Spectroscopy of third-harmonic generation: … of third-harmonic generation: evidence for resonances...

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Spectroscopy of third-harmonic generation: evidence for resonances in model compounds and ligated hemoglobin G. Omar Clay Department of Physics, University of California at San Diego, La Jolla, California 92093 Andrew C. Millard* Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla, California 92093 Chris B. Schaffer Department of Physics, University of California at San Diego, La Jolla, California 92093 Juerg Aus-der-Au Department of Electrical and Computer Engineering, University of California at San Diego, La Jolla, California 92093 Philbert S. Tsai Department of Physics, University of California at San Diego, La Jolla, California 92093 Jeffrey A. Squier** Department of Electrical and Computer Engineering, University of California at San Diego, La Jolla, California 92093 David Kleinfeld Department of Physics, University of California at San Diego, La Jolla, California 92093 Received September 2, 2005; revised November 17, 2005; accepted November 18, 2005; posted November 29, 2005 (Doc. ID 64600) We report on third-harmonic generation (THG) of biomolecular solutions at the fluid/glass interface as a means to probe resonant contributions to their nonlinear absorption spectra that could serve as contrast mechanisms for functional imaging. Our source was 100 fs laser pulses whose center wavelength varied from 760 to 1000 nm. We find evidence of a two-photon resonance in the ratio of third-order susceptibilities, sample 3 3 / glass 3 , for aqueous solutions of Rhodamine B, Fura-2, and hemoglobin and a three-photon resonance in sample 3 3 / glass 3 for solutions of bovine serum albumin. Consistent with past work, we find evidence of a one-photon resonance of sample 3 3 / glass 3 for water, while confirming a lack of resonant enhancement for ben- zene. At physiological concentrations, hemoglobin in different ligand-binding states could be distinguished on the basis of features of its THG spectrum. © 2006 Optical Society of America OCIS codes: 190.4160, 190.4180, 190.4350, 190.4710, 300.6420, 170.3880, 120.6200. 1. INTRODUCTION The nonlinear spectroscopy of fluids has assumed new rel- evance with the advent and proliferation of nonlinear microscopies. 1 In these techniques, an ultrashort pulse of laser light is tightly focused into a material so that optical excitation is confined to a focus where the photon flux is highest. This provides intrinsic three-dimensional optical sectioning for two-photon laser scanning microscopy, 2–4 second-harmonic generation, 5 three-photon laser scan- ning microscopy, 6–9 and third-harmonic generation 10–14 (THG). Whereas contrast in two-photon and three-photon scanning microscopy is typically achieved through the use of fluorescent indicators, contrast in harmonic generation relies almost exclusively on intrinsic chromophores. A pri- ori, THG will depend directly on one-, two-, and three- photon absorption resonances 15 and thus may be expected to report changes in the function properties of biologically active molecules. An understanding of the nonlinear reso- nant properties is of further importance as a means to in- dicate pathways for phototoxicity and shadowing by mul- tiphoton absorption. Under tight focusing conditions, the extent of THG in- 932 J. Opt. Soc. Am. B/Vol. 23, No. 5/May 2006 Clay et al. 0740-3224/06/050932-19/$15.00 © 2006 Optical Society of America

Transcript of Spectroscopy of third-harmonic generation: … of third-harmonic generation: evidence for resonances...

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932 J. Opt. Soc. Am. B/Vol. 23, No. 5 /May 2006 Clay et al.

Spectroscopy of third-harmonic generation:evidence for resonances in model compounds and

ligated hemoglobin

G. Omar Clay

Department of Physics, University of California at San Diego, La Jolla, California 92093

Andrew C. Millard*

Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla, California 92093

Chris B. Schaffer†

Department of Physics, University of California at San Diego, La Jolla, California 92093

Juerg Aus-der-Au‡

Department of Electrical and Computer Engineering, University of California at San Diego,La Jolla, California 92093

Philbert S. Tsai

Department of Physics, University of California at San Diego, La Jolla, California 92093

Jeffrey A. Squier**

Department of Electrical and Computer Engineering, University of California at San Diego,La Jolla, California 92093

David Kleinfeld

Department of Physics, University of California at San Diego, La Jolla, California 92093

Received September 2, 2005; revised November 17, 2005; accepted November 18, 2005; posted November 29, 2005 (Doc. ID 64600)

We report on third-harmonic generation (THG) of biomolecular solutions at the fluid/glass interface as a meansto probe resonant contributions to their nonlinear absorption spectra that could serve as contrast mechanismsfor functional imaging. Our source was 100 fs laser pulses whose center wavelength varied from 760 to1000 nm. We find evidence of a two-photon resonance in the ratio of third-order susceptibilities,�sample

�3� �3�� /�glass�3� , for aqueous solutions of Rhodamine B, Fura-2, and hemoglobin and a three-photon resonance

in �sample�3� �3�� /�glass

�3� for solutions of bovine serum albumin. Consistent with past work, we find evidence of aone-photon resonance of �sample

�3� �3�� /�glass�3� for water, while confirming a lack of resonant enhancement for ben-

zene. At physiological concentrations, hemoglobin in different ligand-binding states could be distinguished onthe basis of features of its THG spectrum. © 2006 Optical Society of America

OCIS codes: 190.4160, 190.4180, 190.4350, 190.4710, 300.6420, 170.3880, 120.6200.

soroptandt

. INTRODUCTIONhe nonlinear spectroscopy of fluids has assumed new rel-vance with the advent and proliferation of nonlinearicroscopies.1 In these techniques, an ultrashort pulse of

aser light is tightly focused into a material so that opticalxcitation is confined to a focus where the photon flux isighest. This provides intrinsic three-dimensional opticalectioning for two-photon laser scanning microscopy,2–4

econd-harmonic generation,5 three-photon laser scan-ing microscopy,6–9 and third-harmonic generation10–14

THG). Whereas contrast in two-photon and three-photon

0740-3224/06/050932-19/$15.00 © 2

canning microscopy is typically achieved through the usef fluorescent indicators, contrast in harmonic generationelies almost exclusively on intrinsic chromophores. A pri-ri, THG will depend directly on one-, two-, and three-hoton absorption resonances15 and thus may be expectedo report changes in the function properties of biologicallyctive molecules. An understanding of the nonlinear reso-ant properties is of further importance as a means to in-icate pathways for phototoxicity and shadowing by mul-iphoton absorption.

Under tight focusing conditions, the extent of THG in-

006 Optical Society of America

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reases dramatically when the focus spans an interfaceetween two optically different materials.10,16 This allowsmaging based on THG to resolve otherwise transparentnterfaces and inhomogeneities within the resolution ofhe confocal parameter and without the use ofyes.11,13,17–19 Mitochondria,20 red blood cells,21,22 embry-nic development,18,23 neurons,13 plasma flows,24,25

uscle fibers,26 and skin biopsy samples27 have been vi-ualized in this manner. Third-harmonic imaging con-rast has also been linked to the density of opticalolids,24 the aggregation state of polymers,28–30 and theoncentration of intracellular calcium in cultured humanlial cells.31 Finally, a near-field THG scanning imagingtudy of a dried red blood cell by Schaller et al.22 qualita-ively showed that their image contrast was best whenheir excitation beam was spectrally tuned near an antici-ated three-photon resonance in hemoglobin. This pastork motivates the need for a systematic study of possible

unctional THG signals.Beyond issues of imaging, nonlinear optical spectros-

opy per se provides insight into the structure and elec-ronic properties of materials that is complementary tohat provided by linear spectroscopy.32–38 Over the pastwo decades, THG has emerged as a useful nonlinearpectroscopy tool39–43 that has been widely used to iden-ify two- and three-photon resonances in solids and thinlms.29,35,37,38,44–48 In addition, this work indicates a sen-itive THG dependence on the molecular structures andnteractions of solutes and solvents.49–51

Here we report on THG at the solution/glass interfaces a means to explore the contribution of electronic reso-ances to THG spectra of solution-phase biocompounds.e first consider several model solutions with known one-

nd two-photon absorption spectra as a means to cali-rate our methodology.52–55 We then focus on physiologi-al solutions of bovine serum albumin (BSA) as well asifferent ligation states of hemoglobin, i.e., oxyhemoglo-in, carboxyhemoglobin, and deoxyhemoglobin. Serum al-umin and hemoglobin are the primary constituents oflood plasma and red blood cells, respectively, and haveeen the subjects of extensive study. Hemoglobin also hasistinct changes in its linear spectrum between ligatednd nonligated states56 that are expected to be reflectedn THG.

. THEORYHG is the coherent conversion of light with frequency �

nto light with frequency 3�, i.e., wavelength � /3, in aaterial that undergoes intense irradiation. It involves

he absorption of three identical photons of energy �� andhe emission of a single photon of energy 3�� within theemporal uncertainty interval of �−1�10−16 s. The result-nt light propagates in the forward direction. A material’susceptibility to a given nonlinear conversion process isescribed by the susceptibility tensors, ��n�, that relatehe polarization field, denoted P, induced in the materialo the electric field, denoted E, of the incident photon. Ofhe 81 independent elements included in the third-orderonlinear susceptibility tensor �ijkl

�3� ��i ,�j ,�k ,�l�, we arenterested only in the terms associated with a uniformlyolarized, single-frequency excitation field, i.e., �j=�k� . This allows the fourth-rank tensor status of the sus-

l

eptibility tensor to be suppressed and the THG polariza-ion field P�3��3�� to be expressed as

P�3��3�� = ��3��3��E3���. �1�

n a solution or other isotropic media, the measured valueor ��3��3�� is averaged over orientation and equal to

13 ��xxxx

�3� �3��+�yyyy�3� �3��+�zzzz

�3� �3���. The susceptibility�3��3�� is the term we seek to measure.

. Resonant Enhancementhe underlying molecules that facilitate THG need notave real states available whose excitation energy corre-ponds to the incident photon energy or any multiplehereof. However, the THG process is resonantly en-anced if real energy levels are present at the fundamen-al ���, second-harmonic �2��, or third-harmonic �3�� fre-uency. Thus the third-order susceptibility tensor may beominated by either resonant or nonresonant mecha-isms, which makes it convenient to write

�Total�3� �3�� � �nonresonant

�3� �3�� + �resonant�3� �3��. �2�

nder the assumption that all molecules are in the elec-ronic ground state prior to excitation, the resonance termenerated in a perturbation expansion is57

resonant�3� �3��

= �l,k,j

N�0l�lk�kj�j0

�3��l0 − 3� − i�l0���k0 − 2� − i�k0���j0 − � − i�j0�,

�3�

here N is the number of molecules and the indices refero different electronic states, �j0 is the electric dipoleransition moment between the jth state and the groundtate, �j0 is the phenomenological damping coefficienthat is inversely proportional to the decay rate from theth state to the ground state, ��j0 is the energy differenceetween the jth state and the ground state, and thej0 , �k0, and �l0 correspond to one-, two-, and three-hoton resonances, respectively. The intermediate statesre those closest to multiples of the incident photon en-rgy, ��, and the energies of the various states satisfy theelation ��l0� ��k0� ��j0. Resonance occurs as �j0→�,k0→2�, or �l0→3� and can significantly increase theagnitude of the susceptibility.17,57 Implicit in this for-alism is the notion that all photons in the excitationeld have the same polarization, or parity, as well as en-rgy.

. One- and Three-Photon Resonanceshe selection rules, based on conservation of parity, fornhancement by a single-photon resonance also apply tonhancement by a three-photon resonance. Thus the pres-nce of peaks in the linear absorption spectrum of the so-ution, at frequencies � and 3�, is a good indication ofhether such resonances are likely to be involved in THG

Eq. 3]. It is important to note that such resonant en-ancement may be self-limiting in thick samples. Whenne- and three-photon resonances are strong, one- and

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934 J. Opt. Soc. Am. B/Vol. 23, No. 5 /May 2006 Clay et al.

hree-photon absorption by the material will deplete thencoming fundamental and outgoing third-harmonicaves, respectively.

. Two-Photon Resonancewo-photon absorption is an even-parity process,hereas, as above, linear absorption is an odd-parity pro-

ess. Although parity selection rules are relaxed in non-entrosymmetric molecules, the two-photon resonant ab-orption remains difficult to predict on the basis of peaksn the linear absorption spectra at frequency 2�. How-ver, parity selection rules are expected to relax in largerolecules.58 As two-photon absorption does not involve

nergy levels that have allowed single-photon transitionsith the ground state, two-photon resonance can lead tonhancements of the susceptibility without a significantoss of optical power. Further, two-photon resonance is notikely to affect the index of refraction and thus the phase

atching of a given nonlinear process.17

. Nonresonant Contributionsn the case that the nonresonant component of ��3��3�� isominant, several semiempirical scaling laws have beenroposed to account for the spectral dependence of�3��3��.57,59–61 Miller’s rule has been found to account foruch of the spectral dependence of ionic crystals, forhich

�nonresonant�3� �3�� � ��1��3�����1�����3 � �n2�3�� − 1�

�n2��� − 1�3. �4�

ang’s rule60 has been found to account for much of thepectral dependence of gases, for which

�nonresonant�3� �3�� � ���1�����2 � �n2��� − 1�2. �5�

astly, Boling’s rule62 includes local-field effects andhould be more generally valid in the fluid phase, i.e.,

�nonresonant�3� �3�� � �n2��� + 2�2�n2��� − 2�2. �6�

. Microspectroscopyhe third-harmonic intensity that is generated from anxially symmetric material with susceptibility ��3��3��hen irradiated by a tightly focused Gaussian beam, de-oted P�3��, is10

P�3�� = C����b���−

d� exp�ib� ����3��3�,��

�1 + i2��2 �2

P3���,

�7�

here C��� is a formulation of prefactors that depend onhe geometry and efficiency of the collection system butre independent of the sample, P��� is the incident power,��� is the confocal parameter, and the integration is overhe normalized distance �=z /b with the focus at �=0. Iniffraction-limited geometries the confocal parameter isiven by

b��� = 2�n���wo

2

�=

2n����

�n2��� − NA2�

NA2 , �8�

here n��� is the index of refraction and wo is the radiusf the beam waist at the focal plane, expressed in terms ofhe numerical aperture (NA) of the objective. Lastly, theave-vector mismatch between the excitation and themitted third-harmonic fields, denoted, � , is57

� = 6�n��� − n�3��

�. �9�

ignificant generation of THG in the far field occurs whenhe fundamental field can constructively drive the third-armonic field and corresponds to small values of theroduct b� . Under the present conditions of tight focus-ng, THG is near its maximal value for b� �1.

Since the elements of the nonlinear susceptibility areenerally small in magnitude, e.g., ��3��3���10−14 esu forany solutions and ��3��3���10−17 esu for gases, THG

ignals from bulk samples tend to be small,15,57 i.e.,�3�� /P����10−8 for incident irradiance of �1010 W/cm2.ore significantly, in an isotropic medium, the Gouy

hase shift encountered as a light wave traverses the fo-us causes the THG produced on one side of a focus to de-tructively interfere with THG produced on the other sidend thus cancel the third-harmonic wave in thear-field.63 However, the cancellation will be imperfect ifhe optical properties of the sample, i.e., the index of re-raction and the nonlinear susceptibility, differ across theocal volume.10,15 Tsang16 and Barad et al.10 have shownhat the far-field third-harmonic intensity can be in-reased by many orders of magnitude when the focuspans an interface between two optically different mate-ials. This renders THG microscopy particularly sensitiveo optical interfaces and inhomogeneities on the spatialcale of the focal volume.11,13,17–19

It follows from Eq. (7) that the THG intensity from aaussian beam focused on a flat interface between two in-nite homogeneous slabs of material is

�3��Slab1/Slab2= C����Slab1

�3� bSlab1J�bSlab1

� Slab1�

− �Slab2

�3� bSlab2J�bSlab2

� Slab2�2P3���, �10�

here we have neglected reflection and absorption andake use of the dimensionless phase-matching integral,

�b� �, defined as

J�b� � � 0

d�exp�ib� ��

�1 + i2��2 . �11�

n absolute measurement of ��3��3�� is complicated byhe need to determine the factors in C���.64,65 Yet a rela-ive value of ��3��3�� is often of sufficient utility. In par-icular, the value of ��3��3�� for a solution is measuredelative to the glass substrate, typically fused silica, thatorms the sample container.15,52,54,66 One implements thisaradigm by collecting third-harmonic light both from thenterface between the sample solution and the glass, withntensity P�3��solution/glass, and from the interface betweenhe glass and the air, with intensity P�3��glass/air. It fol-ows from Eq. (10) that the ratio of these measurements is

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Clay et al. Vol. 23, No. 5 /May 2006/J. Opt. Soc. Am. B 935

P�3��solution/glass

P�3��glass/air= ��glass

�3� �3��bglass���J�bglass� glass� − �solution�3� �3��bsolution���J�bsolution� solution�

�glass�3� �3��bglass���J�bglass� glass� − �air

�3��3��bair���J�bair� air��2

. �12�

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oting that �air�3��3���0, this becomes

P�3��solution/glass

P�3��glass/air

�1 −�solution

�3� �3��bsolution���J�bsolution� solution�

�glass�3� �3��bglass���J�bglass� glass�

�2

.

�13�

olving for the susceptibilities leads to

�solution�3� �3��

�glass�3� �3��

=J�bglass� glass�bglass���

J�bsolution� solution�bsolution���

�1 ± �P�3��solution/glass

P�3��glass/air�1/2� . �14�

he resolution of the sign ambiguity requires additionalnformation that is either gathered through considerationf resonances or, as will be discussed in Section 4, ob-ained by comparative measurements. The general valid-ty of this approach was examined by Barille et al.,52 whoemonstrated remarkable consistency between their fem-osecond measurements at an excitation wavelength of.5 �m and previous picosecond measurements52,53,67 atn excitation wavelength of 1.9 �m.In the case of a solution composed of a solute and a sol-

ent, the different components may contribute to Eq. (14)ith opposite signs. The correct value of the susceptibility

atio of the hydrated solute, defined as �solute�3� �3�� /

glass�3� �3��, may be determined from the measured poweratio of the solution, denoted P�3��solution/glass/�3��glass/air, given knowledge of both the power ratio and

he susceptibility ratio of the solvent, i.e.,�3��solvent/glass/P�3��glass/air and �solvent

�3� �3�� /�glass�3� �3��, re-

pectively. In the case in which the solute and solvent oc-ur with solvated volume fractions of � and 1−�, respec-ively, the measured power ratio of the dissolved solute is

�solute�3� �3��

�glass�3� �3��

=J�bglass� glass�bglass���

J�bsolution� solution�bsolution���

�1 +1

��±�P�3��solution/glass

P�3��glass/air�1/2

− �1 − ��

�P�3��solvent/glass

P�3��glass/air�1/2�� . �15�

ote that the sign of the solvent term has been taken toe negative (Section 4) and the confocal parameter, indexnd dispersion of the dissolved solute are correctly takeno be the same as the solution, as these are properties ofhe bulk. The remaining sign ambiguity must be resolvedndependently.

. METHODS. Imagingur imaging apparatus consists of a laser scanningicroscope68 with the collection of transmitted light forHG imaging and epi-emitted light for simultaneous two-hoton-excited fluorescence laser scanning microscopyFig. 1). The excitation source for imaging was a locallyonstructed 1.054 �m Nd:glass oscillator with an 80 MHzepetition rate and �100 fs duration pulses. We used a00.65 NA Zeiss excitation objective �f=4 mm� and aused-silica collection lens �f=6 mm�. The detectors wereamamatsu R6357 photomultipliers (PMTs) with quartzindows that were connected to a resistive load and am-lified. Colored glass filters (Corning UG-11) were used tolock all but the third-harmonic light from reaching theMT tube. For two-photon-excited fluorescence, bandpass

550±25 nm� and colored glass filters (Corning BG-39)ere used to block extraneous light.

. Microspectroscopy

. Apparatus and Materialspectroscopic measurements were performed without these of the x–y scan mirrors (Fig. 1). The excitation sourceas a Ti:sapphire oscillator (Mira 900-F with a 10 Werdi pump, Coherent, Inc., Santa Clara, California) with

76 MHz repetition rate and �100 fs duration; this

ig. 1. Multiphoton imaging and THG spectroscopy apparatus.mages were collected using a 1.054 �m, 100 fs Nd:glass pulsedaser. Spectroscopic measurements were made using a Ti:sap-hire laser with 100 fs pulses and wavelengths between 760 and000 nm. PD, photodiode; PMT, photomultiplier tube.

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ource was tuned over a wavelength range of 760 to000 nm. We used 400.65 and 0.75 NA Zeiss excitationbjectives. The detector was a Hamamatsu R6353 PMTith quartz windows that was connected to a resistive

oad and amplified. As with imaging, colored glass filtersCorning UG-11) were used to block all but the third-armonic light from reaching the PMT tube. For funda-ental wavelengths below 810 nm, the colored glass fil-

ers were supplemented with a 265 nm bandpass filter.Our sample containers were microcuvettes (3520; Vit-

ocom, Mountain Lakes, New Jersey) with flat 200 �mhick glass walls (Duran 8340) and a 500 �m wide cham-er to hold the solution. The Duran 8340 glass has opticalroperties similar to those of fused silica (Appendix B).Our samples consisted of deionized water, neat benzene

BX0212-6; Omni Solv, Charlotte, North Carolina), andqueous solutions of 1 mM Rhodamine B chlorideR-6626; Sigma-Aldrich, St. Louis, Missouri), 0.5 mM so-ution of Fura-2 pentasodium salt (F-6799; Molecularrobes, Eugene, Oregon) with 3.3 mM ethylene glycolis(�-aminoethyl ether)-N,N,N� ,N� tetra-acetic acidEDTA) (E-478; Fisher Scientific, Pittsburgh, Pennsylva-ia), 0.5 mM Cascade-Blue trisodium salt (C-687; Molecu-

ar Probes), 0.75 mM BSA (81-066-1; Miles Scientific, Na-erville, Illinois), and hemoglobin. The hemoglobinolutions are at physiological concentrations 2 mM�17 g/dL� and represent three different ligand-bindingtates. These include a 98% (v/v) oxyhemoglobin �HbO2�olution (300881R0; Instrumentation Laboratories, Lex-ngton, Massachusetts), a mixed 60% (v/v) carboxylatednd 40% (v/v) oxygenated carboxyhemoglobin (HbCO) so-ution (300879R0; Instrumentation Laboratories), and aeoxygenated (Hb) solution (�80% based on spectroscopiceasurements) that was formed by bubbling N2 through

he oxyhemoglobin solution.

. THG Measuremente seek to derive the third-order susceptibility ratio of

ur solution relative to glass, �solution�3� �3�� /�glass

�3� �3��, byeasuring the ratio of THG power from the solution/glass

nd glass/air interfaces, i.e., P�3��solution/P�3��glass/air.easurements were made in a manner similar to theethod employed by Barille et al.52 We scanned through

he solution-filled microcuvette along the propagationxis of the incident beam and collected third-harmonicight from both the solution/glass and the glass/air inter-aces [Fig. 2(A)]. The third-harmonic power, P�3��, tracesut two bell-shaped profiles as the focus is swept acrosshe two interfaces [Fig. 2(B)]. The peak of the profile cen-ered on the lower solution/glass interface corresponds to�3��solution/glass, and the peak of the profile centered on

he bottom of the glass side corresponds to P�3��glass/airFig. 2(B)]. The half-widths at half-maximum of each pro-le indicates the extent of the confocal parameter [Eq.

8)].10 The THG signal was averaged over �20 suchweeps. The maximum incident irradiance at the sampleas �1010 W/cm2, and the maximum THG efficiency was�3�� /P����510−7.The measurement of peak third-harmonic power was

epeated at different incident powers to form graphs ofsolution/glass�3�� and Pglass/air�3�� versus the incidentower P��� [Fig. 2(C)]. The relation between the two mea-

ured third-harmonic powers was fit as a cubic function ofncident power, i.e., Psolution/glass�3��=�solution/glassP3���Pdark and Pglass/air�3��=�glass/airP3���+Pdark, wheresolution/glass, �glass/air, and Pdark are the fit coefficients. Thearameter Pdark was fit to the two interfaces simulta-eously and corrected for dark noise in the PMT. This pro-edure, as opposed to a measurement of THG at a single

ig. 2. Third-harmonic spectroscopic measurement procedurepplied to deionized water. (A) Close-up of the sample and appa-atus. Third-harmonic generated light is collected from both theample/vessel interface and the vessel/air interface, and their ra-io is used to infer sample properties. (B) A THG signal is gener-ted as an interface is scanned through the focus of the beam.he peak of the THG intensity profile is measured for different

ncident laser powers. The half-width at half-maximum is pro-ortional to the confocal parameter b. (C) The THG intensitiesrom both the sample/vessel interface and the vessel/air interfaceemonstrate the anticipated cubic dependence on laser power.

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Clay et al. Vol. 23, No. 5 /May 2006/J. Opt. Soc. Am. B 937

ncident power, increases the signal-to-noise ratio of oureasurement. It further minimizes potentially confound-

ng effects that have noncubic scaling with the incidentower, such as excited-state absorption and the nonlinearefraction.59

. Data Reductionrior to additional corrections, the ratio of third-harmonicowers is given by RTHG���=�solution/glass��� /�giass/air���.his ratio must be corrected for reflection at interfacesnd linear absorption by the glass cuvette.

. Linear Absorptioninear absorption and transmission spectra, between 250nd 1000 nm, of all model solutions were obtained with aary 50 (Varian, Palo Alto, California) spectrophotometer.hose for the different ligation states of hemoglobin areaken from published measurements56 [Fig. 7(A)]. Theear-infrared absorption spectra of water was furtherulled from the literature.69 Duran glass measurementsre from the manufacturer’s literature (Vitrocom) andorrected to account for reflection at normal incidence bysing the Fresnel equation for the reflectivity, r���, i.e.,

r���SiO2/solution =nglass��� − nsolution���

nsolution��� + nglass���, �16�

nd measurements for benzene [Fig. 10(B)] are a compos-te of data taken over wavelengths that ranged from 0.78o 1.25 �m70 and 1.33 to 1.8 �m.71

. Reflection Coefficientso account for the different third-harmonic and funda-ental powers transmitted through each interface, we

alculated the reflection coefficients r��� and r�3�� by us-ng the Fresnel equation [Eq. (16)]. The absorptivity a���f the glass substrate was extracted from linear transmis-ion measurements, t���, with use of the calculated reflec-ion coefficients, r���, and the formula a���= ��1−r����2

t���� / �1−r����2.

. Linear Dispersionalculation of the reflection coefficients, r���, theiffraction-limited confocal parameter, b��� [Eq. (8)], andhe wave-vector mismatch, � ��� [expression (9)], de-ends on prior knowledge of the dispersion of the linearefractive index, n���. Unfortunately, precise refractivendex measurements and models do not exist for many

aterials. This is especially notable at wavelengthshorter than 400 nm, which are important in estimationsf � ��� and r�3��. The uncertainty in � ��� is graphi-ally illustrated in the case of benzene [Fig. 3(A)], wheree plot the results from two dispersion models for ben-

ene (Appendix A), each of which fits all available disper-ion data equally well at visible wavelengths but whichignificantly diverges for ultraviolet wavelengths.

. Confocal Parameterhe confocal parameter, b���, can be measured directly

rom the axial extent of the THG profile [Fig. 2(B)]10 asoted above. In diffraction-limited geometries, where the

inear dispersion of the sample is known, the confocal pa-

ameter can be calculated with Eq. (8). We use both ap-roaches and note that diffraction-limited THG measure-ents can simultaneously be used as a means to

ndependently measure the linear index through this cor-espondence. Typical confocal parameters for this experi-ent were between 5 and 7 �m.

. Volume Fractionsalculation of the susceptibility ratio [Eq. (15)] for thease of solutions requires an estimate of the hydrated vol-me fraction of the solute under study. The volume of theydrated complex is relevant because the electronic inter-ction between solute and solvent is integral to the solu-ion’s nonlinear optical properties.49,50,73–75 Thus we aressentially interested in measuring the susceptibility ofhe solvated complex.

As a means to estimate the hydrodynamic volume ofhodamine B in water, and thus the volume fraction ofolvated Rhodamine B chloride in a 1 mM aqueous solu-ion, we make use of the rotational relaxation time ofhodamine B in solution74 and approaches based on func-

ional groups.76,77 We note that close to 50% (w/v) of thehodamine B may be dimerized at a concentration ofmM.78,79 We use this estimate for Rhodamine B and the

ig. 3. (A) Theoretical curves of the confocal parameter timeshe wave-vector mismatch, b� . Curves are calculated from lin-ar dispersion models for water, benzene, and Duran glass in thease of diffraction-limited geometry. The band representing ben-ene is bounded by the curves predicted by two different modelsf dispersion.32,72 (B) The phase-matching integral,25 J�b� �.

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atios of volume estimates from functional group-basedpproaches76,77 to calculate the hydrated volume fractionf Fura-2 dye in a 0.5 mM aqueous solution. Literatureeasurements also contribute to our volume fraction es-

imates of BSA and hemoglobin solutions.80,81

. Corrected Ratio of THG Powerhe corrected, fitted ratio of THG power is

RTHG��� ��solution/glass���

�glass/air���

�1 − r2���glass/solution�3�1 − a���glass�3

�1 − r2�3��glass/solution��1 − a�3��glass�.

�17�

his measure controls for linear absorption, reflections,nd some of the intercapillary and intersample variationnd mitigates drift in laser parameters and sample orien-ation. The susceptibility ratio for solvents [Eq. (14)] is re-xpressed as

�solution�3� ���

�glass�3� ���

=J�bglass� glass�bglass���

J�bsolotion� solution�bsolution���

��������� ± �RTHG����, �18�

here the coefficient

���� �J�bglass/solution� glass�bglass/solution���

J�bglass/air� glass�bglass/air����19�

ccounts for the possibility of changes in the confocal pa-ameter of the glass at the two interfaces due to aberra-ions and the coefficient

���� = � �1 − r2���glass/solution�3

�1 − r2�3��glass/solution��1/2

�20�

ccounts for reflections at the interfaces of the cuvette.he former term is typically unity but in some experi-ents was found to be close to 0.8 while the latter term is

reater than 0.9. The phase integral J�b� � [Eq. (11)] cane numerically evaluated25,52 as a function of the product� [Fig. 3(B)]. Lastly, for the case of a solution, the cor-ected susceptibility expression [Eq. (15)] is

�solute�3� ���

�glass�3� ���

=J�bglass� glass�bglass���

J�bsolution� solution�bsolution������������

+1

� �±�R THGsolvent

��� − �1 − ���R THGsolvent

����� ,

�21�

ith ���� and ���� given above [Eqs. (19) and (20)].

. EXPERIMENTAL RESULTSe consider first the image formation characteristics ofHG solely as motivation for our spectroscopic studies.e then consider a systematic study of model solutions,

.e., water, benzene, Rhodamine B, Fura-2, and BSA solu-ions, followed by different function states of hemoglobin

n solution, i.e., oxy-, carboxy-, and deoxyhemoglobin so-utions. In all cases, the above theoretical framework issed to interpret our measurements of THG intensity,�3��, in terms of the third-order nonlinear susceptibility�3��3��.

. THG Imaginghe enhancement of THG at an interface is illustrated

hrough a comparison of two-photon-excited fluorescencend THG imaging of 10 �m diameter fluorescein-labeledicrospheres versus equally sized unlabeled glass beads

hat sit in a drop of water on a glass coverslip [Fig. 4(A)].he microspheres are readily resolved in entirety with

wo-photon fluorescence, while only the interfaces normalo the incident beam, at either the microsphere/water orhe water/glass interface, yield third-harmonic light [Fig.(A)]. The elongation of images for either modality is aonsequence of the difference in axial resolution �zo5.0 �m� compared with lateral resolution �ro=1.0 �m�.he top surfaces of the beads appear dark as a result of

he absorption of the third-harmonic light by the fluores-ent beads. The shadowing on the glass surface resultsrom distortion of the excitation beam as it passeshrough the bead. Critically, there is no fluorescent signalor the case of imaging glass beads, yet THG at the water/lass interface leads to an image of the top and bottomurfaces of the beads [Fig. 4(A)].

As motivation for our studies on the THG by hemoglo-in, we applied THG imaging to human red blood cells inolution without the use of dyes. A maximal projection

ig. 4. Two-photon-excited fluorescence and THG imaging. (A)comparison of two-photon-excited fluorescence and THG im-

ges. Unlike two-photon-excited fluorescence, THG can be col-ected from both fluorescent and nonfluorescent beads. THG cane seen to be primarily produced at interfaces perpendicular tohe excitation beam, including the coverslip beneath the fluores-ent samples. In this case a shadow of the beads is cast on theoverslip due to the distortion of the excitation beam. (B) Third-armonic image showing the high contrast of red blood cells inolution without the use of dyes.

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hrough a 5 �m stack of unprocessed images leads to theell-known view of red blood cells as concave disks [Fig.(B)].

. Microspectroscopye now turn to quantitative spectroscopy of model com-

ounds and hemoglobin in solution. We report our mea-urements in terms of the corrected and fitted ratio ofhird-harmonic power at the solution/glass interface rela-ive to that at the glass/air interface [Eq. (17)]. These aresed, when appropriate, to derive the corresponding ratiof susceptibilities [Eqs. (18) and (19)]. A discussion of thencertainty in all terms is presented toward the end ofhis subsection.

. Model Solventseasurements of THG at the water/glass interface rela-

ive to the glass/air interface show that RTHG���, the ratiof third-harmonic powers [Eq. (17)], decreased as a mono-onic function of wavelength [Fig. 5(A)]. We resolve the

ig. 5. Third-harmonic spectra of water and benzene; each datween 250 to 1000 nm were obtained with a Cary 50 spectrophoater. The term RTHG��� is the ratio of the cubic-fit coefficients

elated to the ratio of the third-order susceptibility ratio by Eq. (nd glass, �H2O

�3� �3�� /�glass�3� (black arrow and left scale), and the line

ight scale). The correspondence between the THG and the linearnset energy diagram (B) The third-harmonic intensity ratio, Ratio of benzene and glass is relatively constant, suggesting that

ign ambiguity in the susceptibility ratio �H2O�3� �3�� /�glass

�3�

Eqs. (18)–(20)] by considering the spectral trend inTHG��� to be related to a one-photon resonance near aavelength of 970 nm [Fig. 5�A��]. The errors bars inigs. 5(A) and 5�A�� capture an �11% uncertainty in theeasurement of RTHG���, whereas the additional system-

tic uncertainty in �H2O�3� �3�� /�glass

�3� is expected to be lesshan 4%.

The third-harmonic spectrum of benzene is essentiallyonstant over the range of measured wavelengths [Figs.(B) and 5�B��], consistent with an absence of one- andwo-photon resonances over the range of our measure-ents. The third-harmonic spectrum does not reflect the

ong wavelength tail of the ultraviolet absorption band inenzene that, in principle, could contribute to a three-hoton resonance; this suggests that the dominant contri-ution to ��3��3�� of benzene is nonresonant. The sign am-iguity in the estimate of �benzene

�3� �3�� /�glass�3� [Eqs. (18) and

19)] is resolved to be positive on the basis of two consid-

he mean ± standard error �±SE�. Linear absorption spectra be-r. (A) The third-harmonic intensity ratio, RTHG���, of deionizedsample/vessel interface to that of the vessel/air interface and is��. We show the derived third-order susceptibility ratio of waterorption of water at the fundamental wavelength (gray arrow andtion spectrum indicates a one-photon resonant enhancement; see, of neat benzene. �B�� The calculated third-order susceptibilityminant contribution to ��3��3�� of benzene is nonresonant.

um is ttometeof the18). �Aar absabsorpTHG���the do

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940 J. Opt. Soc. Am. B/Vol. 23, No. 5 /May 2006 Clay et al.

rations. First, the hyperpolarizabilities associated withouble bonds between carbon atoms in benzene are antici-ated to lead to much larger ��3��3�� values for this mol-cule than for distilled water.51,82,83 Second, a choice of

ig. 6. Third-harmonic spectrum of Rhodamine B, Fura-2, andntensity ratio, RTHG���, of an aqueous solution of 1 mM Rhodahodamine B, �Rhodamine

�3� �3�� /�glass�3� , and the two-photon action cro

ion indicates a strong two-photon resonant enhancement in R

THG���, of an aqueous solution of 0.5 mM Fura-2. �B�� The thihoton action cross section85–87 track each other, indicating a two

THG���, of a 0.75 mM solution of BSA. �C�� The calculated third-o�3��3�� for BSA has a three-photon resonant enhancement fromelevant to three-photon resonance.

he negative root in Eq. (14) leads to comparable valuesor ��3��3�� in water and benzene over the range of 875 to50 nm. The systematic uncertainty in the susceptibilityatio of benzene is �17%.

each datum is the mean ±SE. (A) We show the third-harmonicB. �A�� We show the derived third-order susceptibility ratio ofion.84 The correspondence between the THG and two-photon ac-ine B below 850 nm. (B) The third-harmonic intensity ratio,

er susceptibility ratio of Fura-2, �Fura-2�3� �3�� /�glass

�3� , and the two-n resonant enhancement. (C) The third-harmonic intensity ratio,usceptibility ratio of BSA and glass, �BSA

�3� �3�� /�glass�3� suggests that

850 nm. We display the linear absorption of BSA over the region

BSA;miness secthodam

rd-ord-photorder s

750 to

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. Aqueous Solutionshe third-harmonic spectrum of a 1 mM solution ofhodamine B chloride shows a sharp decrease with in-reasing wavelength, with a break in the slope near50 nm [Figs. 6(A) and 6�A��]. The sign ambiguity in thestimate of �Rhodamine

�3� �3�� /�glass�3� [Eqs. (19)–(21)] is easily

esolved if we assume that the susceptibility of thehodamine B solution is greater than that of pure water.e use Eqs. (21) through (18) to find �Rhodamine

�3� �3�� /

glass�3� and note that it mirrors the two-photon-excited fluo-escent cross-section measurements84 in Rhodamine B;his suggests the presence of a strong two-photon reso-ance [Fig. 6�A��]. The systematic error introduced into

Rhodamine�3� �3�� /�glass

�3� by our estimate of volume fraction,=0.0004, is �50% [Eq. (15)].

The third-harmonic spectrum of a solution of 0.5 mMura-2 pentasodium salt and 3.3 mM EGTA shows aharp decrease with increasing wavelength with a breakn the slope at a wavelength of 800 nm [Fig. 5(C)]. Unlikehe case of Rhodamine B, the RTHG��� solvent backgrounds a 3.3 mM EGTA solution (data not shown). We resolvehe sign ambiguity in the estimate of �Fura-2

�3� �3�� /�glass�3�

Eq. (21)] by assuming that the susceptibility of the dyeolution is greater than that of water alone. Our estimatef the volume fraction of the hydrated Fura-2 complex at0.07% introduces an �70% systematic error in our de-

ived value of �Fura-2�3� �3�� /�glass

�3� . The susceptibility ratio,

Fura-2�3� �3�� /�glass

�3� shows a spectral profile similar to theeasured85–87 two-photon-excited fluorescent cross sec-

ion of Fura-2 [Fig. 6�B��]. This suggests a strong two-hoton resonance.The THG spectrum of a 0.75 mM solution of BSA also

hows a decrease with increasing wavelength [Fig. 6(C)].he sign ambiguity in the estimate of �BSA

�3� �3�� /�glass�3� [Eq.

21)] is resolved if we assume that the susceptibility of thelbumin is enhanced by a three-photon resonance in theinear absorption spectrum of albumin [Fig. 6�C��]. Dis-ersion and volume fraction uncertainties result in a lesshan 12% systematic uncertainty in our value for

BSA�3� �3�� /�glass

�3� .

. Hemoglobin Solutionshe linear absorption spectrum of hemoglobin shows arominent Soret absorption band that peaks near a wave-ength of 420 nm [Fig. 7(A); central gray]. The correspond-ng dip in the measured value of RTHG��� of these solu-ions (Fig. 8) is highly suggestive of a two-photonesonance. We use this correspondence to resolve the signmbiguity in Eq. (21). We use the refractive index esti-ate of oxyhemoglobin [Fig. 7(B); see Appendix A for deri-

ation] to estimate the wave-vector mismatch [expression9)]. We estimate that the volume fraction of hemoglobinn a 2 mM solution to be �12% for the various hemoglobinolutions80,81 and estimate that this introduces aystematic error of �6.5% in our susceptibility ratios

O2−Hb�3� �3�� /�glass

�3� . An unaccounted-for feature at longavelengths may reflect the additional involvement of a

hree-photon resonance [left-hand gray band in Fig. 7(A)]r the solvent.

. Uncertaintyhe standard deviation of the measured peak THG poweras between 1.5% and 5.5% of the peak value across theavelength range of 760 to 1000 nm, with the exact per-

entage dependent on the incident power, the interface,nd the sample. The uncertainties in the cubic fits of theeak THG power led to uncertainties as high as 6% in thealue of RTHG��� [Eq. (17)] within the same session. Mea-urements of the same substance on different days couldead to variations as large as 13% in the values of

THG���. The experimental errors are represented astandard errors (SEs) of the mean in the graphs of

THG��� and �solution�3� �3�� /�glass

�3� (Figs. 5, 6, and 8). They re-ult from an average over two to five estimates ofTHG���; we recall that each estimate involves the ratio of

ubic equation fits through six to ten data points for botholution/glass and glass/air interfaces [Fig. 2(C)]. The SEre of the same order as uncertainties in absolute mea-urements of the susceptibility in glass.65

Additional, systematic uncertainties in the susceptibil-ty ratios (Tables 1 and 2) result from the propagation ofncertainty in the dispersion of relevant materials. Theipersion of Duran 8340 glass [Eq. (A1)], benzene72 [Eqs.

ig. 7. (A) Linear absorption spectrum of oxy-, deoxy-, andarboxyhemoglobin.56 The wavelength bands corresponding tootential one-photon, two-photon, and three-photon resonancesre highlighted and labeled. (B) The estimated refractive index ofxyhemoglobin (Appendix A) and point index measurementsaken by Orttung and Warner88 (500 to 650 nm), Arosio et al.81

750 nm� and Faber et al.89 �800 nm�.

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942 J. Opt. Soc. Am. B/Vol. 23, No. 5 /May 2006 Clay et al.

A2) and (A3)], water91 [Eq. (A4)], BSA [Eq. (A5)],hodamine B, Fura-2, and hemoglobin [Fig. 7(B)] is ap-roximated by numerical formulas (Appendix A). The un-ertainty in the values of the susceptibility ratio intro-

ig. 8. Third-harmonic spectrum of oxy-, carboxy-, and deoeasurements;56 each datum is the mean ±SE. (A) The third-harhe correspondence between the derived third-order susceptibil

rom 375 to 500 nm indicates a two-photon resonant enhancemen0% (v/v) carboxylated hemoglobin solution. �B�� The derive

HbCO�3� �3�� /�glass

�3� , and the linear absorption in the two-photon rehird-harmonic intensity ratio, RTHG���, of a 2 mM, �95% (v/v) deptibility ratio of deoxyhemoglobin and glass, �Hb

�3� �3�� /�glass�3� , and

egime.

uced by these approximations is maximal at the blueide of the spectrum, where there are few published mea-urements of the refractive index to constrain models (Ap-endix A). At an excitation wavelength of 750 nm, we es-

oglobin solutions (this work) together with linear absorptionintensity ratio, RTHG���, of a 2 mM oxyhemoglobin solution. �A��io of oxyhemoglobin, �HbO2

�3� �3�� /�glass�3� , and the linear absorption

We show the third-harmonic intensity ratio, RTHG���, of a 2 mM,d-order susceptibility ratio of 60% (v/v) carboxyhemoglobin,ce range suggest a two-photon resonant enhancement. (C) Thenated hemoglobin solution. �C�� The calculated third-order sus-ear absorption of deoxyhemoglobin in the two-photon absorption

xyhemmonicity ratt. (B)d thirsonaneoxygethe lin

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imate that the uncertainty in �solution�3� �3�� /�glass

�3� �3�� thatesults from uncertainty in the linear dispersion is �3%,17%, �1%, �5%, and �5% for Duran 8340, benzene,ater, BSA, and hemoglobin, respectively (Table 1).A second source of uncertainty in the susceptibility ra-

ios concerns the volume of solution [Eqs. (15) and (21)]ccupied by the solvated form of Rhodamine B, Fura-2,SA, and hemoglobin in 1, 0.5, 0.75, and 2 mM solutions

hat is estimated to be 0.04%, 0.07%, 7%, and 12%, re-pectively. Uncertainties in the volume fraction estimatesominate the systematic uncertainty in the derived sus-eptibility ratios for these solutions (Table 2). This large

Table 1. Dispersion Estimates an

aterial n�3��

�n�3��n�3��(%)

uran glassa 1.530 �0.2enzene72 1.610 1.7ater90 1.379 �0.01yes90 1.384 2SAa 1.390 �1emoglobina 1.410 �1

�=250 nm �=250 nm

aAppendix A.

Table 2. Volume Fraction Estimates

olute

HydrodynamicRadius(nm)

Concentra(mM)

hodamine B74,77 0.5 1.0ura-274,77 0.7 0.5SA80,81 3.14 0.75emoglobin80,81 2.96 2.0

ig. 9. (Color online) Third-harmonic intensity ratio of hemoglo-in in different oxidation states averaged over 20 nm bands. Er-or bars represent two SE; significance at the 95% confidenceevel is indicated by a bar.

ncertainty in values gleaned from the literature is due inart to the presence of a substrate where adsorption maylay a role.73,92–96

. Spectral Discrimination of Hemoglobin Ligand Stateshe final issue concerns the ability to discriminate among

he three ligation states of hemoglobin on the basis ofheir relative THG spectra, RTHG���. In principle, this cane accomplished wherever the spectra do not intercept.owever, for the signal-to-noise ratios achieved in oureasurements, we could distinguish among all three

tates (95% confidence level) in a 20 nm wide band onlyear a center wavelength of 960 nm (Fig. 9). At other cen-er wavelengths, two of the three possible states could beistinguished (Fig. 9).

. DISCUSSIONe confirm that far-field THG is significantly enhancedhen the focal volume is bisected by an optical

nterface11,13,17–19 (Fig. 4). We use this phenomenon to in-estigate the nonlinear spectra of solutions over theavelength range of 750 to 1000 nm by collecting THG

rom the interface of sample solutions and their glassontainers52,54 (Fig. 2). The susceptibility ratio of pure so-utions, �solution

�3� �3�� /�glass�3� [Eq. (16)], is inferred from

ower-dependent measurements of the THG from theolution/glass and glass/air interfaces.11,52,54 This calcula-ion requires sample-specific models of linear dispersionFig. 7(B)], which we generate and collate in Appendix A.

e further derive the susceptibility ratios of hydrated sol-tes, �solute

�3� �3�� /�glass�3� , from THG measurements on solu-

ions, by subtracting the THG due to the solvent from the

certainties at �=250 and 750 nm

n���

�n���n���(%)

Uncertaintyin

�solute�3� �3��

�glass�3� �3��

�%�

1.469 �0.1 �31.480 0.4 171.329 �0.001 �11.332 1 301.337 �0.5 �51.360 �0.05 �5

�=750 nm �=750 nm �=750 nm

ncertainties of Solutes in Solution

VolumeFraction,

� (%)Uncertainty

in � (%)

Uncertaintyin

�solute�3� �3��

�glass�3� �3��

�%�

0.04 45 500.07 50 707 20 7.5

12 11 6.5

d Un

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944 J. Opt. Soc. Am. B/Vol. 23, No. 5 /May 2006 Clay et al.

otal THG from the solution [Eqs. (15) and (21)]. Miller’sule [expression (4)] indicates that the nonlinear suscep-ibility, �glass

�3� , of the glass substrate is approximately con-tant over the 750 to 1000 nm range of wavelengths,

ig. 10. Comparison of THG and linear absorption spectra withemiempirical rules and linear absorption spectra. The data fromHG measurements made here have been shifted by the ratio ofiller’s rules for Duran glass and SiO2 in order to compare themith values reported in the literature (this factor is �1.17, Ap-endix B). (A) Benzene: the THG measurement at 1.06 �m used3 ns pulses and a Maker fringe technique,66 and the 1.9 �measurement used �30 ns pulses and a triple-wedge

echnique.53,67 Linear absorption measurements in benzene areiecewise composed from measurements over wavelengths of.78 to 1.25 �m70 and 1.33 and 1.8 �m.71 Linear absorption val-es for the Duran glass are based on transmission measure-ents and are corrected to account for reflection using theresnel equations [Eq. (15)]. (B) Water: the THG measurementt 780 nm used 100 fs pulses and a variant of the Maker fringepproach,16 those at 1.25 and 1.5 �m used 40 to 130 fs pulses andn experimental protocol similar to that used here,52,54 and theeasurement at 1.06 �m used 13 ns pulses and a Maker fringe

echnique.66 Linear absorption measurements are due toegelstein.69

hich implies that spectral features in the susceptibilityatio �sample

�3� �3�� /�glass�3� reflect features in the susceptibil-

ty, �sample�3� �3��, of the sample (Appendix B).

To evaluate the accuracy of our spectroscopic approachn pure solutions, we compare our measured values of theonlinear susceptibility ratio of deionized water and ben-ene with measurements in the literature52,54,55,66,67 (Fig.0). Most literature measurements are made relative toused silica �SiO2�, so an accurate comparison with our re-ults requires that we first scale our results by the ratio ofhe susceptibility of our Duran glass to that of SiO2. Thiscaling factor is achieved by our applying Miller’s ruleexpression (4)] and indicates that the glass/SiO2 suscep-ibility ratio is �1.17 (Appendix B).

The scaled values of �sample�3� �3�� /�SiO2

�3� for benzene andater found here (Fig. 10) are in good correspondenceith those measured at different wavelengths and withifferent approaches. Literature values are plotted withhe measurements made here, and error bars are in-luded whenever they are available. Systematic errors inur values are not accounted for in the figure (Tables 1nd 2). The close agreement among measurements madeith pulse widths ranging from 30 ns to 40 fs supports thenderstanding of THG as a purely electronic effect, notnduly modulated by the nonlinear index of refraction orhort-time-scale solvation processes.97–100

The microspectroscopy approach52,54,101 adopted hereelies on tightly focused �100 fs pulse-width, �1 nJ laserulses to sample �50 �m3 volumes of solution. It can beerformed with exactly the same pulse shape,102–104 en-rgy, and duration used in laser scanning nonlinear imag-ng. Previous spectroscopic studies based on the Makerringe technique relied on softly focused �1 mJ laserulses, 10 ns or longer, to sample much largerolumes.39,53,66,105 Whereas the Maker fringe techniqueields third-harmonic phase information, which is dis-arded in the present technique, both approaches appearo have similar experimental errors.

We also compare the various semiempirical rules foralculating ��3��3�� values [expressions (4)–(6)] with thoseound here and in the literature for the cases of benzenend water (Fig. 10). These formulations are not expectedo perform well in solutions or near resonance. However,ang’s rule60 [expression (5)] and, to a lesser extent, Bol-

ng’s rule59,62 [expression (6)] predict the relatively flatpectrum of benzene [Fig.10(A)], which may indicate aroader utility for use with nonresonant solutions.

. Nonlinear Spectraomparisons between linear and nonlinear spectra showommon features and demonstrate one-, two-, and three-hoton resonances in THG spectra that correspond to lin-ar absorption features at the fundamental, second, andhird harmonics of the excitation beam as well as two-hoton absorption resonances. We find evidence of a one-hoton resonance in the ��3��3�� spectra of water [Figs. 5A�� and 10(B)]; a two-photon resonance in the ��3��3�� ofhodamine B, Fura-2, and hemoglobin [Figs. 6�A��, 6�B��,nd 7(A)]; a three-photon resonance in the ��3��3�� of BSAFig. 6�C��]; and no resonance in benzene [Fig. 5(B)]. Thewo-photon resonances in the Rhodamine B and Fura-2

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Clay et al. Vol. 23, No. 5 /May 2006/J. Opt. Soc. Am. B 945

pectra are identified by comparison with two-photon-xcited fluorescence cross-section spectra [Figs. 6�A�� and�B��] and confirm that THG may be used as a probe ofwo-photon excited states that are not accessible with lin-ar absorption measurements.87

The degree of modulation in ��3��3�� associated with aesonant enhancement varies dramatically between com-ounds. For example, Fura-2 shows a greater than 20-foldncrease in ��3��3�� associated with a 10-to-102-times in-rease in its two-photon action cross section, whereashodamine B shows an �3-fold increase in ��3��3�� asso-iated with an �102-fold increase in the two-photon crossection (Fig. 6�). These differences follow, in part, from theariable contribution of nonresonant terms to the suscep-ibility [Eq. (2)]. For example, the magnitude of the sus-eptibility ratio of nonresonant benzene�benzene

�3� �3�� /�glass�3� 3.2� is about twice as large as that of

he resonance peaks of water, BSA, and hemoglobin, and,f the materials reviewed here, only Fura-2’s peak reso-ant value equals the nonresonant value of Rhodamine B

�Rhodamine�3� �3�� /�glass

�3� 77�. Thus the resonant modulation

resonant�3� /�nonresonant

�3� �3�� in the susceptibility spectrum isost appreciable for compounds such as oxyhemoglobin

nd Fura-2, where the nonresonant value is relativelyow.

. Potential Application to Imaginghe ratio of THG powers, RTHG���, represents image lu-inosity as collected in a THG microscope. RTHG��� is not

irectly proportional to the nonlinear susceptibility [Eq.18)]; as a result, resonance enhancements may appear asn increase or a decrease in THG luminosity [Figs. 5(A), 5A��, and 6)]. Nonetheless, RTHG��� spectra can be used toistinguish different solutions. We also find that at physi-logical concentrations ��2 mM�, hemoglobin solutionsonsisting of 98% (v/v) oxyhemoglobin, 60% (v/v) carboxy-emoglobin and 40% (v/v) oxyhemoglobin (correspondingith heavy smoke inhalation), or 90% (v/v) deoxyhemoglo-in show significant differences in their RTHG��� spectrahen averaged over 20 nm spectral bands (Fig. 9).Additional factors are needed to enhance the signal-to-

oise ratio before THG can be used to determine the oxi-ation state of hemoglobin in flowing red blood cells. Pos-ibly, THG from red blood cells may provide a higherontrast than the hemoglobin solution/glassnterface,91,106 though such measurements would require

tight focus so as to minimize the orientation effects ofhe cell. It is also possible that successive single-powereasurements might be more useful for discriminating

etween oxidation states. Acquisition of repeated mea-urements at the same power has the advantage allowingapid comparisons across cells while surrendering the po-ential to extract accurate absolute values for the third-rder susceptibility. Finally, the ability to distinguishmong oxidation states of hemoglobin in red blood cellsepends only on the ratio of THG at different excitationavelengths and does not require corrections for linearbsorption and refraction of the incident and THG light.The two-photon absorption resonance in the THG spec-

rum of hemoglobin [Figs. 8�A��, 8�B��, and 8�C��] doesot lead to a significantly larger value for the nonlinear

usceptibility than the value found for BSA [Fig. 6�C��].his suggests that damage induced under nonlinear exci-

ation will not be preferentially driven in either com-ound. In capillaries, whose �5 �m diameter is of the or-er of two confocal parameters, the observed two-photonesonance implies that 820 nm is an optical wavelengthor the visualization of flowing red blood cells againstuorescently labeled plasma.107,108 Conversely, irradiat-

ng a sample at 880 nm may be best to minimize photo-amage to hemoglobin.The large two-photon resonance in the Rhodamine B

nd Fura-2 indicates that common fluorescent dyes usedor two-photon microscopy may have a latent informationhannel available in THG. In all cases the THG channelill preferentially probe dyes in the vicinity of interfaces,ffectively creating a complementary contrast mecha-ism.

PPENDIX Ae discuss the derivation and application of the phenom-

nological formulas used to calculate the refractive indi-es of silicone dioxide, Duran 8340 glass, benzene, water,nd solutions of Rhodamine B, Fura-2, BSA, and hemo-lobin.

. SiO2 and Duran Glasshe dispersion of SiO2 is fit by a well-known formula,109

hereas that for Duran 8340 glass is approximated byhis dispersion equation to fit reported index values in theisible range.110 We have

nSiO2 or Duran��� = �1 +n1

1 − ��1

��2 +

n2

1 − ��2

��2

+n3

1 − ��3

��2�

1/2

, �A1�

here the common parameters are n1=0.897479, �13145.816 nm, n2=0.4079426, and �2=340.9419 nm. ForiO2, n3=0.6961663 and �3=261.5422 nm; for Duranlass, n4=0.7376285665 and �4=279.6276303 nm.

. Benzeneignificant differences in the value of � arise when oneompares refractive index models for benzene constructedn the visible wavelength32,72 [Fig. 2(A)]. Comparison ofhe model calculation with existing refractive index mea-urements does not allow for a clear choice betweenodels.111 We use the average index of the two models.he first is72

nbenzene��� = n0�1 + ��0

��2� , �A2�

ith n0=1.21501 and �0=76.56803 nm, and the seconds32

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946 J. Opt. Soc. Am. B/Vol. 23, No. 5 /May 2006 Clay et al.

nbenzene��� = n0�1 +n1

1 − ��1

��2�

1/2

, �A3�

ith n0=1.205, n1=0.501, and �1=170 nm.

. Waterodels of the refractive index, n��� of water, as in the

ase of benzene, exhibit significant divergence at wave-engths in the ultraviolet part of the spectrum.32,112 Ourhoice of models90 is dictated by favorable comparisonith reported measurements across the full range ofavelengths, 250 to 750 nm. We use112

nwater��,S,T� = n0 + �n1 + n2T + n3T2�S − n4T2

+n5 + n6S + n7T

�− �n8

��2

+ �n9

��3

,

�A4�

here S is salinity in parts per thousand, T is tempera-ure in Celsius, � is in nanometers, and the parameteralues are n0=1.31405, n1=1.77910−4, n2=−1.0510−6,3=1.6010−6, n4=2.0210−6, n5=15.868, n6=1.15510−2, n7=−4.2310−2, n8=66.20, and n9=103.681.

. Dye Solutionse approximate the wavelength dependence of the index

f the dye solutions by scaling the dispersion curve ofaltwater90 [Eq. (A4)] to match an existingeasurement113 of the concentration-dependent index in-

rement, dn��� /dc, of Rhodamine B solutions at a wave-ength of 780 nm. This gives an effective salinity of 2%v/v) �S=20� for 1 mM solutions of Rhodamine B; the samendex increment was used for a 0.5 mM solution ofura-2.

. Bovine Serum Albumine use existing measurements of dn��� /dc at variousavelengths114–116 (see Table 3) to construct a

oncentration-dependent dispersion increment model forSA:

dnBSA���

dc= −

118+ 162 +

15 000

�+ �0.056

��2

, �A5�

here � is in nanometers.

. Hemoglobine estimate the dispersion of oxyhemoglobin solutionsith a Taylor expansion of the Kramers–Kronig integral

hat relates the real and imaginary components of theomplex refractive index89 nc���=n���+ in����. The imagi-ary component of the refractive index is related to theolar absorption coefficient ���� by117

n���� = c ln�10�����

2�, �A6�

here c is the speed of light and �=2�c /�. We approxi-ate the local dispersion features of oxyhemoglobin bytting the n���� absorption spectra in the 250–1000 nmavelength range, with r Gaussians representing r ab-

orption bands, such that n���� can be expressed as theum

n���� = �r

Ar exp� ��r − ��2

2�r2 � , �A7�

here �r������r−�1/2� /�2 ln�2�, �r is the resonance an-ular frequency, �1/2 is the frequency at half of the peakeight, and Ar is the maximum value of n���� for the r�thbsorption band. Variations in the index due to local ab-orption bands can then be expressed as118

�n��� = �2�r

Ar

�r��r − ��exp� ��r − ��2

2�r2 � . �A8�

he results of this approach are then scaled and providedith a linear offset to fit existing measurements ofn��� /dc in oxyhemoglobin over the 450–800 nm wave-

ength range88,89 [Table 4; Fig. 7(B)].

PPENDIX Bchott’s Duran 8340 glass, also designated as Corning740 Pyrex, is a borosilicate glass (81% SiO2, 13% B2O3,nd 4% AlO3) with similar optical properties �n�=1.474nd Abbe number of 65.7) to pure fused SiO2 (n�=1.458nd Abbe number of 67.8).110 Boron is added primarily toeduce the melting temperature and is not thought tohange the nonlinear properties of the glass.119 Nonethe-ess, according to Miller’s rule [expression (4)], the third-rder susceptibility of the Duran glass is 17.9% to 17.2%arger than the value of ��3��3�� for fused SiO2 over the50–1000 nm wavelength range. Measurements of�3��3�� in glasses of different indices support the magni-ude of this estimate,119–121 although the difference in�3��3�� values59,61 may be as large as 100%. Miller’s rule

Table 3. Linear Dispersion Increment of BovineSerum Albumin

avelength436nm

488nm

546nm

578nm

1060nm

n��� /dc 0.1924ml/g

0.192ml/g

0.1854ml/g

0.1901ml/g

0.181ml/g

eference 116 115 116 114 115

Table 4. Linear Dispersion Incrementof Oxyhemoglobin

avelength500nm

650nm

750nm

800nm

n��� /dc 0.198ml/g

0.1900ml/g

0.170±0.01ml/g

0.143±0.02ml/g

eference 88 88 81 89

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Clay et al. Vol. 23, No. 5 /May 2006/J. Opt. Soc. Am. B 947

lso indicates that the value of ��3��3�� for either glassill smoothly decrease by about 10% over the same rangef wavelengths. This has been generally supported byeasurements in fused SiO2 and borosilicate glass atavelengths ranging from 1.064 to 2.1 �m, which show a

ess than 20% change (with 7% to 15% variation) in thealue ��3��3�� for a given glass.59,65

CKNOWLEDGMENTSe thank Zvi Kam for the gift of a quartz lens and Earlolnick for assistance with the electronics. Financial sup-ort was provided by the National Science Foundation,ntegrative Graduate Education and Research Trainee-hip program (G. O. Clay); the Burroughs Welcome–unded La Jolla Interfaces in Science (A. C. Millard and. B. Schaffer); the David and Lucille Packard Founda-

ion (D. Kleinfeld); the National Institutes of HealthNIH), National Center for Research Resources (D. Klein-eld and J. S. Squier); and the NIH, National Institute ofiomedical Imaging and Bioengineering (D. Kleinfeld and. A. Squier).

Corresponding author D. Kleinfeld may be reached athe Department of Physics 0374, University of California,500 Gilman Drive, La Jolla, California 92093, or by-mail at [email protected].

*Present address, Center for Biomedical Imaging Tech-ology, University of Connecticut Health Center, Farm-

ngton, Connecticut 06030.†Present address, Department of Biomedical Engineer-

ng, Cornell University, Ithaca, New York 14853.‡Present address, Spectra-Physics, Inc., Mountain

iew, California 94039.**Present address, Department of Physics, Colorado

chool of Mines, Golden, Colorado 80401.

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