28 single-mode fiber,and the output pulse is analyzed. For low energy val-ues at the input �Ein � 120 pJ� the pulse broadens to1 ps, as shown in Fig. 4(a). The linear contribution isdominant in this case, as evidenced by the parabolicphase profile superimposed on the recovered temporalintensity. In this case the exposure was 70 s, and thetrace was reconstructed to an error G , 0.002 in lessthan 90 s (256 3 256 grid). For higher-intensity inputpulses coupled in the fiber �Ein � 500 pJ�, nonlineareffects counteract the linear dispersion contribution,and soliton formation can be observed, as illustratedin Fig. 4(b), in which the phase is noticeably f lat acrossthe pulse at the output from the fiber and the pulsewidth is comparable with that of the input pulse.

The use of the 16-bit camera allows us to observe allthese pulses in real time by changing the settings ofthe camera. We can observe a pulse that requires 70-s

exposure time with an exposure of 500 ms by looking atthe lower range of the 16 bits. This result is obviouslyunsatisfactory for reconstruction purposes, where thedynamic range of the acquired FROG trace takesprecedence, but is very useful for in situ optimization.

In summary, we have demonstrated that single-shotSHG-FROG can be a valuable tool for the analysisof the temporal and phase profiles of shaped pulsesat a wavelength of 1.55 mm. The single-shot geome-try provides simplicity and an immediate visual rep-resentation of the pulse. This setup measures pulsewidths over a wide range of energies, down to a limitof 12.5 6 2 pJ, and temporal reconstruction has beenverified successfully for pulses of duration in excess of1 ps. These results provide the basis for a tool to ob-serve the phase and temporal structure of ultrashortpulses for phase-control experiments. The adoptionof this technique at this specific wavelength, further-more, has been shown to permit the investigation of thephase evolution of ultrashort pulses in optical fibers,which can lead to a better understanding of the dynam-ics of nonlinear effects and of the fundamental limitsfor higher-capacity fiber-optic communication links.

F. G. Omenetto’s e-mail address is omenetto@lanl.gov.

*Present address, Department of Physics and As-tronomy, University of New Mexico, 800 Yale BoulevardNE, Albuquerque, New Mexico 87131.

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