We demonstrated extraordinary THz transmission through ring apertures on a metal film. Transmission of 60% was obtained with an aperture-to-area ratio of only 1.4%. We show that the high transmission can be suppressed by over 18 dB with a thin layer of free carriers in the silicon substrate underneath the metal film. This result suggests that CMOS-compatible terahertz modulators can be built by controlling the carrier density near the aperture.
©2011 Optical Society of America
Modulators for quasi-optical terahertz (THz) beams have various applications in imaging and communications [1–3]. Different types of THz modulators have been demonstrated including those based on quantum-well structures [4, 5] and those based on metallic antenna structures on semiconductor substrates [6–10]. Among them, the modulators based on the extraordinary optical transmission (EOT) effect [8–10] of sub-wavelength apertures in a metal film are of particular interest, because they can show high extinction ratio up to 40 dB . The switching effects were achieved either with dielectric–metal phase transition of VO2 , or by changing the free-carriers density in a semiconductor substrate underneath the film [9, 10].
In these previous demonstrations, the modulators have a metal layer that is fully connected [8–10]. Therefore, to build an electro-optic switch, the metal layer can only be used as one electrode . With the other electrode placed far away, the speed and power efficiency of the switch is limited. Here we demonstrate a ring aperture design where the metal inside and outside of the ring are electrically isolated and can be used as two electrodes [11, 12]. This capability will allow us to electrically control the carrier density only in the area underneath the aperture. Comparing to controlling the carrier density in the whole area underneath the metal, this design minimizes the power consumption and maximizes the operation speed.
We show experimentally that transmission of 60% can be obtained for an aperture array with only 1.4% open area. The high transmission can be suppressed by over 18 dB with a thin layer of free carriers in the silicon substrate underneath the metal film. Simulations show that the isolated metal film in the center of the aperture can be connected electrically with a metal wire bridged across the aperture on top (Fig. 1(a) ) without significantly affecting the transmission characteristics. A p-i-n junction similar to that used in near-infrared optical switches  can be used to control the carrier density just beneath the aperture (Fig. 1(b)). The p-i-n junction can introduce larger change in the number of carriers in the aperture region than the carrier depletion junctions used in . We expect that a switching speed on the order of 10 Gbps can be achieved with this type of junction . This design is also compatible with pixelation, providing the opportunity for building a high speed high contrast terahertz spatial light modulator . With these capabilities, the electrical control of free-space terahertz beams begins to approach the level of control achieved by conventional modulators in the visible and near-infrared.
2. Principle of operation
EOT is an optical phenomenon in which a structure containing subwavelength apertures in a metal film transmits more light than that expected on the basis of ray optics. EOT through narrow apertures is due to a significantly enhanced electric field inside and around the aperture. Because of the strong local field, the EOT effect is highly sensitive to the change in material properties around the aperture, which is desirable for such applications as molecular sensing, spectroscopy and optical switching [15, 16]. The EOT phenomenon is especially strong in the THz frequency range since apertures with width orders-of-magnitude smaller than the wavelength can be made [17–21].
To understand the principle of operation, the E-field amplitude of the TE11 mode of a ring aperture with a radius r = 50 µm and a width of w = 1 µm is shown in Fig. 1(c). The phase of the Er component of the mode varies by 2π over the circumference of the ring. This mode thus has a cut-off frequency fc = c/(2πr⋅neff), where neff is the effective index. At that frequency, there is no phase variation in the direction perpendicular to the substrate, creating a Fabry-Perot (FP) resonance as waves travelling back and forth inside the aperture, which results in the resonating EOT effect. The yellow arrows in the figure show the direction of E-field of the y-polarized TE11 mode. One can see that the E-field at upper and lower halves of the ring both point to the +y direction; therefore, this mode will efficiently couple to a y-polarized normal-incidence plane wave. The degenerate x-polarized TE11 mode of the aperture provides EOT for the x-polarized normal-incident wave, resulting in polarization-independent operation.
The ring aperture also supports a TEM mode. However, the TEM mode does not have a cut-off frequency to support EOT, and cannot be excited by a normal-incidence plane wave because its E-field at opposite sides of the ring points to opposite directions.
3. FDTD simulation
We performed a 3D finite-difference-time-domain (FDTD) simulation of a normally-incident broadband THz wave passing through the aperture in a gold film on an intrinsic silicon substrate. In the simulation, periodic boundary conditions were used assuming a square-lattice array with lattice constant p = 150 µm. The simulation shows strong E-field enhancement around the aperture. Figure 1(d) shows the side view of the resonant E-field intensity distribution when a plane wave passes through the ring aperture. The E-field distribution is highly confined in and around the aperture, with the peak E-field average intensity (|E|2) in the aperture enhanced by ~2500 times comparing to the incident wave.
The simulated power transmission spectra for different apertures are shown in Fig. 2(a) . As the theory predicts, the cavity resonant frequency scales inversely with the circumference of the rings. The peak transmission varies between 62% and 71% even though the apertures only comprises 1.1%-1.9% of the area. The peak transmission is limited by the large difference in refractive index between air on top of the film and silicon beneath the metal film. The peak transmission would be close to 100% if the refractive indices on both sides of the metal film were the same. When the width of the aperture varying between 20 µm and 1 µm, or when the thickness of metal varying between 2 µm and 100 nm, only small changes (<6%) in the peak transmission of the aperture are observed. These small variations are mainly due to changes in optical loss in the metal. Simulations also confirm that the resonant wavelength is not sensitive to the shape of the aperture. To show that, we computed the simulated transmission spectrum of square rings (dashed lines in Fig. 2(a)). Comparing to the circular rings with the same circumference, the resonant frequency and peak transmission of the square rings only change slightly. We also note that the spectra of all the apertures show smaller and narrower peaks around 0.57 THz. The frequency of these features only changes with the periodicity of the pattern, showing that they are from the grating effect.
To switch off the EOT effect, one can inject free carriers into silicon underneath the apertures [9, 10, 13]. A small increase in free-carrier absorption is significantly enhanced by the FP resonance, resulting in a substantial decrease in transmission. The black solid line in Fig. 2(a) shows the simulated transmission spectrum when free carriers with a density of 3 × 1017 cm−3 are injected into a 1-µm-deep and 4-µm-wide region of silicon under the ring aperture, giving rise to a local conductivity of ~10 Ω–1⋅cm–1. These carriers cause the transmission of the aperture to drop as much as 17 dB, while the one-pass absorption of the free carriers is only ~0.6 dB. Because the E-field is highly confined around the aperture, the p- and n- doped areas shown in Fig. 1(b) do not cause significant loss as long as they are placed a few microns away from the aperture.
To use the metal inside the aperture as an electrode, it needs to be electrically connected to a vertical via and a metal wire going across the aperture on top of a dielectric material. To see how this metal line would affect the transmission of the device, we added a 1-µm-wide gold line on top of a 1-µm-thick SiO2 layer on the metal film, as shown in Fig. 1(a). If the wire crosses the aperture at the position with the minimal E-field, the transmission is barely affected as shown by the blue squares in Fig. 2(b). If the wire crosses the aperture at the position with the maximal E-field, simulations (triangles in Fig. 2(b)) show a ~10% blue shift of the resonant peak and a ~10% drop of the peak transmission.
4. Device fabrication
We fabricated periodic arrays of circular and square ring arrays with various width w and radius r (or side length l for square rings) by E-beam lithography. The period of all the arrays is p = 150 μm. The pattern is first defined on the E-beam resist SU-8 on a 500-µm-thick high-resistivity silicon substrate. A 100-nm-thick gold film is then evaporated on the patterned resist, followed by a lift-off process. The SEM pictures of the fabricated circular and square ring arrays are shown in Fig. 3(a) and Fig. 3(b), respectively. The total size of each array is 4.8 mm × 4.8 mm.
The transmission of the device, measured using a time domain THz spectrometer , agrees well with the simulation results. Figure 4(a) compares the time-domain transmitted field amplitude signals of an aperture array (red) with that of a bare silicon substrate (blue). The time domain signals were truncated at 10 ps after the peak of the initial pulse to remove the signal reflected from the back of the substrate. Then, a Fourier transform with zero-padding  is performed to obtain the transmission spectra. Figure 4(b) compares the measured (solid) and simulated (dashed) power transmission spectra. The blue solid line in Fig. 4(b) shows the measured power transmission spectrum of rings with r = 50 µm, normalized to the transmission of a bare high-resistivity silicon substrate. A transmission peak centered at 0.42 THz can be clearly identified. The measured F-P cavity resonance peak is slightly broader than the simulated one, which may be due to size variation of rings in the array. The narrower surface resonance peak at 0.57 THz cannot be resolved in the measured spectra due to the limited time window length.
Figure 5(a) compares the measured transmission spectra for different aperture patterns. Rings with different circumferences are shown in different colors. Their resonant frequencies scale inversely proportional to their circumference, as expected. Although the transmission decreases as the radius of ring aperture decreases, the normalized-to-area transmission increases due to larger field enhancement inside the ring cavity. We also verify that square-rings (dashed) have the similar resonant frequencies as the circular-rings (solid) with the same circumferences. Moreover, we measured the polarization dependency of the devices, as shown in Fig. 5(b) for circular ring aperture and Fig. 5(c) for square ring aperture. The measured power transmission spectra of ring arrays for different polarization angles of incident THz beam show the same resonant frequency with transmission varying within 10%, verifying polarization independency of the devices due to the symmetry of the ring apertures.
Using an ion-implanted substrate, we show that EOT can be efficiently suppressed with a thin layer of free carriers underneath the apertures. We fabricated the ring apertures on a silicon substrate implanted with boron ions. The designed hole density in silicon resulted from the implantation is shown in Fig. 6(a) , which decreases from ~1019 cm−3 at the surface to almost 0 in a depth of less than 200 nm. With the implantation, the EOT transmission of the ring apertures drops over 18 dB. The measured transmission spectra on the implanted, shown as the dashed lines in Fig. 6(b), are close to the noise level of the measurement system. In comparison, the one-pass absorption of the free carriers is measured to be only ~1.2 dB.
In conclusion, we demonstrate the EOT effect of ring apertures on a metal film for switching THz waves. We show that the transmission can be efficiently suppressed with a thin layer of free carriers in the silicon substrate underneath the metal film. These results suggest the possibility of CMOS-compatible THz-wave modulators with high speed and high on-off contrast ratios.
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