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Abstract
We report experimental observation of strong coupling between surface plasmon polariton (SPP) propagating on a thin silver film and excitons from excited-subband transtitions of single-walled carbon nanotubes (SWNTs). Clear anti-crossing behaviors were observed from attenuated total reflection measurements when the SPP energy approaches the 2nd subband transition of (6,5) SWNTs. The maximum Rabi splitting of the plasmon-exciton mixed states was extracted to be up to ~166.2 meV. Moreover, the splitting was found to be dependent linearly on the square root of the SWNTs concentration, in good agreement with theoretical prediction.
© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Single-walled carbon nanotubes (SWNTs) are competitive candidates for the development of new-generation opto-electronic devices. Superb optical properties are expected due to their unique one-dimensional tubular structures. Indeed, semiconducting SWNTs exhibit very strong oscillator strength and exceptionally large excitonic binding energies that have been reported to be several hundreds of meV [1–3]. However, it was found, amazingly, that radiative quantum yield of SWNTs is extremely low (~10−4 to 10−3) [4, 5]. The existence of low-lying dark excitonic states was later confirmed to be responsible for this low luminescence quantum yield [3, 6–10]. Lots of attentions have thus been paid to the improvement of their optical properties.
One efficient and common way to tailor the optical properties of light emitters is the introduction of optical microcavities [11–14]. Indeed, rapid progresses have been made with significantly improved optical properties of SWNTs, under the concept of optical microcavities. Several types of optical microcavities have been proposed, such as Fabry-Perot planar cavities formed by metallic or dielectric mirrors, waveguide nanocavities and photonic crystal cavities [15–21]. The spontaneous emission of cavity-controlled SWNTs could be readily enhanced up to 316 times [18].
Compared with those conventional optical microcavities as mentioned above, plasmonic nanocavities are attracting more and more attention in recent years. They are particularly attractive due to their ability of supporting resonant modes with sub-wavelength mode volume, which enables the design of ultracompact optical devices [22]. Therefore, it will be very helpful to stimulate the device application of SWNTs if one could tailor their optical properties with plasmonic structures. To this end, thorough understanding and efficient control of the interactions between surface plasmon polariton (SPP) and SWNT excitonic states will be essential. We notice that a few groups have reported their success in tuning the optical properties of SWNTs with plasmonic nanostructures in recent years [23–29]. However, it should be pointed out, that these progresses are essentially limited to the localized SPPs that are supported by metallic nanostructures. Interactions with propagating SPPs, which are important in applications such as information transmission, have not been addressed till now.
Moreover, the efforts reported so far focused on the lowest subband transition of SWNTs (hereafter referred to as E11). As a typical one dimensional material, the excited subbands play an important role in their optical properties as well. Although tailoring these excited subbands through strong coupling with SPP modes share similar physical pictures with that of the E11 subband, bringing it into realization will undoubtedly stimulate better control over the optical properties of SWNTs.
In this work, we report experimental study on the strong coupling between propagating SPPs that exist on a thin silver film and excitons from the 2nd subband transition (referred to as E22) of monochirality (6,5) SWNTs. The system exhibits clearly anti-crossing behaviors when the SPP modes come into resonance with the 2nd subband transition of the (6,5) SWNTs, evidencing the formation of strongly coupled exciton-surface plasmon polaritons. By varying the concentration of (6,5) SWNTs, the observed Rabi splitting reaches ~166.2 meV, which corresponds to ~7.6% of the E22 excitonic transition energy. Moreover, the Rabi splitting was found to increase linearly with the square root of the SWNT concentrations, in agreement with theoretical predictions.
2. Sample and experimental details
The samples we used are monochirality (6,5) SWNTs. They were purified using a technique called single-surfactant multicolumn gel chromatography [30]. High purity of the sample can be confirmed from its absorption measurement. Typical absorption spectrum of the as-prepared sample is shown in Fig. 1(c). As one can see clearly from the figure, the optically-allowed inter-subband transitions of the (6,5) SWNTs can be identified unambiguously up to the 4th subband, showing the high quality of the sample. Absorption from other species are barely visible, as a result of high sample purity. In this work, we focus on its 2nd subband transition, as highlighted by the orange arrow shown in Figs. 1(b) and 1(c). This subband transition lies at ~2.17 eV with a full-width-at-half-maximum (FWHM) of ~78 meV. This transition energy is far away from the bulk plasma energy of Ag which is ħωp ≈3.78 eV [31].
Fig. 1 (a) Schematics showing the structure of our sample and the Kretschmann-Raether geometry for the reflectometry measurements. SPPs were generated at the Ag-PVA interface. (b) Energy subbands for semiconducting SWNTs and the dominant optically-allowed transitions. In this work, we focus on the 2nd subband (E22) transition. (c) Typical absorption spectrum of the purified (6,5) SWNTs. Inter-subband transitions can be identified at least up to the 4th subband. The studied E22 transition was highlighted by an arrow.
Structure of our sample is shown schematically in Fig. 1(a). It is constructed by first evaporating thermally a thin silver film (~55 nm) onto the base of a right angle glass (BK7) prism. To study the SPP-SWNTs interaction, the purified (6,5) SWNTs were dispersed homogeneously into a polyvinyl alcohol (PVA) solution, sonicated for 4 hours, and then spin-coated onto the pre-prepared silver film. Thickness of the PVA/SWNTs film was estimated to be ~100 ± 20 nm using a surface profilometer.
Unlike electronic transitions in atoms or condensed matter, SPPs cannot be excited with light directly. SPPs are hybrid modes formed by the strong interaction between electron oscillations in a metal and an oscillating light field on the metal surface. Momentum of SPPs is always greater than that of a photon with the same energy [22]. Thus, momentum-matchingscheme has to be employed to detect SPPs experimentally. In this work, we employed the prism-coupling scheme, as illustrated schematically in Fig. 1(a). SPPs are generated at the Ag-PVA interface, by the evanescent wave of the incident light during its total internal reflection process. Wave vector of the SPPs can be written as follow:
where np is the refractive index of the prism, λ is the free-space wavelength of the incident light and θ its incident angle in the prism, respectively. Energy of SPP depends on its wave vector and can be tuned into resonance with the E22 transition of SWNTs by changing the incident angle θ.In our experiments, the as-fabricated sample was positioned on a sample holder. Angle-dependent reflectometry measurements were performed by varying the incident angle of a collimated white light beam. The incident light was p-polarized to improve the signal-to-noise ratio in the reflectivity spectrum. The reflected light was guided into a 300-mm spectrometer by optical fibers and detected using a liquid-nitrogen-cooled CCD detector with 1024 × 256 pixels. All measurements were taken at room temperature.
3. Results and discussion
The measured reflectivity spectra of our prism-coupling sample, taken at different incident angles, are shown in Fig. 2. Two reflectivity dips are clearly visible for each incident angle. However, evolutions of these two dips are quite different. For relatively small incident angles, e.g., θ = 48°, the spectrum is completely dominated by the low-energy dip. However, as the incident angle was increased, intensity of the high-energy dip increases gradually, at the expense of the low-energy one. These two dips have roughly the same contributions at θ = 56°. Eventually, the high-energy dip dominates the spectrum for θ ≥ 60°. Moreover, energy positions of these two dips come close at first, and then get farther away again. The minimum separation of these two dips was found at θ = 56°, with a value of ~291.6 meV.
Fig. 2 The attenuated total reflection spectra of the fabricated sample (Ag film thickness ~55 nm) taken at different angles of incidence. The spectra were offset vertically to make the spectral features clearly visible. The vertical dash-dotted line denotes the energy position of the uncoupled E22 exciton of the (6,5) SWNTs. All measurements were taken at room temperature.
Evolutions of these two reflectivity dips show very clearly anti-crossing behaviors. It is now generally accepted, that such avoiding crossings are signatures of strong light-matter coupling [13, 32, 33]. It arises from a reversible energy exchange process that takes place between the SPP mode propagating at the Ag / PVA interface and the excitonic state of the (6,5) SWNTs. However, SWNTs are typical one-dimensional materials, with at least four distinguishable inter-subband transitions in our case, as shown in Fig. 1(c). Thus, one issue to be solved is to clarify which subband transitions are involved in the observed strong coupling behavior. This could be identified from the energy positions of the spectral features. The vertical dash-dotted line shown in Fig. 2 denotes the position of the uncoupled E22 exciton of the (6,5) SWNTs. It can be seen clearly that the avoided crossing phenomena appear when the reflectivity dips approach the E22 exciton. This tells, unambiguously, that it is the 2nd subband transition of the (6,5) SWNTs that couples strongly with the SPP modes. From the fact that the spectra consist of two dips only, we can further conclude that no other subbands are involved in the strong coupling.
The strong photon-emitter coupling leads to the formation of new quasi-particles named “polariton”, which is half-light and half-matter in nature. In the conventional case of strong coupling between a microcavity resonance mode and an excitonic state in semiconductor, the coupled system can be well described using a coupled oscillator model [13, 14, 22]. In the case of SPPs, the coupling also works under the dipole interaction scheme. The electric dipole moment of the exciton in SWNTs interact with the electric field produced by the propagating SPP mode. This picture is very similar to the case of a conventional dielectric optical cavity. Thus, we could also discuss the strongly coupled SPP-SWNT system using the widely accepted coupled oscillator model, by simply replacing the cavity mode dispersion relation by the SPP one. Ignoring damping effects, the new states of the strongly coupled SPP-SWNT system can be written as follow [22, 31]:
where EU (k) represents the upper polariton branch, EL (k) the lower branch, ESP (k) the dispersion relation of the uncoupled SPP mode, EX the E22 exciton energy of (6,5) SWNTs, and ħΩR the vacuum Rabi splitting.Figure 3(a) shows the energy positions of the reflectivity dips as a function of their corresponding wave vector converted using Eq. (1), with a refractive index np = 1.504 + 0.0047 / λ2 − 0.000085 / λ4 (λ in the unit of “μm”). As a comparison, dispersion of the bare SPP mode, obtained from a reference device without SWNT doping, is shown in Fig. 3(b). With this uncoupled SPP dispersion, Rabi splitting of the SPP-E22 Exciton mixed states can be extracted by fitting the experimental data using Eq. (2), which is ~166.2 meV in our case. Besides the anti-crossing behavior, an inversion of the reflectivity dip linewidths can usually be observed when the system enters the strong coupling regime [32, 33]. In our work, the inversion of linewidths is not significant, as the bare SPP mode and excitonic absorption have very similar linewidths (79 meV for SPP mode obtained from reference device and 78 meV for E22 exciton). However, a slight tendency of linewidth inversion can still be identified if checked carefully, as demonstrated in Fig. 3(c). Here, it is also interesting to note, that the Rabi splitting extracted with Eq. (2) is much smaller than the minimum separation of the two reflectivity dips in the angle-dependent spectra as shown in Fig. 2 (~291.6 meV, θ = 56°). This issue could be clarified clearly from the definition of the vacuum Rabi splitting. As shown in Fig. 3(a), as well as in Eq. (2), value of the Rabi splitting equals to the energy separation of the two polariton branches when the uncoupled SPP mode and exciton come into resonance. Keeping this in mind, one may notice that the two reflectivity dips of one particular spectrum do not have the same wave vector, as they have different energies and thus wavelength (k = (2π/λ)·np·sinθ). Therefore, the minimum separation of the absorption peaks in the angle-dependent spectra does not give the real Rabi splitting of the system. Instead, it gives a severely overestimated value (~75% in our case) and should thus be avoided in one’s analysis of strong light-matter coupling.
Fig. 3 (a) Energies of the reflectivity dips, extracted from Fig. 2, as a function of the wave vector. Horizontal dashed line: E22 exciton of (6,5) SWNTs. Olive dash-dot-dotted line: dispersion of the uncoupled SPP mode. Orange solid lines: fitted dispersion curves using the coupled oscillator model for the strongly coupled exciton-surface plasmon polaritons. (b) Dispersion of the bare SPP mode obtained from a reference device without SWNT doping. The olive dash-dot-dotted line represents the best-fit curve for the experimental data. (c) FWHM of the two reflectivity dips in Fig. 2 as a function of their wave vector. Vertical dash-dot-dotted line: position of resonant coupling. (d) Rabi splitting as a function of the amount of linewidth mismatch.
Having extracted the value of Rabi splitting, we now turn to the strength control of the SPP-SWNTs coupling. The value of Rabi splitting measures directly the energy exchange rate between the two systems that are coupled to each other. Achieving stronger coupling is critical both for device application and fundamental physics. As expected theoretically, one efficient way to achieve stronger coupling is to increase the density of light emitters / absorbers [22]. To verify this, we changed the density of (6,5) SWNTs and measured their corresponding Rabi splitting from the attenuated total reflection measurement. The measured Rabi splitting is plotted in Fig. 4, as a function of the square root of the (6,5) SWNTs concentration. Here, concentration of SWNTs is represented directly by its light absorption intensity, based on the assumption that light absorption intensity is proportional to the density of SWNTs. As demonstrated clearly in Fig. 4, the Rabi splitting does show a linear dependence on the square root of SWNT concentration, in good agreement with theoretical prediction. Here, we would also like to point out, that the changes of Rabi splitting are not due to the thickness fluctuation of the PVA / SWNTs film. Thickness fluctuation of the film was confirmed to be less than 10% with a surface profilometer. Compared with the increase of Rabi splitting that reaches 105%, this film thickness fluctuation is small enough to be neglected.
Fig. 4 Rabi splitting of the SPP-SWNTs coupled system as a function of the square root of the (6,5) SWNT concentration. The (6,5) SWNT concentration is represented by its light absorption intensity. The absorption intensity (SWNT concentration) shown here has been normalized to the maximum intensity (concentration) measured in this work.
Finally, we would like to stress again, that the strong coupling we observed happens in the excited subband transition, instead of the lowest subband as usually studied in the past. However, Rabi splitting as high as ~166.2 meV was still observed, which is significantly larger than the E11 Rabi splitting of ~120 meV reported in Ref. 25. There is no doubt that the large oscillator strength of the excitonic transition in SWNTs and the high sample concentration make contributions to the large Rabi splitting. The large field enhancement, which originates from the near field nature of the SPP modes, is also an important factor. Besides these, another key factor, i.e., linewidth matching, play a critical role as well. According to theoretical calculations, coupling strength, i.e., value of Rabi splitting, can be described by the following formula for an SPP-exciton coupled system [22, 34]:
where V is a parameter proportional to the interaction strength of the coupled system, γp andγe the dampling (linewidth) of the uncoupled SPP modes and excitonic transitions, respectively. It could be seen clearly from Eq. (3), that the Rabi splitting will be maximized when the SPP modes and exciton have the same linewidth. To verify this, we fabricated another three devices with smaller Ag film thickness (50, 46 and 42 nm) and thus larger linewidth of SPP mode (86, 95 and 104 meV). The Rabi splitting of these devices under the condition of identical SWNT doping is shown in Fig. 3(d) as a function of linewidth mismatch, where linewidth mismatch is defined as the difference between the SPP mode and exciton linewidths. As can be seen clearly in Fig. 3(d), the Rabi splitting does decrease with the amount of linewidth mismatch, confirming the importance of linewidth matching in the strong coupling regime.4. Summary
In conclusion, we have performed experimental study on the strong coupling between a propagating SPP mode and excitons from excited subband transitions of (6,5) SWNTs. Large Rabi splitting up to ~166.2 meV was observed and it was found to depend linearly on the square root of the (6,5) SWNT concentration, which is in good agreement with theoretical prediction. Physical mechanisms responsible for the large Rabi splitting we observed were also discussed. Plasmonic structures and SWNTs are both promising candidates for the development of new optoelectronic devices. Realizing the strong coupling between them would thus contribute to the development of this emerging field.
Funding
National Natural Science Foundation of China (NSFC) (11404120); The Fundamental Research Funds for the Central Universities, HUST (2017KFXKJC003).
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