1. Introduction

Terahertz (THz) technology is a rapidly evolving field with numerous applications such as stand-off security scanning or high-bandwidth short-range wireless communications [1–5]. Yet, while THz sources and detectors have already reached a high degree of maturity [6–8], the lack of active system components required to dynamically control free-space THz wave propagation still hinders the broad scale success of THz systems. Here we propose a freely programmable diffraction grating based on an electrostatically actuated, computer controlled array of metallic cantilevers. Switching between different grating patterns enables tailoring spatio-temporal profiles of the THz waves. By characterizing the device with spatially resolved THz time domain spectroscopy, we demonstrate that both variable focusing and beam steering over a broad angular range can be attained. The proposed approach could be employed to mimic arbitrary diffraction optics, enabling highly integrated and extremely flexible systems indispensable for THz stand-off imaging and communications.

The capability of dynamically controlling the propagation of free-space THz waves, e.g. by steering or focusing the THz beams, is the key to a variety of applications. For instance, in THz wireless communications, quasi-optical links rely on directed paths between emitters and receivers [2,3]. Beam steering will enable securing reliable communication paths even when the emitters or receivers are changing their positions or objects interrupt the line-of-sight link. Furthermore, in THz sensing or imaging, beam steering devices can replace mechanical scanning stages, and thus dramatically increase the measurement speed and the level of system integration [4,5]. High speed beam steering could also lead to novel THz measurement methodologies such as single pixel THz imaging based on compressed sensing [9] or imaging of moving objects by tracking the targets with THz beams.

So far, THz beam steering has been achieved either by mechanical scanning devices or by spatial phase modulators. The latter operate similarly to phased arrays, which are well known from the microwave regime. First implementations of THz phase shifters relied on free carrier excitation in semiconductors [10–12]. Externally excited free carriers modulate the dielectric function of a semiconductor material so that the THz waves passing through the medium experience a phase shift. However, as the real and imaginary parts of the dielectric function are dependent on each other as described by the Kramers-Kronig relations, the phase modulation results in insertion losses and is inseparable from amplitude modulation [10–12]. The same is true for structures based on resonant metamaterial phase shifters as proposed in [13–15]. Phase shifters have also been implemented using liquid crystals [16–18]. Yet, they operate at rather high voltages and a low speed. Other approaches rely on phase controlled arrays of photoconductive switches [19–21]. However, as this scheme requires ultrashort optical laser pulse excitation, the number of potential applications is limited. At visible light frequencies, spatial phase modulators based on micromachined tunable gratings have been introduced [22–25]. However, a transfer of this technology to the THz regime has so far not been possible as the vertical stroke of each array element must be a hundred times larger due to the longer wavelengths.

Here we propose a THz spatial phase modulator in the form of a freely reconfigurable array of sub-wavelength metallic cantilevers. Computer controlled electrostatic forces individually switch the micromechanical displacement of the sub-wavelength cantilevers so that diffraction grating patterns such as a periodic or a chirped grating can be defined. Tuning the grating pattern allows for both steering and focusing of collimated THz beams as we will experimentally demonstrate in the following sections. We would like to emphasize that the device can be combined with any THz sources regardless of the generation method or the signal intensity. In particular, the combination with quantum cascade lasers or solid-state electronic sources will enable the steering of high power continuous THz waves.

2. Device fabrication

Figure 1 shows (a) a photo and (b) schematics of the device. The cantilever array is fabricated out of a 5 µm thick stainless steel film by periodically perforating narrow rectangular slits with a 180 µm pitch by photochemical etching. After the etching, the remaining frame is employed as the array of 256 cantilevers, all of which are electrically connected. We connect the entire array to the electric ground. The free-standing cantilever array is sandwiched between electrode arrays (Fig. 1(b)). The electrodes are fabricated by patterning copper on a 12.5 µm thick polyimide substrate using a flexible printed circuit fabrication process. Each of the 256 cantilevers is individually addressed and displaced by about 80 µm in the vertical direction when the voltage between the cantilever and the electrode is switched from 0V to 52V. Figure 2(a) shows examples of possible grating patterns. Not only periodic but also chirped grating patterns are available. Figure 2(b) shows a cross sectional profile of the periodic grating measured with a laser displacement meter. The sharp spikes appearing with a 180 µm spacing correspond to the individual cantilevers. Four cantilevers in the up-state followed by four cantilevers in the down-state define a rectangular groove array with a period of 1.44 mm. The up- and the down-state of the cantilevers differ by a vertical displacement of 80 µm, which is roughly a hundred times larger than that of conventional micromachined optical gratings.

 

Fig. 1 (a) Photo of the device. (b) Schematic of the cantilevers and the electrodes.

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Fig. 2 (a) Photos of periodic and chirped grating patterns programmed on the device. (b) Measured cross sectional profile of the periodic grating pattern.

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3. Beam steering experiments

For the characterization of the device we use a fiber-coupled THz time domain spectroscopy system based on a 1560 nm fiber-laser and InGaAs photoconductive antennas. The system delivers short THz pulses with a bandwidth stretching from 0.1 THz to 1.5 THz. As illustrated in Fig. 3(a), a combination of spherical and cylindrical lenses is used to form an almost diffraction limited line-focus illuminating the center line of the programmable diffraction grating. The line-focus is TE polarized and has an incident angle of −55°. We first mount the detector antenna on a goniometer to detect the diffracted beams for angles between −30° and + 30°. A second set of lenses is used to focus the diffracted beam onto the detector antenna.

 

Fig. 3 (a) Experimental setup for beam steering. (b) Beam direction versus frequency plotted for different grating periods p. Measurement (dots) and theory (dashed lines) are compared. The inset shows angular intensity scans at 0.3 THz for three different grating periods p.

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A THz beam, i.e. the first order diffraction from a periodic grating, is steered by changing the grating period p as presented in Fig. 3(b). The main figure shows the relation between the frequency and the beam direction for different values of p. For each frequency ranging from 0.15 THz to 0.9 THz the beam direction is changed depending on the period p. At 0.33 THz the steerable range reaches 42° (from −27° to + 15°) by changing p from 0.72 mm to 1.62 mm. The inset shows the angular intensity distributions at 0.3 THz for three different grating periods p: (A) 1.08 mm, (B) 1.26 mm, and (C) 1.44 mm. The beam width (full width at half maximum, FWHM) is about 3° in all cases. The side lobe levels are (A) −14.5 dB, (B) −12.1 dB, and (C) −14.2 dB, respectively. Both the beam directions and the field profiles agree well with the theoretical predictions (dashed lines) which are calculated by assuming omnidirectional source arrays of the corresponding period and length. As expected from the literature [26], the second order diffraction is hardly observable due to the equally spaced rectangular groove geometry of the grating. The zero order diffraction, i.e. the specular reflection, is roughly 20 dB higher than the first order diffraction. In the next generation of programmable THz gratings the intensity of the zero order diffraction can be considerablyreduced by choosing a groove depth which is close to a quarter of the wavelength [27].

4. Variable focusing experiments

The device also allows for changing the divergence of THz beams. Switching the grating pattern from a periodic to a chirped grating pattern as shown in Fig. 2(a) results in a converging wavefront, and leads to the focusing of THz beams above the device. The chirpedgrating pattern is designed so that the radiation from each groove of the grating contributes to a constructive interference at a single point in free space.

To perform a cross sectional scan of the focus, we mount the detector antenna on a linear stage (Fig. 4(a)). The incident angle is fixed again at −55°. Figures 4(b) and 4(c) show theoretical intensity maps of the diffraction at 0.3 THz with two different chirped grating patterns, in which each groove serves as a point source. The colour bar is valid above the white dashed line. Figures 4(d) and 4(e) show the experimental and theoretical focal intensity profiles corresponding to (b) and (c), respectively. The two patterns are designed so that the focus moves 6 mm horizontally while keeping the distance of 40 mm from the grating. To compensate for the effect of the silicon lens attached to the detector, which would displace the focal distance [28], we set the detector at 44 mm above the grating. The experimental results (dots) agree well with the theoretical predictions (dashed lines). The FWHM defined in the horizontal direction is about 1.8 mm in (d) and 1.0 mm in (e). The FWHM can roughly be estimated by Lλ/D where L and D denote the focal distance and the aperture size, respectively. Considering that L is nearly twice the size of D in our setup, the above formula yields a FWHM of 2 mm at 0.3 THz, which is consistent with the measurement.

 

Fig. 4 (a) Experimental setup for focusing. (b) & (c) Theoretical intensity map of focused diffraction at 0.3 THz for two different chirped grating patterns. The colour bar is valid above the white dashed line. (d) & (e) Intensity profiles of the focus corresponding to (b) and (c), respectively. Measurement (dots) and theory (dashed lines) are compared.

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5. Conclusions

In conclusion, we have demonstrated a freely programmable THz diffraction grating based on an electrostatically actuated array of metallic cantilevers. We showed that switching between different grating patterns enables tailoring the spatio-temporal profiles of the THz waves, which, for instance, can be used to steer or focus the THz radiation. Beam steering has been demonstrated for a wide frequency band extending from 0.15 THz to 0.9 THz. The steerable range at 0.3 THz exceeds 40°. By programming a chirped grating structure, focusing has also been demonstrated with a FWHM below 2 mm at 0.3 THz. Besides beam steering and focusing, other diffraction patterns also enable multi-foci configurations or frequency filtering of certain bands. In future, the proposed concept will be extended to create freely reconfigurable 2D diffraction gratings that enable THz stand-off imaging and communications with highly integrated systems.