We propose an optically controlled reconfigurable hybrid metamaterial waveguide system at terahertz frequencies, which consists of a two dimensional gold cut wire array deposited on top of a dielectric slab waveguide. Numerical findings reveal that this device is able to realize dynamic transformation from double electromagnetically induced transparency like material to ultra-narrow band guided mode resonance (GMR) filter by controlling the optically excited free carriers in gallium arsenide pads inserted between the gold cut wires. During this reconfiguration process of resonance modes, high quality factors up to ~104 and ~118 for the two EIT-like peaks and up to ~578 for the GMR filter are obtained.
© 2016 Optical Society of America
Electromagnetically induced transparency (EIT) in atomic physics is a quantum optical phenomenon, which has plenty of potential applications, such as slow light propagation , bio-chemical sensing  and nonlinear optical processes . Recently, the EIT-like effect in plasmonic metamaterial is attracting increasing attention owing to its advantages of flexible design and easy implementation. However, despite the fact that the ohmic losses in most plasmonic metals are quite low at terahertz (THz) frequencies, it is difficult to achieve the induced transparency peak with high quality (Q-) factor due to the high radiation losses [4, 5]. One strategy to overcome this roadblock is to obtain fano-like lineshape resonance by breaking the symmetry of the metamaterial resonator structure [6, 7]. Another promising way is to build the hybrid metamaterial-waveguide (HMW) system, which supports strong coherent interaction between the plasmonic resonance in metamaterial and the guided mode in the waveguide layer, thereby enabling distinct properties for transmission [8–10]. Additionally, EIT-like metamaterials with multispectral induced transparency windows may find potential applications such as optical information processing, multi-band slow light, filters, delay lines and so on . However, most EIT-like metamaterials reported so far only possess a single transparency peak. Although several designs with multispectral induced transparency windows have been proposed [11–13], complex structures are unavoidable, which present strict requirement for the fabrication technique. Owing to the multi-mode property of the waveguide, the HMW system provides an easy method to achieve multispectral EIT-like design with simple structure. Moreover, in practical applications, dynamically tunable or reconfigurable THz functional devices are highly desired. By introducing optically tunable materials, dynamic switching of the resonance characteristics can be achieved for the HMM system.
In this letter, we present an optically controlled reconfigurable hybrid metamaterial-waveguide (RHMW) system in the terahertz regime with photosensitive semiconductor incorporated into the metamaterial structure. Its optical properties are investigated with theoretical and numerical calculations. Without the pump light, our design exhibits two sharp induced transparency peaks with high Q-factors. It is shown that the double EIT-like transmission results from the destructive interference between the dipole plasmon mode in the metamaterial and the quasi-guided modes in the waveguide layer. As the power density of the incident pump beam increases, this device undergoes a dramatic tuning process, and ultimately becomes an ultra-narrow band guided mode resonance (GMR) filter with Q-factor up to ~578. Our design provides a new method of exploiting THz functional devices and exhibits great potential in THz multi-band slow light technology, THz filters, and switches.
2. The proposed device
Figure 1 shows the schematic of the proposed RHMW system, where a metamaterial array of two-dimensional (2D) gold cut wires is deposited on top of a dielectric slab waveguide. The gold cut wires are arranged in a square lattice with the period of P = 150 µm. Photosensitive elements are inserted between the gold cut wires and connect them in the y direction. In this design, the photosensitive elements are made of gallium arsenide (GaAs), which can achieve high conductivity through reversible photodoping. The length and width of the gold cut wire are l = 80 µm and w = 24 µm, respectively. The heights of the gold and GaAs are both set to be t = 0.2 µm, as shown in Fig. 1(c). In the planar waveguide, two dielectric materials with very low dielectric losses at terahertz frequencies are used. The waveguide layer is made of SU-8 with the permittivity ɛSU-8 = 3.0 . The cladding and the substrate are both made of Polytetrafluoroethylene (PTFE) with the permittivity ɛPTFE = 2.06 . The dielectric losses of these two materials are neglected in the beginning and their impacts on the device performance will be discussed later. The thicknesses of the waveguide and cladding layers are tw = 80 µm and tc = 75 µm, respectively. For the techniques on how to bond the microstructured GaAs on the flexible plastic substrates, please refer to , Lee et al and , Zhou et al.
It is notable that two light beams are incident on the RHMW device. One is the normally incident THz signal beam with the electrical field polarization in the y direction. It is worth mentioning that the polarization of the incidence is always kept along the y direction in this paper. The other is an obliquely incident near-infrared pump beam, which is used to excite photocarriers in the GaAs. In the consideration of the delay between the moment the pump pulse reaches the surface of GaAs and the moment the photo-induced carriers are generated [18–21], the pump pulses should arrive a few picoseconds earlier than the THz pulses to ensure a quasi-steady state for the charge carriers in GaAs. Besides, the pump laser beam needs to be expanded to have a larger spot diameter than the THz beam so as to enable a uniform excitation aperture for the THz transmission. All the electromagnetic response characteristics of the proposed RHMW system are investigated by utilizing the 3D finite difference time domain (FDTD) method. In the simulation, the gold is modeled as the lossy metal with the conductivity of σgold = 4.09 × 107 S/m. The photoconductive GaAs is simulated with εGaAs = 12.7 and a pump power dependent conductivity σGaAs.
3. Results and discussions
First, the electromagnetic response of the proposed HMW system without photosensitive elements is investigated. The black solid line in Fig. 2(a) represents its transmission spectrum. We can clearly observe two distinct narrow transparent windows located at 1.269 THz and 1.302 THz, respectively. For comparison, the transmission spectrum of the gold cut wire array directly on top of PTFE substrate (red dashed line) is also provided in Fig. 2(a). It is obvious that no EIT-like phenomenon occurs in the absence of the waveguide layer and only a wide transmission dip, indicated as the red triangle in Fig. 2(a), appears at 1.284 THz, which is attributed to the excitation of dipole plasmon resonance.
To understand the underlying mechanisms of the EIT-like phenomenon, the role of the waveguide layer is studied. The SU-8 waveguide layer, sandwiched between the cladding and substrate, can be regarded as a slab waveguide that supports transverse electric (TE) and transverse magnetic (TM) quasi-guided modes. According to the slab waveguide theory, theTE and TM modes should satisfy the following eigenvalue equations [22, 23]:Eqs. (1) and (2), we can obtain the dispersion relations of the TEm and TMm, where subscript m represents the mth order of the guided modes. Note that these guided modes cannot be excited by an externally incident wave, because the momentum and energy cannot be conserved simultaneously. Owing to the existence of the metamaterial layer, the periodic arrangement of the gold cut wire can provide the necessary momentum to couple the diffracted waves into the guided modes. In this way, the guided modes are no longer fully confined within the waveguide layer, but leaky in the outer region. These quasi-guided modes manifest themselves as peaks in the transmission spectrum. For efficient coupling, phase matching condition needs to be satisfied:Eq. (3) can be reduced to β = 2π / P (P = Px = Py = 150 µm). By inserting this value to Eqs. (1) and (2), we can obtain the approximate resonance frequencies of the TE/TM quasi-guided modes: fTE0 = 1.266 THz and fTM0 = 1.298 THz, which are consistent with the simulated results (1.269 THz and 1.302 THz, indicated respectively by the dark blue and green triangles in Fig. 2(a)). Essentially, these two transparent peaks are attributed to the interference of the dipole plasmon mode and the TE/TM quasi-guided modes. Therefore, to be more exact, we identify them as hybrid TE/TM modes in the following discussion.
The nature of these resonances can be further confirmed by investigating the field distributions at their resonant frequencies. Figures 2(b) and 2(c) show the distributions of the electric field component Ey on the yOz cross section and the magnetic field component Hx on the xOz cross section of the gold cut wire array without the waveguide layer at 1.284 THz, respectively. Significant field enhancement can be observed near the gold cut wire, demonstrating the excitation of the dipole plasmon mode. Figures 2(d)-2(g) show the distributions of Ey and Hx on the cross section of the HWM system at the two induced transparency peaks. In the HWM system, the plasmon resonance of the gold cut wire are suppressed within the transparency windows, while significantly enhanced electromagnetic fields are confined in the waveguide layer. The TE0 mode along the x direction at 1.269 THz and the TM0 mode along the y direction at 1.302 THz can be clearly observed. According to the above discussion, the physics of the EIT-like phenomenon of the HWM system is clear now. The dipole plasmon resonance of the gold cut wire array can strongly couple with the incident THz waves, serving as the bright state with the low quality factor, whereas the hybrid TE/TM modes can only weakly couple with the dipole mode radiation, functioning as the dark states with significantly longer lifetimes. The destructive interferences between the bright state and two dark states give rise to the double narrowband transparency peaks within a broad transmission dip.
Next, we will discuss the dynamic electromagnetic response of the proposed RHMW system (i.e. with the GaAs insertion). Since the photodoping of GaAs is a reversible process, the conductivity of GaAs can be dynamically tuned via varying the power density of the incident pump beam. Based on the experimental results in , O'hara et al if a Ti: Sapphire laser with the central wavelength of 800 nm and repetition rate of 1 kHz is used as the pump source, the conductivity of GaAs σGaAs can reach up to ~1 × 106 S/m when the energy flux of pump beam is 750 µJ/cm2. Accordingly, the upper limit of σGaAs is set to be 1 × 106 S/m in this paper. Figures 3(a) and 3(b) show the transmission spectra of the RHMW system as a function of σGaAs. As the pump intensity is increased, GaAs gradually transforms from insulator to conductor with the increasing σGaAs, which significantly weakens the strength of the dipole plasmon resonance and red shifts its resonance frequency. When σGaAs reaches 2 × 104 S/m, the plasmon resonance becomes very weak within the observed frequency domain. During the course of continuously increasing σGaAs, it can be observed that the two transmission peaks caused by the hybrid TE and TM modes gradually degrade. These two modes complete disappear when σGaAs reaches 1 × 106 S/m. However, their spectral locations stay the same because of the unchanged lattice constant. Besides, it should be noted that there is a transmission dip between the hybrid TE and TM modes. As shown in Fig. 3(a), as σGaAs increases from 1 × 103 to 2 × 104 S/m, this dip gradually red shifts to the transparency peak caused by the hybrid TE mode and its transmissivity gradually gets higher. When σGaAs continues to increase, as shown in Fig. 3(b), its resonance frequency continues to approach the TE mode transmission peak, while its transmissivity begins to fall. Finally when σGaAs = 1 × 106 S/m a typical GMR filter is obtained—a very narrow transmission dip within a flat transmission background. Furthermore, if all the GaAs elements are replaced by gold, the transmissivity of this dip can reach ~0, as shown in the black dotted curve in Fig. 3(b).
To gain the physical insight into this tuning process, it is instructive to investigate how the electromagnetic field distributions at the transmission dip change along with the changing σGaAs. Figures 3(c) and 3(d) show the distributions of Ey and Hx on the xOz cross section of the RHMW system without GaAs at transmission dip of 1.287 THz located between the TE and TM transmission peaks. From the Ey and Hx distribution, it is clear that both the hybrid TE0 mode and dipole plasmon mode are excited at this frequency. However, the excitation intensity of the TE mode is relatively low, and most of the energy concentrate near the gold cut wire, so the transmission at this frequency exhibits the low-transmissivity plasmon resonance characteristics. As σGaAs increases, the excitation intensity of the dipole plasmon mode greatly decreases, which causes the energy gradually transfer from the plasmon to the TE mode. This can be confirmed by the Ey and Hx distributions when σGaAs = 2 × 104 S/m shown in Figs. 3(e) and 3(f). The maximum value of Hx almost declines by half. The intensity of the TE mode at this dip, by contrast, undergoes a slow rate of increase. As a result, the transmission dip gradually red shifts with the growing transmissivity. Further increase of σGaAs will cause the impact of the plasmon mode on this dip completely disappear, and then the transmissivity of this dip begins to fall. As illustrated by the Ey and Hx distribution when σGaAs = 1 × 106 S/m shown in Figs. 3(g) and 3(h), the majority of energy concentrates in the waveguide layer, and typical field distributions for TE0 GMR mode can be observed. Besides, one can note that the linewidths of the induced transparency peaks are much wider than that of the GMR mode. As mentioned earlier, the transparency peaks result from the interference of the dipole plasmon mode and the quasi-guided modes, where the dipole plasmon mode strongly couples with the incident waves and has relatively large radiation loss and wide linewidth. Thus, the induced transparency peaks have relatively wide linewidth. On the other hand, no plasmon mode is excited when σGaAs = 1 × 106 S/m, and therefore the linewidth of the GMR mode is much narrower.
The dielectric losses of the waveguide materials may affect the performance of our proposed devise. Based on the experimental results reported in , Arscott et al and , Hejase et al, the loss tangents of SU-8 and PTFE are 6.3e-6 and 8e-4 around 1 THz, respectively. The loss tangent tanδ is defined as the tangent of the loss angle δ, which is the ratio between the imaginary part ɛ” and real part ɛ’ of the dielectric constant, i.e. tanδ = ɛ”/ɛ’. Accordingly, the transmission spectra of the HMW system and the RHMW system when σGaAs = 1 × 106 S/m with the loss tangent of the waveguide tanδw = 6.3e-6 and loss tangent of cladding layers tanδc = 8e-4 are plotted as the orange curves in Figs. 4(a) and 4(b). By comparing these two spectra with the ones when tanδw and tanδc = 0 (dark blue curves in Figs. 4(a) and 4(b)), it can be found that the dielectric losses do not change the resonant frequencies. However, the transmissivities of the two induced transparency peaks slightly reduce (Fig. 4(a)) and the transmissivity for the GMR dip (Fig. 4(b)) slightly increase. Besides, their Q-factors slightly decrease from 105.8 to 104 for the TE mode transparency peak, from 120.6 to 118.4 for the TM mode and from 636 to 578 for the GMR mode. We also provide the transmission spectra of the HMW system and the RHMW with σGaAs = 1 × 106 S/m when the loss tangent of the waveguide tanδw is increased to 1e-3, as the cyan curves in Figs. 4(a) and 4(b). As expected, the resonance strengths further decrease along with the increasing tanδw, but the resonant frequencies still keep unchanged.
EIT effects have been well demonstrated to significantly slow down the speed of the light while reduce the absorption of the medium for the light signal, revealing potential applications in optical signal processing and nonlinear optics [25, 26]. Figure 4(c) shows the group delay spectrum of the the HMW system in absence of GaAs with the loss tangents of the waveguide and cladding layers tanδw = 6.3e-6 and tanδc = 8e-4. The group delay is defined as the opposite slope of the transmission phase response, what is obtained by taking the negative derivative of the transmission phase with respect to the angular frequency, i. e. tg = −dφ/dω . It is more suitable to use tg instead of the group index to identify the light slowing capability of a device because utilizing tg does not require the effective thickness of the device, which is generally difficult to define due to the influence of the substrate. From Fig. 4(c), it can be found that the group delays at the two transparency windows are 24.2 ps at 1.27 THz and 26.6 ps at 1.30 THz, indicating good group delay properties and slow light capability. To our best knowledge, the maximum group delays obtained in the previously reported THz metamaterial designs [12, 28, 29] are several picoseconds, which are much lower than that in our design. Compared with the ever reported THz metamaterials, the quasi-guided modes in our design are weakly coupled with the incident waves through the grating diffraction, resulting in the ultranarrow band dark mode and correspondingly high group delay. In addition, the proposed RHMW system can realize in situ optical tuning of the group delay, as shown in Fig. 4(d). With the increase of the GaAs conductivity σGaAs caused by increasing the pump intensity, the group delays at the two transparency windows experience reverse changing processes. In accordance with the earlier discussion, the TM transparency peak at 1.30 THz gradually degrades until it eventually disappear when σGaAs reaches 1 × 106 S/m. Consequently, a decreasing group delay is obtained and it drops to almost zero when σGaAs = 1 × 106 S/m, as illustrated by the dark blue squares in Fig. 4(d). On the other hand, the TE transparency peak at 1.27 THz accumulates more dispersion as σGaAs increases, and eventually evolves into an ultra-narrow bandstop GMR mode. Accordingly, the group delay at 1.27 THz (red triangles in Fig. 4(d)) grows larger along with the increasing σGaAs.
An optically controlled reconfigurable hybrid metamaterial-waveguide system is proposed in the THz regime. By numerical simulations, we have demonstrated that it can realize the conversion from a double EIT-like system to an ultra-narrow band GMR filter by varying the pump illumination. Without the pump illumination, the transmission spectrum exhibits two sharp induced transparency peaks resulting from the destructive interference between the dipole plasmon mode and TE and TM quasi-guided modes. Large group delays are obtained in vicinity of the two transparency windows: 24.2 ps at 1.27 THz and 26.6 ps at 1.30 THz. As the pump illumination is increased, the TM transparency peak continually weakens and eventually disappears whereas the TE transparency peak gradually evolves into a GMR mode with a very high Q-factor of 578. If the TE transparency peak is regarded as a bandpass filter, our device can realize the change from a bandpass to a bandstop filter at ~1.27 THz. The proposed reconfigurable design is expected to work as optically controllable multi-band slow light devices, delay lines and nonlinear devices. Moreover, our device is also very promising for developing high-performance THz functional devices, such as tunable filters, switchers, and modulators. Furthermore, considering the multi-mode property of waveguide, it is possible to achieve more induced transparency peaks by appropriately designing the waveguide parameters and introducing more quasi-guided modes in the waveguide layer.
This work is supported by the National Basic Research Program of China (973) (2015CB755403). X. Zhao also acknowledges financial support from the China Scholarship Council.
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