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Dispersion control of excitonic thin films for tailored super-absorption in the visible region Byeong Hun Woo, In Cheol Seo, Eunsongyi Lee, Seo Young Kim, Tae Young Kim, Sung Chan Lim, Hoon Yeub Jeong, Chang Kwon Hwangbo, and Young Chul Jun ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.6b01044 • Publication Date (Web): 03 Apr 2017 Downloaded from http://pubs.acs.org on April 8, 2017

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Dispersion control of excitonic thin films for tailored super-absorption in the visible region Byeong Hun Woo1, In Cheol Seo1, Eunsongyi Lee1, Seo Young Kim2, Tae Young Kim2, Sung Chan Lim1, Hoon Yeub Jeong1, Chang Kwon Hwangbo2 , Young Chul Jun1, † 1

School of Materials Science and Engineering, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, Republic of Korea 2

Department of Physics, Inha University, Incheon 22212, Republic of Korea †

[email protected]

ABSTRACT Strong light absorption in ultrathin films has been of great interest for both fundamental studies and device applications. Here we demonstrate and analyze controllable super-absorption in excitonic thin films in the visible region. By adjusting the concentration of J-aggregate dyes, we control the dispersion of excitonic films (from optically metallic to non-metallic ones), and show that this leads to drastic changes in the optical response of organic thin films. We find that planar excitonic films can have various optical features in the visible region – e.g. surface polaritons, epsilon-near-pole, asymmetric Fabry–Perot type resonances, etc. We leverage these diverse features to study perfect absorption in planar films without additional structural patterning. We also demonstrate that strong light absorption can even occur away from an excitonic absorption peak (i.e. maximum optical loss position) due to cavity-like resonances in the high dielectric constant region. Our work demonstrates that there are unique opportunities for dispersion control in the visible region with easy-to-handle organic molecules, and this can be useful for novel nano-optical studies or energy conversion devices. Collaborative synergy between molecular photonics and nanoscale optics has been demonstrated throughout this work.

KEYWORDS: perfect absorption, excitonic films, J-aggregates, dispersion control, surface polaritons, Fabry– Perot resonances

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Absorption spectrum control is one of the fundamental issues in photonics, and is important for both basic light-matter interaction studies and energy conversion (or light detection) applications. Especially, perfect absorption (PA) has attracted much attention recently. It can be accomplished by blocking the transmission (T = 0) with a reflective metallic substrate and finding the destructive interference condition of reflected light (R = 0). Subsequently, PA can be achieved: Absorption A = 1 – R – T = 1. Although PA has been studied in various configurations, most of them are based on delicate nanostructure patterning.1-7 Another approach for PA employs planar films without structural patterning. For example, a highly lossy film (e.g., Ge) can be deposited on metal to induce asymmetric Fabry–Perot (F–P) type resonances even with a nanometer scale film thickness.8-10 However, the absorption spectrum in this case is very broad. Moreover, because it requires very lossy films, material choice is highly limited. Planar metal–dielectric–metal films can be also used in large area perfect absorbers without lithographic patterning; this would provide a simple and costeffective solution for certain applications (e.g., color filters).11,12 However, the dielectric spacer layer between the top and bottom metal cladding needs to be sufficiently thick to ensure F–P resonances at a target wavelength, and a significant amount of incident light can be absorbed in the metal clads instead of the dielectric region. Therefore, these films have limited applicability for efficient energy conversion or light detection based on PA. Another method to achieve PA in planar films is to employ an epsilon-near-zero (ENZ) layer (e.g., ITO in the near-infrared region).13-16 Using this approach, PA can be achieved in low-loss, ultra-thin layers near the ENZ frequency of an absorbing film with a p-polarized, oblique incidence of light. This method is advantageous because ENZ frequencies are tunable by film growth conditions (e.g., adjusting the doping level in ITO). However, it is difficult to extend this approach to the visible region because it requires extremely high carrier density for ENZ frequencies in the visible range. In this study, we demonstrate and analyze controllable super-absorption in excitonic thin films. J-aggregates have very sharp excitonic absorption lines that can be tuned over the whole visible region by changing their molecular designs.17,18 J-aggregates also support coherent exciton transfer, which can be useful for optical energy harvesting. The large oscillator strength in J-aggregates has been used in various strong-coupling experiments.19-22 Herein, we adjust the concentration of J-aggregate dyes and control the dispersion of excitonic thin films; this causes drastic changes in the optical response of organic thin films. We show that planar excitonic films can have various optical modes and features in the visible region. We leverage these features to demonstrate PA and control strong absorption in metallic and non-metallic excitonic films. Our studies demonstrate that we have unique opportunities for dispersion control in the visible region with easy-to-handle organic molecules. Figure 1(a) shows the molecular structure and absorption spectrum of a water-soluble cyanine dye used in our experiment (TDBC:5,6-dichloro-2-[[5,6-dichloro-1-ethyl-3-(4-sulphobutyl)-benzimidazol-2-ylidene]-propenyl]1-ethyl-3-(4-sulphobutyl)-benzimidazoliumhydroxide, sodium salt, inner salt).23 TDBC monomers have an absorption peak around 520 nm (Fig. 1(b)). However, when they dissolve in water, they form J-aggregates and the absorption spectrum becomes very sharp, strong, and the absorption peak red-shifts to ~590 nm (Fig. 1(b)). Poly-vinyl alcohol (PVA) provides a similar environment to water and when TDBC molecules mix with PVA, 2


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they form J-aggregates again. The fraction of J-aggregate formation in a PVA matrix is smaller than that in water, but we can still have strong and sharp absorption near 590 nm. The large oscillator strength in J-aggregates can result in strong absorption at a specific wavelength. It can induce an optically metallic response (Re[ε] < 0) within a certain wavelength range, if the TDBC concentration is large enough. This is easily understood from the Kramers–Kronig relation. Figure 1(c) shows the picture of two excitonic films prepared by spin-coating (see Method for details). Two samples have different TDBC concentrations, and show different optical responses in the visible region (non-metallic vs metallic). The metallic one has a clear appearance like gold; due to a large Im[ε] at the exciton line, we can obtain a metallic response from an organic thin film in the visible region.24-29 This metallic film supports excitonic surface polaritons (SPs), similar to surface plasmon polaritons (SPPs) on a metal surface. Although they are generated by different physical mechanism, they show similar optical responses. A layer-by-layer (LBL) method can also be used to create thin films of J-aggregate dyes.26,30 This method can produce a better film quality, but the thickness of the film prepared by LBL-assembly is usually limited to a few nanometers due to the timeconsuming processes. However, when J-aggregate dyes are mixed in a polymer matrix and are spin-coated, we are able to adjust the concentration of dyes arbitrarily. As a result, we can control the dispersion of the excitonic film, ranging from optically metallic ones (Re[ε] < 0) to non-metallic ones (Re[ε] > 0). We can then modify the optical response of the film significantly. This has inspired us to investigate the optical properties of excitonic films with engineered dispersion. In this paper, we study controlled super-absorption in planar excitonic films. We consider both metallic and non-metallic excitonic films, which are controlled by TDBC concentrations in a PVA matrix. We experimentally demonstrate and theoretically analyze strong absorption in the visible spectral region. We consider two different configurations. First, we use the attenuated total reflection (ATR) configuration (i.e., [Prism/Excitonic film/Air]) for clear mode coupling studies. In this case, by working beyond the critical angle, we can naturally suppress transmission (T = 0). Secondly, we employ a metal substrate without a glass prism (i.e., [Air/Excitonic film/Silver]). A reflective substrate is often used for PA studies to block transmission (T = 0). We find that strong absorption can occur even away from the excitonic absorption peak due to cavity-like resonances in ultra-thin organic films. We present various experimental absorption spectra together with the theoretical calculations and simulations supporting them.

RESULTS AND DISCUSSION Figure 2(a) shows the dielectric constants of the excitonic film, extracted from the reflection-transmission measurements (see Method for more details). The reflection and transmission raw data are given in Supporting Information (Fig. S1). The imaginary part of the dielectric constants (Im[ε]) has a pole near 590 nm that corresponds to excitonic absorption, and we have the optically metallic (Re[ε] < 0, 530–590 nm) region right below this peak absorption wavelength. This metallic excitonic thin film shows various features in the visible region; SP resonance (Re[ε] ≤ -1), ENZ point (Re[ε] ~ 0), epsilon-near-pole (ENP) or excitonic absorption pole (Im[ε] ~ peak), large-ε region, etc. The spectral positions for these features can be tuned by adjusting the 3


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concentrations of TDBC and PVA in the films or by using other cyanine dyes with different excitonic absorption wavelengths. Figure 2(b) shows the absorption spectra from this excitonic film (thickness: t ~ 50 nm) for several different incidence angles. We first perform p-polarization measurements in the attenuated total reflection (ATR) configuration to investigate SP mode coupling. Working beyond the critical angle (θc ~ 42°), the transmission is naturally suppressed. By measuring reflection spectra, we can deduce absorption spectra (A = 1 – T – R). Here to compensate for reflections from prism surfaces, background reflection spectra are also measured for each incident angle without a film. They are then subtracted from the measured spectra of organic films. The angles here refer to internal angles inside the prism. The same configuration is often used to measure the dispersion of SPPs on metal (silver or gold) films, because a high-index prism can provide additional momentum required for the excitation of surface bound waves. In the ATR configuration, we can access a bound mode beyond the light line in air. In Fig. 2(b), we observe clear PA near 563 nm (Re[ε] < -1) in the p-polarized spectrum. The maximum absorption reaches about ~ 99.5 % for the incidence angle of ~52º. This wavelength and incidence angle correspond to a critical coupling condition (γdamping = γradiative), which can be explained with temporal coupled mode theory.31-33 At this condition, incident light can be absorbed maximally without reflection. Such an absorption peak appears only in p-polarization spectra (not in s-polarization ones), as expected for SP mode coupling. Figure S2 in Supporting Information is the p- and s-polarization absorption spectra maps in the ATR configuration as a function of incident angle, which are obtained using the dielectric constants in Fig. 2(a). We can clearly see the SP mode dispersion in the p-polarization spectrum, while it is missing in the s-polarization spectrum. In fact, SP modes in J-aggregate films have been also studied in Ref. [27], and we observed similar features in our samples. Because there was a previous report on SP modes, we briefly discussed it here. We rather focused on dispersion control and the resulting perfect absorption in various contexts. We also see another sharp peak at the ENP position, which corresponds to the peak of Im[ε] (i.e. maximum loss position). It occurs at the J-aggregate exciton wavelength (~ 590 nm). We have a sharp absorption peak at the ENP wavelength due to this high loss.

We prepare another excitonic film with smaller TDBC concentration in a PVA matrix (t ~ 40 nm), so that it becomes almost non-metallic (Re[ε] > 0) and thus no SP mode exists. Figure 3(a) and (b) show the dielectric constants and the p-polarized absorption spectra measured in the ATR configuration. As expected, PA at the SP position (around 560–565 nm) does not appear. However, we find another PA peak (~ 583 nm) appears closer to the ENP wavelength. This PA peak reaches about 99.5 % around the incidence angle of 60º. Figure 3(c) compares the angle dependence of peak absorption in metallic and non-metallic films. Two samples show a clear difference. The metallic one has an absorption peak near 52º, but the non-metallic one has near-PA at larger incidence angles with a broader angular response. Two films show a clear difference in the angle dependence as well as PA wavelengths. These imply that PA has different physical origins in two cases. Figure S3 in Supporting Information is the p-polarized absorption spectra maps, which correspond to Fig. 2(b) and Fig. 3(b). We can notice clear differences between metallic and non-metallic excitonic films. In metallic 4


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films, the prominent absorption peak appears around 560 ~ 575 nm only for p-polarization, and this corresponds to SP mode coupling (Fig. 2). However, in non-metallic films, PA occurs around 580 ~ 590 nm, which is much closer to the ENP wavelength (maximum loss position). Moreover, we can see that these two samples show different angular dependencies, in agreement with Fig. 3(c). As will be discussed below (Fig. 4 ~ 5), PA in the non-metallic film (Fig. 3) can be explained as asymmetric F–P type resonances. F–P type resonances can occur in deep subwavelength films, if materials are lossy [8-10]. Loss can relax the minimum thickness requirement for such resonances. In Fig. S3, we have also indicated the field profiles in metallic and non-metallic samples. The clear differences between them again confirm our descriptions on PA in these samples. We have also observed similar PA from other non-metallic samples with different film thicknesses (Supporting Information Fig. S4). Even in a 25 nm-thick film, near-perfect absorption (A ~ 96%) is observed (corresponding to the thickness to wavelength ratio: t/λ ~ 4.3 %). We can analyze this PA near the ENP position using the partial reflected wave calculations8,34 (Fig. 4). Reflected light from a highly absorbing layer can have a complex reflection coefficient with its phase deviating significantly from π, which means the phasor in the complex reflection coefficient diagram (Re[r]-Im[r]) is not along the horizontal Re[r] axis. This can enable cavity-like resonances even in deep subwavelength films. Note that, in typical lossless dielectric films, the film thickness t needs to be thick enough to satisfy the resonance condition (t ≈ q·λ/2n, where q is an integer). Near the ENP, we have large absorption loss (i.e., a peak of Im[ε]), and thus we can have asymmetric F–P type resonances even in very thin organic films (t/λ ~ 6.86 % for t = 40 nm). Considering the fact that typical refractive indices of organic films are around n = 1.6, the thickness to wavelength ratio (t/λ) should be at least 1/2n ~ 31.25% in conventional, lossless dielectric films. Figure 5 shows the complex phasor diagram of the reflection coefficient for the excitonic film studied in Fig. 3. We consider the ATR configuration with p-polarized light as used in experiments. We assume the same wavelength (λ0 = 583 nm), incidence angle (θ = 60º), but vary the film thicknesses (t = 30–60 nm) to investigate the resonance condition. These wavelength and incidence angle are the ones used in Fig. 3. Phasors corresponding to each partial reflected wave (r0, r1, r2, …) are indicated as arrows and connected together headto-tail. The final position of the phasor shows the amount of reflection (R = |r|2) from the film, and is related to the absorption (A = 1 – R – T = 1 – R, here T = 0 beyond the critical angle θc). The reflection coefficient from a general three-layer system (Layer 1, 2, 3) can be expanded as follows34:

= ∑ , = + ∑

(1)

where rm is the roundtrip reflection coefficient (rm =

for m ≥1, and r0 = r12) and

β = 2/ cos . Here rmn and tmn are the Fresnel reflection and transmission coefficients from medium m to medium n given by ! = "# − #! %/"# + #! % and ! = "2# %/"# + #! % with the admittance # = /cos for p-polarization, # = cos for s-polarization, and = sin sin / . The four phasor diagrams show a clear trend. As the film gets thicker, the r1 vector becomes shorter and is rotated counter-clockwise. The first reflection coefficient vector (r0) remains the same for all four cases, because it represents the reflection from the top surface and thus is not affected by the film thickness. At t = 40 nm, the 5


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total phasor returns to the closest point to the origin (i.e., achieving the strongest absorption). This thickness matches the experimental data in Fig. 3 exactly, which shows PA at t ~ 40 nm. The absorption peak occurs around 583 nm, which is slightly shorter than the J-aggregate excitonic line (~590 nm). From further calculations, we find this absorption peak position varies a little depending on the film thickness and incidence angle. It is because the F–P type resonance condition is affected by those factors. Supporting Information Figure S5 shows another phasor diagram. Here, the film thickness and wavelength are fixed as t = 40 nm and λ0 = 583 nm, but the incidence angle is varied. This time the r0 vector is also rotated, and its size varies a little. However, when the incidence angle becomes θ = 60º, the total phasor returns to the origin closest again. We have the smallest reflection (close to zero) and thus achieve PA. Therefore, our partial reflected wave calculations reflect our experimental result in Fig. 3 very well, and show that PA indeed results from the cavity-like resonances in thin organic films (not simply due to high material losses).

We also study light absorption of TDBC/PVA films on a silver substrate. In this case, the transmission is naturally blocked by the reflective substrate, and thus we can maximize the absorption by minimizing the reflection. This time, we can observe another kind of cavity-like resonances for both p- and s-polarization in a longer wavelength region (> 600 nm), which has smaller optical losses (Im[ε]). The imaginary part of the dielectric constant has a peak near the ENP position, but drops rather quickly away from it. The real part fluctuates rapidly (e.g., from negative to positive) around this absorption pole. We can have a high dielectric constant value with lower losses in a longer wavelength region. This is another interesting point in excitonic thin films, and we have investigated optical resonances in this wavelength region too. We could find various optical features appear, depending on the film composition and thickness. Here, we compare metallic and non-metallic films with similar thicknesses, and demonstrate that they can be drastically different in their optical behavior. An optically thick silver layer (tAg ~ 200 nm) was deposited on a quartz wafer, and then TDBC/PVA films were spin-coated on a silver substrate. Figure 6(a) and (b) show the p-polarized and s-polarized absorption spectra from the sample (t ~ 40 nm) for different incident angles. This excitonic film shows the optically metallic response (Re[ε] < 0) in the visible region (550–600 nm) (Supporting Information Fig. S6(a)). At longer wavelengths, we can achieve very large values for the dielectric constant (Re[ε] > 5) with much smaller losses than the ENP position. Both p- and s-polarization spectra show optical resonances in the wavelength region of 600–650 nm. To look at the nature of this feature more, we numerically investigated how the absorption peak position (i.e., the resonance wavelength) changes with the film thickness (Fig. 7(a)). We clearly see the resonance wavelengths get longer in thicker films, as expected for cavity-like resonances (such as F-P resonances). This condition can be again analyzed using the partial reflected waves. Figure 7(b) is the complex phasor diagram of the reflection coefficients for s-polarization (incident angle: 55º). Here, we compare two cases: on-resonance (~ 626 nm) and off-resonance (~ 700 nm) conditions to see differences. At onresonance, the total phasor returns to the origin closely, while it remains far away at off-resonance. This verifies that a cavity-like resonance occurs in the on-resonance condition. We also perform more TMM calculations,35 and obtain the absorption maps as a function of wavelength and angle (Supporting Information Fig. S7(a) and 6


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(b)). We find these agree well with our experimental data. In addition to these optical resonances, sharp Jaggregate exciton lines are also visible at the ENP position. We have observed similar resonances in other samples (Supporting Information Fig. S8). In this case, resonance peaks can even extend beyond the 700 nm region. We also prepared another excitonic film on silver (t ~ 35 nm), where we decreased the TDBC concentration. This sample has a non-metallic response (i.e. Re[ε] > 0 in all region), as shown in Fig. S6(b). We have measured angle-dependent absorption spectra again for both p- and s-polarizations (Fig. 8). This time the strong absorption peaks centered around 600 nm for both polarizations regardless of incident angles. This is in agreement with our TMM calculations (Supporting Information Fig. S7(c) and (d)). The measured spectra in Fig. 8 are clearly different from those for the metallic sample with a similar film thickness (Fig. 6). We also see very different angle dependencies from these two samples. The s-polarization absorption spectra in the metallic sample showed an opposite trend compared to the non-metallic sample. In Fig. 6(b), the absorption peak intensity gradually increased with larger incident angles, while it decreased in Fig. 8(b). These angle dependencies agree well with TMM calculations, as shown in Supporting Information Fig. S7(b) and (d). The drastic difference in the optical response is essentially originated from different dispersions of the two samples.

Except Figure 2, all other spectral resonances in our work can be understood as cavity-like optical resonances (asymmetric F–P type resonances in our case). Figure 2(b) was obtained from p-polarized ATR measurements of a metallic sample, and shows mode coupling to a bound SP mode within the optically metallic region. We also want to mention that the features we observed are not from monomer response. For example, the spectral feature around 560 ~ 575 nm in Fig. 2 appears only for p-polarized ATR measurements. The spectra from air-incidence or s-polarization ATR measurements do not exhibit such prominent features. And they are far away from the monomer absorption wavelength (~ 520 nm). Therefore, we can clearly tell that these drastic spectral features are not due to monomer response. Actually, in all of our absorption spectra, we have weak shoulders around 520 ~ 530 nm, which could be originated from the monomer response. In this work, we have demonstrated large area super-absorption in planar films without lithographic patterning. This is possible because excitonic films can have various optical modes and features in the visible region. Current studies based on TDBC can be readily extended to other J-aggregate molecules that can cover the entire visible range. Eventually, to convert absorbed optical energy into useful photocurrents, we need to further improve the composition of organic films for carrier extraction, or we need another carrier transport layer, as commonly used in organic optoelectronic devices. This could be an important, future research direction. In the current work, we presented basic optical studies on dispersion control with easy-to-handle organic molecules. This demonstrates that collaborative synergy can be obtained between molecular photonics and nanoscale optics, which can benefit from each other in various ways.

CONCLUSIONS In conclusion, we have demonstrated controlled perfect absorption and super-absorption in planar excitonic 7


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films without additional structural patterning. We have adjusted the concentration of J-aggregate dyes and controlled the dispersion of excitonic thin films, ranging from optically metallic to non-metallic ones. We find that this leads to drastic changes in the optical response of organic thin films. Planar excitonic films can have various optical modes and features in the visible region: SPs, ENP, ENZ, asymmetric F–P type resonances, large dielectric constant region, etc. We experimentally demonstrated and theoretically analyzed strong light absorption in metallic and non-metallic films. For that, we have considered both the ATR configuration ([Prism/Excitonic film/Air]) and the silver substrate ([Air/Excitonic film/Silver]). We find that strong absorption can even occur away from the excitonic absorption peak due to cavity-like resonances in the large dielectric constant region. Our work demonstrates that there exist unique opportunities for dispersion control in the visible region with organic molecules, and this can be useful for various nanophotonics applications (such as efficient energy conversion or light detection devices).

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METHODS TDBC molecules were dissolved in water and mixed with PVA, and spin-coated on a quartz substrate. Both TDBC and PVA were first prepared as water-based solutions. For dispersion control, TDBC and PVA concentrations in water were varied within the ratio of 1–3 wt% and 1–6 wt%, respectively. To fully dissolve PVA in water, PVA solutions were heated for several hours at 90 ºC before mixed with TDBC solutions. Final TDBC/PVA solutions were prepared by mixing them in the 3:1 volume ratio and agitating for about 1 hour using a vortex machine. Before spin-coating, a quartz substrate was sonicated in DI water, acetone, and isopropanol for 5 minutes, respectively. After cleaning, to enhance the wettability of the substrate surface, we had the UV ozone treatment of quartz substrates for 10–15 minutes. Finally, TDBC/PVA solutions were spincoated on quartz substrates with the spin speed of 4000 rpm for 30 seconds. To obtain thinner films, higher spin speeds with longer spinning time (up to 5000 rpm for 60 seconds) were also used. The thicknesses of excitonic films were measured using either a surface profiler (P6, KLA Tencor) or AFM (DI-3100, Veeco). We first made 5–6 scratches on the organic film, scanned the surface over scratches, and took an average of the measured values to determine the final film thickness. For our optical measurements, we used either spectroscopic ellipsometer (VASE, J.A. Woollam) or spectrophotometer (Cary 5000, Varian). In both cases, the light source was white light with a large spot. Because the illumination spot size is orders of magnitude larger than the SP propagation length, incident light can be considered as a near-uniform plane wave in our case. We obtained the dielectric constants of excitonic films by fitting the experimentally measured reflection and transmission spectra to the Fresnel’s equation.26,27,36 Under the normally incident beam with the frequency ω, the reflection Rcal and transmission Tcal of the multilayer structure can be expressed as the follows. We assume the thin film has the complex refractive index n~1 (ω ) = n1 (ω ) + ik1 (ω ) and thickness d.

Rcal = RNUM

RNUM T , Tcal = NUM D D 2 2 2 k1 qd =e [(n0 − n1 ) 2 + k1 ][( n1 + n2 ) 2 + k1 ]

+ e − 2 k1qd [( n0 + n1 ) 2 + k1 ][( n1 − n2 ) 2 + k1 ] 2

2

2

+ 2 cos(2n1qd )[( n 20 − n12 − k 12 )( n12 − n22 + k 12 ) − 4n0n2k1 ] − 4k1 sin(2n1qd )[(n0 − n2 )( n12 + n0n2 + k 12 )] TNUM = 16n0n2 ( n12 + k 12 ) 2

2

D = e 2 k1 qd [(n0 + n1 ) 2 + k1 ][( n1 + n2 ) 2 + k1 ] + e − 2 k1qd [(n0 − n1 ) 2 + k1 ][(n1 − n2 ) 2 + k1 ] 2

2

2

+ 2 cos(2n1qd )[( n 20 − n12 − k 12 )( n12 − n22 + k 12 ) + 4n0n2 k1 ] + 4k1 sin(2n1qd )[( n0 + n2 )( n12 − n0n2 + k 12 )] where n0 and n2 are the refractive indices of the air and the substrate, respectively. q = 2π / n0 λ0 , where λ0 is the wavelength of incident light in air. We have experimentally measured the reflection ( Rexp ) and transmission ( Texp ) spectra. Therefore, we can define the following function (Fresnel residual function) at a 9


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given frequency,

f (n1 , k1 , ω) = Rcal (n1 , k1 , ω ) − Rexp + Tcal (n1 , k1 , ω ) − Texp . n~1 minimizing f (n1 , k1, ω ) should be close to the real values of the complex refractive index of the thin film. Through iterations for all the experimental frequencies, we can obtain the complex refractive indices. However, since such Fresnel residual function sometimes has more than one solution, we need to correct the obtained value via Kramers–Krönig (K–K) relation based on k1 which has less uncertainty. Note that we applied the following K–K relation including noffset (instead of 1),

n(ω ) ≅ noffset +

2

π

P∫

ωU

ωL

ω ' k (ω ' ) dω ' , ωL ≤ ω ≤ ωU ω '2 −ω 2

to consider the background contributions beyond the experimentally obtained spectra. We used noffset around 1.7 for our excitonic films.

ACKNOWLEDGMENTS We acknowledge financial support from National Research Foundation (NRF) grants (No. 2015001948, NRF2016R1D1A1B03933827), Research fund (1.150036.01, 1.160087.01) of UNIST (Ulsan National Institute of Science and Technology). CKH acknowledges the supports from the Inha University Research Grant and the Basic Science Research Program through NRF of Korea (NRF-2016R1D1A1A09919495).

ASSOCIATED CONTENT Supporting Information Raw data (reflection and transmission spectra) used for the dielectric constant calculations; absorption spectra map obtained from TMM calculations (corresponding to Fig. 2); absorption spectra map and field profiles (corresponding to Fig. 2 and 3); the p-polarized absorption spectra of optically non-metallic samples in the ATR configuration; phasor diagrams for complex reflection coefficients; the dielectric constants of metallic and nonmetallic samples (corresponding to Fig. 6 and 8); absorption spectra map obtained from TMM calculations (corresponding to Fig. 6 and 8); the s-polarized absorption spectra of optically metallic samples in the ATR configuration.

AUTHOR INFORMATION Notes The authors declare no competing financial interest.

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36. Phillips, R. T. A numerical method for determining the complex refractive index from reflectance and transmittance of supported thin films. J. Phys. D: Appl. Phys. 1983, 16, 489.

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Figure 1

Fig. 1 (a) Molecular structure of the TDBC dye. (b) The absorption spectra of the TDBC monomer (black) and J-aggregate in water (red). When monomers dissolve in water, they form J-aggregates; the absorption peak becomes very sharp and red-shifts to ~590 nm. We can still see weak absorption near 520 nm due to monomer residues. (c) A picture of PVA/TDBC films prepared by spin-coating. Two samples have different TDBC concentrations, and show different optical responses in the visible region (non-metallic vs metallic). The metallic one has a clear appearance like gold.

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Figure 2

Fig. 2 (a) The dielectric constants of the metallic excitonic film (t ~ 50 nm). Strong and sharp absorption in Jaggregates result in optically metallic responses (Re[ε] < 0) in the visible region. Planar excitonic films can have various optical modes and features in the visible region: excitonic surface polaritons (SPs), asymmetric FabryPerot (F–P) resonances, epsilon-near-zero (ENZ), epsilon-near-pole (ENP), large dielectric constant region, etc. (b) The p-polarized absorption spectra for different incident angles in the ATR configuration. It shows PA near ~ 563 nm due to SP mode coupling.

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Figure 3

Fig. 3 (a) The dielectric constants of the non-metallic (i.e. Re[ε] > 0 at all wavelengths) excitonic film (t ~ 40 nm) (b) The p-polarized absorption spectra for different incident angles in the ATR configuration. We have PA near 583 nm, which is rather close to the ENP position (~590 nm). Note that this non-metallic sample does not support SP modes. (c) Peak absorption values as a function of incidence angle for metallic (black line) and nonmetallic (red line) films. Two films show a clear difference in the angle dependence as well as PA wavelengths. This implies that PA in those two cases has different physical origins.

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Figure 4

Fig. 4 Schematic of partial reflected waves (with complex reflection coefficients r0, r1, r2, …). Phasors corresponding to each partial reflected wave are indicated as arrows and connected together head-to-tail. To achieve PA, the final position of the phasors should come back to the origin; i.e. R = |r|2 = 0, so that A = 1 – R = 1. Reflected light from an absorbing layer can have a reflection coefficient with its phase deviating significantly from π - i.e., the phasor in the complex reflection coefficient (Re[r]-Im[r]) diagram is not along the horizontal Re[r] axis. This can enable asymmetric F–P type resonances even in deep subwavelength films.

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Figure 5

Fig. 5 Partial reflected wave calculations for different film thicknesses (t = 30–60 nm). We consider the ATR configuration as used in experiments. We assume the same wavelength (λ0 = 583 nm) and incidence angle (θ = 60º) for four complex phasor diagrams. At t = 40 nm, the phasor returns to the closest point to the origin (i.e. achieving the strongest absorption), in good agreement with experimental data in Fig. 3.

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Figure 6

Fig. 6 Absorption spectra of the metallic excitonic film on a silver substrate (t ~ 40 nm): (a) p-polarization and (b) s- polarization. We could observe cavity-like resonances for both p- and s-polarization in a longer wavelength region (> 600 nm), which has smaller optical losses (Im[ε]). We have high dielectric constant values in the longer wavelength region, which could lead to optical resonances in very thin organic films.

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Figure 7

Fig. 7 (a) Calculation results showing how the absorption peak position changes with the film thickness (Incidence angle: 55º). The resonance wavelengths get larger (i.e. red-shift) in thicker films, as expected for typical cavity resonances. (b) Partial reflected wave calculations for Fig. 6(b). We compare the on-resonance (~ 626 nm) and off-resonance (~ 700 nm) cases to see differences. The incidence angle is 55º.

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Figure 8

Fig. 8 Absorption spectra of the non-metallic excitonic film on a silver substrate (t ~ 35 nm): (a) p-polarization and (b) s-polarization. The strong absorption peaks are centered near 600 nm for both polarizations, showing different behavior from Fig. 6. Especially, the absorption peak intensity gradually increases with larger incident angles in Fig. 6(b), while it decreases in Fig. 8(b).

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