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Abstract
Enhanced extraordinary optical transmission (EOT) is generated by a gold hole array with a concentric hemisphere in the terahertz (THz) region. By introducing hemispherical particles and using the plasmon coupling effects of surface plasmon polaritons and localized surface plasmon resonances, it can be found that not only the transmission intensity is greatly enhanced to 0.97 and the bandwidth is nine times wider than that of a non-particle in a hole, but also the size of the structure can be significantly reduced. Additionally, optical characteristics of the hemisphere-in-hole structure are thoroughly analyzed by the schematic diagram, transmission spectra, and optical field distribution. In addition, with the diameter of the hemisphere increasing, the transmission peak maintains at a high value and the peak position redshifts correspondingly. Finally, we alter the shapes and sizes of the central particles to verify the influence on the enhanced THz EOT. Our results provide a reference for theoretical understanding and expand the application prospects for many THz plasmonic devices.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Plasmon coupling effects have gradually become a promoting research field in enhanced extraordinary terahertz (THz) transmission. The extraordinary optical transmission (EOT) phenomenon, is firstly discovered by Ebbesen [1] at a two-dimensional hole array in the visible-infrared region in 1998. Immediately, it attracted extensive research interest due to an immense breakthrough of the standard aperture theory [2,3]. More and more studies have confirmed that the generation and propagation of surface plasmons in structures is the main reason for the enhancement of sub-wavelength metal hole transmission [4–6]. Surface plasmon polaritons (SPPs) is a kind of surface electromagnetic wave, which is generated by coupling excitation of cluster oscillating free electrons propagating along the metal-dielectric surface. It can overcome the classical diffraction limit, effectively control the energy of the evanescent field and enhance the surface local electromagnetic field. When the period of the metal hole array matches the wavelength of the SPPs, the electrons will couple with each side of the metal hole and then convert into photon radiation, which greatly improves the transmission [7–10]. So, many metallic film structures perforated with holes of different shapes have been reported, such as cone-shaped hole arrays [11], triangle-shaped hole arrays [12], as well as bull’s eye arrays [13]. In 2004, Kazuo and others designed an I-shaped aperture in a thick metallic screen and obtained high near-field intensity. It is shown that the interesting characteristic is due to the SPPs excited on the surface of the aperture [14]. Tavakol’s research group in 2015 proposed a new type of bull’s eye structure based on a polygonal star-shaped aperture and concentric star-shaped grooves. It can consistently provide UV-band response as well as the fundamental SPPs resonance in the visible range [15].
Importantly, it has been revealed that localized surface plasmon resonances (LSPRs) generated in the particles or inner surface of metallic holes can effectively contribute to the EOT phenomenon. In 2005, Degiron and others showed the experimental results of how LSPRs modes contribute to the light transmission [16]. In particular, it is shown that the SPPs of the periodic structure dominates the spectral signature and the LSPRs of each hole can be controlled by appropriate arrangement of the apertures. In addition, since the intercoupling between the SPPs and the LSPRs can further enhance the transmission [16–19], many studies have focused on the hole arrays with central particles. A compound Ag nanohole structures with a nanorod in the middle of nanohole was investigated by Wang in the infrared region [20], and they showed that the new EOT mode results from the enhanced local radiation of the nanorods as well as the electromagnetic coupling to the nanoholes. In visible band, Steven discovered when a hexagonal silver nanohole array is covered by a tilted silver nanorod array, the resonant wavelength of the EOT mode red-shifts with respect to the normal EOT mode predicted by plasmon-grating coupling theory [21]. These configurable structures have a relatively concentrated electric field distribution and provide higher adjustable flexibility than hole arrays [22]. However, it has been discovered that the plasmon intercoupling between particle and hole arrays in the infrared and visible exhibits distinct enhanced EOT properties, some of which are less considered in the THz region [23–25]. Besides, further investigations analyzed by Liu [26] demonstrate that the surface plasmons model clarifies the physics of the EOT phenomenon and the contribution proportion is not the same in different frequency regions.
In this paper, we propose a hemisphere-in-hole (HIH) modified structure that can greatly enhance the transmission and broaden transmission linewidth in the THz region. By introducing hemisphere in gold hole arrays, the combination of SPPs and LSPRs effects can efficiently improve the energy conversion, and the size of the structure can be significantly reduced. In addition, when the diameter of hemisphere is 15 µm, the transmission could be enhanced to 0.97, which is much greater than the transmission of non-particle in hole (NIH) structure. The normalized transmission factor exponentially increases which means that a smaller aperture area can achieve a higher transmission. Also, the transmission linewidth is nine times larger than the NIH structure when the diameter of hemisphere is 14 µm. Furthermore, the mechanism of the enhanced THz EOT is analyzed by schematic diagram, electromagnetic field distribution and Poynting vector profile. With the increasing of hemisphere parameters, the transmission rises at first and then maintains at a high value, and the frequency of the transmission peak gradually redshifts. Moreover, different sizes and shapes of central particles have been verified to have influence on enhanced THz transmission. Through the modulation of the LSPRs resonance mode of the particles, it can be concluded that not only the position of the EOT peak changes accordingly, but the enhancement effect of transmission becomes more obvious as the particle size increases. Currently, the demand for high-performance sensors, filters and active modulators has increased rapidly. The resonant coupling at the analytes can be significantly enhanced by THz EOT, thus improving the sensor sensitivity. These favorable THz plasmonic approaches with enhanced EOT could also enrich other potential applications.
2. Structure and simulation
Figure 1(a) illustrates the schematic representation of the proposed structure. The gold hole array is modified by concentric gold hemispheres fixed on the support column (HIH structure). Figure 1(b) depicts the XZ-cross section of the unit cell. The square period P and the hole diameter D are 50 µm, 18 µm respectively. The thickness of Au film H (that is the depth of supported column) is set to be 5 µm, which is much larger than the skin depth and opaque to the incident plane wave [27]. The frequency-dependent permittivity of the gold (yellow part) is described by the Drude model [28]. The lossless dielectric permittivity of the supported column and substrate (blue part) is 1.4. Three-dimensional finite-difference-time-domain (FDTD) solutions are performed to calculate the transmission spectra and electromagnetic field distribution. Perfectly matched layer boundary condition is used on the Z direction and periodic boundary conditions are placed on the X and Y directions. The incident plane wave is perpendicular to the surface of the structure with the electric field parallel to the X-axis.
Fig. 1. Schematic representation of the proposed structure. (a) The gold hole array is modified by concentric gold hemispheres fixed on the support column, and the array is deposited on the substrate. The propagation direction of the illumination source used in the numerical calculations is shown in the figure. (b) The XZ-cross section of the unit cell with a periodicity P = 50 µm, the hole diameter D = 18 µm, depth H = 5 µm, and dc is the hemisphere diameter. (c) The structural diagram of the support column placed in the gold hole array (SCIH structure). (d) The structural diagram of the metal hole etched on the gold plate (NIH structure).
3. Results and discussion
Under the vertical irradiation of the THz wave, the excitation and resonant coupling of SPPs and LSPRs in the HIH structure is represented in Fig. 2(a). It has been proved that periodic hole arrays in a metallic film can help to excite SPPs and selectively transmit light according to wavelength. The transmission peak position in the EOT spectrum approximately obeys the grating coupling condition [7,29],
Fig. 2. (a) A simple schematic diagram shows the transmission enhancement mechanism in the HIH structure. (b) The transmission characteristics of NIH structure (black line), SCIH structure (green line) and HIH structure (blue line). (c) The XZ-cross electric field distributions of the NIH structure at f1 = 5.95 THz when D = 18 µm, H = 5 µm and P = 50 µm. (d) Relative electric field distributions of the HIH structure at transmission peak f2 = 5.15 THz when the hemisphere diameter dc is 15 µm.
As shown in Fig. 2(c), for NIH structure, the XZ-cross electric field at transmission peak (f1, T1) is discretely distributed on the upper and lower surfaces of the gold hole. It is the direct transmission and SPPs mode that plays a dominant role in THz transmission [33,34]. Figure 2(d) presents the electric field distributions of the HIH structure at transmission peak (f2, T2). The resonance at 5.15 THz yields a strong field distribution at the gap between the top sharp corner of hole and hemisphere. This implies that the LSPRs mode from the hemisphere interacts with the SPPs mode from the aperture and then the gap has a strong local charge accumulation. In fact, the HIH structure at 4.25 THz shows a high-efficiency in extraordinary THz transmission, which is due to that the SPPs mode is excited not only on the upper but also on the lower surfaces of the gold. The surface plasmon is first coupled at the gap and then discretely propagates down to free space. The electromagnetic field and Poynting vector profile distribution of HIH array at 4.25 THz is detailed analyzed and shown in Fig. S3 in Supplement Document.
To better verify and reveal the origin of the enhanced THz EOT, the electric field on the XY plane, the magnetic field and Poynting vector distributions on the XZ plane are displayed at the corresponding frequencies. As shown in Figs. 3(a) and 3(b), it can be found that the electric field in HIH structure at 5.15 THz is mostly confined near the hole wall along the vertical direction of the incident polarized light, while the electric field in NIH structure at 5.95 THz is relatively weak, indicating that the hemisphere can trap more THz energy through the intensive surface plasmon coupling among particles and holes. The stronger convergent electric field energy can have stronger THz radiation to the far field, which contributes to the further enhanced THz EOT for HIH structure. Although the transmission in NIH structure gradually increases as the hole size increases, for the HIH structure, the same transmission can be achieved in a smaller hole, which could further reduce the device size (Corresponding transmission spectra shows in Fig. S4 in Supplement 1). Meanwhile, in Fig. 3(c), the magnetic field in NIH structure is distributed at the gold top surface. This means that the field energy cannot be mostly coupled into the hole. But for the modified structure, as shown in Fig. 3(d), the strong magnetic field is confined at the bottom of the hemisphere due to the coupled effects of SPPs and LSPRs modes. In other words, the light field energy is mostly trapped into the hole that responsible for the enhanced THz EOT. From another point of view, the white arrows in Figs. 3(c) and 3(d) represent the Poynting vector profiles, which clearly reveal how the electromagnetic wave propagates in the structure before it is transmitted. In the HIH structure, the energy is strongly coupled into the hole, flows spread downwards along the Z-axis and then converges into the bottom of hole, where exactly the magnetic field concentrates. Finally, the energy converts into photon radiation, which reflects that this modified structure provides an efficient pathway to re-emit THz waves.
Fig. 3. Under the vertical irradiation of incident light polarized along the X direction, the electric field is in the XY plane with (a) NIH structure at 5.95 THz and (b) HIH structure at 5.15 THz. The magnetic field distributions are combined with the corresponding Poynting vector (white arrows) along the Y = 0 plane for the (c) NIH structure and (d) HIH structure.
In order to optimize enhanced transmission quality of the modified structure, while keeping P, D and H the same as before, Fig. 4(a) shows the EOT curve with hemisphere diameter varying from 12 µm to 16 µm, and the color map of transmission spectra from dc = 11 µm to 17 µm is depicted in Fig. 4(b). As the diameter of hemisphere increasing, the distance between gold hole walls and hemisphere decreases. It can be seen that the transmission first arises and then maintains at a high level, which corresponds to the gradual darkening of the color in Fig. 4(b). The reduced distance strengthens the near-field interaction of plasmon modes. Both the SPPs and the LSPRs waves on slit walls react with each other to form gap plasmon polariton. The propagation coefficient of the gap plasmon polariton is sensitive to the gap distance. So, the smaller the gap distance, the bigger the nearfield coupling degree. The stronger nearfield coupling effects between adjacent units enable more charges to transfer, leading to the enhancement of the plasmon resonance. When the diameter of the hemisphere changes from 15 µm to 16 µm, the peak intensity does not continue to increase. Although the plasmon resonance coupling is strong, it is also affected by the gradual increase in the loss of the metal hemisphere. An obvious red-shifts, accompanied by the relatively broader symmetric line shape, are observed from the transmission color map and curve. The symmetry coupling allows the EOT to have a broader adjustable resonance frequency range. And due to enhancement of the secondary radiation, the electrons lose energy experiencing a damping effect, which makes the peak broaden and redshift. As a result, the intensity and position of the THz EOT peaks could be modulated through the hemispherical particle.
Fig. 4. Transmission curve (a) and the color map of transmission spectra (b) for the HIH structure (P = 50 µm, D = 18 µm, and H = 5 µm) with different hemisphere diameter dc.
Figure 5 summarizes the overall transmission properties of the HIH structure. The transmission peak intensity (denoting absolute transmissivity, the left axis) as a function of the hemisphere diameter dc is shown in Fig. 5(a). It can be seen that the peak intensity increases from 0.77 to 0.97 with the increase of the hemisphere diameter from 11 µm to 15 µm. However, for larger hemispheres, the transmission slightly decreases, which results from the increasing metal loss. Also, the transmission still maintains higher than 0.95. For comparison, the right axis in Fig. 5(a) presents the aperture area ratio k as a function of the hemisphere diameter. It is obvious that the transmissivity is far larger than the k of the array. When hemisphere diameter increases to 17 µm, the open fraction of the unit cell is only 0.003, but the peak intensity remains high at 0.95. It indicates that the HIH structure can achieve a higher transmission in a smaller aperture area due to the stronger coupling between SPPs and LSPRs modes [35,36]. The phenomena of enhanced THz EOT through apertures in the metal film are usually characterized by the normalized transmissivity, defined as [18],
Fig. 5. (a) Peak intensity (left axis) and aperture area ratio k (right axis) as a function of hemisphere diameter dc. Insert: normalized transmission efficiency Tn as a function of hemisphere diameter dc. (b) Frequency of the transmission peak (left axis) and FWHM (right axis) as a function of hemisphere diameter dc.
The transmission peak position (the left axis) and the full widths at half maximum (FWHM, the right axis) as a function of the hemisphere diameter are depicted in Fig. 5(b). The result shows that the optical transmission peak shift from 5.86 THz to 4.41 THz obviously with increasing hemisphere diameter. When the hemisphere diameter increases, the radiation effects become more important, and high multipolar charge distributions are produced in hemisphere. Furthermore, the accelerated electrons produce an additional polarization field that depends on the ratio between the hemispherical particle size and the frequency of the incident light. Therefore, this field reacts against the quasi-static polarization field, causing the position of the transmission peak to gradually redshift [39,40]. Besides, it can be seen that the FWHM presents a non-monotonic variety trend. The FWHM ($\Gamma $) of SPs mode is simply given by the lifetime ($\tau$) of the SPs mode as,
where $\tau$ is inversely proportional to FWHM. As the hemisphere diameter increases from 11 µm to 14 µm, the FWHM increases from 0.26 THz to 0.53 THz. The efficiently coupling effect between the SPs mode and the red tail (from non-SPs transmission) began to increase gradually. Noting that the SPPs modes play a dominant role in the total transmission. And the shorter $\tau$ of the SPPs and the LSPRs mode lead to the broader the THz transmission bandwidth. When the hemisphere diameter changes from 14 µm to 17 µm, the FWHM decrease to 0.30 THz. It is worth mentioning that for the modified structure with a hemisphere diameter of 14 µm, the maximum FWHM is about 0.53 THz, which is nine times broader than the FWHM of 0.059 THz for NIH structure with the same hole diameter of 18 µm. With the gold hemisphere diameter increasing, the LSPRs of the individual metal particle gradually play a dominant role. As is known, multipolar charge interactions are present in hemisphere for all the positional arrangements. The more the multipolar modes fluctuations, the larger the frequency shift, the longer the SPs resonance lifetime, resulting in the decrease of the FWHM in THz transmission spectrum. As the hemisphere size increases, the non-monotonic change of FWHM would be due to the successive dominant role first from the SPPs and then from the LSPRs contribution [41–43].In fact, the transmission peak position and amplitude can be tailored in a large range through the modulation of the LSPRs mode. Therefore, we alter different central particles to study the influence on enhanced EOT in the THz region. The hole diameter D, height of support column H and period P are fixed as before. The illustration in Figs. 6(a)–6(c) is the unit cell of the compound structure in the XY cross section. The central particle fixed on the support column is based on the length L of 12 µm, the width W of 4 µm, and the height of 2 µm. Figure 6(a) shows the enhanced THz EOT generated by placing a rectangle particle in the center of the hole, and the transmission is about 0.85 at 5.61 THz. As shown in Fig. 6(b), when placing another same rectangle particle to form a T-shape particle, the enhanced transmission emerges at 5.28 THz and the peak intensity increases to 0.90. Similarly, the enhanced THz EOT spectrum in Fig. 6(c) is produced by the square particle. The maximum transmission of the square particle structure can reach above 0.93 at 5.37 THz. Although the aperture area ratio decreases as the particle size increases, it can be clearly seen that the transmission is enhanced accordingly. However, in this square particle structure with a diagonal length of 16.97 µm, the transmission peak intensity is still smaller than that of HIH structure with a diameter of 17 µm. In order to better analyze this changing trend, we compare the electric field diagram of three compound structures in the XY plane at their corresponding transmission peak. As shown in Figs. 6(d)–6(f), with the particle size gradually increases, the number of charges transferring from particles to apertures augments, and the number of strong coupling electric field hotspots also increase obviously. Furthermore, compared with the electric field shown in Fig. 3(b), the hemispherical particle structure obviously has more coupling electric fields that render the intensity of the EOT enhanced dramatically. Consequently, it can be concluded that the increased number of the concentrated electric field hotspots in the hole array could give rise to the enhancement of THz EOT peak amplitude. By adjusting the particle size and shape, the position of the EOT peak not only changes accordingly, but each plasmon resonance mode in the modified structure could produce an enhanced EOT in the THz region.
Fig. 6. Calculated further enhanced THz EOT spectra of a gold hole array with (a) rectangle, (b) T-shape and (c) square particle. The insert in (a)-(c) is the view of each unit’s structure in the XY plane. (d-e) The corresponding electric field of three compound structures along the XY-cross section at their transmission peak.
4. Conclusions
In this work, the plasmon-induced enhanced THz EOT properties have been introduced in detail through a gold HIH structure employing the FDTD methods. The significantly enhanced THz EOT is a complex phenomenon, which results from various coupling effects, including non-SPs transmission and constructive interference between SPPs and LSPRs modes. It has been obtained dual-band THz transmission due to the plasmon resonance excited on different interfaces. Especially at 5.15 THz, the transmission is significantly enhanced to 0.97 when the hemisphere diameter is 15 µm. It is much higher than the transmission of NIH structure in the same hole diameter. The normalized transmission enhancement factor grows exponentially, up to 3033 when hemisphere diameter is 17 µm. And the FWHM exceeds nine times wider than NIH structure when the diameter of hemisphere is 14 µm. The optical characteristics of HIH structure are thoroughly analyzed by the schematic diagram, transmission spectra and optical field distribution. Meanwhile, as the hemisphere diameter increases, it has been observed that the transmission peak frequency gradually redshifts and the peak intensity is enhanced obviously due to the contribution of super-coupling between the SPPs and LSPRs modes. Furthermore, the hole arrays modified by different central particles have been found to exhibit distinct electric field enhancement properties. With the particle size increasing, the number of concentrated coupling electric hotspots increase gradually, as well as the enhancement of transmission. All in all, these results could expand our fundamental understanding of the EOT phenomenon in the THz region and offers a scientific reference for the potential optoelectronic applications.
Funding
Postdoctoral Innovation Project of Shandong Province (201602017); China Postdoctoral Science Foundation (2015M582073); Fundamental Research Fund of Shandong University (2018TB002); Natural Science Foundation of Shandong Province (ZR2019BF014); National Natural Science Foundation of China (61805127).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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