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Adjustable exciton-photon coupling with giant Rabi-splitting using layer-by-layer J-aggregate thin films in all-metal mirror microcavities

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Abstract

Developing of highly absorbing thin films is essential for exploration of light-matter interaction and polariton-based applications. We demonstrate here layer-by-layer assembled J-aggregate thin films of (DEDOC) cyanine dyes that have high absorption coefficient and controlled thicknesses, leading to adjustable exciton-photon coupling and Rabi splitting exceeding 400 meV at room temperature in all-metal mirror microcavities.

© 2013 Optical Society of America

1. Introduction

In recent years, strong exciton-photon coupling in optical cavities has become of significant scientific and technological interest for applications such as low-threshold polariton lasers [13]. The cavity structure increases the photon lifetime and hence the exciton-photon coupling rate as the exciton transition energy approaches to the confined photon mode. In the strong coupling regime, the exciton-photon coupling rate becomes faster than the decoherence or dissipation of two modes, resulting in Rabi oscillation of hybrid exciton-photon states and creation of polariton modes at different energy branches in the cavity dispersion with a minimum energy separation at resonance, known as Rabi-splitting [4,5]. Resolution of strong coupling usually requires active materials with long exciton lifetime and narrow transition linewidth. In contrast to the weakly bound excitons in most inorganic semiconductors, the tightly bound excitons in organic semiconductors have relatively long lifetime that allows the occurrence of strong coupling with large Rabi splitting at room temperature [6,7]. However, since the typical characteristics of disorders and strong intermolecular interactions in organic films will lead to broadening of exciton linewidths [8], only few classes of organic systems such as highly ordered small molecule films [9,10] and molecularly doped films [11] have been intensively employed for polariton research. In particular, amorphous films with J-aggregate dye molecules are one of most recognized systems in this area of study, primarily due to their unique characteristics of strong transition dipoles and well-defined band structures that yield high absorbance and narrow absorption/emission linewidths. Another interesting attribute of J-aggregate films is due to their simple solution processability. Following the work for the first discovery of organic polaritons by Lidzey et al. in 1998 [6], there have been numerous optical studies of polaritons based on spin-cast J-aggregate films of sufficient thickness as the absorbing cavities [1215]. In 2005, Bulovic et al. otherwise used layer-by-layer (LBL) assembly to produce highly absorbing J-aggregate films [16]. Compared to conventional spun films, the LBL technique permits the reduction of film thickness such that electrical excitation of J-aggregate films to create polariton emission becomes feasible [17]. This breakthrough paves a promising way for practical device applications.

Up to date, much progress has been made to gain better understanding of organic polaritons, in particular with regard to their optical properties, energetic distributions, and correlations with the exciton and phonon properties of materials [1825]. However, some important issues still need to be addressed further to accelerate the prospect of realizing innovative polaritonic devices such as electrically pumped organic lasers. For example, the materials available for optoelectronic device applications are still very limited. Also, how charges affect the organic polaritons is not well understood, particularly under conditions of intense electrical excitation. It is therefore desirable to develop organic materials that possess optoelectronic functions compatible with device engineering and the ability of large Rabi splitting, thus allowing polariton stabilization at high excitation densities. The LBL-assembled J-aggregate films are well suited for this demand as they offer capability of electroluminescence, unique properties for strong coupling, variety of dye molecule options, and simple, well-controlled fabrications.

In this paper, we introduce a high-performance LBL-assembled J-aggregate films with a cyanine dye molecule, [5-chloro-2-(2-[(5-chloro-3-(3-sulfopropyl)-2(3H)-benzoxazolylidene) methyl]-1-butenyl)-3-(3-sulfopropyl)-benzoxazo-lium inner salt, sodium salt] (DEDOC), as shown in Fig. 1(a). The LBL assembly method is employed to deposit sequential cationic poly(diallyldimethylammonium chloride) (PDAC) and anionic DEDOC layers, resulting in formation of DEDOC J-aggregates in PDAC/DEDOC active films with controlled thicknesses and high absorption coefficient of >106 cm−1. We demonstrate a giant Rabi splitting of exceeding 400 meV at room temperature, higher than most of organic materials reported so far. Our results suggest that PDAC/DEDOC J-aggregates films can be applied for future exploration of strong- and even ultrastrong-coupling optoelectronic applications.

 figure: Fig. 1

Fig. 1 (a) Chemical structure of DEDOC dye molecule. (b) Absorption spectra of DEDOC dye monomers dispersed in NaOH solution (dotted line) and a LBL-assembled P(DP)1 film with DEDOC J-aggregates (solid line). (c) Absorption spectra of PDAC/DEDOC J-aggregate films with various adsorption cycles, N.

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2. Fabrication and characterization of J-aggregate films

The LBL-assembled J-aggregates thin films were deposited on glass or thermally evaporated SiO2 layers of cavity devices. Prior to the film deposition, substrates were cleaned using UV ozone to create prevalent hydroxyl groups on the surface. Substrates were then sequentially immersed in PDAC and DEDOC solutions for cationic and anion adsorptions, and finally finished with PDAC adsorption to produce an assembled thin film in a sequence of PDAC-(DEDOC-PDAC)N (notated as “P(DP)N” for rest of the paper, N represents the number of PDAC/DEDOC adsorption cycles). Figure 1(b) shows the normalized absorption spectra of DEDOC monomers dispersed in NaOH solutions and a P(DP)1 J-aggregate film. Compared to the monomer absorption band peaking at 495 nm, the P(DP)1 film exhibits a red-shifted, sharp J-band absorption peak at 546 nm, indicating the formation of DEDOC J-aggregates in the assembled film. The full-width at half-maximum linewidths (FWHM) of the J-band is approximately 88 meV. A rather broad spectral shoulder (sideband) at wavelengths of 450~520 nm could be attributed to the absorption of residual monomers in the assembled film.

Figure 1(c) shows the absorption spectra of PDAC/DEDOC J-aggregate films with different adsorption cycles N. The absorption spectra were extracted from the reflectance (R) and transmittance (T) spectra by 1-R-T. It can be noticed that the J-aggregate films with N≤5 have similar absorption features, which comprise a primary J-band and a weaker sideband with the peak positions independent of N. The peak intensity of the J-band absorption increases constantly with N up to a maximum at N = 4 and starts to level off for N = 5. However, the growth quality of J-aggregate films slightly decreases with N, as evidenced by the increased intensity ratio of the sideband to J-band. For the films with N>5, the J-band does not increase further in intensity but appears to be slightly red-shifted, while the sideband keeps increasing in intensity and bandwidth with N, resulting in an apparently different absorption lineshape from those with N≤5. The evolution of these optical spectra is supported by the atomic force microscopy (AFM) measurements performed on the identical samples. As the images shown in Fig. 2(a), the films with N≤5 all have an amorphous surface topography with small roughness, whereas beyond N>5 the roughness increases sharply [Fig. 2(b)] and much larger granular microstructures, even discontinuous islands appear. The combination of optical and morphological measurements suggest a transition from the layered growth for N≤5 to a rough growth (similar to Stranski-Krastanov growth observed in crystalline semiconductors) for N>5. Such trend is similar to the previous studies on TDBC dye molecules [16].

 figure: Fig. 2

Fig. 2 (a) Tapping-mode atomic force microscopy (AFM) images of the PDAC/DEDOC J-aggregate films with various adsorption cycles. The image size is 5 μm × 5 μm. (b) The estimated thickness and roughness of the PDAC/DEDOC J-aggregate films as a function of adsorption cycles from the AFM measurements. The inset is the AFM image of the first DEDOC layer adsorbed on a PDAC layer (N = 0.5). The image size is 2 μm × 2 μm.

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The thickness and roughness of J-aggregate films versus adsorption cycles N from AFM measurements are summarized in Fig. 2(b). The film thickness is increased by roughly 5-7 nm per cycle. We have also investigated the morphology of the first PDAC layer (denoted as N = 0) and the first DEDOC layer adsorbed on a PDAC layer (denoted as N = 0.5). The PDAC layer adsorbed on glass is 3-4 nm thick and rather smooth (Ra roughness <1 nm). On the other hand, the DEDOC layer exhibits randomly packed granular structures of J-aggregates (the inset in Fig. 2(b)), and the surface roughness of ~4 nm is relatively large compared to the average film thickness (2-4 nm) estimated from the difference between N = 0.5 (6-7 nm) and N = 0 films, implying a discontinuous film formation of DEDOC J-aggregates.

Further, we used variable-angle spectroscopic ellipsometry (M-2000U, J. A. Woollam) and associated CompleteEASE software to obtain the optical constants of the J-aggregate films. In principle, for a uniform film made of single material, ellipsometry enables simultaneous calculation of the physical thickness and complex refractive index N = n-ik. However, for LBL J-aggregate films, the ellipsometry software tends to yield the “effective” (n,k) spectra of the assembled films but significantly underestimates the entire film thicknesses as compared with the AFM data. Moreover, the peak (n,k) values of the J-aggregate films are much larger than those of a neat PDAC film. All of these reflect that the optical properties of J-aggregate films are dominated by the DEDOC layers.

Instead of treating an assembled J-aggregate film as a single material, here we consider a more realistic case where a J-aggregate film is alternatively stacked with uniform DEDOC and PDAC layers. Therefore the optical modeling of J-aggregate films can be constructed with practical thicknesses and (n,k) spectra of each DEDOC and PDAC layer. The (n,k) spectra of a PDAC layer were directly obtained from the ellipsometry software. On the other hand, the (n,k) spectra of a DEDOC layer were evaluated based on an iterative approach combining the Kramers-Kronig (KK) transformation [26] and transfer-matrix method. In the first step of iteration, the (n,k) spectra of a P(DP)1 film calculated from the ellipsometry software were taken as the initial (n,k) spectra of a DEDOC layer. The (n,k) spectra were then iteratively modified to minimize the difference between the measured transmittance and that calculated using transfer-matrix method, with (n,k) values of PDAC and DEDOC layers as inputs and their thicknesses (assumed to be unchanged for more adsorption cycles) as fitting parameters. Figure 3(a) shows the (n,k) spectra of a DEDOC layer obtained from the optimized fitting of the transmittance spectrum of a P(DP)1 J-aggregate film [Fig. 3(b)]. The thicknesses of each PDAC and DEDOC layer used for the fitting are 3 nm and 3.2 nm, respectively, in excellent agreement with the AFM measurements.

 figure: Fig. 3

Fig. 3 (a) (n,k) spectra of a DEDOC J-aggregate layer, obtained from the KK regression in an iterative algorithm to reach an optimized fitting of the transmittance spectrum of a P(DP)1 J-aggregate film, as the result shown in (b). Fitting of the reflectance spectrum was also performed for reference. The inset in (b) is the fitting of R and T spectra of a P(DP)5 J-aggregate film using (n,k) spectra in (a).

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It should be noted that the above algorithm to extract optical constants from spectral measurements may yield slight sample dependence of (n,k) spectra of a DEDOC layer. Concerning J-aggergate films with different adsorption cycles, here we simplify the optical modeling by assuming that the (n,k) spectra and thicknesses of DEDOC and PDAC remain the same as more adsorption cycles are progressed, and the only fitting parameter is the average thickness per DEDOC layer (PDAC thickness is fixed at 3 nm in all cases). Based on this assumption, the (n,k) spectra in Fig. 3(a) can be used to fit the optical spectra of J-aggregate films from 2 to 5 adsorption cycles with satisfactory precision, and the average thicknesses per DEDOC layer for all the samples are reasonably within a range of 2.5-3.2 nm (The inset of Fig. 3(b) shows the fitting result of a P(DP)5 film). This confirms the validity of our model and the (n,k) spectra to capture essential optical features of J-aggregate films. Nevertheless, delicate modification of the (n,k) values in the sideband region (400~520 nm) is sometimes required to gain better optical modeling for samples with intensive sideband absorption such as P(DP)5 films, as will be discussed in the next section. From the peak k value of ~4.5 at λ = 546 nm, we could deduce the peak absorption coefficient α = 4πk/λ~1.03 × 106 cm−1. This high absorption coefficient makes PDAC/DEDOC films suitable for applications in strong coupling systems.

3. Polaritonic properties of J-aggregates in cavities

To investigate the polaritonic properties of PDAC/DEDOC J-aggregates, we performed the angle-resolved measurements for s-polarized reflectivity at room temperature on λ/2 microcavities, which consist of the J-aggregate film sandwiched by two SiO2 buffer layers and two Ag mirrors [Fig. 4]. It has been demonstrated that all-metal mirror microcavities are advantageous to yield larger Rabi-splitting energies over DBR microcavities due to better optical confinement [27]. The design of microcavities is to maximize the exciton-photon coupling by placing the J-aggregate film at the electric field antinode of the cavity mode, as the simulated field shown in Fig. 4. The thicknesses of two SiO2 buffer layers are approximately the same and designed such that the cavity mode energy at the surface normal, Eph(0), is lower than the exciton transition energy of the J-aggregates (Eex = 2.27 eV). Therefore, increasing incident angle θ allows the cavity mode to be tuned to higher energy following the dispersion relation [28]

Eph(θ)=Eph(0)[1(sinθ/neff)2]1/2,
where neff is the effective refractive index of the uncoupled cavity, and become resonant with the exciton mode, which is angle-independent, at the angle between 30∘to 50∘.

 figure: Fig. 4

Fig. 4 Schematic diagram of the microcavity structure consisting of a 150 nm thick Ag as the bottom mirror, 60 nm thick SiO2 as spacer layers, a PDAC/DEDOC J-aggregate film, and a 20 nm thick Ag as the top mirror. The electric field superimposed on the cavity was calculated by finite-difference time-domain method with spatial resolution of 1 nm for the wavelength of 550 nm.

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The angle-resolved reflectivity spectra of a microcavity containing P(DP)1 film reveal clear polaritonic features [Fig. 5(a)]. Two resonant dips arising from the exciton-photon coupling, one at energy higher than Eex and another at energy lower than Eex, correspond to upper (UP) and lower (LP) polariton branches, respectively. At small angles, UP mode is exciton-like and LP mode behaves more photon-like with stronger reflectivity dip. As increasing angles, LP mode moves closer to the exciton mode with decreased dip intensity, while UP mode moves away from the exciton mode and becomes photon-like with increased dip intensity. The angular dependence of the resonant dips yields the UP and LP dispersions with pronounced anticrossing at an angle of 33∘[Fig. 5(d)]. Upon the best fit of the polariton dispersion curves with a conventional two-mode coupled oscillator model [29]

EUP,LP(θ)=Eph(θ)+Eex2±12(Eph(θ)Eex)2+4V2,
where V is the interaction potential, we can deduce the Rabi splitting energy (Ω = 2V) for P(DP)1 J-aggregate film to be 180 meV.

 figure: Fig. 5

Fig. 5 (a)-(c) Angle-resolved reflectivity spectra for microcavities containing P(DP)1, P(DP)4, and P(DP)5 J-aggregate films and 60 nm SiO2 spacers. (d)-(f) LP/UP dispersions (solid circles) extracted from the reflectivity spectra in (a)-(c). The black lines are fit to the polariton dispersions using a two-mode coupled oscillator model. The gray lines indicate the dispersions of the uncoupled photon and exciton modes deduced from the fit to the polariton dispersions. In (f) the experimental LP/UP dispersions of P(DP)5 device (black open circles) were simulated with the J-band-only model (green solid circles) using the k spectrum denoted as “J” in (g), and the model including both J-band and a Guassian sideband absorption (red cross) using the k spectrum denoted as “J+sideband” in (g). As shown in (c) and (f), the “J+sideband” model agrees well with the angular evolution of UP reflectivity spectra and experimental LP/UP dispersions. However, the J-band-only model can recover the UP energy of J-band in the sideband region (2.5~2.7 eV). The arrow in (f) indicates the Rabi splitting between LP and UP dispersions of the J-band.

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Similar polaritonic features can also be observed in the microcavities containing thicker J-aggregate films, e.g., P(DP)4 and P(DP)5 [Fig. 5(b) and 5(c)]. In general, the Rabi splitting is proportional to (Lactive)1/2 [4], where Lactive is the entire thickness of the DEDOC J-aggregate layers in the assembled films. Here the SiO2 thickness is fixed at 60 nm for all three devices, therefore more adsorption cycles will result in thicker active layers and longer cavities, and hence larger Rabi splitting energies and increased resonant angles can be expected. Indeed, fitting of the P(DP)4 device with Eq. (2) yields Ω = 370 meV with anticrossing at an angle of 41∘[Fig. 5(e)]. P(DP)5 device is expected to yield the largest Rabi splitting energy in the layered growth regime. However, as shown in Fig. 5(f), P(DP)5 devices usually exhibit an irregular UP dispersion in the sideband region (2.5~2.7 eV), which cannot be simply fit by the two-mode coupled formalism. In order to interpret the dispersion data correctly, we simulated the UP/LP dispersions of P(DP)5 device with two models: (1) using the k spectrum in Fig. 3(a) to count as J-band absorption only (denoted as “J” in Fig. 5(g)); (2) using a linear superposition of “J” spectrum and a Gaussian sideband absorption (denoted as “J+sideband” in Fig. 5(g)). We found that with properly defined sideband, the “J+sideband” model agrees well with the experimental UP reflectivity spectra [Fig. 5(c)] and UP/LP dispersions [Fig. 5 (f)]. On the other hand, the “J” model produces nearly identical UP/LP energies as the “J+sideband” model except slightly lower UP energies in the sideband region. Our simulation elucidates that the sideband absorption mainly contributes to a spectral dip overlapped with UP reflectivity in the sideband region, resulting in an apparent energy shift of the overall spectral dip, but does not affect the UP energy of the J-band excitons. Accordingly, the J-band-only model can be used to rule out the sideband effect and recover the intrinsic UP dispersion of the J-band, which shows good fitting by Eq. (2) [Fig. 5(f)]. This analysis allows us to extract Ω = 430 meV at θ = 48∘for the P(DP)5 device.

Table 1 lists the parameters used to model the polariton dispersions of all the studied samples. A little decrease in Eph(0) and neff is as expected for slightly thicker cavities as increasing adsorption cycles of J-aggregate films. The correlation of Rabi splitting energies between samples can be quantitatively analyzed using an analogical model for quantum wells placed at an antinode of the electric field in planar microcavities [30]. The Rabi splitting predicted by the model is proportional to a function of [αLactive/neff2Leff]1/2, where Leff is effective cavity length. To include the angular dependence of optical lengths, Lactive and Leff can be rewritten as Lactive/cosθ' and Leff × cosθ', respectively, where θ' is the internal angle within the cavity. By combining snell’s law (neff × sinθ' = sinθ) and constructive interference conditions (neffLeff∝1/Eph(0)), we can further derive the Rabi splitting to be proportional to [αLactive/neffEph(0)]1/2. Assume that the absorption coefficient α is invariant while Lactive is linearly increased with adsorption cycles, the scaled Rabi-splitting energies of the P(DP)4 and P(DP)5 devices with respect to Ω = 180 meV of the P(DP)1 device are highly consistent with their experimental values (see Table 1), demonstrating the good repetition of the layered growth up to 5 adsorption cycles. We have also fabricated another P(DP)4 device with a longer cavity length (~70 nm SiO2) for comparison [Fig. 6], which yields a slightly larger Rabi splitting of 400 meV than that of the P(DP)4 device with 60 nm SiO2. The Rabi splitting energies of two P(DP)4 samples also follows the scaling with [neffEph(0)]-1/2. Obviously, the major factor to influence the Rabi splitting energy is the absorbance (αLactive) of J-aggregate films, though design of longer cavities may lead to a minor enhancement [17]. From simulation of devices in Fig. 5 and 6, we estimated the average thickness of each DEDOC layer to be around 1.5-1.7 nm, somewhat thinner than those deposited on glass probably due to a higher roughness of thermally evaporated SiO2 bottom spacers. By better device and LBL-assembly manipulations that improve the absorption coefficient and thickness control of J-aggregate films, we believe that it is possible to further enhance the Rabi splitting energies.

Tables Icon

Table 1. Fitting parameters for the UP/LP dispersions in Fig. 5 and 6. Ωscaled is the scaled Rabi-splitting energy with respect to the P(DP)1 sample.

 figure: Fig. 6

Fig. 6 The LP/UP dispersions of a microcavity containing a P(DP)4 J-aggregate film and 70 nm SiO2 spacers. The black lines are fit to the polariton dispersions using a two-mode coupled oscillator model. The gray lines indicate the dispersions of the uncoupled photon and exciton modes deduced from the fit to the polariton dispersions. The arrow indicates the Rabi splitting of 400 meV between LP and UP dispersions at 62°.

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4. Conclusions

We present detailed studies on optical and morphological properties of PDAC/DEDOC J-aggregate films and their applications on strong exciton-photon coupling devices. Using layer-by-layer assembly method, we can obtain J-aggregate films with a high absorption coefficient of > 106 cm−1 and controllable film thicknesses varying over a few tens of nanometers. Integration of PDAC/DEDOC J-aggregate films into properly designed all-metal mirror microcavities yields pronounced polariton phenomena. From detailed analyses of polariton dispersions, we demonstrate unambiguously that Rabi-splitting energies exceeding 400 meV can be achieved. Moreover, it is noteworthy to mention that the exciton transition of PDAC/DEDOC J-aggregate films coincides with the emission bands of many organic semiconductors with high luminescence efficiencies, e.g., a well-known light-emitting polymer “Super Yellow” [31]. Such a highly absorptive, nanometer-scale J-aggregate film therefore not only serves a good candidate for physical research of light-matter interaction as approaching ultrastrong coupling regime, but also offers great potentials to develop high-performance exciton-polariton optoelectronic devices with versatile material combinations.

Acknowledgments

The authors gratefully acknowledge the National Science Council of Taiwan for financial support under Contract No. NSC100-2112-M-008-016-MY3 and NSC99-2923-E-008-002-MY2.

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Figures (6)

Fig. 1
Fig. 1 (a) Chemical structure of DEDOC dye molecule. (b) Absorption spectra of DEDOC dye monomers dispersed in NaOH solution (dotted line) and a LBL-assembled P(DP)1 film with DEDOC J-aggregates (solid line). (c) Absorption spectra of PDAC/DEDOC J-aggregate films with various adsorption cycles, N.
Fig. 2
Fig. 2 (a) Tapping-mode atomic force microscopy (AFM) images of the PDAC/DEDOC J-aggregate films with various adsorption cycles. The image size is 5 μm × 5 μm. (b) The estimated thickness and roughness of the PDAC/DEDOC J-aggregate films as a function of adsorption cycles from the AFM measurements. The inset is the AFM image of the first DEDOC layer adsorbed on a PDAC layer (N = 0.5). The image size is 2 μm × 2 μm.
Fig. 3
Fig. 3 (a) (n,k) spectra of a DEDOC J-aggregate layer, obtained from the KK regression in an iterative algorithm to reach an optimized fitting of the transmittance spectrum of a P(DP)1 J-aggregate film, as the result shown in (b). Fitting of the reflectance spectrum was also performed for reference. The inset in (b) is the fitting of R and T spectra of a P(DP)5 J-aggregate film using (n,k) spectra in (a).
Fig. 4
Fig. 4 Schematic diagram of the microcavity structure consisting of a 150 nm thick Ag as the bottom mirror, 60 nm thick SiO2 as spacer layers, a PDAC/DEDOC J-aggregate film, and a 20 nm thick Ag as the top mirror. The electric field superimposed on the cavity was calculated by finite-difference time-domain method with spatial resolution of 1 nm for the wavelength of 550 nm.
Fig. 5
Fig. 5 (a)-(c) Angle-resolved reflectivity spectra for microcavities containing P(DP)1, P(DP)4, and P(DP)5 J-aggregate films and 60 nm SiO2 spacers. (d)-(f) LP/UP dispersions (solid circles) extracted from the reflectivity spectra in (a)-(c). The black lines are fit to the polariton dispersions using a two-mode coupled oscillator model. The gray lines indicate the dispersions of the uncoupled photon and exciton modes deduced from the fit to the polariton dispersions. In (f) the experimental LP/UP dispersions of P(DP)5 device (black open circles) were simulated with the J-band-only model (green solid circles) using the k spectrum denoted as “J” in (g), and the model including both J-band and a Guassian sideband absorption (red cross) using the k spectrum denoted as “J+sideband” in (g). As shown in (c) and (f), the “J+sideband” model agrees well with the angular evolution of UP reflectivity spectra and experimental LP/UP dispersions. However, the J-band-only model can recover the UP energy of J-band in the sideband region (2.5~2.7 eV). The arrow in (f) indicates the Rabi splitting between LP and UP dispersions of the J-band.
Fig. 6
Fig. 6 The LP/UP dispersions of a microcavity containing a P(DP)4 J-aggregate film and 70 nm SiO2 spacers. The black lines are fit to the polariton dispersions using a two-mode coupled oscillator model. The gray lines indicate the dispersions of the uncoupled photon and exciton modes deduced from the fit to the polariton dispersions. The arrow indicates the Rabi splitting of 400 meV between LP and UP dispersions at 62°.

Tables (1)

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Table 1 Fitting parameters for the UP/LP dispersions in Fig. 5 and 6. Ωscaled is the scaled Rabi-splitting energy with respect to the P(DP)1 sample.

Equations (2)

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E ph ( θ )= E ph ( 0 ) [ 1 ( sinθ/ n eff ) 2 ] 1/2 ,
E UP,LP ( θ )= E ph ( θ )+ E ex 2 ± 1 2 ( E ph ( θ ) E ex ) 2 +4 V 2 ,
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