Coupling Mechanism between Tamm Plasmon Polaritons and Monolayer WS2 Embedded in Metal/Dielectric Bragg Reflector Hybrid Architecture

JIA Guangyi, YUE Ke, YANG Wenxin, HUANG Zhenxian, LIANG Qiqi, LI Yin

(School of Science, Tianjin University of Commerce, Tianjin 300134, China)

Abstract: To reveal and utilize the interaction between Tamm plasmon polaritons (TPPs) and twodimensional materials are promising for exploiting next-generation optoelectronic devices. Herein, the coupling mechanism between metal TPPs and monolayer WS2 along with its differences from that between metal TPPs and graphene was studied in detail by using the transfer matrix method. The experimental results show that it is difficult to excite TPPs at the boundary between monolayer WS2 and dielectric Bragg reflector (DBR) such that the strong coupling mainly stems from the interaction between metal TPPs and exciton in monolayer WS2. However, the coupling in graphene/DBR/metal hybrid structure derives from the interaction between two different TPP resonance modes. Thus, evolutions of Rabi splitting with various structural parameters including spacer thickness, incident angle and DBR period greatly differ from those observed in graphene/DBR/metal hybrid structure. In addition, the discrepancies induced via metal Ag and Au films as well as the possible influence mechanism were also discussed.

Key words: Tamm plasmon polaritons; monolayer WS2; Rabi splitting; coupling mechanism

1 Introduction

In 2005, Kavokinet alfirstly proposed the concept of optical Tamm states through making an analogy with Tamm states for electrons at crystal boundaries[1]. In 2007, Kaliteevskiet alpredicted a new plasmon polariton state at the boundary between a metal film and a dielectric Bragg reflector (DBR), and referred to it as the Tamm plasmon polaritons (TPPs)[2]. In comparison with conventional surface plasmon polaritons, TPPs are endowed with many superior optical properties. To name a few, TPPs can be directly excited by both TE and TM polarizations of incident light without the limitation of prisms and/or incident angles[3,4]. Coupling of TPPs with other resonance modes holds unique Rabi splitting which can be employed to manipulate the resonance wavelength and navigate the design of artificial microconfigurations[5,6]. Thus far, the easily realizable TPPs promise great potential in optical sensors[7,8], solar cells[9], plasmonic filter[10], ultrafast all-optical modulator[11], and so forth.

In particular, two-dimensional materials,eg, graphene, phosphorene, and transition metal dichalcogenides (TMDCs), have been igniting tremendous enthusiasm from both the academic and applied communities to exploit various exotic optical characteristics in recent years[12-16]. Thanks to their ultrathin thickness and robust response with incident photons, they demonstrate an excellent platform for investigating the light-matter interaction in nanoscale. For example, Lundtet al[17]and Huet al[18]confirmed the strong coupling between TPPs and the A excitons in monolayer WSe2and MoS2, respectively. Zhanget al[19]proposed the manipulation of exciton-polaritons in the WS2and Tamm plasmon hybrid structure based on the spin-selective optical Stark effect. Nonetheless, all of these previously studies are limited to use only one metal film[17-19]. The discrepancy in monolayer TMDC-TPPs interaction induced via different metals is still elusive. Besides, the latest researches showed that TPPs can be created in a graphene/DBR hybrid architecture such that they can strongly couple with the traditional metal TPPs at the interface between Ag film and DBR[20,21]. Then, several completely open questions may emerge. For instance, previous studies mainly attribute the strong coupling to the interaction between metal TPPs and excitons in monolayer TMDCs[17-19,22], are there TPPs to be produced at the TMDC/DBR interface? Is the evolution of resonance frequencies induced via metal/TMDC/DBR along with the underlying coupling mechanism the same with or different from that induced by graphene/DBR/metal hybrid structure?

In view of these, we investigated the interaction between metal TPPs and WS2in a hybrid architecture consisting of metal layer, polymethyl methacrylate (PMMA) spacer, monolayer WS2upon a DBR in this work. The discrepancy in optical properties induced by noble metal Au and Ag was analyzed in detail. Moreover, impacts of various parameters including PMMA thickness, incident angle and DBR period on the optical properties of the proposed hybrid architecture were thoroughly studied. The coupling mechanism between metal TPPs and WS2as well as its difference from that between metal TPPs and graphene was clarified.

2 Model and theoretical method

As depicted in Fig.1(a), our proposed hybrid architecture consists of a metal layer, a PMMA spacer, monolayer WS2, and the DBR from left to right. The metal layer is a commercial Ag or Au film with a thickness of 40 nm thickness. Complex permittivities of bulk Ag or Au published by Johnson were employed[23]. PMMA is a transparent thermoplastic, which is often used in sheet form as a lightweight alternative to glass. Here, the thickness of PMMA spacer is initially set as 71.78 (or 64.10) nm for the multilayer structure with Ag (or Au) film. The refractive index of PMMA is chosen as 1.49. Monolayer WS2has a thickness of 6.18 Å, and its complex dielectric constant was fitted from the experimental result[24]. To more intuitively gain the optical properties of metal and WS2films, Fig.1(c) presents the fitting dielectric functions of Ag, Au, and monolayer WS2. The DBR is composed of 10 periods of alternately stacked SiO2and TiO2layers. The SiO2and TiO2layers in each unit have thicknesses of 106.2 and 66.0 nm, respectively, which satisfy the Bragg condition at the central wavelengthλ0= 620 nm. The refractive indices of SiO2and TiO2are 1.46 and 2.35, respectively.

One monochromatic plane wave with TM polarization impinges from air upon the metal film surface with an incident angleθi. The exit medium is air. Without the PMMA layer and monolayer WS2, the interface between metal film and DBR is accepted as a virtual plane microcavity, as shown in Fig.1(b). The propagating light waves could be resonantly trapped between the two imaginary cavity mirrors, corresponding to TPP modes. The TPPs as well as the optical Tamm states were first proposed and investigated on the basis of transfer matrix theory[1,2]. Until now, lots of theoretical predictions by transfer matrix method (TMM) have been confirmed via experiments[11,17,18,21]. And the TMM has been widely applied in simulating new optical phenomena in stratified media without magnetic activity[3,4,7,20]. Utilizing the TMM, one can solve the eigenmode equation for optical field in the virtual microcavity and haverleftrrightexp(2iΦ) = 1. Then, the phase of TPP modes should satisfy Arg[rleftrrightexp(2iΦ)] ≈ 2mπ, where,rleftandrrightindicate the amplitude reflection coefficients for propagating waves at the left and right interfaces, respectively,Φis the phase shift of wave propagating across the cavity, andmimplies the order of TPP resonance.

Fig.1 (a) Schematic representation of metal/PMMA/WS2/DBR hybrid architecture; (b) Illustration of the virtual plane microcavity at the interface between metal film and DBR; (c) Complex dielectric functions ε1+iε2 of metal Ag, Au and monolayer WS2, refer to the left and right vertical coordinates for solid and dash lines, respectively

The configured DBR is approximately a complete photonic crystal with a bandgap between 540 and 725 nm, as shown by the solid line in Fig.2(a). According to the TMM[25-27], one stacked multilayer structure containsN+2 materials andN+1 interfaces. Here,Nis the number of layers and thejth layer holds the dielectric functionεj=nj2and thicknessdj. The film layers are stacked along thezaxis that is perpendicular to the interfaces. Then the electromagnetic waves propagating in each layer can be expressed by a characteristic matrix

where,δj= 2π/λnjdjcosθj,λis the incident wavelengthandθjindicates the refraction angle in thejth-layer medium.Fr[j-1]jandFt[j-1]jare the Fresnel reflection and transmission coefficients at the interface between thej-1th and thejth layers, and

Thereby, the total reflection coefficient of the multilayer structure can be calculated viar=M21/M11, and the intensity-based reflection is derived byR= |r|2.

3 Results and discussion

The reflectance spectra for the multilayer structures of metal/PMMA/DBR and PMMA/WS2/DBR are shown in Fig.2. One can find that a dip appears at 607 nm in the spectra of metal/PMMA/DBR, indicating the creation of TPP modes. In particular, the TPPs in Au/PMMA/DBR structure gives near-zero reflectance. The reflectance spectrum of PMMA/WS2/DBR exhibits one dip at 616.5 nm which is closely related to the excitonic resonance absorption of A exciton in monolayer WS2. After inserting monolayer WS2into the metal/PMMA/DBR structure, a prominent resonance dip splitting is observed.

One can see from Fig.1(c) that both real and imaginary parts of metal Au are larger than those of metal Ag. In particular, the imaginary partε2describes the energy dissipation, and a largerε2value generally leads to a stronger absorption. Therefore, the reflectance dip of multilayer structure with Au film is smaller than that of hybrid architecture with Ag film, as shown in Fig.2. The electric field distributions along thezaxis, as illustrated in Fig.3, further exemplify that an excess of energy dissipation induced by metal Au makes against the enhancement of local optical field.

Fig.2 Reflectance spectra for the multilayer structures of DBR(solid line), metal/PMMA/DBR(dash dot line), PMMA/WS2/DBR(dot line), and metal/PMMA/WS2/DBR(dash line)

Fig.3 Electric field |E| distributions at the wavelength of left dip, and the TPP resonance when monolayer WS2 is removed

In addition, the damping constant Γ (0.037/fs) of Au is larger than that (0.027/fs) of Ag[28,29]. The damping arises from the scattering of electrons at phonons, impurities, lattice defects,etc., and Γ stems from the average of the respective collision frequencies of the electrons. This indicates that the relaxation time of carriers, which is affected by the external excitation field, is shorter for metal Au in comparison with that for Ag. In consequence, the reflectance dip of multilayer structure with Au film is broader than that of hybrid architecture with Ag film (see Fig.2). The discrepancy induced via Ag and Au can be further witnessed from the reflectance mapping with respect to the incident wavelength and the thicknessdPMof PMMA spacer in Fig.4. It is seen that the bandwidth of reflectance dip of Au/PMMA/WS2/DBR is about twice that of Ag/PMMA/WS2/DBR.

Besides, a conspicuous wavelength splitting, which matches well with the characteristics of Rabi splitting[17,18,20], can be observed around 616.5 nm in Fig.4. Moreover, as the thickness of PMMA deviates from 71.78 (or 64.10) nm for the hybrid structure with Ag (or Au) film, the reflectance spectra in Fig.4 varies from the symmetric line shape to the asymmetric ones. In order to inspect the origin of this coupling splitting, Figs.5(a) and 5(b) show the reflectance mapping of Ag/PMMA/DBR and PMMA/WS2/DBR. AsdPMincreases, it is clear that the TPP resonance wavelength in Fig.5(a) gradually shifts toward long wavelength while the reflectance dip in Fig.5(b) keeps unchanged at the resonance wavelength 616.5 nm of A exciton in PMMA/WS2/DBR. This is greatly different from recently reported coupling mechanism in graphene/spacer/DBR/Ag hybrid structure[20]. In the graphene/spacer/DBR structure, TPPs are excited at the boundary between graphene and DBR such that the resonance frequency gradually shifts to low frequency as the spacer thickness increases. Therefore, the Rabi splitting originates from the coupling between two kinds of TPP modes in graphene/spacer/DBR/Ag[20]. In the present work, however, the resonance wavelength of PMMA/WS2/DBR is unaffected by the thickness of PMMA since it originates from A exciton resonance in monolayer WS2.

Fig.4 Reflectance spectra of metal/PMMA/WS2/DBR as a function of the incident wavelength and the thickness of PMMA spacer. Metals in panels (a) and (b) are Ag and Au, respectively

Fig.5 Reflectance spectra of (a) Ag/PMMA/DBR and (b) PMMA/WS2/DBR with respect to the incident wavelength and the thickness of PMMA spacer

Furthermore, both the resonance peaks of TPP modes in graphene/spacer/DBR/Ag shift to the short wavelength with increasing the incident angle, and the Rabi splitting spacing gradually increases with reducing the period of DBR[20]. In marked contrast, the right dip position of metal/PMMA/WS2/DBR in Fig.2 is almost uninfluenced by the incident angleθiwhile the TPP resonance dip bends towards the short wavelength direction asθiincreases (see Fig.6). Additionally, when the period of DBR increases to be 3 (or 2), the coupling double dips emerge for hybrid architecture with Ag (or Au) film, as exhibited in Fig.7. As the period increases to be 5 or larger, the reflectance at dip positions approach saturation and the dip positions are unaffected by the period. According to the model in Fig.1(a), both metal film and monolayer WS2locate at the left side of DBR. Resultantly, it could has little impact on the resonance dip positions through changing the period of DBR. Nevertheless, when we put monolayer WS2on the right side of DBR in Fig.1(a), the reflectance dip associating with A exciton resonance cannot be observed until the period of DBR decreases to 1 (not shown here). This hints that it may be difficult to excite TPPs at the boundary between monolayer WS2and DBR at the studied wavelength range. Herein, the resonance dip splitting mainly results from the coupling between TPPs and exciton resonance rather than two kinds of TPP resonance modes.

Fig.6 Reflectance spectra of metal/PMMA/WS2/DBR as a function of the wavelength and the incident angle. Metals in panels (a) and (b) are Ag and Au, respectively

Fig.7 Reflectance spectra of metal/PMMA/WS2/DBR as a function of the incident wavelength and the period of DBR. Metals in panels (a) and (b) are Ag and Au, respectively

4 Conclusions

In conclusion, we theoretically investigate the interaction mechanism between TPPs and monolayer WS2embedded in a metal/DBR hybrid architecture. Results show that the bandwidth (or reflectance value) of reflectance dip from hybrid structure with Au is larger (or smaller) than that from hybrid structure with Ag due to the relatively larger damping constant (or higher energy dissipation) of metal Au. Because the resonance wavelength associating with A exciton absorption in PMMA/WS2/DBR keeps nearly unchanged, evolutions of Rabi splitting with the structural parameters of spacer thickness, incident angle and DBR period greatly differ from those observed in graphene/DBR/metal hybrid structure. This may also imply that it is difficult to excite TPPs at the boundary between monolayer WS2and DBR around the exciton resonance wavelength. These findings could be helpful for understanding the fundamental properties of monolayer TMDC-TPPs interaction and may provide guidance for designing optically tunable Tamm plasmonic devices.