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Abstract
In this work, a periodic bowtie structure based on black phosphorus (BP) is theoretically proposed and characterized. It is demonstrated that localized surface plasmons can be excited in the BP nanoantennas at terahertz (THz) frequencies. Numerical investigations, using the numerical method finite-difference time-domain (FDTD), have been utilized to analyze the the dimensions’ impact on absorption spectra. Furthermore, the electric field distribution is plotted and discussed to explain the resonance wavelength tuning by different geometrical sizes of the structure. Results reveal that the optimized BP bow-tie structure can be allowed for the realization of two-dimensional nanophotonics at terahertz frequencies.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Recently, exploiting plasmonic antenna has attracted much attention, largely due to their capacity for coupling free-space electromagnetic excitation into nanoscale volume and producing highly localized electromagnetic fields. By controlling localized surface-plasmon resonances (LSPR) in a small volume, it can achieve two important goals under incident illumination [1], diffraction limit breakthrough [2] and local field intensity enhancement [3]. These phenomenons can support potential applications such as biochemical sensing and detection [4–8], food quality analysis [9], optical trapping [10] and manipulation [11], and quantum optics [12,13] etc. In the last few years, different plasmonic antennas have been proposed and investigated [14–16]. Among them, the bowtie structure received extensive attention for its unique geometry [17,18]. Two triangular antennas are placed on a dielectric material with a gap between them. Large field enhancements can be achieved at the sharp corners of the individual triangular monomers [19,20]. Importantly, this field enhancement depends on the angle of the bowtie, the gap between the antenna arms, the length of the antenna arm and so on. Therefore, by designing its dimensions, this strong near-field can have significant applications in many fields, like near-field optical microscopy [21], near-field trapping techniques [22,23], nanolithography [24–26] and other optical applications.
Previously, both numerical simulations and experimental measurements show that great progress has been made in bow-tie nanostructures based on metals (e.g. silver and gold) [27,28]. However, the existence of the Joule loss in metals limits its practical applications [29]. As a result, new materials have been studied to excite plasmon polaritons [30–32]. Simultaneously, two-dimensional (2D) materials are known for the tunability of electronic and optical properties with the change of their thickness [33–36]. Importantly, 2D materials provide an opportunity to solve the trade-off between light-matter interactions and the thickness of materials, which allows new progress in ultracompact devices. Black phosphorus (BP) is a recently exfoliated and extensively investigated 2D material [37–46]. It was reported that plasmonic excitations can be realized in BP [40]. Moreover, the plasmon frequency can scales as nβ, where n is the carrier concentration and β represents the effective couplings between the conduction band and valence band [40]. Considering the scaling relation between plasmon frequency and n, the control of the carrier density has made possible the realization of plasmonic excitations in BP films at terahertz frequencies. For instance, when n is 4.5 × 1013cm−2, plasmon frequency can reach 36THz for the monolayer BP film [40]. Consequently, a bowtie structure based on BP can be very meaningful, which opens a door to achieve novel 2D electronic and photonic devices in THz frequencies.
In this paper, we report a plasmonic bowtie structure based on black phosphorus. The performance of the antenna is investigated in THz frequencies using numerical simulations. A highly localized electric field intensity distribution, which results from the LSPR, can be observed around the antennas. In addition, the relationship between optical characteristics and dimensions is thoroughly analyzed by absorption spectrum, optical field intensity, and power flow distribution. Numerical modeling results illustrate that the localized surface plasmon resonances can be adjusted by changing the dimension parameters of the bowtie. This strategy can contribute to the development of new 2D plasmonic nanoantennas in THz regime.
2. Simulation
Figure 1 depicts a bowtie structure constructed by a gold (Au) mirror and a top BP nanoantenna array separated by a dielectric layer. The metallic mirror is set to be 1μm to eliminate the optical transmission. Consequently, the absorption can be expressed as A(λ) = 1-R(λ), where A(λ), R(λ) are absorption and reflection, respectively. A dielectric layer is introduced between the BP bowtie array and Au mirror. It can reduce the reflection and enhance the absorption of BP by compensating the phase mismatch [47]. The absorption can be improved by adjusting the dielectric thickness. The BP nanoantennas are periodically placed on the dielectric layer and their thicknesses are set as 1nm. The dielectric function of the BP is given as follows [48]:
In (1), εr is the relative permittivity and was set as 5.76, σj is the conductivity and j denotes the direction concerned, ε0 is the permittivity of the free space, ω is angular frequency, and a is the thickness of the BP. As the BP crystal structure shown in Fig. 1, the atomic arrangement yields two inequivalent directions within the lattice: the zigzag and the armchair. It leads to the unusual in-plane anisotropic properties, which can be potential to achieve novel anisotropic optoelectronic applications. To determine the optical characteristic, here we employ the finite-difference time-domain (FDTD) method in the simulation. The refractive indexes of Au and dielectric are extracted from ref [49]. For simplicity, one parameter was varied and the other were kept constant in the simulation. Furthermore, we employed two polarized incidences (i.e. x-polarized and y-polarized) to explore polarization-dependent behavior in BP.
Fig. 1 A schematic diagram of the proposed bowtie structure. The angle of the bowtie, the gap between the antenna arms, the length of the antenna arm, and the thickness of dielectric layer are denoted by θ, g, L, and t, respectively.
3. Results and discussion
As a multilayer structure based on Fabry-Perot cavity, the dielectric layer will influence the absorption in BP. Consequently, we first focus on the impact of the dielectric thickness on the absorption spectra. Figures 2(a) and 2(b) compare the absorption maps of the bowtie structure for two different polarized incidences, showing a strong dependence of the absorption resonance on t. It is clear that the absorption resonance for x and y cases are at about 28.6 and 38.8μm, respectively. We can see that resonance peaks occur at the same wavelength with the change of thickness. It turns out that the resonance wavelength depends on the BP bowtie instead of the dielectric layer. To understand this resonance behavior, the plasmon dispersion of BP is given by [40]:
where q is wave vector, Dj is the Drude weight, j denotes x, y directions and i denotes the subbands, k describes the effective dielectric constant, ε0 is the permittivity of the free space, q is the momenta, and mj is the electron effective mass. In summary, the difference in the plasmon dispersion is caused by the mass anisotropy of BP and there is a negative correlation between the plasmon dispersion and the effective mass. The effective masses along x-direction are smaller than that along y-direction, leading to a shorter wavelength. It can also be seen that the absorption reaches the maximum at several thicknesses for both figures. To answer this question, we calculated the effective wavelength of the resonance. For simplicity, we only consider the y case here. The refractive index of the dielectric layer is 1.7, so the effective wavelength is 22.8μm. The quarter and half lengths of effective wavelength are 5.7μm and 11.4μm, respectively. Then, the thicknesses are set as 5.7μm and 11.4μm, which correspond to the strongest/weakest of absorption. Figures 2(c) and 2(d) present the electric field distribution in X-Z plane. At the thickness of 5.7μm, both the electric field intensity and absorption reach the maxima. The situation completely reverses at t = 11.4μm. The explanation for this phenomenon is that the BP nanoantennas are placed exactly at the maximum/minimum of the field intensity in these thicknesses. In order to reduce calculation time and achieve a comparatively large absorption enhancement, t is set as 5μm in the following simulation.Fig. 2 Modeled the absorption spectra as a function of the dielectric thickness with θ = 100°, g = 10nm, and L = 100nm, respectively. (a) x-polarized light, (b) y-polarized light. Electric field intensity distributions with two fixed thicknesses for y case. (c) t = 5.7μm, (d) t = 11.4μm. Inset of (c) is the side view of the bowtie structure.
Figure 3 displays the absorption spectra of nanoantenna arrays as a function of the bow angle, θ. As shown in Figs. 3(a) and 3(b), the absorption spectra almost keep the same when the θ varies from 20° to 60° for both polarized lights. As shown in Fig. 3(a), there are two resonant wavelengths for x-polarized light. For a larger θ, only one resonant wavelength can be observed and the resonant peak is redshifted obviously for both polarized incidences. To interpret this phenomenon, we plot the field distributions in the bowtie with θ = 60°/80°/100° at corresponding resonance wavelengths. Under the illumination of x-polarized incidence [see Figs. 4(a)-4(c)], all the response fields appear at the corners and gaps of the bowtie antennas and the oscillating electric charges are concentrated in these areas. The additional resonant wavelength in Fig. 3(a) results from the field distribution across the gap. At smaller angles, this fleld distribution is dominant and leads to a resonance peak at 31.8μm. When the angle is larger than 60°, the intensity of the electric field at the extremity edges enhances along with θ, which implies that isolated LSPR is pronounced at each edge. These plasmonic modes interfere and even lead to a standing wave [28]. The resonance wavelength of the standing wave is related to the distance between two corners. In such cases, the absorption characteristic begins to be affected. To verify the above analysis, we also plot the Poynting vector distribution at θ = 100° for x-polarized light in Fig. 4(h). It is clear that the plasmonic modes are excited at sharp corners of the bowtie and they influence each other. Moreover, as shown in Fig. 4(g), there is an equal strength distribution of electric field with opposite signs separated by the gap, indicating that this symmetric field distribution is the dipole. Its moment is along the external electric field. For a y-polarized case, the response fields only appear at the corners, as displayed in Figs. 4(d)-4(f). Considering the direction of the polarized electric field, it cannot form a dipole across the gap, which can also be confirmed in Fig. 4(i). As the increase in θ, the isolated LSPR appears at the corners and the distance between them increases. Finally, the LSPR performs a red shift for a small separation between isolated plasmonic modes according to plasmon hybridization theory [50]. By varying θ, it is possible to adjust absorption characteristic for both polarized incidences.
Fig. 3 Modeled the absorption spectrum as a function of the bow angle, θ. (a) x-polarized light, (b) y-polarized light. L and g are fixed at 100nm and 10nm, respectively.
Fig. 4 (a)-(c) Normalized field distributions for different θ at corresponding wavelengths of 31.8/23.6/29.7μm for x-polarized light. (d)-(f) Normalized field distributions for different θ at corresponding wavelengths of 24.4/30.3/38.3μm for y-polarized light. (g) Normalized field distributions at X-Z plane for x-polarized light. The distributions of the Poynting vector for (h) x-polarized and (i) y-polarized incidences, respectively. The color of the arrows indicates the power intensity.
We next study the absorption spectrum of the structure with a gap distance varying from 4 to 20nm. Figures 5(a) and 5(b) describe 2D map of the absorption spectrum as a function of the incident wavelength and g for x-polarized and y-polarized incidences, respectively. Three remarkable resonance peaks (see the black circles) are found for x-polarized light [see Fig. 5(a)], but no such feature is found for y-polarized light [Fig. 5(b)]. These remarkable resonance peaks appear at g = ~8nm, ~14nm, and ~20nm, respectively, which are indicated by the black circles in Fig. 5(a). Besides, the value of the resonance peak decreases slightly as g increases. To interpret the resonance characteristic, the field distributions are plotted in Fig. 6. We first focus on the y-polarized incidence. It can be seen from Figs. 6(a)-6(c) that, as the gap increases, all the response filed appear at the corners and there is little change in the filed intensity. In our earlier discussion, the resonant wavelength depends on the LSPR of the bowtie structure. Therefore, the resonant wavelength almost keeps the same. For sake of comparison, Figs. 6(d) and 6(e) show the E-field distribution when the plasmonic resonance generates for x-polarized light. One can see that the intensity of the E-field decreases because a larger g weakens the formation of the dipoles. The formation of the dipoles is caused by the electrostatic lightning-rod effect [51]. Due to this effect, the charges can accumulate around the sharp edges of the bowtie structure more easily. Particularly, the accumulating charges across the gap with opposite signs form the electric dipoles and the direction of dipole moment is along the incident electric field. It has been confirmed by the electric field in Fig. 4(g). According to pervious analysis, at a larger θ, the absorption characteristic depends on the standing wave. Actually, though there is no change in the distance between two corners, the resonance peaks exhibit (approximately) periodicity accompanied by the decline in absorption with the increase in g. Therefore, we consider another coupling effect. A close examination of Fig. 6(f) indicates that the standing waves (the black circle) and the dipoles (the red circle) do interact on each other. Within the framework of the dipole-dipole approximation, the effects of Young’s interference should be taken into account to explain this absorption characteristic [50]. The most important effect of Young’s interference in plasmonic structures is the enhancement in absorption [50]. Summarizing above discussions, the approximately periodic resonance is arising from the existence of the dipole across the gap. At a small g, the intensity of the dipole is large and it appears an obvious interference phenomenon. When g increases, it weakens the formation of the dipoles, which also has a significant effect on the interference between the dipole and standing wave. Finally, it leads to the decline in absorption, corresponding to the attenuation of the resonance peak with the increase in g as shown in Fig. 5(a). This effect provided by this design can help facilitate the potential applications in THz regime.
Fig. 5 Modeled the absorption spectrum as a function of the gap, g. (a) x-polarized light, (b) y-polarized light. θ and L are fixed at 90° and 100nm, respectively.
Fig. 6 (a)-(c) Normalized field distributions for different g at corresponding wavelengths of 34.7/33.8/34.7μm for y-polarized light. (d) and (e) show the normalized field distributions for different g at corresponding wavelengths of 28.4/28.1 for x-polarized light. (f) The distribution of the Poynting vector at g = 8nm for x-polarized light. The color of the arrows indicates the power intensity.
Now we aim at the length of the antenna arm, L. The absorption spectrum is modeled as a function of L as depicted in Fig. 7. As shown in Figs. 7(a) and 7(b), when L increases, the resonance wavelength exhibits a blue shift for both polarized lights. Actually, the distance between two edges was kept at a constant of 280nm with the increase in L. That is, the bow angle is always larger than 50° when the L varies from 50nm to 130nm. The effect of the increase in L on the absorption spectrum, to some extent, should be similar to that of the decrease in bow angle. One can see in Fig. 7 that both the resonances are blue shifted, which does show an opposite trend compared with Fig. 3. The data also clearly demonstrates that there is an improvement in absorption as L increases. This behavior can be explained by the enhancement in the intensity of electric field. To verify this, the field distributions for both two polarized incidences are shown in Fig. 8. It can be clearly seen that the intensities of electric field at gaps and corners increase along with the L for both polarized lights. A possible explanation is that as a Fabry−Perot cavity, a larger L, which means a larger absorption cross section, leads to more oscillating electric charges. It finally contributes to the charge accumulation at the gap and edges of the bowtie. With regard to the high-order resonance at 23.5μm for x-polarized light [Fig. 7(a)], it is believed that this resonance results from the electric dipole at the gap. The peak of this high-order resonance increases slightly along with L, which is consistent with the character of the enhancement in electric field intensity in Figs. 8(a)-8(c). It is worth noting that a standing wave can be clearly observed at edges for larger θ, which is in good agreement with the explication of angle variation. As for y-polarized light, one can see in Figs. 8(d)-8(f) that there is no electric dipole at the gap owing to the polarization direction of the electric field. Hence, there exists only one resonance, attributed to the field distributions at corners. For a fixed length between edges, L should be seriously considered to achieve the different resonance wavelength and absorption enhancement.
Fig. 7 Modeled the absorption spectrum as a function of the length of the antenna arm, L. (a) x-polarized light, (b) y-polarized light. g is set as 10nm and the distance between two edges is set as 280nm.
Fig. 8 (a)-(c) Normalized field distributions for different L at corresponding wavelengths of 32.6/31.8/31.4μm for x-polarized light. (d)-(f) show the normalized field distributions for different L at corresponding wavelengths of 45.5/44.0/42.6μm for y-polarized light.
Finally, we would like to discuss the experimental implementation of this work. There are two critical problems. The first one is the material growth in the manufacture. In fact, lots of work has been done in bulk growth of BP, including the high-pressure route [52,53], recrystallization from bismuth flux [54], chemical vapor transport [55], and mechanical milling [56]. The liquid-phase exfoliation technique can be used to fabricate the few-layer BP film [57–59]. What’s more, a large-area thin BP film was also reported [60]. With the growing interest in BP, the author is confident that more breakthroughs in the growth of ultrathin film will come. The other question is the fabrication of the bowtie. To our knowledge, BP is less stable in air because it is very sensitive to oxygen and water. Thereby, all the experiment should be carried out in the condition of insulating air. It is also necessary to remove tape residues before the device fabrication by soaking the BP film in acetone [61]. The bowtie nanoantenna can be patterned by electron beam lithography (EBL), which is a flexible system to make the nanodevices with critical dimensions below 10nm [62]. Consequently, both L and g can be controlled. It was reported that a narrow gap could be obtained at 3 nm [63]. As for θ, the corner of the bowtie structure is not sharp due to the imperfect side wall during the manufacture, which can affect the characteristic of the LSPR. Actually, according to related work [64,65], it seems that the rough corner only has a small impact on the characteristic of the LSPR. A possible explanation is that compared with the inside region of BP, the rough corner still can accumulate more charges due to the electrostatic lightning-rod effect. We hope that the comment on the experimental implementation can be helpful to implement this device.
4. Conclusion
In summary, we propose and numerically demonstrate our simulation results on localized surface plasmons in BP bowtie nanoantennas at THz frequencies. It is found that the electric field is mostly localized around the tips of the structure and this field localization is related with the tip geometry. Importantly, by optimizing the parameters of the bowtie structure, we can improve the near-field enhancement and adjust the pronounced resonance. Besides, two polarized incidences were employed to explore anisotropic behavior of the BP bowtie structure, which can be helpful to achieve polarization sensitive application. The research provided by this work confirms the dependence of performance on the geometric parameter of the structure, which can guide the BP based bowtie structures to plasmonic applications in THz regime.
Funding
National Natural Science Foundation of China (61534004, 61604112, and 61622405).
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