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Abstract
Surface plasmons (SPs) is the cornerstone in terahertz (THz) near-field photonics, which play crucial roles in the miniaturization and integration of functional devices. The excitation and manipulation of SPs, however, is currently restricted to electric SPs paradigm, while magnetic SPs receive less attention despite the importance of magnetic light-matter interactions. Here, a scheme is proposed to simultaneously convert the propagating waves in free space into magnetic and electric SPs using a single ultracompact device. First, a plasmonic structure composed of connected slit rings is designed and demonstrated to support both electric and magnetic SPs, which is ascribed to the two distinct eigenmodes of oscillating electrons and vortex currents, respectively. Second, with the assistance of an anisotropic and gradient metasurface, orthogonal linear polarized components of incident THz beams are coupled into different electric and magnetic SP channels with little crosstalk. Furthermore, by encoding two distinct polarization-dependent phase profile into the metasurface, it is shown that the resulting meta-device can individually tailor the wavefronts of magnetic and electric SPs, thus simultaneously engineering magnetic and electric near-field distributions. This work can pave the road to realize bi-channel and on-chip devices, and inspire more integrated functionalities especially related to near-field manipulations of magnetic SPs.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The development of modern optics has brought forward higher requirements for compact size, high integration and multiple functionalities. Traditional optical components (e.g., lens, prism and wave plate) are excessively bulky in size, making them inconvenient for on-chip applications. Recently, the concept and advances of metasurfaces [1,2] open a new route to realizing compact devices with desired functionalities due to the subwavelength thickness, however, they have little effect in compressing propagation space of electromagnetic (EM) waves in the systems. The surface plasmonic waves (SPWs) offer a solution to this problem, whose unique properties of large wave vector and field confinement enable an efficiency platform for chip-scale transmitting and processing [3]. Since SPWs are eigen EM modes bounded at dielectric/metal interfaces [4], replacing space propagating waves with SPWs can greatly reduce the systems from three dimensions to two dimensions. While travelling along the interface, the field enhancement and high-resolution make SPWs promising in many fascinating applications such as surface sensing, sub-diffraction-limited imaging and surface-enhanced Raman scattering [5–8]. Moreover, SPWs can also propagate along one-dimensional line-guided structures [9–12], which endows them great potentials in integrated plasmonic components for energy transport and communications [13,14].
In recently years, much attention has been paid to the electric surface plasmons (ESPs), which originate from the collective oscillations of electrons, while magnetic surface plasmons (MSPs) are less focused due to the lack of magnetic materials. With the rapid development of metamaterials, artificial materials that can extend the magnetic responses to THz and even optical frequencies receive special interest [15,16]. Different from ESPs, MSPs arise from vortex currents, and the low radiation loss of magnetic dipole makes it a promising candidate for EM energy transfer of long distance [17]. In practical cases, the tailor of electric and magnetic fields may greatly facilitate some applications, such as spontaneous radiation transition [18,19], optical trapping [20,21], and enhanced nonlinear effect [22]. Therefore, guiding MSPs and ESPs simultaneously, although challenging, becomes highly required due to the ever-growing demand in both plasmonic research and applications. Up to now, various kinds of “plasmonic metal” have be proposed and demonstrated [9,23,24], however, most of them support single ESP mode. The signal propagation and processing for both MSPs and ESPs are unattainable using the common textured metal surface [25,26]. Along with the ongoing efforts to synthesize plasmonic metal that support propagating SPs, we also notice that there are some optical architectures that modify the magnetic and electric modes relevant to localized plasmons. The clusters composed of closely packed metal nanoparticles are demonstrated to manipulate both electric and magnetic resonances [27,28]. The localized electric and magnetic modes excited in hyperbolic nanoparticles is coupled with an external magnetic field to realize tunable magneto-optical response [29]. Via exploiting different nature of the localized hyperbolic Bloch-like modes, the full control of scattering and absorption in magnetic and electric decay channels is demonstrated over a broad spectral range [30,31]. Two types of electric and magnetic hot spots originating from the excitation of localized surface plasmons are formed by switching the internal coupling method in a dimer antenna [32]. Furthermore, the plasmon-induced artificial magnetism has been demonstrated to trigger active magneto-plasmonic metamaterial at optical frequencies controlled by light [33].
On the other hand, due to the lack of direct SPW sources, typically a slit grating is integrated with waveguide to couple the free-space wave into propagating SPWs [34], however only the incident TM component is converted into ESP beams without modulation (Fig. 1(a)). Metallic slit resonators based on Pancharatnam-Berry (P-B) phase concept are among the most commonly used coupler, which show excellent flexibilities to steer the wavefront of SPWs by carefully designing their locations and orientations [35]. But the chirality-locked effect results in the simple and symmetric splitting of the opposite chirality, thus hindering them from generating arbitrary and independent SPW profiles for the two spins. Specially, metasurfaces with properly arranged phase gradient have shown the unprecedented capabilities to excite SPWs with high efficiency [36–39]. When further combining P-B phase with resonance phase, the incident orthogonal circular polarization (CP) can be independently modulated [40]. However, since the driven surface waves remain CP, it’s hard to apply different manipulation to ESPs and MSPs. Usually only one SPW can be successfully excited, while the other is just scattered off due to the mode mismatch. In other words, the information capacity carried by the SPWs is far from completely exhausted. To realize more variety of functional plasmonic devices, the exploration for new approaches to simultaneously manipulating ESPs and MSPs has thus been an intrigued research topic, which could promote the design and fabrication of next level integrated plasmonic circuits.
Fig. 1. Schematics of the bifunctional meta-device achieving wavefront reshaping for both MSP and ESP. (a) Schematics of ESP excitations by a grating coupler. TE component of incident beam is reflected and only TM component is converted into ESP. (b) Schematics of SP excitations and wavefront tailoring by a single meta-device. Orthogonal linear polarizations are converted into focusing MSP and launching ESP, respectively. The bottom insets indicate MSP and ESP traveling on the plasmonic structure with different wavefront, where the purple, the red and the gray arrows represent magnetic fields, electric fields and currents, respectively.
In this work, we propose a new plasmonic structure (PS) supporting the propagation of both MSPs and ESPs with little crosstalk between the electric and magnetic channels, which shows potential in integrated plasmonic chips and communication systems [24,41]. Besides, a reflection-type metasurface is designed to convert space propagating waves into surface waves. The decoupling of anisotropic phase response of the meta-atom offers a simple method to modulate the phase profiles for orthogonal linear polarized waves. Via combining the SP and metasurface, a meta-device is shown to simultaneously excite both MSP and ESP, and the ratio of energy transferred in the magnetic and electric channel can be readily adjusted by rotating the incident polarization orientation. Furthermore, individual engineering of magnetic and electric near-field distributions can be realized by encoding two distinct polarization-dependent phase profile into the metasurface. Based on the above concept, a bifunction meta-device is designed and demonstrated to achieve two wavefront modulation (anomalous launching and focusing) in different channels (see Fig. 1(b)). This work provides a new platform for the full usage of EM signals and it may stimulate more studies about the manipulations of near-field plasmonics.
2. Results and discussion
2.1 Design and characterization of a plasmonic structure supporting both ESP and MSP
We start from designing a THz PS supporting both ESP and MSP. Magnetic metamaterials constructed from nonmagnetic metallic element such as split ring resonator [15] have been demonstrated to support MSPs, which can largely enhance magnetic light-matter interactions. However, the single- or double- splits along one direction introduce the unnecessary anisotropy, thus affecting the wavefront modulation functionality of MSPs. To circumvent this issue, herein we introduce four splits in a single metallic ring to form the unit cell with fourfold rotational symmetry. In this way the isotropic magnetic plasmonic structure can be constructed from the four-split ring-based array. One may notice that such isolated metallic rings are unfavorable for transmitting ESPs because they originate from the collective oscillations of charges, which is different from the coupled circular currents of MSPs. In order to design the transmission channel for ESP, a pair of metallic bars is utilized to connect the adjacent rings, which provides pathway for the oscillating charges. The inset in Fig. 2(a) shows the details of the connected split rings (CSRs), where the brown and gold regions indicate the gold rings and dielectric substrate, respectively. Here, P = 60 μm, hs = 28 μm, r1 = 15 μm, r1 = 28 μm, ws = 14 μm, g = 8 μm, and the thickness of the gold film is 170 nm. The substrate is polyimide with permittivity of ɛ = 3.55 + 0.035i [42].
Fig. 2. Design and characterization of the plasmonic structure. (a) The designed plasmonic structure consists of connected split ring array. The inset shows the details of the CSPs, brown and gold regions indicate the gold rings and dielectric substrate, respectively. (b) Dispersion relations of SP modes supported by the present plasmonic structure, where the solid red and blue lines indicate MSP and ESP, respectively, and the dashed black line is the light line in free space. The surface currents distributions of (c) current loop and (d) oscillatory current alone horizontal direction correspond to the characteristics of MSP and ESP, respectively.
To study the EM response of the proposed CSRs, we employ the eigenvalue module of the commercial software Computer Simulation Technology (CST) and obtain the dispersion relations of first two modes for the plasmonic structure. As depicted in Fig. 2(b), the MSP has lower cut-off frequency at the boundary of the first Brillouin zone and larger wave vector, which corresponds to stronger field confinement and lower radiation loss. The surface current distributions of these two modes are plotted in Fig. 2(c), and 2(d), where the circular current excites magnetic dipolar resonance for MSP and the oscillatory current alone horizontal direction excites the x-propagating ESP. Multipolar analysis is further performed to confirm that magnetic and electric dipole moment dominates the radiation at different modes, respectively (see Fig. S2 in Supplement 1). Therefore, both magnetic and electric responses can be induced using a single PS. We also calculate the corresponding EM field distributions, which reveals the TE and TM characteristics of these two SP modes (see Fig. S3 in Supplement 1). Besides, to further verify the ability of transmitting the two-mode signals, two dipole antennas with orthogonal orientations are simply employed to excite this structure. As expected, the external radiations are successfully coupled into the propagating MSP and ESP confined at the interface (see Fig. S4 in Supplement 1). For the considered configuration and operating frequency of 0.9 THz, we determined the propagation loss at 0.0007 dB/μm and 0.002 dB/μm for MSP and ESP, respectively. Through numerical studies we find that the propagation loss mainly results from the absorption in the dielectric substrate for MSP and radiation loss for ESP, which indicate the signal attenuation for MSP can be improved further by using low-loss dielectrics.
2.2 Bi-channel excitation of MSP and ESP
Although we have employed dipole antennas as the source to excite both MSP and ESP, however, the conversion efficiency is quite low. Thus, it’s necessary to explore more efficiency excitation scheme. Innovative metasurfaces with abrupt phase discontinuities have shown unprecedented capabilities of manipulating electromagnetic waves, which can be applied to compensate the momentum mismatch between free space waves and SPWs [43–45]. Here we consider a reflective meta-atom which consists of a metallic cross and a metallic plate separated by the same dielectric spacer (polyimide) with thickness hm= 15 μm and period P = 60 μm. The length, l, and width, wm, of metallic cross are 56 and 2 μm, respectively, as shown in the inset in Fig. 3(a). For simplicity, the isotropic metasurface is first investigated, that is gx = gy, from which the reflective beam is endowed the same phase shift for both TE and TM polarization. When illuminated by incident waves, the anti-parallel electric currents induced on top cross and bottom plate form a magnetic dipole (see the insert in Fig. 3(b)). Near the magnetic resonance the reflection phase undergoes a phase change of 2π while the amplitude maintains a relatively high level as shown in Fig. 3(b), where gx = 35 μm. According to equivalent circuit theory [46], this metal-insulator-metal system can be regarded as a LC resonance circuit, in which the effective inductance L and capacitance C are determined by the geometry. Such equivalent model provides us a method to control the phase retardation simply by adjusting length of the metallic arm gx. Figure 3(c) gives the amplitudes and phases of the reflected electric fields for the metallic crosses with different parameter gx at the designed frequency of 0.9 THz. As gx varies from 2 μm to 50 μm, the 2π phase coverage is obtained with the reflection amplitude more than 0.85. Based on this, a spatial distribution of phase discontinuities at the interface can be constructed freely, which renders an addition parallel wave vector to the reflective waves [36].
Fig. 3. Schematics of the meta-device composed of metasurface and plasmonic structure. (a) Structure of the metasurface consisting of a periodic array of meta-atoms with geometry shown in the inset. (b) Reflection spectrum for the meta-atom with gx = 35 μm, the insert shows the surface current distributions on top cross and bottom plate at magnetic resonance. (c) Reflection amplitude and phase shift of meta-atom with varying dimension parameter gx at 0.9 THz. By adjusting the arm length of the metallic cross, a phase shift over an entire 2π range can be achieved. Illustration of the (d) MSP- and (e) ESP-typed meta-device illuminated by the y- and x- polarized wave, producing high-efficiency MSP and ESP, respectively. Field patterns of (f, h) Hz component and (g, i) Ez component on a reference plane 20 µm underneath the meta-device, which corresponds to (f, g) MSP and (h, i) ESP.
With the design schemes of plasmonic support and meta-atom at hand, we now construct a meta-device to achieve high-efficiency excitations of MSE and ESP. By properly arranging the metasurface’s phase gradient ξ to match the wave vector kSP of SPs, the input free-space waves are first converted to driven surface waves and then coupled into SP modes supported by the plasmonic structure. The matching condition is written as
where k0 is the wavenumber of free-space light, and θi is the angle of the incident light. Under normal illumination, Eq. (1) is simplified as kSP=ξ. Therefore, the phase distribution of metasurface can be described in the following form where Φ0 is a constant phase. From the dispersion relation of the SP modes (see Fig. 2(b)), the wavenumbers of MSP and ESP at 0.9 THz are obtained as kMSP = 1.49k0 and kESP = 1.03k0. To realize the required phase gradient, 12 × 12 meta-atoms exhibiting the same phase gradient in each row are employed to build the metasurface, which is jointed with the PS consisting of 12 × 50 CSRs on the left (see Tables S1 and S2 for geometric parameters and phase of each meta-atoms). As schematically shown in Fig. 3(d) and 3(e), for the metasurface with ξ=kMSP and kESP, the y- and x-polarized beams are converted into MSP and ESP bounded on the PS, respectively. To visualize the excitation of SPs of different modes, 3D full-wave simulations in the time domain module of the CST is performed by considering a THz beam normally impinging on the metasurface. Simulation results of Ez and Hz field patterns on the reference plane 20 μm below the PS are shown in Fig. 3(f)-3(i). For the MSP-typed meta-device shined by a y-polarized beam, a well-defined MSP beam is generated on the PS propagating along x direction indicated by the Hz field pattern, and the Ez field hardly exists. Meanwhile, the case is reversed for the ESP-typed meta-device shined by a x-polarized beam. From the field pattern, we can quantitatively determine the wavelength of the excited SPs, λMSP≈221 μm and λESP≈326 μm, and the corresponding parallel wave vector, kMSP≈1.49k0 and kESP≈1.03k0 at 0.9 THz, are in good agreement with the dispersion relation. What’s more, we numerically integrate the total powers carried by the excited SP beams and the impinging wave beam, and then calculate the working efficiency as the ratio between them. The efficiency reaches 55% and 70% for MSP and ESP, respectively, which can be further increased by adjusting the waist and position of incident beam [45].Although having demonstrated the capability of launching SPs, however, the excitation of different SP modes requires the redesign of meta-device. The underlying cause is the mismatch of wave vector of MSP and ESP, which requires different phase gradient to match the momentum. Therefore, it’s highly desired to obtain a polarization-dependent phase response. To solve this problem, we extend the meta-atom into an anisotropic one by rendering gx≠gy. Parametric sweep of both gx and gy is performed to obtain the phase response of orthogonal linear polarized waves. The simulation result is shown in Fig. 4, where horizontal axis represents the dimension parameter gx and gy, and vertical axis represents the reflection phase at 0.9 THz. It’s found that not only the polarization-locked phase, but also the decoupling of anisotropic magnetic resonance is achieved through this metallic cross-based meta-atom. In detail, the reflection phase for x-polarization (y-polarization) is only related to length of the metallic arm gx (gy) which is perpendicular to the polarization, while is hardly influenced by the other arm length gy (gx). This scheme implies a solution to the bi-channel excitation of both MSP and ESP.
Fig. 4. Reflection phase variation for anisotropic meta-atoms illuminated by (a) x-polarized and (b) y-polarized waves as a function of metallic arm length gx and gy. The decoupling of anisotropic phase response offers a simple method to modulate the phase profiles for orthogonal linear polarized waves individually.
Next, we proceed to demonstrate the bi-channel meta-device that can achieve excitation of MSP and ESP simultaneously. Considering the incidence-polarization dependence of the metasurface, such device should exhibit the following phase distribution for x- and y-polarized normal incidence
The phase gradient ξESP and ξMSP equals to kESP and kMSP, respectively. Figure 5(a), b illustrates the required phase profiles of the metasurface under y- and x-polarization excitations, respectively. Via fully exploiting the additional freedom provided by the in-plane anisotropic magnetic response, the structural parameters gx and gy of 12 × 12 meta-atoms (as depicted in Fig. 5(c)) are carefully optimized to compensate two kinds of momentum mismatch (see Table S3 for geometric parameters and phase of each meta-atoms). Shining the meta-device by a 45° linearly polarized beam, we performed simulations to study the near-field patterns generated on the plasmonic structure. Since the normally incident plane wave does not exhibit any Hz and Ez components, the computed Hz and Ez field patterns depicted in Fig. 5(d), e clearly demonstrated the expected generation of both MSP and ESP. Ascribing to the different eigen modes, MSP and ESP waves propagate on the single device simultaneously. Moreover, the ratio of energy transferred in the magnetic and electric channel can be readily adjusted by rotating the polarization orientation of incident wave. As the polarization angle decreases, more input energy is converted into ESP travelling in the electric channel, while the energy carried by MSP increases as the polarization angle increases. Specifically, by switching the polarization angle between 0° and 90°, the two-mode SP signals can be selectively excited in the same meta-device with little crosstalk (see Fig. S5 in Supplement 1 for more details). This bi-channel excitation and transmission can become a promising platform to explore more functionalities and applications of both magnetic and electric SPs.
Fig. 5. Characterizations on the THz meta-device enabling bi-channel excitation of both MSP and ESP. The required phase profiles of the anisotropic metasurface when shined by normally incident (a) y-polarized and (b) x-polarized waves. (c) Schematics of the meta-device illuminated by a 45° linearly polarized beam. (d) Hz and (e) Ez distributions on a plane 20 µm underneath the meta-device, which corresponds to the excitation of (d) MSP and (e) ESP.
2.3 Independent and anomalous SP launching in different EM channels
So far, we have verified that the coupling and excitation of bi-channel SPs can be achieved through appropriately designing the anisotropic meta-atoms to satisfy momentum matching. The next goal is to realize the complex and anomalous SP launching simultaneously, which requires the phase gradient along both x and y directions. Specifically, the phase distribution of each row of the meta-atoms along x direction still satisfies dΦ/dx = kSP, indicating that each row can convert an impinging beam into a SP. Meanwhile each column of meta-atoms along the y direction are tailored with the desired value of dΦ/dy to ensure that the SP waves excited by different rows have different phases. The interferences between these SP waves, excited by different rows, can form a new SP beam with a desired wavefront, and thus SP coupling and anomalous SP launching can be simultaneously achieved.
To illustrate this assumption, we follow the above strategy to design a meta-device which exhibits a linear phase profile along the y direction for both x- and y-polarized incidence
Fig. 6. Characterizations on the THz meta-device enabling coupling and anomalous launching of both MSP and ESP. The required phase profiles of the anisotropic metasurface when shined by normally incident (a) y-polarized and (b) x-polarized waves. (c) Schematics of the meta-device illuminated by a 45° linearly polarized beam. (d) Hz and (e) Ez distributions on a plane 20 µm underneath the meta-device, which corresponds to the anomalous launching of (d) MSP and (e) ESP.
2.4 Bifunctional meta-device achieving wavefront reshaping for both MSP and ESP
While the meta-device in last subsection successfully achieves both SP excitation and anomalous launching simultaneously, we further expand it into a bifunctional device achieving different wavefront reshaping for MSP and ESP. To demonstrate this scheme, a specific example is designed which exhibits a focusing and linear phase profile along the y direction for MSP and ESP, respectively. The equation of phase distribution can be written as
The required phase profiles of the metasurface under y- and x-polarization excitations are plotted in Fig. 7(a) and 7(b), respectively. Retrieving the gx(x, y) and gy(x, y) distributions from the parameter sweep results in Fig. 4, we design the metasurface with two distinct polarization-dependent phase profiles (see Fig. 7(c)). Shining the meta-device by a 45° linearly polarized beam under normal incidence, the full-wave simulation is performed, and the Hz and Ez field patterns on the reference plane are plotted in Fig. 7(d), e to characterize the excited MSP and ESP. The near-field patterns do clearly demonstrate two distinct wavefront modulations, which is in good consistent with prediction. These two different functions of anomalous launching and focusing can also be selectively excited by switching the polarization angle between 0° and 90° (see Fig. S7 in Supplement 1 for more details). Therefore, our methodology provides a platform to simultaneously engineer the 2D magnetic and electric near-field distributions.
Fig. 7. Characterizations on the THz meta-device enabling coupling and wavefront reshaping of both MSP and ESP. The required phase profiles of the anisotropic metasurface when shined by normally incident (a) y-polarized and (b) x-polarized waves. (c) Schematics of the meta-device illuminated by a 45° linearly polarized beam. (d) Hz and (e) Ez distributions on a plane 20 µm underneath the meta-device, which corresponds to the excitation of (d) MSP and (e) ESP.
3. Conclusion
In summary, we propose a new strategy to simultaneously convert the propagating waves in free space into magnetic and electric SPs using a single ultracompact meta-device. The meta-device consists of a metasurface which provides momentum matching between space waves and SPs, and a plasmonic structure supporting the propagation of both electric and magnetic SPs. The decoupling of anisotropic phase response of the metallic cross-based meta-atoms offer a simple method to modulate the phase profiles for orthogonal linear polarized waves individually, which can be employed to obtain any polarization-locked gradient phase distributions. By making fully use of the 2D anisotropic phase discontinuities along x and y directions, the excitation and wavefront modulation of both MSP and ESP are successfully achieved within the same device. Following the above strategy, several meta-devices are designed to demonstrate the bi-channel excitation with little crosstalk and the dual functions achieving distinct wavefront reshaping for MSP and ESP. Specifically, the ratio of energy transferred in the magnetic and electric channel can be readily adjusted by rotating the polarization orientation, enabling the switchable dual functions that can be selectively activated by changing the polarization angle between 0° and 90°. Our universal design bridges the gap between free-space waves and SPs, which can be easily expanded to other spectra such as microwave and medium infrared, and provides a promising way for developing various on-chip integrated circuits. We believe the capability of engineering magnetic and electric near-field distributions can stimulate more comprehensive studies about manipulations of SPs and obtain other advanced functionalities that are unattainable with only ESP.
Funding
National Natural Science Foundation of China (51872154).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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