Near-infrared dual-wavelength plasmonic switching and digital metasurface unveiled by plasmonic Fano resonance

3.1 Plasmonic FR in the near-infrared region

Here, we study the hybridized modes, under the condition of the polarization of the incident light being along the Z-direction, in the periodic arrays with individual PH and CRA unit cells, as well as the hybrid metasurface, respectively. As shown in Figure 2a, the electric dipolar (D _PH) mode interacts with the electric quadrupolar (Q _PH) mode in the PH structure. This process gives rise to the presence of hybridized bonding mode (D _PH + Q _PH) [43], owing to the selective excitation that the incident light with specific polarization gives access to the pure bonding mode [44]. Meanwhile, as shown in the inset of Figure 2a, the charge distribution of the PH structure at the related wavelength is presented, where the top panel shows the charge distribution at the Ag/air interface, while the bottom panel shows the charge distribution at the Ag/quartz interface [12]. This interaction of the hybridized modes, as mentioned above, can be confirmed from the charge distribution (marked by the red dot) in the inset of Figure 2a. For simplicity, the bonding mode can be considered as the effective electric dipolar mode D ₁, although the hybridized plasmonic wave functions contain an admixture of D _PH and Q _PH modes [45]. However, as depicted in Figure 2b, there are electric quadrupolar (Q _CRA) and hybridized bonding (D _CRA + Q _CRA) modes [43] occurring in the CRA structure, which can also be confirmed by the charge distribution (marked by blue and purple dots) in the right and left insets of Figure 2b, respectively. Likewise, the hybridized bonding mode (D _CRA + Q _CRA) is weak excitation (see the left inset in Figure 2b), but it can also be viewed as the effective electric dipolar mode D ₂. One can notice that the electric dipolar D ₁ and D ₂ modes possessing different quality factors; thus, they can be regarded as the superradiant and the subradiant modes [46], [ 47], respectively. When there exist spectral overlapping between the two electric dipolar modes in the transmitted spectrum, the realization of the plasmonic FR originates from the interaction between the electric dipolar D ₁ and D ₂ modes in the near-infrared region, leading to the two new hybridized bonding (D ₁ + D ₂) and antibonding (D ₁ − D ₂) modes in the hybrid metasurface. This behavior can also be confirmed from the charge distributions (marked by orange and green dots, respectively) in the left inset of Figure 2c.

Figure 2:

The origin of the near-infrared plasmonic FR in a hybrid metasurface.

Transmitted spectra correspond to periodic arrays with individual (a) PH and (b) CRA unit cells, as well as (c) the hybrid metasurface. The insets of (a) and (b) show the charge distribution of the individual PH and CRA structures at the marked wavelength, respectively. The left inset of (c) shows the charge distribution of the hybrid metasurface. While the right inset of (c) shows the related transmitted spectra (black dashed box) of the hybrid metasurface, with the blue dots and red solid curve being the simulation and fitting, respectively. The geometrical parameters are set as follows: P _x  = P _z  = 600 nm, R ₁ = 242.5 nm, D = 10 nm, L = 300 nm, W = 200 nm, a _p  = 0.25, and b _p  = 20. FR, Fano resonance; PH, parabolic-hole; CRA, circular-ring-aperture.

To further understand the plasmonic FR in our scheme, the TCMT is used [48], [ 49]. It is known that TCMT is a simple and effective tool to model the interaction between resonator and incident light, which is capable of being used to study the Fano-type transmission phenomena in the hybrid metasurface. By doing so, the dynamic equations of the related resonance amplitude in this system can be written as,

where Ω = ( ω 1 − k − k ω 2 ) , Γ e = ( Γ e 1 0 0 0 ) , Γ i = ( Γ i 1 0 0 Γ i 2 ) , C 1 = ( 0 1 1 0 ) , and C 2 = ( j Γ e 1 0 j Γ e 1 0 ) . a ₁ and a ₂ are the normalized resonance amplitudes of bonding (D ₁ + D ₂) and antibonding (D ₁ − D ₂) modes; S ₁₊ and S ₂₊ (or S ₁₋ and S ₂₋) are normalized amplitudes of incoming (or outgoing) light at the input and output ports; | S 1 + | 2 and | S 2 + | 2 (or | S 1 − | 2 and | S 2 − | 2 ) correspond to the power of the incident (or transmitted) light; ω ₁, Γ _e1, Γ _i1 (or ω ₂, Γ _e2, Γ _i2) represent the resonant frequency, radiative decay rate, and nonradiative decay rate of the bonding (antibonding) mode, respectively. k describes the direct coupling coefficient between the bonding and antibonding modes. C ₁ denotes the direct scattering matrix without resonance modes. C ₂ is the coupling between the resonance modes and the incident/transmitted light. In our scheme, we assume that the radiative loss in the case of plasmonic FR is mainly dominated by the bonding mode (D ₁ + D ₂). For the antibonding mode, there is no direct energy exchange with the related environments, so the radiative loss is negligible (i.e.,  Γ e 2 ≈ 0 ). When the C ₁, C ₂, and Γ _e satisfy the relationships, namely, C 1 C 2 * = − C 2 , and C 2 + C 2 = 2 Γ e , the transmittance of the hybrid metasurface can be given by [50],

Hence, by using the TCMT to fit the transmittance of the hybrid metasurface, the fitting (red solid line) agrees well with the numerical simulation (see the blue dot), as shown in the right inset of Figure 2c. Herein, the fitting parameters of the hybrid metasurface are obtained as ω 1 = 2 π × 1.974 × 10 14   rad / s , ω 2 = 2 π × 2.144 × 10 14   rad / s , Γ e 1 = 2 π × 0.099 × 10 14   rad / s , Γ i 1 = 2 π × 0.047 × 10 14   rad / s , Γ i 2 = 2 π × 0.027 × 10 14   rad / s , and k = 2 π × 0.154 × 10 14   rad / s . In brief, the plasmonic FR that results in the hybridized modes of the hybrid metasurface can be implemented in the near-infrared region.

In the following, we explore the tunable plasmonic FR by considering different geometric configurations of the unit cells in the hybrid metasurface. For a more quantitative analysis, the W _Fd and D _Fd are defined as the width and depth of the Fano dip, respectively (see Figure 3a–c). In Figure 3a, by changing the coefficient b _p from 20 to 80 divided into four groups, there exists a fixed wavelength of the Fano dip, whereas the W _Fd and D _Fd are varied. This behavior is concomitant with the opposite shifts of the two adjacent peaks, which can also be regarded as the radiation-sensing monitoring of the depth of the Fano dip [51]. As shown in Figure 3b, when the widths of PH (W) are set as 100, 150, 200, and 250 nm, the wavelengths of the Fano dip and one of the peaks of the doublet are fixed, while the other peak of the doublet can be evidently broadened with the variation of D _Fd and W _Fd. As depicted in Figure 3c, by varying the width of the CRA unit cells (D), which is set as 6, 10, 14, and 18 nm, it is found that the wavelength, W _Fd, and D _Fd of the Fano dip can be significantly all changed. It is worth mentioning that the fixed wavelengths of the Fano dip in Figure 3a and b can be ascribed to the parameters of the CRA unit cells remaining unchanged [47]. These results imply that the wavelength, width (W _Fd), and depth (D _Fd) of the Fano dip can be controlled by modulating the related geometric configurations of the unit cells in the hybrid metasurface, in which the wavelength mainly depends on the relevant geometric parameters of the CRA unit cells.

Figure 3:

The designability and polarization dependence of the near-infrared plasmonic FR in a hybrid metasurface.

(a) Transmitted spectra of the hybrid metasurface with different geometric parameters (a) b _p , (b) W, and (c) D in the near-infrared region, respectively. (d–f) Polar plots of the transmittance at the related three wavelengths (corresponding to the blue square, black dot, and red triangle in (a), (b), and (c), respectively) in the hybrid metasurface with (d) b _p  = 40, (e) W = 150 nm, and (f) D = 10 nm. The other parameters are the same as Figure 2. FR, Fano resonance.

Next, when the geometric parameters of the unit cells are fixed, the modulated polarization direction of the incident light could potentially induce the change of the coupling strength of the electric field with the hybrid metasurface [11]. As shown in Figure 3d–f, the polar plots of the transmittance at the related three wavelengths (corresponding to the blue square, black dot, and red triangle in Figure 3a–c, respectively) in the hybrid metasurface with b _p  = 40, W = 150 nm, and D = 10 nm are considered. The polarization angle θ is defined as the angle between the polarization and the positive Z-direction, which can be changed from 0 to 360° in a 15° step. In Figure 3d, the transmittance at 1262 nm (marked with blue squares) reaches a maximum of 0.7607 at θ = 0° and θ = 180° and a minimum of 0.302 at θ = 90° and θ = 270°. Likewise, the transmittance at 1487 nm (marked with red triangles) reaches a maximum of 0.4433 at θ = 0° and θ = 180° and a minimum of 0.1461 at θ = 90° and θ = 270°. But the transmittance at 1394 nm (marked with black dots) reaches a maximum of 0.1595 at θ = 90° and θ = 270° and a minimum of 0.06755 at θ = 0° and θ = 180°. As shown in Figure 3e and f, a similar conclusion can be made on the related wavelengths (see the blue square, black dot, and red triangle) in Figure 3b and c, respectively. The results elucidate that, when the geometric parameters of the unit cells are fixed, the transmittance at the related three wavelengths can be regulated by changing the polarization direction of the incident light. In other words, the polarization-dependent transmittance at the related three different wavelengths that result from different degrees of anisotropy [52] holds great promise for plasmonic sensing and switching [3], as well as polarization-dependent digital metasurface in the metasurfaces [53].

3.2 Polarization-dependent passive plasmonic switching and digital metasurface

In view of the fact that the line shape and position of the plasmonic FR can be effectually designed by changing the geometric parameters of the hybrid metasurface. Moreover, the properties of the transmitted spectrum can be controlled by adjusting the polarization angle of the incident light (θ). In this scenario, as shown in Figure 4a, by varying the θ between 0° (along the Z-direction) and 90° (along the X-direction), the passive plasmonic switching can easily change the “ON” and “OFF” states at the telecom O-band (1260 ∼ 1360 nm) and L-band (1565 ∼ 1625 nm). Here, the ON/OFF ratio η can be defined as [54].

where T _ON and T _OFF are the transmittance of the “ON” and “OFF” states at the marked wavelengths, respectively. The marked wavelength in Figure 4a presents at the telecom L-band with the center wavelength being 1571 nm, where T _ON = 0.3908 and T _OFF = 0.0099. The ON/OFF ratio η based on Equation (4) can be obtained as 15.96 dB, where the modulation depth at the marked wavelength can be obtained around 97% [19]. In particular, there exists the marked wavelength appearing at the telecom O-band with the center wavelength of 1276 nm. In this case, T _ON = 0.5045, while T _OFF is only 0.0032, leading to the ON/OFF ratio η being as high as 21.98 dB with the modulation depth being nearly 99%. It should be noted that the passive plasmonic switching can work simultaneously at the marked dual-wavelength, but the “ON” states are not realized simultaneously. Once the “ON” state of one of the dual-wavelength occurs, the “OFF” state is achieved at another wavelength under the same conditions and vice versa. Besides, by adjusting the geometric parameters of the unit cells, the “ON” and “OFF” states at a working wavelength of 1267 nm in a single-wavelength passive plasmonic switching can obtain T _ON = 0.8144 and T _OFF = 0.007464 with the ON/OFF ratio being 20.38 dB (the modulation depth is around 99%). This means that a novel compact dual-wavelength passive plasmonic switching can be realized in the near-infrared region, which is a passive device without adding another active pump light field in the hybrid metasurface. Such a high ON/OFF ratio for the polarization-dependent passive plasmonic switching allows for potential applications in optical communication with high flexibility and designability.

Figure 4:

The polarization-dependent dual-wavelength passive plasmonic switching and 1-bit digital metasurface.

(a) The polarization-dependent dual-wavelength passive plasmonic switching in the near-infrared region, with the ON/OFF ratio being 21.98 and 15.96 dB at a wavelength of 1276 and 1571 nm, respectively. (b) The 1-bit digital metasurface can be obtained by encoding the elements “1” and “0” in two ways at the related wavelengths. The four subplots show the polarization of the incident light and the related E-field distributions. The parameters of the unit cells of the hybrid metasurface are set as R ₁ = 122.5 nm, D = 20 nm, L = 130 nm, W = 100 nm, a p = 1 , and b p = 5 , and the other parameters are the same as Figure 2.

In addition, we further consider the hybrid metasurface to be encoded as the binary digital elements of “0” and “1.” The physical realization of digital elements requires distinct responses to obtain significant amplitude changes of the transmitted spectra, which can own dramatic freedom to control the transmission of the pulsed light field. As shown in Figure 4b, for the “ON” state at 1276 nm, the E-field distribution implies that both the CRA and the PH unit cells of the hybrid metasurface are excited, whereas the strongest resonance is activated at the center of the PH unit cells. Likewise, there is no obvious strong resonance occurring in the E-field distribution for the “OFF” state at 1276 nm. With respect to the case of the “ON” and “OFF” states at 1571 nm, the CRA unit cells are evidently excited when the plasmonic switching operates independently in the “ON” and “OFF” states, but the PH unit cells are only obviously excited when the plasmonic switching works at the “ON” state. In our scheme, the hybrid metasurface here can function as a 1-bit digital metasurface, where the “ON” and “OFF” states can be named as “1” and “0” elements, respectively. With the hybrid metasurface working at a wavelength of 1276 nm, the “1” (see the upper left of Figure 4b) and “0” (see the lower left of Figure 4b) elements refer to the case of the polarization angle of the incident light at 0° (along the Z-direction) and 90° (along the X-direction), respectively. However, with the hybrid metasurface operating at 1571 nm, the “1” (see the upper right of Figure 4b) and “0” (see the lower right of Figure 4b) elements refer to the case of the polarization angle of the incident light at θ = 90 ° and θ = 0 ° , respectively. In this way, the amplitude response of the “0” and “1” elements can be readily defined as A n = n ( T ON − T OFF ) , with n = 0 , 1 . Therefore, we can control the amplitude response of the transmitted spectra by adjusting the polarization direction of the incident light to realize the freely switching between coding elements “0” and “1.” By encoding the “0” and “1” elements with a controlled sequence (1-bit coding), it is possible to fulfill the digital metasurface in the telecom dual-wavelength with different functions in the near-infrared region.

It is obvious that the polarization-dependent digital metasurface can be extended from 1-bit to 2-bit or more. In the case of 2-bit coding, four types of polarization states with distinct amplitude responses in the transmitted spectra are required to mimic the “00,” “01,” “10,” and “11” coding elements. As for the 2-bit digital metasurface, one can obtain greater flexibility in controlling the coding sequences with extensive applications. Similar to the case of 1-bit digital metasurface, the amplitude responses are defined as A n = n ( T ON − T OFF ) / 3 , ( n = 0 , 1 , 2 , 3 ) . As shown in Figure 5a, to realize 2-bit digital metasurface, the polarization angles with four different amplitude responses in the transmitted spectra are set as θ = 0 ° , θ = 37 ° , θ = 56 ° , and θ = 90 ° , respectively. When the hybrid metasurface works simultaneously (dual-wavelength 2-bit) at the telecom O-band with the center wavelength being 1276 nm and L-band with the center wavelength being 1571 nm, the amplitude responses in the transmitted spectra of θ = 0 ° , θ = 37 ° , θ = 56 ° , and θ = 90 ° are defined as “10” (see the red curve in Figure 5a), “11”(see the black curve in Figure 5a), “00” (see the orange curve in Figure 5a), and “01” (see the blue curve in Figure 5a) coding elements, respectively. With the hybrid metasurface working at wavelength 1276 nm (single-wavelength 2-bit), the “11,” “10,” “01,” and “00” coding elements refer to the case of the polarization angle of the incident light at θ = 0° (see the red pentagram in Figure 5b), θ = 37 ° (see the black pentagram in Figure 5b), θ = 56 ° (see the orange pentagram in Figure 5b), and θ = 90 ° (see the blue pentagram in Figure 5b), respectively. However, with the hybrid metasurface working at wavelength 1571 nm (single-wavelength 2-bit), the “11,” “10,” “01,” and “00” coding elements refer to the case of the polarization angle of the incident light at θ = 90 ° (see the red triangle in Figure 5b), θ = 56 ° (see the black triangle in Figure 5b), θ = 37 ° (see the orange triangle in Figure 5b), and θ = 0 ° (see the blue triangle in Figure 5b), respectively. As shown in Figure 5b, for the CRA unit cells of the hybrid metasurface, the E-field distributions at 1276 or 1571 nm illustrate that the orientations of the distributions are consistent with the polarization direction of the corresponding incident light. For the PH unit cells of the hybrid metasurface at 1276 and 1571 nm, the E-field is mainly distributed on the center (on both sides) of the H-shaped hole unit cells in the case of θ = 0 ° ( θ = 90 ° ) . Meanwhile, the E-field distributions are asymmetric in the case of θ = 37 ° and θ = 56 ° , which is due to the geometric configuration of the PH unit cells being asymmetric along the polarization direction of the incident light (see the projection of the E-field intensity in Figure 5b). When the 2-bit digital metasurface works at the single-wavelength or dual-wavelength, not only are their coding methods different but can achieve different functions. These plasmonic optical behaviors indicate that the proposed hybrid metasurface device can possess multifunctionalities and provide for the possibility of applications in optical sensors, optics digital processing, optical communication, and optical switching in the near-infrared region.

Figure 5:

The amplitude responses in the transmitted spectra of the dual-wavelength 2-bit digital metasurface, as well as their coding elements.

(a) The amplitude responses in the transmitted spectra of the dual-wavelength 2-bit digital metasurface by encoding the polarization state of the incident light with the polarization angle θ being 0, 37, 56, and 90°, respectively. (b) The “11,” “10,” “01,” and “00” coding elements realized at the related wavelengths. The eight subplots show the polarization of the incident light and the related E-field distributions, as well as the projection of the E-field intensity (along the polarization direction) on the X- or Z-direction.

Moreover, it is known that magnetron sputtering has been proven to be an extremely versatile tool for coating deposition in the application field of coatings with specific optical or electrical properties [55], [56], [57]. The magnetron sputtering films are superior to the films deposited by other physical vapor deposition processes in many cases, which provide the feasibility for the fabrication of high-quality metallic Ag films. In order to tailor the unit cells with the required geometric configurations in the Ag film, a focused-ion beam system can be used to generate highly symmetrical nanohole with a diameter of sub-5 nm, thus forming arrays with the multiple nanohole [58]. By doing so, a 50-nm-thick Ag film can be sputtered on the polished quartz substrate, and then, the hybrid metasurface with CRA and PH unit cells can be fabricated by using a focused-ion beam method. The transmission spectra can be measured by using a homebuilt optical system [59]. Therein, a pair of the near-infrared objective lens can be used to focus the incident ultrashort Gaussian pulse and collect the transmitted signal. Thus, the transmitted signal can be delivered to a spectrometer equipped with a charge-coupled device detector. In brief, the proposed hybrid metasurface can be fabricated, and the dual-wavelength passive plasmonic switching and digital metasurface can possibly be observed in the experiment.