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We demonstrate a terahertz (THz) beam steering method using difference frequency generation that is based on the principle of phased array antennas. A strip-line photoconductive antenna was illuminated by two spatially dispersed beams produced from an ultrafast laser. THz radiation with a bandwidth of 65 GHz was generated from the overlapping area of the two beams, between which the frequency difference was approximately constant. We confirmed that the THz beam can be steered by tilting one of the incident pump beams so as to change their relative phase relation. The steering range of the THz beam was 29 degrees when the angle between the incident pump beams was only varied within a range of 0.155 degrees, that is, 187 times less. In addition, by laterally shifting one of the pump beams, the frequency of the THz radiation could be tuned from 0.3 to 1.7 THz. This technique can be applied to high-speed terahertz imaging and spectroscopy systems.
©2008 Optical Society of America
1. Introduction
Terahertz (THz) imaging holds a high potential for non-destructive inspection and other applications due to the property of THz radiation to pass through various materials such as paper, cloth, plastics, and wood, and a submillimeter spatial resolution [1,2]. In recent years, the advantages of THz imaging have been shown in many reports such as the detection of weapons concealed underneath clothes, illicit drugs in mail, and the inspection of foods [1, 3–5]. For commercial applications, quick measurements will be desired when the THz imaging technique is applied, for example, to the inspection of a large number of targets. Conventionally, the THz images are acquired by moving the samples through the focused beam or by scanning the emitter and detector in the case of fixed samples. Quicker and more efficient ways of steering the THz beam are required for practical applications because the measurement speed is mainly limited by the speed of the mechanical devices.
Additionally, the possibility of applying the THz radiation to short-range wireless communications has been discussed in recent years [6]. It has the advantage of offering the greater communication bandwidth than in the conventional microwave regions. It has been proposed that the THz radiation be omnidirectionally emitted from a base station in order to cover the entire communication area [7]. It is, however, more effective to focus the transmission power of the THz radiation on the mobile terminals because the atmospheric attenuation at THz region is stronger than at the microwave region. This method also avoids the multipath fading caused by the reflection on objects in the communication area. Thus the THz beam should be steered to track the mobile terminals.
So far, there are some reports of THz beam steering. For example, it was achieved by changing the incident angle of an ultrafast laser beam when THz pulses were generated from a wide-gap photoconductive antenna [8]. It was, however, difficult to steer the beam quickly and over a wide angle. In another report, a photoconductive antenna array illuminated by an optical pulse train was utilized with applying periodic bias voltages. The THz beam emitted from the array was steered by varying the bias period [9]. It is, however, necessary for steering at each tuning frequency to control not only the period of the bias, but also the period of the optical pulses in the train. Besides there is a report of the beam steering by the micromechanical method [10]. In the microwave region, a phased array antenna has been established as a non-mechanical beam steering technique. It consists of antenna elements and phase shifters for each element. The microwave beam is steered by controlling the phase of each element with high speed and a wide angle [11]. Optical phase shifters are also available in steering the microwave beam from the antenna array when the microwave is generated by the difference frequency generation between two lasers [12]. Many phase shifters are, however, required for a large scale array.
In this paper, we propose a technique for generating a THz beam that allows simultaneous and independent control of both the direction and the frequency. The generation of the narrow-band THz radiation is demonstrated via photomixing by using spatially dispersed beams produced from an ultrafast laser. The THz beam can be steered based on the phased array antenna principle.
2. Principle
Our proposed method includes three ideas: The first is to produce the phase relation between the THz radiation and the pump laser light in difference frequency generation (DFG), the second is to control the wavefront of the THz radiation based on the principle of the microwave phased array antenna without any phase shifters, and the third is to generate the narrow band THz radiation by pumping with spatially dispersed beams.
2.1 Phase relation in difference frequency generation
One of the general methods of generating narrow-band THz radiation is photomixing [13, 14], or DFG with pulsed or continuous-wave (CW) lasers. Two laser beams with different wavelengths are focused on a photoconductive antenna or other nonlinear device such as an optical crystal. Then, the mixing process can be expressed by the following formula,
where E 1 and E 2 are the electric fields of two laser beams, respectively, |E 1| and |E 2| are their amplitudes, ω 1 and ω 2 are their angular frequencies, t is time, and Δϕ is a phase difference between two laser beams. The terms represent the components of DC, second harmonic generation, sum frequency generation, and DFG, respectively. The THz radiation is generated as the 4th component and then it is given by,
where ωT=ω 1-ω 2 is the frequency of the THz radiation. Note that this formula means that the local phase difference between the two pump beams is directly reflected in the local phase of the THz radiation. In other words, the phase of THz radiation can be shifted by changing the phase of one pump beam.
2.2 THz wavefront control
Fig. 1. (a) Conventional microwave phased array antenna and (b) the proposed method of THz beam steering. The wavefront is tilted by changing the direction of one laser beam; this plays the same role as the array of variable phase shifters in (a).
Fig. 2. Principles of generating monochromatic THz radiation and its frequency tuning, (a) a spatially dispersed beam produced from an ultrafast laser, (b) overlapping two spatially dispersed beams with a relative shift, for difference frequency generation, (c) tuning to a lower frequency by shifting one of the beams, and (d) tuning to higher frequency.
Figure 1 shows the comparison between the conventional microwave phased array antenna and our proposed method. In case of the phased array antenna depicted in Fig. 1(a), the microwave is generated from an oscillator and distributed to the array elements. The wavefront is controlled by using variable phase shifters connected to each element. On the other hand, in our method, the wide area on a single nonlinear optical device is illuminated by two pump beams with different wavelengths, and the THz radiation is generated from the whole area as shown in Fig. 1(b). In this case, the phase difference between the two pump beams is continuously varied at each position on the device when one of the pump beams is tilted. According to Eq. (2), the phase of the THz radiation is identical to the phase difference of two pump beams. The wave front of the THz radiation is, therefore, also tilted. This means that the THz beam can be steered by changing the incidence angle of one pump beam.
As shown in Fig. 1(b), the phase difference at each position on the device is given by
where ki is the wave number of the pump laser beam, x is the position on the material, and θi is the angle between the two pump beams. Similarly, the phase distribution of the THz radiation generated from the device is given by
where kT is the wave number of the THz radiation, and θT is the THz radiation angle [11]. As mentioned of Eq. (2), ϕT(x)=Δϕi(x) based on the phase relation in DFG. Consequently, the relation between the incidence angle of one pump beam and the THz radiation angle is derived by
Commonly, infrared radiation is often utilized as the pump laser to generate THz radiation. Thus the THz beam can be steered within an angle several hundred times as wide as the tilting of the incident pump beam, the angular magnification being given by the ratio between the THz and pump wavelengths. The principle is similar to the analytic result for a photoconductive antenna array reported in Ref. [15]. Our idea is different from that report in terms of the use of a single wide nonlinear optical device, without any array.
2.3 Generation of the THz radiation and the frequency tuning
As shown in Fig. 2(a), a spatially dispersed beam, with a linear distribution of frequencies, is produced from an ultrafast laser, for example using a diffraction grating. The beam is split in two equal parts and overlapped again with a relative spatial shift, as shown in Fig 2(b). Note that the frequency difference between the pump beams is constant along the overlapping area. When a nonlinear optical device is pumped with these beams, a monochromatic THz radiation is generated from the entire overlapping area, even if the frequencies along strip-lines are not constant.
Furthermore, the frequency difference, and thus the THz wavelength, can be controlled by shifting one of the beams, as depicted in Fig. 2(c) and (d). The spatially dispersed beams are, therefore, available for not only generating the monochromatic THz radiation from a broadband pump laser, but also tuning the frequency of the THz radiation by the simple method of beam shifting.
2.4 Beam steering by using the spatially dispersed beams
In this report, the ideas mentioned in the two sections above are combined. The length of the gap along a strip-line photoconductive antenna is illuminated with two spatially dispersed beams as shown in Fig. 3(a) [16, 17]. The DFG occurs and monochromatic THz radiation is emitted from along the gap. Because the phases of all wavelength components in the ultrafast pulse are synchronized at the pulse peak, it is considered that the phases of each spatially dispersed beam are linearly distributed in the planes labeled “phase fronts” in Fig. 3(b). When one of the beams is tilted, the phase difference does not vary linearly with position because the frequencies themselves depend linearly on the position. Equation (3) becomes
Fig. 3. Combination of the ideas shown in Fig. 1(b) and Fig. 2(b). (a) Illumination of a strip-line photoconductive antenna with spatially dispersed beams, and (b) tilting one of the incident beams for THz beam steering. And also the frequency can be tuned by shifting one of the beams.
Hence the phase front of the THz radiation actually has a parabolic shape. It can be, however, regarded as linear because the frequency bandwidth of the ultrafast laser is much smaller than the center frequency. Hense the conditions in Fig. 1(b) are satisfied for the THz beam steering. The THz beam, therefore, can be steered with an angle several hundred times as wide as the incidence angle of one pump beam.
3. Experimental setup
Fig. 4 shows an experimental setup for THz-wave generation that allows both the steering of the output beam and tuning of its frequency. The spatially dispersed beams were produced by ultrafast pulses which were obtained from a Ti:sapphire laser (pulse duration 100 fs, repetition rate 90 MHz, center wavelength 803 nm, band FWHM 8.7 nm). The laser beam was diffracted off a 1200 lines/mm grating to obtain the spatially dispersed beam. This was then collimated by a cylindrical lens. The wavelength resolution of the diffracted beam is determined from
where λ is wavelength, Δλ is the resolution, m is the order of diffraction and N is the number of the grating lines in the beam spot [18]. In our experiment, the size of the beam spot was 2.4 mm and so Δλ is 0.28 nm (130 GHz). The resolution affects the linewidth of the THz radiation.
The spatially dispersed beam is divided in two beams that are subsequently overlapped with a slight shift. These two beams illuminate the emitter through two spherical lenses and a cylindrical lens. For THz beam steering, the incidence angle of one pump beam was controlled by mechanically rotating a mirror. The setup is adjusted such that the spot of the pump beam on the antenna surface does not depend on the incidence angle of the beam. The spot of the other beam is shifted by moving a pair of mirrors enclosed with a dotted rectangle depicted in Fig. 4, in a way that keeps a constant optical path length to the emitter.
Fig. 4. Experimental setup for both THz beam steering and frequency tuning. The dashed lines show the optical paths for the case where the two pump beams are superimposed without any shift.
The photoconductive antenna consists of a strip line with a length of 6 mm and a gap of 80 µm on a substrate of low-temperature grown gallium arsenide (LT-GaAs) mounted on the back on a silicon hemisphere lens. A voltage of 200 V is applied across the gap and the pump beams with a total average power of 130 mW illuminate the whole gap length. The THz radiation was detected by a dipole-shaped photoconductive antenna after reflection on two off-axis parabolic mirrors with both a focal length and a diameter of 50.8 mm. The waveform of the THz radiation was measured by sequentially delaying the ultrafast pulses of a probe beam focused on the detector antenna [19].
4. Results
4.1 THz radiation generated by spatially dispersed beams
Figure 5(a) shows a typical spatial distribution of the wavelength and the intensity of two pump beams for a radiation frequency of 0.7 THz. The shift between the beams is 2 mm. Two lines appear in the figure. The wavelength of one line ranges from 801 nm to 810 nm over a spatial width of 12 mm. The other line ranges from 799 nm to 810 nm over 14 mm. The overlapping length is 12 mm and the frequency difference is constantly around 0.7 THz, as shown in Fig. 5(b). The features of the distribution were close to the drawing in Fig. 2(b).
Figure 6(a) shows a typical waveform of the THz radiation at 0.6 THz after cutting the frequency band below 0.38 THz, using an analog filter after the lock-in amplifier. It is pulse-shaped, with an oscillation period of 1.67 ps and an envelope width of about 8 ps. The inset of Fig. 6(a) shows the waveform without filtering. Another signal with a long oscillation period of about 30 ps was simultaneously detected besides the pulse of THz radiation. As this signal is also seen when one pump beam is blocked, we believe it is produced by DFG occurring between the wavelength components of each beam.
Figure 6(b) shows the spectrum of the waveform calculated by fast Fourier transform. The center frequency was 0.6 THz and the bandwidth was 80 GHz, which is close to the predicted width obtained by the wavelength resolution of the diffraction grating given by Eq. (7). This bandwidth is clearly narrower than that of the THz radiation generated by the general method with an ultrafast laser focused on the antenna [19].
Fig. 5. (a). The spectral distribution of the spatially dispersed beams for the generation with a frequency of 0.7 THz measured with an optical spectrum analyzer, (b) The corresponding frequency difference.
Fig. 6. (a). Typical waveform of the emitted THz radiation and (b) its spectrum given by the fast Fourier transform in case of the generation at 0.6 THz.
4.2 Beam steering
Figure 7(a) shows the THz beam patterns for different incidence angles of the adjustable pump beam. These patterns were measured by the knife-edge method midway between the two parabolic mirrors. The horizontal axis indicates the angle of the direction from the emitter, calculated as the arc tangent of the ratio of the knife displacement to the effective focal length of the parabolic mirror. The spots of the pump beams on the emitter were set for an output radiation frequency of 0.6 THz. The incidence angle was estimated by the rotating angle of the mirror reflecting one pump beam; each division of the manual tilting is 0.031 deg. We can see in Fig. 7(a) that the whole pattern of the THz radiation was shifted when the pump beam was tilted. All the patterns in the figure are normalized individually. The pattern for the incidence angle of 0 degree has maximum peak intensity. The peak ratios of other patterns were 48, 41, 32, 24 and 22 % for the incidence angles of -0.031, 0.031, 0.062, 0.093 and 0.124 degrees, respectively.
Figure 7(b) shows the relationship between the THz radiation angle and the incidence angle of the adjustable pump beam. The radiation angle was defined as the angle at the peak of Gaussian distribution fitted for the beam pattern. A solid curve represents the theoretical radiation angle calculated by Eq. (5), considering the refraction at the interface between the LT-GaAs substrate and the silicon hemispherical lens. The steering range of the THz beam was 29 degrees when the incident pump beam was tilted within a range of only 0.155 degrees, which represents an angular magnification factor of 187. The error of the THz radiation angle is caused by the angular sensitivity of the rotating mirror, whose smallest division corresponds to a THz beam steering angle of 5.8 degrees. The covering range of the THz beam is ±27 degrees taking into account the size and the focal length of the parabolic mirror. This is the reason why the THz radiation could not be detected out of the range, even though our method theoretically has the ability to steer the beam within ±90 degrees. Also the range was not symmetrical, but shifted to about +10 degrees. These results may be caused by a pulse front tilting of the pump beams diffracted on the grating [20].
Fig. 7. (a). Normalized THz beam patterns for different incident angles of one pump beam, and (b) the relation between the incident angle of the pump beams and THz radiation angles.
Fig. 8. (a). Spectra of the THz radiation for different relative positions of the pump beams and (b) the center frequency as a function of the beam shift.
4.3 Frequency tuning
Figure 8(a) shows how the spectra of the THz radiation depend on the shift between the two spatially dispersed beams; one of the pump beams is fixed while the other is shifted with a pair of mirrors as shown in Fig. 4. All spectra were measured with a frequency resolution of 10 GHz and a high-pass cut-off frequency of 0.13 THz. The frequency of the THz radiation was found to be tunable from 0.31 to 1.69 THz. The maximum output power was obtained around 0.6–0.7 THz. The average linewidth was 65 GHz.
Figure 8(b) shows the relation between the beam shift and the frequency of the THz radiation, and the comparison with a curve calculated from the wavelength distribution of the pump beams shown in Fig. 5(a). The vertical axis indicates the center frequencies of Gaussian distributions fitted to the measured spectra shown in Fig. 8(a). The calculated data are in good agreement with the measurements. The average error was 20 GHz, which is comparable with the measurement resolution of 10 GHz. For each 0.25 mm step in the relative position of the pump beams the THz radiation changes on average by 92 GHz.
5. Discussions
The merits and the differences of our idea compared with the conventional techniques are as follows: (1) The array structure is not required; (2) many phase shifters are not required; (3) the steering angle of the THz beam is magnified several hundred times compared to the pump beam incidence angle; and (4) the frequency tuning of the THz beam is also possible and the beam is steered at each frequency with a low angular dispersion.
The THz beam direction also changes when both pump beams are tilted together while keeping them parallel, but the incidence angle needs to be controlled over a wide range, because the radiation angle of the THz radiation is approximately equal to the incidence angle of the two pump beams [21]. Comparatively, our proposed method allows obtaining a large phase shift and thus achieving a THz beam steering greatly amplified relative to the incidence angle.
Although in this experiment a manually rotated mirror was used for tilting the incidence of the pump beam, non-mechanical steering can also be achieved by an optical deflector. The deflecting angles of usual electro-optic (EO) and acousto-optic (AO) deflectors are small, with a range under 1° and several degrees, respectively. These performances are sufficient for wide-range THz steering because of the angular magnification effect. Furthermore, the deflecting frequency of the AO deflector is up to 1 MHz, while that of mechanically moving mirrors is about 1 kHz. Also, the angular resolution of an optical deflector is about 0.2 millidegrees. This means that a high-speed and high-resolution imaging system could be realized using the beam steering technique described here.
In conventional photomixing, two monochromatic lasers with different wavelengths have been used for generating a monochromatic THz radiation. Our method of using spatially dispersed beams allows us to utilize many components of the wavelengths compared to that of the pump laser used for the conventional photomixing and DFG. A narrower linewidth of the THz radiation than that reported here is expected to be achieved by improving the resolution of the diffraction grating, as expressed by Eq. (7). Besides steering, simple and stable tuning is possible just by shifting one of the pump beams. The technique is then available not only for THz beam steering, but also for THz spectroscopy.
When the frequency of the THz radiation is tuned, especially in the higher frequency region, the THz output intensity decreases because the emission area becomes smaller as illustrated in Fig. 2(d) and the total pump power which contributes to the DFG is reduced. This fact is similar to the optical rectification in terms of the DFG between the various combinations of two wavelengths included in the spectrum of an ultrafast laser [22]. However, we believe that the optical rectification is comparatively difficult to use in steering the THz beam with high speed and in a wide angular range.
The divergence of the THz beam is not expected to change even if the overlapping area becomes smaller at higher THz frequencies, because the diffraction depends on the ratio of the THz wavelength to the length of the emission area. Therefore, beam steering can be achieved with constant divergence over a wide range of frequencies.
In case of the short-range and indoor wireless communications, it is important for the THz beam steering to expand the angular range and reduce the beam divergence rather than to improve the speed, taking account of the walking speed of the person carrying the mobile terminal. Our basic methods of the beam steering could lead to developing the techniques of automatic tracking and multi-beam forming for practical communication devices [23].
8. Conclusion
We demonstrated a method of THz beam steering based on the phased array antenna theory. Narrow-band THz radiation was generated by DFG between two spatially dispersed beams produced from the beam of an ultrafast laser. Taking advantage of the relation between the phase of THz radiation and the phase difference between the pump beams, the THz beam could be steered by tilting one of the pump beams. The THz beam steering to occur in an angle 187 times larger than the relative tilting of the pump beams. Additionally, the frequency of THz radiation could be tuned from 0.3 to 1.7 THz by controlling the lateral shift between the pump beams. These results have the potential to contribute toward realizing a high-speed THz spectroscopic imaging system.
Acknowledgment
The authors wish to thank Drs. Masatsugu Yamashita and Hiromichi Hoshina from RIKEN for their valuable advices and comments. They also appreciate Dr. Adrian Dobroiu for carefully reading the manuscript, as well as Mr. Takayuki Shibuya, Drs. Koji Suizu and Kodo Kawase from Nagoya University for their kind cooperation.
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