optical reflection response of dye-aggregate films in the absorption bands

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Wakamatsu et al. Vol. 23, No. 9 /September 2006 /J. Opt. Soc. Am. B 1859

Optical reflection response of dye-aggregate filmsin the absorption bands

Takashi Wakamatsu

Department of Electrical and Electronic System Engineering, Ibaraki National College of Technology, 866 Nakane,Hitachinaka-shi, Ibaraki 312-8508, Japan

Susumu Toyoshima and Kazuhiro Saito

National Institute of Advanced Industrial Science and Technology, Central 2, 1-1-1 Umezono, Tsukuba-shi, Ibaraki305-8568, Japan

Received March 7, 2006; revised April 21, 2006; accepted May 2, 2006; posted May 17, 2006 (Doc. ID 68348)

Optical reflection properties of strongly absorbing dye-aggregate films are discussed with respect to spectro-scopic experiments and numerical calculations based on classical wave optics. The dye-aggregate films exhibitenhanced reflection in the wavelengths of the absorption bands and exhibit reflection spectra analogous in pro-file to the absorption spectra. Although film thickness is much smaller than the wavelength of light, the simplesimulations based on a dielectric model reproduced well the essential features of the reflection spectra. Themacroscopic analysis, which involved using a complex refractive index, indicates that the enhanced reflectioncan be expressed by increasing the extinction coefficient with respect to absorption. The spectrally distinct be-haviors of reflection at low absorption on wavelengths on either side of the absorption bands are attributed tothe changing refractive index with an anomalous dispersion due to the absorption bands. © 2006 Optical So-ciety of America

OCIS codes: 120.4530, 120.5700, 160.4890, 300.1030, 310.6860.

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. INTRODUCTIONbsorbing dye thin films are typically applied to opticalemories or optoelectronic devices.1–3 The macroscopic

ptical properties of these dye thin films in the linear re-ion, such as absorption and transmission, are basicallytilized in these applications. Their optical properties cane described quantitatively by the complex refractive in-ex, n=n+ ik, (n, refractive index; k, extinction coeffi-ient). The general focus on absorbing dye films is, how-ver, mainly on the structure of the absorption bandsoncerned, with respect to the quantum electron state inhe molecules, or molecule interactions on a microscopiccale. Additional information about the complex-efractive-index characteristics of the dye films is usefuln further applications.

An interesting optical response associated with dyeolecules occurs in the wavelengths of the absorption

ands when the light is reflected by the dye monolayers athe air–water interface. These reflection spectra are en-anced around the absorption wavelengths and are simi-

ar in profile to the absorption spectra.4–8 Furthermore, asrst presented in this paper, dye-aggregate films of sev-ral molecule layers also yielded an enhanced reflection inhe absorption wavelengths.

The reflection responses of the dye-aggregate layersith a very small size (thickness d��) have been inter-reted by using a microscopic viewpoint in terms of quan-um theory. Namely, the origin of the enhanced reflectionroduced by the dye-aggregate monolayers has been ex-lained as coherent resonance scattering of light by theye molecules in the absorption bands.4 The microscopic

0740-3224/06/091859-8/$15.00 © 2

nterpretation has been particularly valid for the reso-ance light scattering of isolated atoms in vapor, or mol-cules in solution due to the weak interactions.9–11 Fur-hermore, a point dipole model based on the microscopicnteractions between the molecular dipole assembly andhe incident light has been developed by Orrit et al.5 Theodel, however, has been applied to the monolayers of

ye molecules at the air–water interface only.The typical properties of enhanced reflection response

n dye aggregate ultrathin films in solid-state assemblies,hich will be described in detail in this paper, are as fol-

ows: (1) The reflection of the dye-aggregate films hasefinite polarization dependence; the reflection responses higher for p-polarized oblique incident light rather than-polarized light. (2) The reflection increase depends onhe layer thickness of the dye aggregates. (3) At low ab-orption on the short-and long-wavelength sides of thetrong absorption bands, the reflection exhibits a spec-rally characteristic behavior.

A more complicated analysis is probably required forhe microscopic interpretation of the enhanced reflectionroduced by the dye-aggregate multilayers. These charac-eristic reflection responses can, however, be understoody using a light wave viewpoint of the macroscopic inter-ctions between light and the dye-aggregate layers, whichre expressed with n��. In this case, the dye-aggregatessemblies are treated as a simple macroscopic dielectricedium in which the macroscopic average of certain com-

lex electromagnetic interactions, such as molecule inter-ctions with the incident light and intermolecular inter-ctions, is considered with respect to n��.

006 Optical Society of America

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1860 J. Opt. Soc. Am. B/Vol. 23, No. 9 /September 2006 Wakamatsu et al.

To explain the characteristics of enhanced reflection inerms of classical wave optics, a series of spectroscopic ex-eriments on both a dye-aggregate monolayer and a dyeggregate comprising several molecule layers is demon-trated, together with numerical simulations, based on aimple layered-structure model. The polarized reflectionnd absorption spectra of two dye-aggregate film typeswith a particular absorption spectrum), J-aggregatelms of merocyanine (MC) and H-aggregate films ofquarylium (SQ), both fabricated by using the Langmuir–lodgett (LB) technique, have been investigated. The re-ection spectra are compared with the absorption spectran the basis of spectral shape, and the spectroscopic char-cteristics of reflection are discussed with respect to n��stimated by using the Kramers–Kronig (K–K) analysisor absorption spectra. Furthermore, numerical calcula-ions based on Fresnel’s formula are performed by using aorentz dielectric function for the absorbing films. It was

ound that the reflection characteristics of the dye-ggregate absorption bands can be explained adequatelyrom the macroscopic wave optics.

. EXPERIMENT. Sample Preparationhe chemical structures of the amphiphilic dye moleculessed here, MC dye and SQ dye, are shown in Figs. 1(a)nd 1(b), respectively. A further dye, arachidic acidAA:CH3�CH2�18COOH� was also used. These dyes werehosen because of their ability to form typical aggregatest the air–water interface and their particular absorptionpectra.

These aggregate ultrathin films were fabricated care-ully in order to avoid strong optical anisotropy, such asn-plane or uniaxial orientations of the transition dipole

oments. MC was mixed with AA in the ratio MC:AA1:2 to form stable LB films, while SQ was used as is.he MC:AA and SQ dyes were each dissolved in chloro-

orm at a concentration of about 3�10−3 mol/L, and thenpread on water containing about 2�10−3 mol/L ofdCl2, with KHCO3 for adjusting the pH value

�pH 6.4�, and on pure water with no CdCl2, respectively.

ig. 1. Chemical structures of dye molecules: (a) merocyanineMC), (b) squarylium (SQ).

he water temperature was kept at about 20 °C. The MConolayer was slowly transferred onto a BK-7 glass sub-

trate whose surface was hydrophilic due to the predepo-ition of AA layers by a vertical dipping technique, at aurface pressure of 3.0�10−2 N/m. The SQ monolayeras transferred onto a hydrophobic glass substrate, pre-

oated with AA layers, by using the horizontal dippingechnique at the same surface pressure. The MC and SQggregate layers were yielded as LB films of Y- and-type structures, respectively.

. Spectral Measurements of Reflection and Absorptionue to the very thin film thicknesses �d�� used, the re-ection spectra of the dye-aggregate layer films were ob-ained relative to a transparent glass substrate. Figure 2llustrates the reflection measurement method used inhis study. The relative reflection spectra of the dye aggre-ate layers for s- or p-polarized light at an incident angle, were estimated from the intensity ratio of the reflectionight produced by the dye layer films on the glass sub-trate Ir��, with respect to the intensity of the reflectionight produced by the glass substrate only Ir

sub��. Theeasured Ir /Ir

sub represents the ratio of the absolute re-ection spectrum R�� of the dye-layer covered glass slideo that of the bare glass substrate Rsub��, namely R /Rsub.he measured relative reflection R /Rsub corresponds to�� if Rsub experiences a slow change in wavelength.his can apply to the case of the glass substrate becausef its slow dispersion in the refractive index. Note herehat the obtained R /Rsub excludes the wavelength depen-ence of the reflection from the substrate, owing to thepectrum intensity ratio Ir /Ir

sub. If the wavelength depen-ence by the substrate is completely neglected, the refrac-ive index of the substrate is considered to be constant,nd the influence expressed in the reflection spectra is ob-erved in wavelength regions far from the absorptionands.In the spectral measurements of reflection, collimated

hite light from a glass optical fiber was incident on theye aggregate samples at �=45°, and the reflected lightrom the samples was measured through a linear polar-zer. A Xe lamp was used as white-light source, and thepectrum of the reflection light was detected with a fiber-oupled photodiode-array spectrometer (IMAC-7000, Ot-uka Electronics, Osaka, Japan). The sample glass sub-trates coated with the dye-aggregate films were attachedo a BK-7 glass plate of 15 mm thickness by using an im-ersion oil with a refractive index similar to that of the

ig. 2. Reflection measurement method used in this study. Ii,ncident light; Ir, reflected light produced by the dye layer filmample; Ir

�, reflected light from the back interface of the sub-trate; It, transmitting light.

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K-7 glass substrate, so that the reflected light Ir pro-uced by the dye ultrathin films can be separated from Ir

�,esulting from the back interface of the substrate ashown in Fig. 2. This enables only the reflection light af-orded by the dye-aggregate films to be detected.

The absorption spectra A�� of the dye-aggregate filmsere estimated by ordinary transmission measurements.onpolarized and collimated white light from a halogen

amp was irradiated through an optical fiber at the inci-ence normal to the dye-layer covered substrate, and theransmitted light was detected by using the fiber-coupledpectrometer. The transmission spectrum was estimatedrom the ratio of the transmitted light intensity producedy the dye film samples It��, with respect to that pro-uced by the glass substrate only It

sub��. The obtainedt /It

sub represents the relative transmission with respecto the bare glass substrate, T /Tsub, where T and Tsub arehe transmittances associated with the dye-layer coveredubstrate and the bare substrate, respectively. Note herehat the correction for reflection by the transparent glassubstrate is valid in the nonabsorption wavelengths ofye thin films, whereas in the absorption-band wave-engths, the reflection correction by the glass substrate isenerally insufficient because of the enhanced reflectiony the dye thin films, as mentioned in this paper. In thease of very thin layers of dye aggregates �d��, however,he reflectivity is still small ��6% �, as compared with theransparent loss due to the film absorption, and as such,he reflection loss can be neglected on the semiquantita-ive discussions. As a result, A�� was estimated from anxpression of −ln�T /Tsub�, according to the revised law ofambert and Beer for natural logarithms. Moreover, toiscuss semiquantitatively the reflection responses of theye-aggregate films, we estimated k�� from A�� and ob-ained n�� from the revised K–K transform12 of k��.

. EXPERIMENTAL RESULTS ANDISCUSSIONS. Merocyanine Aggregate Filmse first describe in detail the measurement results of theC aggregate films. Figure 3 shows the s-polarized rela-

ive reflection spectra �R /Rsub�s at �=45° (solid curve, val-es represented as a percentage) and the absorption spec-ra A�� (dotted curve) of the MC LB films: Fig. 3(a),onolayer films; Fig. 3(b), five-layered films. Here, the

tandard value of 100% in �R /Rsub�s corresponds to the re-ection intensity of the bare glass substrate. The largebsorption spectra with a peak near 590 nm are red-hifted absorption bands from those of the isolated mono-er states of the MC molecules located at about 525 nm,hich are attributed to the J-aggregate formations12–14 ofC molecules. The J-aggregate films are found to exhibit

o other absorption bands on the long-wavelength side ofhe J band, so that the absorption spectral curves of the-aggregates on the long-wavelength side are approxi-ately Lorentzian in shape. In contrast, additional ab-

orption bands produced by the monomer, the dimer, andthers, exist on the short-wavelength side, the spectra ofhich are not Lorentzian.The relative reflection spectrum curves are enhanced

round the wavelengths of the strong J absorption bands,

nd are fairly similar in profile to the corresponding ab-orption spectra, although the wavelength positions of theeaks of both spectra are somewhat different. In addition,he spectral properties are considerably analogous tohose of the relative reflection associated with the dyeangmuir monolayer at the air–water interface.4–8 From

hese data, the reflection response of the dye aggregatelms has clearly a strong relationship with the absorp-ion, exhibiting light energy loss by the dye aggregates. Ithould be noted here, however, that the reflection curvesn the long-wavelength side of the J band are high, whilehose on the short-wavelength side are rather low. Sincehere is little absorption by the MC aggregates in eitheravelength region, this indicates that the reflection re-

ponse in these regions is not a direct cause of the absorp-ion. Therefore, it is necessary to discuss the reflectionpectra by discriminating between the wavelength re-ions either side of the absorption bands at low absorp-ion.

The polarization dependence of R /Rsub at �=45° for theve-layered MC LB films is shown in Fig. 4. The-polarized curve is also enhanced at the wavelengths as-ociated with the J absorption band, and is spectrally un-hanged with respect to the s-polarized curve. In contrast,he relative reflection for the p-polarized incident light isarger than that for the s-polarized light by a factor of 1.6t the peak positions. The MC films with the J-aggregatesre expected to exhibit rather large absorptions when ir-adiated with s-polarized light because of the tendency of

ig. 3. Typical s-polarized relative reflection spectra �R /Rsub�st �=45° and absorption spectra A�� of MC J-aggregates: (a)onolayer films, (b) five-layered films. Solid and dotted curves

re �R /Rsub�s represented as a percentage, and A�� estimatedrom the measured transmission at �=0°, as an expression ofln�T /T �, respectively.
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he transition dipole moments to orient parallel to theubstrate, namely the uniaxial orientation,12–14 in spite ofhe care taken in fabricating LB films to avoid strong an-sotropy. If the reflection response produced by the dye-ggregate layers was associated simply with the absorp-ion itself, the J-aggregates would induce a largereflection when irradiated with s-polarized light. Con-rary to expectation, the measurement results give the re-erse characteristic, as shown in Fig. 4. Thus, for the dyeggregates, a larger absorption does not necessarily causelarger reflection, but the reflection response is higher

or p-polarized light, despite lower absorption.Since the p-polarized light has an electric-field compo-

ent parallel to the thickness direction of the filmamples, the reflection response is supposed to haveayer-thickness dependence. This fact is confirmed for thealues of �R /Rsub�s in Figs. 3(a) and 3(b); the s-polarizedelative reflection of the five-layered films is clearly ofarger intensity than that of the monolayer. Additionally,n the case of the p-polarized relative reflection, a similarayer-thickness dependency was also observed.

The amount of resonance scattering in the absorptionands of the dye molecules is strongly dependent on thebsorption.11 As evidenced by the absorption data in Fig., the absorption associated with the five-layered MC ag-regate films is about five times greater than that of theonolayer, at a fixed concentration of MC aggregates.herefore if the enhanced reflection in the absorption

ig. 5. Complex refractive index, n=n+ ik, of the five-layeredC aggregate films, as a function of wavelength. Solid and dot-

ed curves represent k�� estimated from the A�� data in Fig.(b), and n�� obtained from the K–K transform of k��,espectively.

ig. 4. Polarization dependence of R /Rsub spectra for the five-ayered MC LB films.

ands was owing to the resonance scattering, the increasen reflection experienced by the five-layered films wouldppear to be of the order of 5 times higher, while the ratiof the reflection increase of the five-layered films to that ofhe monolayer remains by a factor of 1.5 times higher athe peak position, as shown in Fig. 3. From the layer-hickness dependence, we find that the reflection re-ponse of the three-layered (air–dye layers–glass sub-trate) structure is simply generated not only by theeflection from the first interface of the air–dye layers,ut also from the second interface of the dye layers–glassubstrate. Thus, the reflection associated with the dye-ggregate films has a definite film-thickness-dependence,amely a finite size effect, in spite of d��.Figure 5 shows a typical n�� of the five-layered MC ag-

regate films, estimated from A�� in Fig. 3(b). In the es-imation of k�� (Fig. 5, solid curve), we adopted the opti-al path length L in the absorbing films of five-layeredC aggregates, as L=5l=14 nm, based on the entire

ength of the MC molecule, l=2.8 nm established from-ray diffraction measurements. In the K–K analysis12,15

f n�� (Fig. 5, dotted curve), a background refractive in-ex of nb=1.5 was employed based on previous experi-nce, because the measurement wavelength range of ab-orption is limited within the visible region, as shown inig. 3(b).Comparing the �R /Rsub�s spectral curve in Fig. 3(b)

ith the n�� and k�� curves in Fig. 5 reveals that thenhanced reflection response experienced by the dye ag-regates is connected mainly with k��. From Fig. 5, theC aggregate films exhibit a changing n (the value from

.25 to 2.21) with an anomalous dispersion around thetrong J band. Here, the influence of changing n on theeflection in the J band becomes smaller than that of k.n the contrary, the reflection at low absorption for wave-

engths either side of the J band is clearly attributed tohe effect of refractive index; the increase in reflection onhe long-wavelength side is attributed to the refractive in-ex being higher than that of glass �n�1.51�, while theorresponding decrease in the short-wavelength region isttributed to the lower n. At around �=575 nm, n�� has ainimum value, but any effect of the low n is not exhib-

ted in the reflection due to the large k. Thus, the anoma-ous dispersive n�� provides an explanation for the spec-ral behaviors of reflection at low absorption on bothavelength sides.

. Squarylium Aggregate Filmsext, we present the measurement results for the SQ ag-

regate films. The SQ dye in the LB films tends to form-aggregates, which exhibit a blueshifted absorption

rom that of the monomer state,15,16 in contrast to the-aggregates of the MC molecules that exhibit a red-hifted absorption band, as mentioned in the previousubsection. Figure 6 shows �R /Rsub�s at �=45° (solidurve) and A�� (dotted curve) of the SQ five-layered ag-regate films. The large and broadened absorption with aeak near 530 nm is attributed to the H-aggregates of SQ,nd is blueshifted from that of the SQ monomer state lo-ated at about 650 nm. On the short-wavelength side, thebsorption spectra are Lorentzian in shape, while on theong-wavelength side, the corresponding absorption spec-

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ra are non-Lorentzian, due to the presence of other ab-orption bands associated with the monomer, the dimer,nd others.The �R /Rsub�s spectrum exhibits a remarkable increase

n the large H absorption band, and except for the long-avelength side of the H band, its curve is fairly similar

n profile to that of A��, as previously observed in the MC-aggregate films presented in Fig. 3. Hence, in the casef the SQ H-aggregate films, the reflection response islso strongly connected with the absorption propertiesnd can be directly expressed by k�� to represent the ab-orption.

In contrast, the relative reflection on the short-avelength side at very low absorption ��475 nm� de-

reases drastically to about 78% of its original value. Thispectral behavior is probably attributed to the lower re-ractive index caused by the strong H absorption band.he origin of the decreasing reflection is clearly a result ofhe refractive index with an anomalous dispersion, as pre-ented in a previous paper.15 According to the n�� curvehown in Ref. 15, which was estimated for SQ LB samplesabricated in a similar manner here, the n of the SQ ag-regate films is lower than that of glass �n�1.52� on thehort-wavelength side. On the contrary, on the long-avelength side (near 650 nm) of the H band, the relative

eflection is found to increase somewhat. In this wave-ength region, the n�� increases with a probable anoma-ous dispersion due to the strong H-aggregate absorption,hile the absorption bands of the monomer or dimer re-

ig. 6. Typical s-polarized �R /Rsub�s spectrum at �=45° (solidurve) and A�� spectrum (dotted curve) for the five-layered SQB films.

ig. 7. Polarization dependence of R /Rsub spectra for the five-ayered SQ LB films.

ain. As a result, the enhanced reflection is influenced byhe increasing k�� of the monomer absorption bandather than the increasing n.

As evidenced by the polarization-dependent reflectionpectra for the MC J-aggregate films (see Fig. 4), the-polarized reflection response was higher than the-polarized, with little relation to the absorption. The po-arization dependence on the SQ five-layered films ishown in Fig. 7. The p-polarized reflection experiences aarger increase (by a factor of 1.9 at the peak of 530 nm)han the s-polarized, in the same way as that of the MC-aggregate films, though no difference in spectral profiles observed in both polarized reflection curves.

. SIMULATIONS AND DISCUSSION. Calculation of Reflection and Absorption Spectrarom the experimental results, we have so far indicated

hat the reflection response of the dye-aggregate films cane explained from a macroscopic viewpoint; the enhance-ent of reflection in the absorption bands is attributed to

he absorption effect expressed by the increasing k��,nd the spectral behaviors on both wavelength sides atow absorption are caused by the changing n��, with annomalous dispersion due to the strong absorption bands.Next, in order to further understand the reflection

haracteristics of the dye-aggregate films, we consider theeflection response of the strongly absorbing films by us-ng numerical calculations based on the macroscopic waveptics. Here we adopt a plane-parallel structure of threeayers with an optically isotropic absorbing film as aimple calculation model: air–absorbing film–glass sub-trate, corresponding to the measured dye-aggregatelms. Although the transition dipoles in the measuredye-aggregate films could be weakly anisotropic withniaxial orientation,12–16 the numerical calculationsased on the isotropic model can still be compared withhe experimental results for the essential points on theeflection properties. Here, we adopted the following di-lectric functions based on angular frequency �: (a) forhe absorbing thin film, �L��, by the well-known Lorentzscillation model with a single resonant absorption bandnd a damping constant, (b) for the glass substrate, �C��,y a Cauchy normal dispersion. The dielectric functionsor the absorbing film and for the glass substrate are re-pectively given by

�L�� = �b +f0��0

2 − �2�

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+ if0�

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, �1�

here �b is the background dielectric constant, �0 the an-ular frequency of resonant absorption, f0 the amountroportional to oscillator strength, and the dampingonstant, and

�C�� = a0 + a1�2 + a2�−2 + a3�−4 + a4�−6 + a5�−8, �2�

here the above various parameters are summarized inable 1, and the unit of the wavelength � isicrometers.17

Figure 8 shows an example of the calculated Lorentzomplex-refractive-index spectrum nL�� (n, dotted curve;, solid curve), based on � of Eq. (1) given by the param-
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ters �b=2.25 �n=1.5�, �0=2.2 eV ��=564 nm�, f01.2 eV2, =0.16 eV, and derived from the related ex-ression of n= �1/2. The calculated n�� changes largelyith an anomalous dispersion near the wavelengths of anbsorption band with a 564 nm peak. Here, one finds thathese parameters correspond to the n�� characteristics ofhe dye-aggregate films, especially the MC J-aggregatelms mentioned in Section 3 (see Fig. 5).We utilized the well-known Fresnel formula18 for theacroscopic wave optics to calculate both R /Rsub spectra

nd A�� derived from the transmission. For the three-ayered structure, we obtained an expression for absoluteeflection R

R = � r12 + r23 exp�i2kz�2�d�

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ith

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ig. 8. Lorentz complex-refractive-index spectrum, nL��, with aingle resonant absorption band at �=2.2 eV ��=564 nm� forbsorbing thin films. Solid and dotted curves represent k�� and��, respectively.

Table 1. Parameter Values for Estimations of BK-7Glass Refractive Indexa

Parameter symbol Values

a0 2.2718929a1 −1.0108077�10−2

a2 1.0592509�10−2

a3 2.0816965�10−4

a4 −7.6472538�10−6

a5 4.9240991�10−7

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kz�i� =2�

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here n�i� is the complex refractive index of the ith layer,z�i� is the z component of the wave vector perpendicularo the surface, and � is the incident angle of light. d is thehickness of the absorbing film and n�1� is the refractivendex of the first layer, where n�1�=1 for air. ri�i+1� repre-ents the complex reflection coefficient at the i / �i+1�ayer interface, which has a different expression for theolarization of incident light, represented by Eqs. (4) and5). To compare the numerical simulations with the ex-erimental results of the dye-aggregate films, we calcu-ated Rsub�� and R�� spectra for the air–glass and air–bsorbing film–glass structures, respectively, andbtained the relative reflection spectra to the glass sub-trate: R /Rsub.

When we calculated the absorption spectra, we ob-ained the following expression for the transmittance T athe normal incidence ��=0° �:

T =n�3�

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ith

ti�i+1� =2kz�i�

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here ti�i+1� represents the complex transmission coeffi-ient at the i / �i+1� layer interface. n�1� and n�3� repre-ent the refractive indices of air and the glass substrate,espectively. Successively, we calculated the ratio of theransmittance T�� for the air–absorbing film–glass, withespect to that of the air–glass Tsub:T /Tsub�� and thenetermined A�� from the expression of −ln�T /Tsub�, inhe same way as the experimental evaluations.

. Simulation Results and Discussiony using the simple model mentioned above, we calcu-

ated first R /Rsub�� and A�� of the absorbing thin filmsith nL�� in Fig. 8. Figure 9 shows �R /Rsub�s at �=45°

solid curve), and A�� (dotted curve), for the 10 nm thick-ess absorbing films. The thickness is comparable withhat of the dye-aggregate LB films described here. The

ig. 9. Calculated �R /Rsub�s spectrum at �=45° (solid curve) and�� spectrum (dotted curve) estimated from the calculated

ransmission at �=0°, for three-layered structure of air–bsorbing film �d=10 nm�–glass substrate.

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alculated �R /Rsub�s curve is analogous to the A�� and�� curves (respectively, in Figs. 9 and 8). Clearly, the ab-orption itself causes the enhanced reflection, and the re-ection behavior can be understood from the k�� spec-rum. This simulation provides excellent support for theye-aggregate films, especially for the MC J-aggregatelms (see Fig. 3). In addition, from Fig. 9 it is found thathe relative reflection becomes higher on the long-avelength side of the absorption band, and it is slightly

ower than the absorption curve on the short-wavelengthide. Consequently, the spectrum disagreement tendencyn the reflection and absorption curves of the experimen-al data (Figs. 3 and 6) can also be observed in the simu-ations, and from the nL�� in Fig. 8, this tendency is at-ributed to the changing n with anomalous dispersion.

Second, in Fig. 10, the polarization dependence of/Rsub at �=45°, is calculated by adopting the same pa-

ameters used in Fig. 9. As expected, the p-polarized rela-ive reflection �R /Rsub�p (Fig. 10 solid curve) is larger thanhat of s-polarized light (Fig. 10 dotted curve), except forne part of the short-wavelength side �500–530 nm� ofhe absorption band. The ratio of �R /Rsub�p to �R /Rsub�s athe 564 nm peak is equal to 1.9, which is comparable tohe experimental values obtained for the dye-aggregatelms. In addition, the �R /Rsub�p curve becomes high onhe long-wavelength side, and it decreases drastically onhe short-wavelength side. From consideration of theL�� in Fig. 8, these behaviors are clearly affected by thenomalous dispersive n of the absorbing layer. The effectf the refractive index on the reflection spectra for the ab-

Fig. 10. Polarization dependence of calculated R /Rsub spectra.

ig. 11. Absorbent-film-thickness dependence of calculatedR /Rsub�s spectra.

orbing films is found to be much larger for p-polarizedight than for s-polarized light. Thus the p-polarized re-ection of the absorbing films appears as the higher re-ponse. Although the spectral profile of the p-polarized re-ection is altered by the anomalous dispersion effect of n,s compared with no spectral change in the experimentalata (Figs. 4 and 7), this simulation also essentially sup-orts the measured reflection data for the various types ofye-aggregate films.From the experimental data, the increasing thickness d

f the dye-aggregate films causes increases in the reflec-ion intensities. Third, the calculated �R /Rsub�s at �=45°or the various d of absorbing films are presented in Fig.1. The same set of parameters mentioned above was alsosed in the calculations. In the thickness range of d1 to 10 nm, the relative reflection is enhanced near thebsorption wavelengths, and increases with increasing d.hose film thicknesses are almost comparable with thosebtained experimentally for the dye-aggregate layer filmsescribed earlier. Obviously, the increases in relative re-ection have no linear relation with d. This simulation re-roduces the absorbent-layer-thickness dependence on re-ection particularly well, as shown in Fig. 3.When the thickness is increased further, however, d

50 and 100 nm (more than 1/10 of �), although the rela-ive reflection is enhanced near the absorption wave-engths, in the same way as observed for d=1 to 10 nm,he intensities on the long-wavelength side are found toncrease while those on the short-wavelength side de-rease. Such behaviors are simply explained from the ef-ect of the changing n with anomalous dispersion, as seenrom the spectral profile of the nL�� curve in Fig. 8. It isherefore found that the anomalous dispersion effect isxhibited remarkably in the reflection at the thicknessore than 1/10 of �. Furthermore, in the case of d100 nm (comparable with �), an optical interference ow-

ng to the two reflected light beams from the first and sec-nd interfaces (respectively, air–absorbing-film and ab-orbing film–substrate) appears on both wavelength sidesf the absorption band.

Finally, to confirm the effect of absorption on the en-anced reflection in the absorption bands, the dependencef the parameter f0 on enhanced reflection is representedn Fig. 12, where f0 is proportional to the oscillatortrength of absorption, and gives a scale of absorption in

ig. 12. Calculated R /Rsub spectra (at �=0°) for nL�� with vari-us values of f : 1, 1.5, and 2. Inset, corresponding n �� curves.
0 L

twusswttswsmtt

5Tcfitsirssicatttr

@

R

1

1

1

1

1

1

1

1

1


he Lorentz dielectric function. The simulation resultsere calculated at the normal incidence for various val-es of f0 given in Eq. (1): 1, 1.5, and 2. The inset of Fig. 12hows the corresponding nL�� used in the reflectionimulations. Evidently, although the n changes largelyith the f0 value near the absorption band, as shown in

he inset of Fig. 12, the intensities of the calculated reflec-ion spectra are strongly dependent on f0, and increase inpectrally unchanged shape when the f0 value increasesith respect to the absorption. Thus the simulation re-

ults indicate that the origin of the reflection enhance-ent in the strong absorption bands is directly related to

he absorption effect, and the enhanced reflection charac-eristics can be expressed mainly in terms of k��.

. CONCLUSIONShe polarized reflection and absorption spectra of mero-yanine J-aggregate and squarylium H-aggregate thinlms have been investigated. The macroscopic wave op-ics provides a good explanation for interpreting the es-ential features of the spectroscopic reflection responsesn the absorption bands, in spite of d��. From the mac-oscopic analyses of the experimental data and simpleimulations, we have confirmed that the reflection re-ponse of the dye-aggregate films include two factors: thencreasing k�� expressing the absorption itself, and thehanging n�� with an anomalous dispersion due to thebsorption bands. The enhanced reflection observed onhe absorption wavelengths, and the characteristic reflec-ion behaviors on both wavelength sides at low absorp-ions, is attributed mainly to the former and latter effects,espectively.

T. Wakamatsu’s e-mail address is wakamatuee.ibaraki-ct.ac.jp.

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optical reflection response of dye-aggregate films in the absorption bands

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