Deep subwavelength manipulation of THz waves by plasmonic surface

Deep subwavelength manipulation of terahertz (THz) wave is a key method to realize compact on chip THz devices. It is demonstrated that the refractive index change in a deep subwavelength region of a dielectric layer can effectively manipulate the surface THz wave propagation by the simulation study. The feature size of this area is only 10 μm (∼1/8 λ). A slight change of refractive index, position or size of this region is enough to manipulate the surface THz waves with high efficiency, such as the transmissivity or reflectivity of different THz frequencies. Moreover, the change of the deep subwavelength region can be controlled by an ultrafast laser to achieve ultrafast dynamic manipulation of THz waves. This is a concise and efficient method of manipulating electromagnetic waves on the deep subwavelength scale and to fabricate more compact integrated optical devices.


Numerical simulation
The dispersion property of a metal grating with rectangular grooves (figure 1) is determined by its depth (d), width (w), and period (p). Hence, the metal waveguide can be designed to propagate and slow down EM waves of different frequency simply by adjusting the three parameters of depth (d), width (w), and period (p) [11,13,45]. In addition, the refractive index (n) of the groove material (like air or silica) is another factor to control the propagation of the surface waves. Here, the refractive index (n) in the grooves is not changed, but only the refractive index (n) of the layer attached on the metal grating is changed in a deep subwavelength region, which means only refractive index (n) of the covered dielectric layer is changed. The dielectric layer can be deposited on the metal grating to form a hybrid waveguide experimentally. The femtosecond laser pulses with different energies can be focused on the subwavelength region to change the local refractive index (n) dynamically, so as to control the surface wave in the order of femtosecond [52,53]. The grating model with a special region that have different refractive index (n) and different positions (P1, P2, P3) is built (figure 1) and simulated via finite difference time domain (FDTD) modeling. The FDTD method is a rigorous solution to Maxwell's equations and does not have any approximations or theoretical restrictions, which has been widely used as a propagation solution technique in integrated optics [41][42][43][44][45][46]. The size of this region is equal to the size of the grating groove. The meshed size or the uniform cell of the simulation model is Δx=Δz=1 μm. At THz frequencies, metals behave like a perfect conductor, and the negligible penetration of the EM fields leads to highly delocalized SPPs, which is also called spoof SPPs [43]. Hence, the material of the grating waveguide is modeled as a perfect electric conductor (PEC), and the whole simulation region is surrounded by a perfectly matched absorbing layer. The position and refractive index of the single deep subwavelength region are the main parameters to be studied. A ppolarized (Hy, Ex, Ez) end fire excitation source is introduced at the beginning of the PEC model, which located at 1000 μm away from the single deep subwavelength region (P1), to excite the surface plasmonic EM waves.
According to reference [45], the cutoff frequency is below 4.6 THz for metal grooves with period of 20 μm, width of 10 μm, and depth of 10 μm. Hence, a 3.75 THz (wavelength of 80 μm) excitation source is used to excite and generate the propagated surface EM wave along the periodic metal grating. The generated surface EM wave is propagated smoothly along the grating until it meets a special region with controllable refractive index (n) (marked with grey in figure 1). Here, only the refractive index and position of the special region are changed to run the simulation. Two monitors (M1, M2) are located before and after the special region to record the before and after intensity of the surface EM wave, respectively.

Simulation results and discussion
According to the FDTD simulation results (figure 2), the surface wave intensities before (reflection) and after (transmission) the special region are all controllable with the increase of refractive index (Δn) or positions (P1, P2, P3). Here, Δn means the increase of refractive index relative to air (n=1).
At the zero point of figure 2, Δn=0, the grating becomes a uniform waveguide grating, and the intensity of M1 and M2 are all approximately equal, which is a base intensity of the surface wave that is propagated on the uniform waveguide. When the refractive index (Δn) gradually increases, the intensity of M1 increases and the intensity of M2 weakens, which can be attributed to the reflection of the surface wave by the special deep subwavelength region. The intensity of reflection wave can be more than 2 times of base values and reach at '1' (square dotted black line in figure 2(a)). The reason is the intensity we monitored is localized near field intensity that can be enhanced by interference and localized SPPs as shown in figure 3. If the special region is located at position 1 (square dotted black line), the intensity of M1 and M2 show the most dramatic change, which means that a small change of refractive index (∼0.3) is enough to control the transmissivity or reflectivity of different THz frequencies. Hence, if people want to manipulate the surface EM wave with high efficiency, the most effective position to change the refractive index (Δn) is position 1 (P1). When the refractive index (Δn) increases to '0.4', the M2 intensity (square dotted black line in figure 2(b)) drops to nearly '0', which means that the special deep subwavelength region can approximately block all the surface waves. If the special region moves to other positions like P2 (circle dotted red line) and P3 (triangle dotted bule line), the intensity of M1 and M2 change more and more slow. The mechanism for effective THz wave control at different groove position (P1, P2, P3) is the excitation of resonant modes. The change of refractive index in the dielectric layer forms a new localized dielectric EM mode. At P1, the refractive index changing area is covered on a single groove and forms a new cavity. The resonant modes between the new localized dielectric mode and groove mode are excited in the new cavity. At P2, only half of cavity is working, so the efficiency is slightly lower. At P3, the controlling efficiency becomes much lower. Because, there is no cavity any more, and the controlling of surface waves only depends on the dielectric mode. This mechanism can be also used for the surface refractive index sensing with high spatial sensitivity. Figure 3 shows the two-dimensional surface EM wave distribution obtained through the metal waveguide with a deep subwavelength region at position P1 of varying refractive index. The frequency of the excitation source is 3.75 THz. When Δn=0.0 ( figure 3(a)), the grating works as a normal waveguide. When Δn=0.2 ( figure 3(b)), only part of the surface wave can be propagated through the special region. When Δn=0.4 ( figure 3(c)), the surface wave is totally blocked by the deep subwavelength region with high efficiency. It demonstrated again that the deep subwavelength region can easily manipulated the surface EM wave with  changing refractive index (Δn). Importantly, the changing refractive index (Δn) can be controlled by an ultrafast laser to realize the ultrafast manipulation of surface EM wave [52,53]. In addition, the position and size of the special region also can be controlled by simply moving the position and size of the laser focal point.
The surface EM waves with different frequencies can also be controlled by the refractive index. For example, a source of 3 THz (wavelength of 100 μm) is tested ( figure 4) for comparison. The control effect of the deep subwavelength region for longer wavelength (lower frequency) is reduced. Thus, the refractive index or size of the special deep subwavelength region must be increased to obtain a high efficiency manipulation. For the frequency of 3 THz, the most efficient blocking effect occurs at the refractive index (Δn) of '∼0.75' (square dotted black line in figure 4(b)), which is larger than that of 3.75 THz.

Conclusion
The numerical results demonstrate that the propagation of plasmonic EM waves can be efficiently controlled by a single deep subwavelength region (< 1/8 λ) with changing refractive index or positions, which has advantages over metamaterials or photonic crystals that rely on large-scale periodic structures. The refractive index, position, and size of the region can be controlled by an ultrafast laser to manipulate the EM waves of different frequencies at a high speed and high efficiency. For example, the femtosecond laser pulses with different energies can be focused on the subwavelength region to change the local refractive index (n) dynamically, so as to control the surface wave in the order of femtosecond. In addition, the intensity of the reflected waves is enhanced by the localized SPPs and interfering of incoming and reflected waves. When coupling with the composite antennas [54], the dynamic controllable subwavelength waveguide can become a more effective on-chip platform for THz applications. It can be used in fast optical switch or high sensitivity detection. This control method of surface EM waves can also be combined with semiconductor-based plasmonic waveguides that is compatible with the current complementary metal-oxide-semiconductor (CMOS) fabrication technique [55][56][57][58], for subwavelength THz transmission and manipulation in a real CMOS plasmonic platform. Hence, controlling plasmonic EM waves and fabricating more compact integrated optical devices such as nonlinear wave switches, local enhanced slowing waveguides, dynamic filters, and amplifiers for future integrated THz circuits is considerably easier by this method, and will further promote the research of material identification for THz-sensitive molecules or cells, as well as surface THz metamaterials and quantum dots.