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## Bulk and surface sensitivities of surface plasmon waveguides

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In general, the higher carrier mobility is, the lower intrinsic loss of plasmons would be. Furthermore, the dielectric functions of BDS can be actively tuned by changing its Fermi energy. The good news is that BDS, such as Na 3 Bi [ 19 ], Cd 3 As 2 [ 20 ], and AlCuFe quasicrystals [ 21 ], are easier to process and more stable compared with graphene, which is expected to be a new generation of plasmonic material after graphene.

## "Metal-insulator-insulator-metal plasmonic waveguides and devices" by Jing Chen

Our recent work has investigated the manipulation of the THz SPPs in double-layer BDS sheet waveguide, which indicates that the symmetric coupling mode has better confinement than the plasmonic waveguide mode in monolayer BDS film [ 22 ]. The mode index of the symmetric mode is 1. In this paper, we propose a deep-subwavelength BDS-insulator-metal BIM waveguide with enhanced confinement, relatively low loss, and desirable tunability.

Dispersion relation, propagation loss, and filtering application of this highly confined mode are investigated. Interestingly, there is an optimized frequency range with an enhanced confinement as well as a reduced loss, which has rarely been reported in the traditional SPP mode in metal structure. By taking two silicon ribbons as reflection mirrors, a dynamically tunable optical resonator has been achieved. The resonant frequency of the resonator can be dynamically tuned by varying the Fermi energy of BDS, which may find applications in THz switching and filtering.

The proposed BIM plasmonic waveguide is schematically presented in Fig. For the TM-polarized incident light, the plasmonic waveguide mode confined in the metal-insulator interface can propagate along the x direction with a wavevector k SPP and exponentially decay along the y direction into the free space. By combining proper boundary conditions, the wavevector k SPP of the BIM waveguide can be obtained from the following dispersion relation: [ 23 ]. By solving Eq. For the highly confined plasmonic waveguide modes, the real part of effective refractive index Re n eff roughly describe the mode confinement, while the imaginary part Im n eff is directly proportion to the mode propagation loss: The larger Re n eff is, the higher the confinement.

The complex conductivity of BDS is presented in methods Eqs 3 — 4. The TM-polarized plasmonic waveguide mode propagates along the x direction and decays along the y direction. Schematic depiction of the E x distribution is depicted by the red line. As depicted in Fig. The similar tendency can be observed in the dependence of propagation loss on the gap width g , as depicted in Fig. Thus, there is an optimized frequency region where the mode confinement is strongly enhanced while the propagation loss is gradually reduced.

This characteristic has rarely been observed in traditional plasmonic waveguide modes at metal-insulator interface. Similar with the case of a monolayer and double-layer waveguide, the mode confinement and propagation loss continuously decrease with the increase of Fermi energy, which can be attributed to the enhanced metallicity and prolonged carrier relaxation time of BDS.

For example, the confinement factor of plasmonic waveguide mode at 2. Therefore, relying on frameworks that have already been discussed above would increase mode confinement with a relatively low loss, which can be utilized to the design of integrated optical filters, buffers, and Mach-Zehnder interferometer. To examine aforementioned analysis, we perform numerical calculations about the transmission intensity and field distribution of the proposed waveguide structure. The simulation setting is described in methods.

On the other hand, as indicated in Fig. To visualize this statement, the magnetic field Hz distributions of these modes are presented in Fig. It can be clearly found that the highly confined plasmonic mode in BIM waveguide shows shorter oscillation period than that of the monolayer BDS case. Among all the applications mentioned above, optical resonator is the essential element for tailoring THz plasmonic waveguide mode.

As illustrated in Fig. Only the incident frequency satisfies the resonance condition of the standing wave, the plasmonic waves can transmit to the output of the waveguide via coupling with the designed optical resonator. The magnetic field distributions H z 2 of the transmission peaks are depicted in Fig. The first- and second-order resonance can be clearly found in the FP cavity. The incident plasmonic wave near the resonance frequency can be coupled into the FP cavity and then transmits through the BIM waveguide, which generates the transmission peak in the spectrum.

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While, for the non-resonant frequency region, the standing wave cannot be formed and thus the incident waves are prohibited in the left port of BIM waveguide, as shown in Fig. Moreover, combined with the dispersion relation of BIM waveguide, the transmission intensity can be analytically calculated by coupled mode theory CMT [ 17 ]:. The analytical results based on CMT hold good agreement with the numerical simulations, as depicted in Fig.

The width of each silicon ribbon is d , and the distance between the ribbons is L. The transmission peak tends to red-shift with the increase of L , as presented in Fig. As shown in Fig. According to Eq. With the increase of g , the resonant peak in same order exhibits a blue shift. This phenomenon can be attributed to the dramatic decrease of Re n eff as shown in Fig. The tuning of Fermi energy of BDS can be realized by alkaline surface doping in experiment. As the Fermi energy increases, the transmission peak presents a blue shift, which can also be involved in the standing wave resonance picture.

That is the reason why the transmission peak tends to blue-shift with the increase of Fermi energy. Meanwhile, the bandwidth of the transmission peak is narrowed, which can be attributed to the decrease of Im n eff , i. Transmission spectra for different gap width g a and Fermi energy E F b , where the other parameters are same as Fig. In summary, we have demonstrated the highly confined terahertz plasmonic mode supported by a BIM waveguide.

The mode confinement and loss characteristics have been discussed with the variations of BDS-metal separation and Fermi energy, which indicates that there is an optimized frequency range with enhanced mode confinement as well as reduced propagation loss, which has rarely been reported in traditional SPP mode in metal structure.

By taking two silicon ribbons as reflective mirrors, a dynamically tunable band-pass filter has been achieved, where the resonant frequency can be actively controlled by adjusting the Fermi energy of BDS film without re-optimization of its structural parameters. Numerical results are obtained by using 2D finite-difference time-domain FDTD method, where the perfectly matched layers are set to absorb the scattering light in the x and y directions.

The frequency-dependent conductivity of BDS is described by Kubo formula with random phase approximation [ 12 , 25 ].