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Second harmonic ellipsometry

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2003 Meas. Sci. Technol. 14 508

(http://iopscience.iop.org/0957-0233/14/4/315)

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INSTITUTE OF PHYSICS PUBLISHING MEASUREMENT SCIENCE AND TECHNOLOGY

Meas. Sci. Technol. 14 (2003) 508–515 PII: S0957-0233(03)52333-5

Second harmonic ellipsometryAndrew J Timson, Rowland D Spencer-Smith,Alexander K Alexander, Robert Greef and Jeremy G Frey1

Department of Chemistry, University of Southampton, Southampton SO17 1BJ, UK

E-mail: j.g.frey@soton.ac.uk

Received 14 August 2002, in final form 23 January 2003, accepted forpublication 18 February 2003Published 17 March 2003Online at stacks.iop.org/MST/14/508

AbstractApparatus suitable for variable wavelength and incident angle secondharmonic ellipsometry (SHE) studies of solid and liquid interfaces isintroduced, with particular attention drawn to the calibration of theexperiment. Preliminary results obtained from the study of the chiralmolecule 1, 1′-bi-2-naphthol located at the air/water interface are used toindicate the suitability of SHE as a surface probe for resonant systemsincluding the determination of the interfacial refractive index at theharmonic frequency.

Keywords: ellipsometry, second harmonic generation, interface,surface layer, chiral

1. Introduction

There are now several established optical techniques to studyair–liquid and liquid–liquid interfaces. One such techniqueis the surface or interfacial second harmonic generation(SHG), which along with sum frequency generation (SFG),has been used to probe a wide variety of liquid systems (andindeed solid interfaces) due to its interface specificity, rapidresponse times and submonolayer coverage sensitivity [1].We concentrate here on equipment designed to obtain themost polarization information from resonant SHG experimentsby extending the polarization measurements typically madein SHG experiments to those more often associated withellipsometry.

SHG arises from the second order polarization P(2)

induced in a non-centrosymmetric medium by the electric fieldE(ω) of the incident fundamental radiation given by the tensorequation,

P (2)(ω) = χ(2)E(ω)E(ω) (1)

where χ(2)

i jk is the third rank second order surface susceptibilityof the material. In a centro-symmetric medium no second orderpolarization is possible in the dipole approximation. Higherorder quadroplar terms, and terms involving the electric fieldgradient or magnetic terms, can still contribute. At an interfacethe inversion symmetry is broken and a dipole contribution toP (2) is allowed.

1 Author to whom any correspondence should be addressed.

The intensity, I (2ω), of the SHG signal observed from aninterface between two isotropic bulk phases illuminated withfundamental radiation of intensity I (ω) is given by [2]

I (2ω) = 32π3ω2

c2

√ε1(2ω)

ε1(ω)(ε(2ω) − ε1(2ω) sin2 θ1(2ω))

× |e(2ω) · χ(2) · e(ω)e(ω)|2 I 2(ω) (2)

where e(ω) and e(2ω) are the polarization vectors for thefundamental and harmonic beams and include the appropriatecombination of Fresnel factors. The refractive indices andpermittivities, εi , are defined for each layer of the three-layer model (figure 1) and θ1 is the angle of reflectionof the harmonic beam in the upper layer. As writtenequation (2) applies when the permittivities are real anda more general expression is given by Brevet [3]. Asexplained in Brevet (chapter 7) for the three-layer model itis the real parts of the permittivity that are significant forthe leading terms in equation (2) though the full complexquantities are involved in the calculation of the Fresnelfactors.

For an isotropic (in plane) interface only four of the tensorcomponents, χZ Z Z , χZ X X , χZ X Z and χXY Z , where Z is thenormal to the interface, contribute to the observed harmonicsignal. The electric fields of the s (Es

2ω) and p (E p2ω) polarized

components of the harmonic beam, as a function of the linearpolarization angle (γ ) of the fundamental wave (assuming apure linear polarization), are given by

Es2ω = C(a1χX Z X sin 2γ + a6χXY Z cos2 γ ) (3)

0957-0233/03/040508+08$30.00 © 2003 IOP Publishing Ltd Printed in the UK 508

Second harmonic ellipsometry

1

2

1( )

( )

(2 )

1(2 )

ε

ε

ε

1

2

ω

ω

ω

ω

θ

θθ

θInterface region

Figure 1. Three-layer model with the permittivities associated witheach layer. The upper bulk phase is region 1 and the lower bulkphase surrounding the interface is region 2. The interface isconsidered as a microscopically thin region between the two bulkphases. For the experiments reported in this paper the upper phasewas always air. Therefore the refractive indices for the fundamentaland harmonic waves in this region do not differ significantly andθ1(ω) = θ1(2ω). In general for a liquid–liquid or liquid–solidinterface dispersion may be significant and the reflection angle forthe harmonic will differ slightly from the angle of incidence of thefundamental.

E p2ω = C((a2χX Z X + a3χZ X X + a4χZ Z Z ) cos2 γ

+ a5χZ X X sin2 γ − a7χXY Z sin 2γ ). (4)

The χXY Z component is only non-zero for chiral surfaces; thevalue of χXY Z for two enantiomers will be equal in magnitudebut opposite in sign. As the tensor components can becomplex quantities (especially near resonance) the harmonicwave can be elliptically polarized even for a linearly polarizedfundamental, just as in conventional ellipsometry. This resultsin a variety of interesting effects of non-linear optical activitybeing observable in SHG [4]. The majority of observations ofthis type have been made on chiral films [5].

The ai coefficients are combinations of Fresnel factorsrelating the electric fields in the interfacial region to the externalfield and depend on the exact model for the interface chosen.For the second harmonic calculations a simple three-layermodel (figure 1) is used. The non-linear region is the thinlayer between bulk immersion medium layers. It is importantto realize that this layer is assumed always to be vanishinglythin, being on the order of the molecular dimension of thetarget, because thicker assemblies of molecules are usuallycentro-symmetric and do not generate even harmonics. Thesecond harmonic calculations therefore assume that there isno significant light interference in this layer, although there isreflection at its upper and lower boundaries. This is in contrastto macroscopic layered structures often investigated by linearellipsometry, where interference effects within the layer cancontribute dominantly to the overall polarization changes.

The dipole allowed nature of the interfacial processmeans that, despite the relatively small amounts of materialcontributing to the interfacial signal, it is usually larger than theresidual higher order contributions from the bulk, even whenthe bulk phase contains the same molecules in solution thatare present at the interface. For resonantly enhanced signalsthe interface or surface component dominates. Analysis of thetensor elements yields information both on surface coverageand adsorbate molecular orientation.

The interfacial SHG effect is inherently weak, being a non-phase-matched system, and therefore electronically resonant

systems are often investigated so that the signal may be morereadily detected. This introduces the added complication thatχ

(2)

i jk and indeed the interfacial refractive index are complexquantities. Hence, in order to elucidate the real and imaginarycomponents of χ

(2)i jk , knowledge of the polarization and phase

of the surface SHG response is required [6]. A sufficientlyextensive set of SHG intensity measurements for a rangeof different input/output beam polarization combinations canprovide the information needed. However a more elegantapproach is to introduce a rotating quarter-wave plate intothe experiment to continuously modulate the polarization stateof the fundamental beam incident at the interface [7]. Thishas allowed the SHG response of several chiral systems to beinvestigated.

The alternative applied in this work is to employ a rotatingoptical compensator (quarter-wave plate) in the analysis ofthe SHG radiation generated at the surface to allow thefull polarization characteristics of the reflected light to bedetermined by a Fourier analysis. The configuration we usehere has been analysed by Hauge [10] applied to the linear-optical ellipsometry case under the title of generalized rotating-compensator ellipsometry. A rotating compensator has theadvantage over the more often employed rotating analysersystem in that it enables the unambiguous determination ofthe polarization state of the light. An important practical pointis that optical compensators usually have low beam deviation.Polarizers, by contrast, very often display beam deviation, andthis is particularly true of high-power polarizers which mustbe used in these experiments. Further developments of thetechnique are alluded to in the conclusion section of our paper.A condensed version of the derivation is presented here tointroduce our notation.

1.1. Linear ellipsometry with a rotating compensator

Using the Jones calculus, the incident light componentsparallel to and perpendicular to the plane of incidence aredenoted by E pi and Esi while the reflected components areE po and Eso. In general these are complex quantities. Theeffect of the sample upon the incident light is represented bythe normalized Jones matrix of complex quantities [8]:

(E po

Eso

)=

(1 ab c

) (E pi

Esi

). (5)

In our case where we have a non-depolarizing sample, thematrix is diagonal (a = b = 0), and we can use the alterna-tive representation of the c term, conforming to the usualellipsometric notation:

c = tan ψ exp i� (6)

where tan ψ is the modulus of the ratio of the p and s amplitudereflection coefficients, and � is the difference between thephase changes of the p and s components. We measure theintensity as the compensator rotates to a number of azimuthalpositions C at fixed azimuths of the polarizer of 45◦ or −45◦and of the analyser of 0◦. The detected light intensity atposition C is proportional to I (C):

I (C) = A0 + A2 cos 2C + B2 sin 2C + A4 cos 4C + B4 sin 4C(7)

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where

A0 = 2 + qS1, A2 = 2s(S1 + 1),

B2 = 2sS2 − 2r S3, A4 = (2 − q)S1,

B4 = (2 − q)S2

(8)

and

q = 1 + sin 2ψC cos �C , r = sin 2ψC sin �C ,

s = cos 2ψC

(9)

are compensator defect parameters. ψc and �c are defined fortransmission in a similar way to those for reflection. Theseterms are necessary because no compensator is achromaticwith exactly π/4 retardance over the wide wavelength rangeof these experiments. A perfect compensator would haveq = r = 1 and s = 0.

The S1, S2 and S3 terms are the Stokes parameters(normalized to S0 = 1) in the alternative Stokes/Mullercalculus for representing polarization transformations. Theyare related to the quantities used here by

tan 2ψ = −(S22 + S2

3)1/2/S1, tan � = −S3/S2. (10)

The An terms are obtained by carrying out discrete Fouriertransforms at every wavelength, and the q, r and s values areobtained by a calibration process described below. The aboveequations then allow calculation of the target quantities ψ and�. This methodology is used in the established linear surfacetechnique of ‘rotating compensator Fourier ellipsometry’,and has led to this experiment becoming known as ‘secondharmonic ellipsometry (SHE)’. In addition, our instrumentallows the angle of incidence to be varied.

1.2. Second harmonic ellipsometry with a rotatingcompensator

In conventional linear ellipsometry the measured angles (ψ,�)

relate to the change in polarization on reflection. The secondharmonic wave is a ‘new’ wave generated at the interfaceand the rotating compensator analysis is used to measure thepolarization state of this wave. The polarization angle, ψ ,and the phase difference, δ, between the s and p componentsof the harmonic wave are measured. The lower case δ isused to distinguish these measurements from the differencemeasurement made in the linear case.

The polarization parameters determined are the relativeamplitude ratio tan ψ and the phase difference δ. With theseterms the second harmonic electric field can be expressed inthe form of Jones vectors,

E2ω =(

E p2ω

Es2ω

)=

( |E p2ω|eiδ

|Es2ω|

)= |E2ω|

(cos ψeiδ

sin ψ

)(11)

where E p2ω and Es

2ω are the second harmonic electric fieldamplitude components in the p- and s-planes respectively. Theoverall phase of the SHG wave relative to the fundamentalwave is not measured or described here. This could still bedetermined by comparison with for example a quartz sampleusing an interference technique. The angles ψ and δ are tobe determined as a function of the angle of incidence at the

interface and the wavelength of the fundamental in order tounderstand all the parameters of the resonance and thus makethe extraction of geometric data (i.e. orientation distributions)more reliable.

From the expressions given in equations (3) and (4)it is seen that in general there is no direct correlationbetween the measured ‘ellipsometric’ parameters and thetensor components. For the isotropic liquid surface somesimplifications occur. Thus for p-polarized fundamentalradiation (γ = 0)

tan ψP = |E p2ω(0)|

|Es2ω(0)| = |a2χX Z X + a3χZ X X + a4χZ Z Z |

|a6χXY Z | (12)

which will be the same whichever enantiomer is present at theinterface, but the phase difference

δP = arg(a2χX Z X + a3χZ X X + a4χZ Z Z ) − arg(a6χXY Z ) (13)

will depend on the enantiomer (R/S) via the sign of χXY Z .For incident fundamental radiation with ±45◦, ψ is given

by

tan ψ±45 = |a2χX Z X + (a3 + a5)χZ X X + a4χZ Z Z ∓ 2a7χXY Z ||2a1χX Z X ± a6χXY Z | .

(14)In this form it is seen that the sign change that occurs with±45◦ is associated with χXY Z and thus the same term thatchanges sign on exchanging enantiomers, which exemplifiesthe symmetry of the experiment to reflection in the planecontaining the fundamental and reflected harmonic beams.

As well as a description of the apparatus we report herethe preliminary results obtained from this new technique, in thestudy of the chiral molecule 1, 1′ -bi-2-naphthol (BN) located atthe air/water interface. Binapthol was one of the first molecularsystems in which large non-linear chirality was observed inSHG [9].

2. Experimental details

The SHE experiments used two laser sources. For 532 nmthe frequency doubled output of a Nd:YAG laser (ContinuumModel: Minilite 10, maximum energy of 10 mJ/pulse, afrequency of 10 Hz and pulse width of 5–7 ns) was used. Otherexperiments used the frequency doubled output (532 nm) ofa Nd:YAG laser (Continuum Model: 661-10) to pump a dyelaser (Continuum Model: TDL60). This generated laser lightwith a maximum energy of 15 mJ/pulse, a frequency of 10 Hzand pulse width of 5 ns. The light was linearly polarized andtuneable over the wavelength range offered by the laser dye,which in this case was Rhodamine 6G (552–586 nm).

The laser radiation was brought in along the rotation axisof the ellipsometer arms and directed up one arm using amirror that rotated with the arm. This arrangement ensuredthat the laser path did not need to be re-aligned as the armswere moved. Two mirrors translate and reverse the direction ofthe light sending it back down the ellipsometer arm. Precisionstepper motor units coupled via reduction gearboxes were usedto select the angle of incidence. As we wish to study liquidinterfaces it was desirable to have the sample horizontal. Thismeans that the ellipsometer arms must move in a vertical plane

510

Second harmonic ellipsometry

Clinometer

HeNe

Polariser

FaradayModulator

Glass plate or Water

Photodiode or PMT

θ

θ

Figure 2. A schematic of the optical arrangement used in thecalibration of the input polarizer. The clinometer is used to set theellipsometer arm to the Brewster angle for the sample. Nulling thereflection from the surface can then set the p-polarization orientationof the polarizer.

and thus they were counter-balanced carefully and aligned withshims to ensure that the optical axes of the two arms matchedand stayed in line as they were rotated.

The polarization state of the laser light was controlled witha half-wave plate (Ealing Optics) and Glan–Taylor polarizercombination. The light beam was then focused 2 mm abovethe sample surface to a beam diameter of about 0.3 mm usinga f = 20 mm achromatic lens. A yellow Schott glass UVfilter was also present to remove any SHG generated by thepreceding optics. The signal generated by the surface wasrecollimated using a fused silica lens, whilst the reflectedfundamental was blocked by the use of several UG5 glassfilters. A compensator, mounted in a Newport rotary stage,was introduced in front of a UV polarizer, which was fixed toallow only p-polarized light through.

After a monochromator (PTI International) the beamentered the detection system, which consisted of a PMT (ThornEMI: 9828B), a pulse pre-amplifier (Thorn EMI: A2) and aboxcar integrator (SRS: SR250). A photodiode signal, takenfrom a reflection from one of the optics, was simultaneouslyaveraged by a second boxcar integrator (SRS: SR250) forpower normalization. A delay/pulse generator (PAR: 9650)triggered the detection system between laser pulses to allowbackground readings to be taken. Intensity measurementswere taken typically with ten laser shots at each angle, andthe compensator was rotated up to a maximum of 40 completerevolutions in steps of 3.6◦. The signal was then processedusing a Visual Basic program running on a PC.

2.1. Polarizer calibration

The arms of the ellipsometer were moved to set the angle ofincidence to the Brewster angle for water (as this automaticallygives a horizontal surface) or glass; the angle is set using aclinometer. All the subsequent alignment and calibration weretraced back to this one mechanical measurement. The height ofthe sample was adjusted so that the surface was aligned with theaxis of the ellipsometer. Light from a small HeNe or diode lasermounted on the input arm was passed through the polarizer.The reflected light from the water or glass sample surface wasdetected with a photodiode. Since at the Brewster angle plane

p-polarized light is transmitted and not reflected (figure 2), thecalibration of the first polarizer can be achieved by rotating thepolarizer to null the reflected signal. In order to improve thesensitivity of the nulling process, a Faraday modulator in theincident beam was used. This consisted of a glass core woundwith several hundred turns of wire and driven at 50 Hz from a12 V transformer. The detected signal consists of a mixture ofsecond and fourth harmonics of the driving frequency. Whenthe polarizer axis coincides exactly with the incident plane ofthe reflecting surface, the second harmonic disappears, leavinga symmetric fourth harmonic response. This null point canbe judged by eye on an oscilloscope screen to give a precisenull within a few hundredths of a degree, which is adequatefor the present study. If required, the precision can be furtherimproved by using a phase-sensitive detector to zero the secondharmonic component.

Both arms were then returned to the horizontal position toallow the analysing polarizer on the output arm to be calibratedby nulling it against this polarizer on the input arm, whichhad been calibrated by using the Brewster angle proceduredescribed above.

2.2. Compensator calibration

Typically quarter-wave plates are not achromatic and onlybehave ideally for a fixed wavelength. Even then, any residualstress in mounting the plate can lead to deviations from idealbehaviour. If as in our experiments the wavelength is to bescanned, it is essential to account for these deviations fromideal behaviour. In the standard ‘rotating compensator Fourierellipsometry’ the calibration is achieved by passing 45◦ linearlypolarized light through the quarter-wave plate. Knowing thatin the straight-through position (where the sample is air) �

is 0◦ and ψ is 45◦ allows [10] the determination of the threedefect parameters q, r and s from the A- and B-coefficients ofthe observed variation of I (C) (equation (7)).

One further parameter, not dealt with in the Hauge and Dilltreatment, is recorded at each wavelength and is defined as thestatic phase angle (θc). This angle relates the position of thecompensator fast–slow axis to the zero reference of the encoderof the rotary stage. When the mounting of the compensatorwithin the encoder motor housing is inaccessible or difficult toadjust, as in our case, the offset of the compensator axis can beobtained by analysis of the Fourier components of the detectedsignal in the straight-through position (arms horizontal). Bysetting � = 0 and ψ = 45◦ corresponding to empty spaceinto the Hauge and Dill formulae, which assume that thecompensator is set with its fast axis at zero azimuth, it can beshown that the fourth harmonic phase component is invariant atπ/2. Any offset of the compensator can therefore be computedfrom the offset of this component in the measured straight-through response. There is however a remaining ambiguity inits determination (θc ±90◦), which we resolved by performingan ellipsometry measurement on a standard system (e.g. agold plate, where � ≈ 100◦) and correcting θc accordingly.Measurements of the compensator offset across the spectrumconfirmed its constancy to within a few hundredths of adegree, and an average value was therefore subtracted fromits azimuthal position in the analysis program.

This procedure is sufficient for determining thecompensator response at the fundamental wavelength but for

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A J Timson et al

Nd:YAG

Dye Laser

Z-cutquartzplate

Polariser45o

Rotating/4-plate

Polariser0o

Visibleblockingfilter

Monochromator

PMT

Nd:YAG

Dye Laser

Z-cutquartzplate

Polariser45o

Rotatingλ/4-plate

Polariser0o

Visibleblockingfilter

Monochromator

PMT

Figure 3. Experimental set-up for the acquisition of the defectparameters at the harmonic wavelength. The z-cut quartz flatgenerates a large enough SHG signal that it can be used as the UVlight source at 2ω. The first polarizer (on the input arm) ensures thatthe light reaching the λ/4-wave plate is polarized at 45◦. A visiblefilter blocks the fundamental laser light and the monochromatorensures the detection of only the harmonic wave (for exampleexcluding nearby two-photon fluorescence). The signal intensity isrecorded as a function of the rotation of the wave plate.

278 280 282 284 286 28830

40

50

60

70

80

90

100

angl

e/de

g

λ / nm

defe

ct p

aram

eter

1.10

1.05

-0.05

0.00

0.05

0.85

0.90

0.95

1.00

Figure 4. The measured defect parameters for the retarder as afunction of wavelength. The defect parameters are q (•), s ( ) andr (�) with values shown on the left hand y axis and angles ψC (��)and �C (◦) with value shown on the right hand y axis.

SHE the response at the harmonic wavelength is needed. It isimportant to use the same type of light source for the calibrationmeasurement as for the actual SHE measurements. Sufficientharmonic intensity for the corresponding defect measurementsin the UV can be generated very simply by transmission thougha z-cut quartz flat. The configuration used is shown in figure 3.A quartz flat is placed before the initial polarizer (for thispurpose we need to ensure this polarizer is UV transmitting)which is set to 45◦. The polarization generated by the quartzflat is largely wavelength independent, but the use of thepolarizer ensures we are not dependent on the polarizationcharacteristics of the generated harmonic. The harmonic isgenerated collinearly with the fundamental beam and continueson into the output arm (both arms are horizontal for thisexperiment).

The filters and monochromator ensure that the detectorresponds to the harmonic wavelength and not the moreintense fundamental, but otherwise the measurements are asdescribed for the fundamental. With the beam polarizationstate known (45◦) the intensity variation of the signal as the

compensator is rotated gives the required defect parameters.These experiments were repeated for the wavelength used inthe study. If the compensator was remounted or aligned thestatic phase angle had to be re-determined. The other defectparameters that are largely properties of the wave plate ratherthan how it was mounted were found to be constant. Themeasured defect parameters in the harmonic wavelength regionare shown in figure 4.

One important issue is that in determination of thedefect parameters it is important to know the baseline forthe intensity measurements (A0), as well as the variation.Once these parameters are known the ellipsometric anglesfor the detected wavelength (harmonic or fundamental) canbe obtained just from the variation (i.e. the value of thesecond and fourth harmonic components) in the intensity asa function of the compensator rotation. The absolute value isnot required. However, for interfacial harmonic generation,especially followed as a function of the incident angle, it isvery useful to be able to compare the intensity as well as thepolarization properties of the harmonic wave. To ensure thecomparison can be made reliably the boxcar was triggeredbetween laser pulses to measure the background value, as thereare various electrical offsets present that can drift with time.The background can then be subtracted from the measuredadjacent laser derived signals and normalized to the laserintensity (squared).

2.3. Sample preparation

All solutions were prepared using water obtained from awater purifier (Purite Analyst HP: 17.5 M� cm) and R-/S-binaphthol (BN) supplied by Lancaster (99%). Due to possibleoxidation of the BN and the long dissolution times requiredto prepare the samples, all solutions were kept in the dark,prepared using water purged of oxygen and stored in an inertenvironment i.e. under nitrogen. The interfaces were createdby placing 35 ml of the solution in a specially designedcovered cell which allowed the sample to be kept at a constanttemperature of 17 ± 1 ◦C. The top layer of the interface wasaspirated using a pipette (Eppendorf) prior to measurementsbeing taken. As a further precaution the sample area was thenflooded with either N2 or Ar gas.

3. Results and discussion

Checking of the polarization response extraction and systemalignment was carried out using the Xe arc lamp source anda pure Si wafer sample (Wacker-Chemitronic) between 250and 320 nm. The results were found to be within 0.1◦ in� of those from the standard data for Si overlaid with a2 nm thick native oxide layer [11]. Further checks usingthe Nd:YAG pumped dye laser source on Au and water at564 nm, angle of incidence 70◦, gave values in agreementwithin 0.03◦ with values extracted from the literature [12].For water � = 359.58◦ (i.e. 0.02◦ away from the theoreticalvalue of 0◦) and ψ = 24.07◦ , while for Au, � = 104.61◦ andψ = 43.59.

SHE measurements were made on an air/water (achiral)interface and then on a chiral binapthol(aq)/air system [6].Figure 5(a) shows the variation of SHG intensity withcompensator angle, which indicates that the SHG signal

512

Second harmonic ellipsometry

0 30 150 180 210 240 270 3000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

S-BN/Air Interface

Air/Water Interface

0 30 90 120 150 180 210 240 270 300 330 3600.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

360330

60

Compensator angle / deg

Compensator angle / deg

60 90 120

(a)

(b)

Figure 5. (a) The plot shows the variation in SHG intensity as afunction of rotation of the compensator for input light of +45◦polarization at 560 nm for the air/water interface and S-binapthol atthe air/water interface. Signal averaging is performed by summingthe signals from ten laser pulses at each angle and then repeating thecycle of rotation of the compensator. The curves above show theresult of a single cycle. (b) The variation in SHG intensity from theair/solution interface of a 10 µM solution of S-BN as a function ofthe rotation of the compensator. The upper curve is the result ofusing p-polarized fundamental radiation at 560 nm with the twopeaks per cycle showing the harmonic wave is predominantlycircularly polarized. The lower curve corresponds to s-polarizedfundamental radiation at 560 nm with the four peaks per cycleindicating predominately a linearly polarized harmonic wave.

originating from the pure water surface is linearly polarizedand the signal generated at the BN interface is ellipticallypolarized. Figure 5(b) shows that the polarization of theharmonic wave generated by the binapthol solution interfacedepends on the polarization of the incident fundamental. Ap-polarized fundamental wave generates a largely circularlypolarized harmonic while the s-polarized fundamental resultsin a plane polarized harmonic wave. This result is consistentwith the binapthol being chiral and the SHG process having atwo-photon resonance close to the wavelengths used.

The ellipsometric parameters were determined by rotatingthe compensator using the wavelength dependent defectparameters from the calibration phase of the experiment. Thevalues obtained at a fundamental/harmonic wavelength of560/280 nm for the air/water interface are shown in table 1and the binapthol solution in table 2. In subsequent work,this investigation was extended to cover the entire wavelengthrange of the laser dye R6G, for both the R- and S-enantiomers,

276 278 280 282 284 286 288 29020

25

30

35

40

R-BN (+45)S-BN (-45)R-BN (-45)S-BN (+45)Spline fit

/°

Wavelength / nm

δ

Figure 6. The plot shows the variation in the phase difference, δ,between the s- and p-components of the second harmonic wavegenerated by for binapthol at the air/water interface plotted as afunction of the harmonic wavelength. The results for the +45◦polarization of the fundamental beam and R-binapthol areessentially the same as for the mirror image situation with −45◦fundamental polarization impinging on the solution of S-binapthol.Error bars = ±2σ .

Table 1. Values of the SHE parameters ψ and δ for the air/waterinterface for a fundamental wave at 560 and harmonic at 280 nm for+45◦ and −45◦ incident fundamental polarizations. The errors arecalculated using standard statistical methods on a series ofmeasurements made at each input polarization setting.

WaterInputpolarization (deg) ψ (deg) 2σ δ (deg) 2σ

+45 49.1 1.2 360 1.2−45 42.4 0.8 180.3 1.1

Table 2. Values of the SHE parameters ψ and δ for the air/solutioninterface for 10 µM solutions of R-BN, and S-BN interface for afundamental wave at 560 and harmonic at 280 nm for +45◦ and−45◦ incident fundamental polarizations. The errors are calculatedusing standard statistical methods on a series of measurements madeat each input polarization setting. Within the uncertainties thesymmetry on exchanging the ±45◦ and the R/S enantiomer isdemonstrated. Some systematic differences can be observed and aredue to the slightly different enantiomeric purity of the two samples.

R-BN S-BNInputpolarization ψ δ ψ δ(deg) (deg) 2σ (deg) 2σ (deg) 2σ (deg) 2σ

+45 40.6 2.2 26.3 2.2 52.8 2.9 32.3 2.9−45 51.0 2.8 211.3 2.1 38.0 2.8 204.3 2.1

p 45.7 2.1 97.6 2.6 44.8 2.6 279.7 2.7s 89.1 2.6 16.8 2 88.3 2.3 16.2 2.9

using the input polarizations of +45◦ and −45◦. The valuesmeasured for the parameter δ are shown in figure 6.

The results show that for a given input polarization setting,e.g. +45◦, the R- and S-enantiomers of BN have differentvalues of δ. When the polarization is changed, e.g. to −45◦,this has the effect of switching the response of the twoenantiomers; this is consistent with viewing the change in

513

A J Timson et al

40 50 60 70 800

10

20

30

40

50

60

-45°IN

PIN

/°

Incident Angle / °

Figure 7. Variation in the parameter ψ as a function of incidentangle for the second harmonic wave generated from S-BN located atthe air/water interface for a fundamental polarization of −45◦ (◦)and p (+) at a fundamental/harmonic wavelength of 532/266 nm.Each scan was repeated twice.

polarization to taking a mirror image of the experiment andthus of the molecule. These observations can be rationalizedin terms of the surface second order susceptibility having achiral component (χ

(2)

XY Z ) that has different signs for the twoenantiomers. In more recent work the parameters ψ and δ andthe SHG intensity have been measured for S-BN as a functionof incident angle [13]. Figure 7 shows ψ as a function ofthe angle of incidence. A consistent fit to the ellipsometricangles and the SHG intensity can only be obtained by adjustingthe interfacial refractive index at the harmonic wavelength inequation (2) [14]. A value of Re (n(2ω)) = 0.99 was obtainedat 266 nm, which is consistent with being close to resonancefor a concentrated binaphthol layer.

As has been demonstrated in this paper, it is interestingin certain cases, e.g. when chiral materials are adsorbed, toanalyse the second harmonic response of the system to morethan one incident polarization state. By an extension of theinstrumental methods used here, the whole of the opticalresponse to all polarization states can be determined. Aninstrument for achieving this can be called a generalizedellipsometer (or Mueller matrix ellipsometer), and the variousconfigurations available have been described [15]. The mostappropriate of these, the dual rotating compensator, couldbe implemented by adding one component, a second opticalcompensator (together with appropriate stepper motor drivecircuitry and software changes), to the incident beam of theconfiguration we used [16]. This instrument also incorporatesan optical multi-channel analyser, which replaces the scanningmonochromator.

4. Conclusion

SHE is a new and powerful tool in surface analysis. Notonly has it been used to probe the chiral molecule 1, 1′-bi-2-naphthol (BN) at the air/water interface, it has also been ableto distinguish between its R- and S-forms. The technique hasseveral distinct advantages over the current SHG experimentalmethodology. The set-up is such that the detection system

analyses light of the same polarization throughout, henceeliminating any bias in the monochromator/PMT combination.The polarization parameters ψ and δ are measured directlyindependent of the absolute SHG signal intensity as a functionof both the angle of incidence and the wavelength.

Acknowledgments

We are pleased to acknowledge the support of theUK Engineering and Physical Sciences Research Council(EPSRC) and Natural Environment Research Council(NERC). AJT thanks the EPSRC for a studentship and AKAthanks GlaxoSmithKline (at the time Glaxo-Wellcome) fortheir contribution to his support.

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