270 OPTICS LETTERS / Vol. 27, No. 4 / February 15, 2002

Two-photon spectroscopy and analysis with a white-lightcontinuum probe

Raluca A. Negres, Joel M. Hales, Andrey Kobyakov, David J. Hagan, and Eric W. Van Stryland

School of Optics/Center for Research and Education in Optics and Lasers, University of Central Florida,4000 Central Florida Boulevard, P.O. Box 162700, Orlando, Florida 32816-2700

Received August 27, 2001

We present a powerful experimental tool and analysis for characterization of two-photon absorption (2PA) spec-tra. We demonstrate this method with ZnS and then apply it to organic dyes in solution. We also comparethe results with those from other methods such as two-photon f luorescence spectroscopy. This femtosecondpump–probe method uses a white-light continuum (WLC) as the probe to produce a nondegenerate 2PA spec-trum. The extreme chirp of the WLC requires that transmittance data be collected over a range of temporaldelays between pump and probe pulses. These data then need to be corrected for the effects of this chirp aswell as for the temporal walk-off of the pulses in the sample that result from the frequency nondegeneratenature of the experiment. We present a simple analytic solution for the transmitted f luence through thesample, which is applicable for most practical cases. © 2002 Optical Society of America

OCIS codes: 320.7150, 190.4710.

The quest for materials that exhibit high nonlinearoptical (NLO) absorptivities has increased dramati-cally over the past several years. Two-photon ab-sorption (2PA) is an object of interest in chemistry,photonics, and biological imaging. Several currentand emerging technologies, including optical powerlimiting, two-photon f luorescence imaging, two-photon photodynamic cancer therapy, and two-photonmicrofabrication, exploit 2PA.1

With the advent of tunable, short-pulse lasersources, many experiments that are of use in NLOmaterials characterization have become possible.One method of interest is femtosecond pump–probespectroscopy, in which a broadband, weak, white-lightcontinuum2 (WLC) pulse is used to probe a mediumthat has just been subjected to an intense pump pulse.This pump–probe technique yields a frequency non-degenerate NLO absorption spectrum. It could, inprinciple, be a single-shot technique because thelarge spectral extent of the probe beam allows for fullcharacterization of the sample. In practice, becauseof WLC chirp, the temporal delay between pulses mustbe scanned. An alternative method for obtainingthe spectral dependence of the nonlinearity involvesthe often more time-consuming process of tuningand calibration of the probe and (or) pump pulses atvarious different wavelengths, e.g., in pump–probeexperiments or in degenerate Z scans.3 Furthermore,one can, under certain conditions, use the nondegen-erate NLO spectrum to infer the spectral dependenceof the nonlinear refraction through Kramers–Kronigrelations.4

The WLC probe is chirped because of positivegroup-velocity dispersion (GVD) of optical elementsincluding the WLC generating element, and there-fore the transient spectra suffer from a wavelength-dependent time-delay distortion. To extract the truedynamics, we must vary the relative pump–probe timedelay and rescale the data as discussed below. Thisis important, especially in the case of short-time-scaleprocesses, such as 2PA, in which the nonlinear in-teraction takes place only during the time overlap of

0146-9592/02/040270-03$15.00/0

the probe and pump pulses. The information con-tained in the time-delay measurements is also usefulfor determining the origin of the nonlinearity, e.g.,differentiating between 2PA and long-lived processessuch as excited-state absorption.

The nondegenerate character of the experiment alsoleads to a temporal walk-off between the pump andthe probe within the sample that reduces the effec-tive interaction length. This walk-off is due to thegroup-velocity mismatch in the sample and causes a re-duction in the nonlinear signal as the frequency differ-ence between pump and probe increases. Spencer andShore5 give a theoretical treatment of the pump–probeinteraction in a lossy Kerr medium to describe thecross-phase modulation and chirp imposed on the probeowing to excitation. Ziólek et al.6 show how the realtemporal response function of a pump–probe appara-tus can be determined if the linear properties of thesample (dispersion of the refractive index) are known.Here we present a general model, including linear andnonlinear effects, of the pump–probe interaction inKerr media for a 2PA process. Whereas the group-velocity mismatch between pump and probe can sig-nificantly reduce the nonlinear signal strength, GVDcan have a negligible effect on the probe pulse propaga-tion. An analytic solution of this propagation in Kerrmedia for the normalized f luence transmittance of theprobe can be found in this limit of negligible GVD forthe probe. How this can be true for the WLC is de-scribed in more detail below. This limit is valid formost practical cases, e.g., a sample thickness L of afew millimeters, and for probe pulses near 100 fs. Thenormalized f luence transmittance, T , is then given by

T s, td,W , r,G exp22sW

pp

Z `

2`

expΩ2

µt 1 td 2 r

W

∂2

2Gp

p

rerft 2 erft 2 r

ædt ,

(1)

© 2002 Optical Society of America

February 15, 2002 / Vol. 27, No. 4 / OPTICS LETTERS 271

where s aL (a is the linear absorption coeff icient),

r L

wpc

µn 2 np 1 lp

dndl

Çlp

2ldndl

Çl

∂

is the temporal walk-off parameter (wp is the pumppulse width, n is the sample refractive index atwavelength l, and c is the speed of light), andG LnnpIp0b describes the nonlinearity.7 Heretd is the ratio between the relative time delay and thepump’s temporal width HW1eM, W is the ratio ofprobe and pump temporal widths, Ip0 is the pump’speak irradiance (in watts per square meter), and b

is the nondegenerate 2PA coeff icient (in meters perwatt). All subscripts p refer to the pump. We usethis analytic solution to f it the experimental data at10-nm increments over the bandwidth of the probe.As stated, Eq. (1) is valid over spectral ranges at whichthe GVD is negligible; although this is certainly nottrue for the entire continuum, it is true for portions ofthe WLC. We verified this through calculations andobservations of the WLC chirp by making the opticalKerr effect (OKE) measurements, as described below.Our spectrometer resolution is limited to 4 nm, buta bandwidth-limited pulse of 100 fs has a bandwidthof 5 nm (in the visible range), thus limiting ourresolution. The analysis treats the continuum asmade up of a group of bandwidth-limited pulses.This works well, but analyzing the pulses as spectrallybroader also works up to the point where the GVDbecomes important. In our case our analysis is validfor bandwidths of as much as 15 nm FWHM.

To characterize the WLC we performed an OKEexperiment on a thin piece of fused silica, L 50 mm.It is convenient to use OKE in transient spectroscopybecause the experimental setups involved are thesame except for simple rotations of the pump polar-ization and probe analyzer.8 This experiment mapsthe frequency content of the continuum in the timedomain. One more advantage of the method is that,as with white-light interferometry, one can measurethe GVD of an unknown sample inserted into theWLC’s path. From OKE measurements, with andwithout the sample in the probe path, the differencein arrival time for a fixed frequency component of thecontinuum gives the group index of the material. Itis necessary to know this value for materials whosedispersion is not yet in any database. Looking at aplot of an OKE signal as a function of wavelengthand time shows that for any fixed l the pulse widthis equal to the width of the pulse used for continuumgeneration, i.e., 100 fs.8 The fact that the pumpalso interacts simultaneously with other spectralcomponents does not inf luence the interaction withthe narrow frequency band.

We measured the spectral energy of the probe tobe 1 nJnm, with a chirp of 3.5 fsnm. For a 5-nmbandwidth this makes the probe 40 times less intensethan the pump, given that the probe is more tightly fo-cused than the pump. This input is too low to lead tononlinearities by itself, even when nondegenerate 2PA

from other portions of the probe is included; i.e., the2PA induced by the pump on the probe dominates.

The samples that we used to demonstrate thismethod were ZnS L 0.84 nm and an alkyl-f luorenederivative L 1 mm whose molecular structure andsynthesis are given in Ref. 9. The ultrafast nonlinearspectroscopy measurements were made with two inde-pendently tunable optical parametric sources pumpedby a regeneratively amplif ied 120-fs (FWHM) sourceat 775 nm. The transmittance of the WLC probe(obtained by focusing of 1 2-mJ, 100-fs pulses at1400 nm into a 1.5-mm-thick fused-silica window) wasmonitored after the pulses passed through a 0.15-mspectrometer. A TE-cooled silicon dual-diode arraywas used for detection. The excitation was set at awavelength less than half the bandgap of the samplebeing studied to avoid degenerate 2PA of the pump.

We obtained the transient absorption spectrum of a2PA sample by varying the pump–probe delay time in20-fs increments and monitoring the reduced trans-mittance for those wavelength for which the probe andthe pump overlapped in time. As in the analysis per-formed on OKE traces, we built the cross-correlationsignals, i.e., nonlinear absorption signals at fixed probewavelengths versus time delay. The amplitudes andwidths of these curves depend not only on the strengthof the nonlinearity but also on the relative speed ofthe pulses in the sample. For pulses of significantlydifferent wavelengths, the GVM led to a relatively fastdifferential speed between pump and probe, resultingin a shortened effective interaction length withinthe sample; i.e., pulses walk through one another.This walk-off translates to a reduced nonlinear sig-nal strength, which must be accounted for by useof Eq. (1).

To illustrate the f itting procedure, in Fig. 1 we showthe cross-correlation signals obtained in ZnS Eg 3.54 eV at probe wavelengths of 480, 532, and 580 nmwith lp 750 nm. The energy for the pump was5 mJ, and the beam width was 500 mm HW1e2M.Experimental data were f itted to Eq. (1), yielding b.

Fig. 1. Normalized probe f luence transmittance T at l 480, 532, 580 nm in ZnS. Solid curves, fits of experimen-tal data (dashed curves) with Eq. (1); the correspondingmaterial and nonlinearity parameters are given in the text.Curves are vertically offset for ease of viewing.

272 OPTICS LETTERS / Vol. 27, No. 4 / February 15, 2002

Fig. 2. Nondegenerate 2PA coeff icient, b, of ZnS versusprobe wavelength: (a) WLC spectral measurement,pump–probe walk-off not included; (b) WLC spectralmeasurement with walk-off correction; (c) theoreticalmodel for ZnS, Eg 3.54 eV. Experimental parametersare L 0.84 mm, wp 72 fs HW1eM, W 0.85,lp 0.75 mm.

Fig. 3. Nondegenerate cross section d (open squares) anddegenerate 2PA cross sections from 2PF (f illed circles) ver-sus photon energy (pump 1 pump, solid curve) verticallyscaled linear absorption spectrum.

The walk-off parameter was calculated from Sell-meier’s equation. The material r and nonlinearityG parameters that correspond to the wavelengthsin Fig. 1 were 16.4 and 4.5 at 480 nm, 9.9 and 1.9 at532 nm, and 6.2 and 0.6 at 580 nm. We note thattemporal walk-off can also be a fitting parameter forunknown samples, where the starting values in theprocess are those obtained in the OKE experiment.The results for b (centimeters per gigawatt) in ZnS,along with the theoretical prediction of Ref. 10, areshown in Fig. 2, illustrating the large correctionrequired for accounting for GVM at wavelengths farfrom that of the pump.

An alternative to the pump–probe method pre-sented in this Letter, which works well for f luorescing

samples, is two-photon f luorescence spectroscopy.The results are calibrated against a well-known refer-ence standard, e.g., f luorescein.11 Figure 3 shows theresults of our nondegenerate measurement for whichwe used the WLC probe lp 1.2 mm along with thedegenerate 2PA spectrum obtained as described abovefor our organic dye solution. The linear absorptionspectrum of our sample is shown for reference. Agree-ment of the two methods with the linear spectrum isexpected for an asymmetric molecular structure witha large dipole moment.12

The WLC pump–probe method of materialscharacterization presented here is particularly ad-vantageous for rapidly building a database of spectraof organic dyes applicable in the investigation ofstructure–property relations. The nondegeneratenonlinear absorption spectrum is also of use inpredicting the dispersion of the ultrafast nonlinearrefraction.4

We thank Kevin Belf ield and Katherine Schaferfor synthesizing the organic samples. We gratefullyacknowledge the support of the Joint Services AgileProgram (contract N00421-98-C-1327) and of theNational Science Foundation (grant ECS 9970078).J. M. Hales’s e-mail address is hales@creol.ucf.edu.

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