Emission and detection of terahertz pulses from a metal-tip antenna

Walther et al. Vol. 22, No. 11/ November 2005 / J. Opt. Soc. Am. B 2357 Emission and detection of terahertz pulses from a metal-tip antenna Markus Walther, Geoffrey S. Chambers, Zhigang Liu, Mark R. Freeman, and Frank A. Hegmann Department of Physics, University of Alberta, Edmonton, Alberta T6G 2J1, Canada Received March 21, 2005; revised manuscript received May 12, 2005; accepted May 16, 2005 We investigate the antenna characteristics of a metal tip coupled to terahertz (THz) pulses generated from a photoconductive switch. Enhanced terahertz pulse emission is observed with the metal tip in contact with one of the electrodes of the photoconductive switch. Measurements of the angular dependence of the emitted THz radiation show that the metal tip acts as a highly directional antenna with radiation patterns well described by the theory for long-wire traveling-wave antennas. Similar behavior is observed for the metal tip acting as a THz pulse receiver, in accordance with the reciprocity principle. Effects related to the broadband nature of the THz pulses are discussed. 2005 Optical Society of America OCIS codes: 180.5810, 230.7020, 230.7370, 300.6270, 350.4010. 1. INTRODUCTION To overcome the spatial resolution limit for microscopy in the long-wavelength region at terahertz (THz) frequencies, near-field methods were recently introduced that use metal tips to interact with the electric field of pulsed THz radiation in the vicinity of the sample. 1 8 In such a configuration, the metal tip not only locally interacts with the incident electric field but also acts as an antenna that couples THz radiation into or out of the region close to the apex of the tip. Similar metal wire antennas have routinely been used to concentrate radiation to micrometersized electronic elements, such as submillimeter whisker diodes, for which the wire acts as an antenna with highly directional radiation characteristics. 9 13 In such devices, properties such as directional sensitivity 10 12 and antenna gain 13 could be explained by long-wire antenna theory. In all these studies, however, narrowband cw radiation sources were used. More recently, 6 ps farinfrared pulses from a free-electron laser with tuning from 5 to 12 THz were coupled to a superlattice detector through a metal wire antenna, 14 but the corresponding bandwidth of each far-infrared pulse in this case was less than 100 GHz. Important differences are expected, with THz sources emitting picosecond pulses with typical bandwidths extending from 100 GHz to several THz, because, for example, antenna efficiencies and radiation patterns of wire antennas are strongly frequency dependent. As a result, the broad bandwidth of THz pulses has direct consequences for optimal coupling angles and preferred wire lengths, and a detailed understanding of the characteristic radiation patterns and their frequency and wire-length dependence would provide useful information for the optimization of systems that couple THz pulses to metal tips. The properties of metal wires or tips interacting with THz pulses have been studied by several research groups, and many interesting aspects of this interaction have been addressed, including effects on the THz pulse bandwidth, 3 the influence of the tip shape, 4 and THz pulse propagation issues. 2 Further studies have demonstrated high spatial resolution in scanning near-field microscopy with THz pulses and have revealed resonant processes between the tip and the radiation field. 5 7 Despite these achievements, angle-dependent effects associated with the broadband nature of the THz pulse radiation used in these investigations have not yet been reported. As a result, the coupling angles in apertureless near-field imaging, for example, have been dictated mainly by experimental constraints rather than by optimization issues. Understanding how to optimize the coupling angle will help in the design of more-efficient THz near-field microscopes. In this paper we demonstrate the efficient coupling of THz pulses out of and into a micrometer-sized photoconductive (PC) switch by using a metal tip. We investigate the angular dependence of the emitted and detected radiation and observe effects related to the broad bandwidth of the THz pulses, which can be explained by the frequency dependence of the characteristic radiation patterns of the metal tip acting as a highly directional antenna. A detailed analysis of the angle dependence of the emitted frequency spectra allows us to determine the frequency-dependent radiation patterns, which can be successfully modeled by long-wire antenna theory. Owing to the reciprocity principle, the polar properties for an emitting antenna are similar to those obtained when it is used as a receiving antenna. By operating the same system of PC switch and metal tip in emission and detection mode, we are able to qualitatively demonstrate reciprocity. Placing the metal tip far away from the photoconductive switch region allows us to spatially and, because of additional propagation of the electric field pulse along the metal strip transmission line, temporally delay the THz emission from the tip with respect to the THz pulse emitted directly from the PC switch alone. As a result, by successively changing the position of the metal tip on the strip line, we can directly follow the propagation of the electric field pulse on the transmission line. We point out 0740-3224/05/112357-9/$15.00 2005 Optical Society of America

2358 J. Opt. Soc. Am. B/ Vol. 22, No. 11/ November 2005 Walther et al. that this technique represents a new approach to sampling voltage pulses propagating along coplanar transmission lines. 15 18 Interestingly, various circular metallic waveguides, such as metal tubes, 19,20 submillimeter coaxial transmission lines, 21 and bare metal wires, 22 have been shown to exhibit excellent wave-guiding properties for broadband THz radiation. Recently, propagation of cylindrically symmetric radial surface modes along metal wires has been observed. 22 In light of these recent observations, we point out that in the limit of an infinitely long, lossless wire the radiation patterns and traveling-wave description presented in this paper do indeed extrapolate to these radial polarized modes. In this respect, our results help to elucidate the properties of short metal tips used in THz nearfield microscopy applications as well as long metal wires used for THz pulse waveguides. 2. EXPERIMENT For our investigations we used a THz time-domain spectroscopy setup, as shown in Fig. 1. In Fig. 1(a), a PC switch (PC1) generated pulsed THz radiation, and a metal tip in contact with one of the electrodes of PC1 acted as a transmitting antenna. Photoconductive switch PC1 consisted of two gold coplanar metal strip lines with a width of 10 m separated by an 80 m gap on a 500 m thick semi-insulating GaAs (SI GaAs) substrate. The bias voltage applied across the strip lines was 50 V. The metal tip was made from platinum iridium wire (10 mil =254 m diameter) by mechanical cutting with pliers. Observation under a microscope showed a sharply pointed, asymmetric tip. The wire was bent at a right angle at distance L=5.1 mm from the apex, which defined the active length of the wire antenna. The tip could be contacted either to one of the strip lines, with the angled portion of the wire acting as a spring or withdrawn by several millimeters with roughly 50 m precision. The switch and the tip were rigidly mounted together on a mechanical stage such that they could be rotated together about the y axis by angle with respect to the z axis, as indicated in Fig. 1. The axis of rotation intersected the point where the tip was in contact with the strip line. The output of a mode-locked Ti:sapphire laser (50 fs, 800 nm, 75-MHz repetition rate) was focused to a spot size of 50 m in the gap between the two coplanar strip lines by a focusing lens with a focal length of 15 mm. This focus defined the origin of the coordinate system x=y=z=0 in Fig. 1(a). The excitation beam from the laser source illuminated the gap at an angle of 25 from the z axis to avoid placing a mirror in the path of the THz pulses and to minimize clipping of the excitation beam by the tip. Varying the angle of incidence of the excitation beam had no apparent effect on the emitted THz radiation. In par- Fig. 1. Experimental setup: A photoconductive switch (PC1) with a metal tip in contact with one of the strip lines acts as a wire antenna emitting and receiving THz pulses. PC1 can be rotated together with the tip about the y axis. (a) The radiated THz pulses are collected and focused by two off-axis parabolic mirrors onto a detector where the electric field is electro-optically sampled in a ZnTe crystal. Two photodiodes (PD1 and PD2) are used for balanced detection. The inset shows a more detailed view of the metal tip in contact with one of the strip lines of the photoconductive switch. The z axis is in the direction of propagation toward the THz detection setup, and is the angle of the metal tip with respect to the z axis by rotation about the y axis. (b) In a second arrangement, THz pulses are generated from a photoconductive switch equipped with a hyperhemispheric silicon lens (PC2) and focused onto the switch with the metal tip (PC1). In this case, PC1 is used as a THz detector.

Walther et al. Vol. 22, No. 11/November 2005 / J. Opt. Soc. Am. B 2359 ticular, no directional dependence of the emitted THz radiation power was observed as a function of excitationbeam illumination angle, which we note is not the case for large aperture antennas. 23 An off-axis parabolic mirror at a distance of 1 focal length f=4 in. =10.16 cm from PC1 collected and collimated the THz radiation emitted in the z direction. A second parabolic mirror focused the pulses to a spot at the position of the THz detector, where the THz pulses were electro-optically sampled in a 1 mm thick ZnTe crystal by use of balanced photodiodes PD1 and PD2. 24,25 The 2 in. clear aperture and the 4 in. focal length of the first parabolic mirror collected THz radiation emitted from PC1 and the metal-tip antenna within ±10 of the z axis, which limited the angular resolution of our experiment. Introducing an additional aperture to improve the angular resolution resulted in a dramatically reduced signal and was therefore not practical. In a second experiment, the same PC switch with the metal tip shown in Fig. 1(a) was used as a THz pulse detector, as described in Fig. 1(b). In this case a separate PC switch equipped with a hyperhemispheric silicon lens [PC2 in Fig. 1(b)] was placed at the position of the former THz detector to generate free-space THz pulses. 26 The parabolic mirrors focused the THz pulses emitted from PC2 to a diffraction-limited spot at the position of PC1. In this case the generated photocurrent across the unbiased photoconductive gap of PC1 was measured and used to reconstruct the time-dependent electric field of the incident THz pulses. Note that, because of the long carrier lifetime in SI GaAs, our antenna basically detects the time integral of the THz field, and we have to recover the actual THz waveform by differentiating the detector signal. 27 3. RESULTS AND DISCUSSION Using the setup shown in Fig. 1(a), we examined the influence of the tip on the emitted THz radiation with the tilt angle of the switch at =0. Curve (a) of Fig. 2 shows the typical bipolar THz waveform emitted from the PC switch in the z direction when the metal tip is not in electrical contact with one of the electrodes (in this case at a distance of 0.2 mm). The additional weak oscillations immediately after the main pulse are due to water-vapor absorption in the THz beam path, and the slightly weaker second pulse after 12.2 ps is the THz pulse that was radiated into the GaAs substrate and reflected from the dielectric interface at the back of the substrate. Contacting the tip to one of the electrodes leads to a significantly larger THz output and a modified waveform, as shown in curve (b) of Fig. 2. Note that, in contrast to that of the main pulse, the THz pulse reflected from the back of the substrate is essentially unaltered by the presence of the tip. The change in shape of the main pulse is the result of a superposition of the THz pulse radiated from the excitation spot on the photoconductive switch and an additional component radiated from the metal tip. Thus we can isolate the contribution from the tip by simply subtracting the two waveforms with and without the tip in contact. The resultant difference waveform is shown in curve (c) of Fig. 2. Remarkably, the peak-to-peak amplitude of the main pulse is 1.7 times larger than the original field amplitude emitted without the tip in contact, Fig. 2. THz pulses emitted by the combination of a PC switch and a metal tip at =0. For (b) the tip was in contact with one of the strip lines of the switch. The second pulse at later times is due to internal reflection at the back surface of the substrate of the switch. (c) We isolated the THz pulse radiated from the metal tip alone by taking the difference of the two waveforms in (a) and (b). The waveforms are vertically offset for clarity. demonstrating the radiative efficiency of the metal tip as a wire antenna. As is shown below, because of the directional properties of the antenna we can further improve the coupling efficiency by adjusting the angle of the wire with respect to the z axis. Note that in our configuration the wire extends somewhat out of the focal plane of the first parabolic mirror. As a result we found that, by slightly defocusing the PC switch, i.e., by a translation in the z direction away from the mirror, we were able to preferentially enhance the contribution from the tip slightly while we reduced the signal from the switch. Contacting the opposite electrode resulted in a sign reversal of the waveform, as expected. In our experiment we exclusively contacted the positive electrode, which resulted in a slightly larger signal owing to the electric field enhancement at the anode. 28 As in a conventional linear long-wire antenna, an oscillating current distribution along the axis of the metal tip radiates an electromagnetic field. In our case the current in the wire is driven by the transient voltage pulse launched by the photocurrent flowing between the strip line electrodes after switching by the excitation laser pulse. The electric field from this transient partly radiates into free space, generating the THz waveform shown in curve (a) of Fig. 2, and partly drives a transient current in the wire, leading to an additional THz pulse radiated from the metal tip acting as a wire antenna, which is then superimposed upon the original THz pulse [Fig. 2, curve (b)]. This contribution to the THz pulse radiated from the metal tip is expected to exhibit characteristic directional properties. 10 12 In addition to the radiation coupled into free space, an electric field pulse also propagates along the metal strip lines, which represent a coplanar transmission line, 15 18 in both directions along the y axis away from the exciting laser focus at the origin. Thus moving the apex of the tip in the y direction along the strip line introduces an additional path length for the voltage pulse driving the current in the wire and consequently generates an extra delay for the THz pulse radiated from the tip. Displacing the tip from the origin therefore temporally offsets the contri-

2360 J. Opt. Soc. Am. B/ Vol. 22, No. 11/ November 2005 Walther et al. butions from the PC switch and the metal tip. In our experiment we achieved this displacement by simply translating the strip line together with the tip in the y direction with respect to the stationary laser focus. By using this procedure, rather than moving the tip or the laser focus, we eliminated any unwanted effects caused by changes of the contact properties between the tip and the strip line and effects caused by changes of the laser focus. However, by doing this we also moved the tip slightly out of the focus of the first parabolic mirror, which limited the practical range of the displacement to ±250 m. The result of such an experiment in which the tip and the PC switch were shifted in the positive and negative y directions with respect to the position of the laser focus at y=0 is shown in Fig. 3(a). We observed attenuation and dispersive pulse broadening with increasing propagation length along the transmission line, as observed in studies with similar transmission line structures. 15 18 In Fig. 3(b) we plot the y position of the metal tip versus the relative time delay of the peak of the THz pulse emitted from the metal tip with respect to the peak at y=0. We obtained a linear time dependence, from which we estimated a mean group velocity of the field pulses propagating along the coplanar strip lines of v= 99±4 m/ps, which corresponds to 0.330±0.013 c, where c is the speed of light in vacuum. For comparison, we calculated the group velocity through v=c/ eff, using the theoretical effective dielectric constant eff determined from an empirical model for coplanar transmission lines, 29,30 the geometry of our strip lines, and a group refractive index for GaAs of 3.5 for a pulse with a central frequency of 1 THz. 31 As a result, we get v=98.4 m/ps, in excellent agreement with our measurement. Note that our measured value is also consistent with previous studies of comparable coplanar wave guides on GaAs substrates. 18 We point out that our metaltip antenna method represents an alternative approach to traditional sampling techniques of picosecond electrical pulses propagating along transmission lines. 15 18 Fig. 3. (a) Radiated THz waveforms as a function of the y position of the metal tip with respect to the position of the laser focus y=0. The waveforms are vertically offset for clarity. (b) Relative delay of the maximum of the THz pulses radiated from the metal tip versus tip position along the y axis. The straight lines are linear fits from which the mean group velocity for the propagation along the coplanar transmission line could be extracted. We now investigate in more detail the radiative properties of the metal tip acting as a wire antenna. As demonstrated, for example, in submillimeter whisker-contact diode receivers, the wire can act as a highly directional antenna with a characteristic radiation pattern that has been modeled by antenna theory, which considers the metal tip as a long-wire antenna supporting a travelingwave current distribution. 10 12 Theoretically, the radiation patterns of linear antennas that support either a stationary current distribution (standing wave) or a progressive one (traveling wave) are symmetric about the wire axis and consist of lobes, which are cones of radiation centered on the wire and tilted toward the wire axis. The result is a directional characteristic with a lobe in the radiation pattern for each half-wavelength of wire length. 32 Whereas the lobes of a wire with a standing-wave current distribution are tilted in the forward and the backward directions with respect to the middle of the wire, a traveling-wave current supports only lobes in the forward direction. Motivated by the observations for submillimeter whisker diodes, 10 12 we determined the angular dependence of the radiated THz pulse from the metal tip and compared the results to the theory for a travelingwave antenna. For this purpose, the emitter, including tip, could be rotated freely about the y axis, as indicated in Fig. 1(a), to change angle between the axis of the metal tip and the z direction. We excited the PC switch at the position of the metal tip (i.e., at y=0) to ensure that we did not lose the high-frequency components in the spectrum that would have been lost if the tip had been placed far away from the excitation spot owing to propagation losses down the transmission line. This, however, limited the range of experimentally accessible angles to =0 45, because for negative angles part of the excitation beam was clipped by the tip and for angles larger than 45 the laser focus on the switch became significantly distorted. The angle-dependent THz waveforms are shown in Fig. 4(a), and the corresponding spectral amplitudes, obtained by Fourier transforming the time-domain signals, are shown in Fig. 4(b). The time-domain traces of the THz pulses in Fig. 4(a) already reveal some of the antenna characteristics of the radiating metal tip. As is increased, the peak-to-peak amplitudes of the THz pulses become larger until a maximum is reached near 10, after which the signal amplitudes start to decrease. This angular dependence is a direct consequence of the directional antenna properties of the metal tip and can be explained by the characteristic spatial radiation patterns. As a second effect, the radiated pulses temporally broaden when gets larger. This behavior is directly related to the broadband nature of the THz pulses and leads to a spectral narrowing of the THz radiation emitted at large, as illustrated in the spectra at =40 and 45 in Fig. 4(b). We will address these two effects and show that both can be explained by the characteristic radiation patterns of the antenna and their frequency dependence. It has been shown that the metal wire of whiskercontact diodes exhibits the antenna characteristics of a traveling-wave long-wire antenna, and its radiation properties can be well described by the conventional theory for

Walther et al. Vol. 22, No. 11/ November 2005 / J. Opt. Soc. Am. B 2361 this type of antenna. 10 12 In the far field, the electric field can be well described by 32 E sin 1 cos sin L 1 cos, where L is the length of the antenna, is the wavelength, and is the angle between the direction of the emitted radiation and the wire axis. The resultant radiation pattern 1 consists of a main lobe and several weaker sidelobes, as shown in Figs. 5 and 6. Note that the electrical field reverses its direction in each successive lobe. This effect is analogous to the reversal of the phase of the currents in successive half-wavelength portions of the wire. 32 The characteristic angles for the main lobes and the number of lobes depend on L and. The radiation pattern is cylindrically symmetric about the wire axis, giving rise to radiation cones. The angle between the first (main) lobe and the wire axis can be approximated by 10,32 max = cos 1 1 0.371 /L. 2 Fig. 4. Angular dependence of the radiated THz pulses for the metal tip at the position of the laser focus y=0. (a) THz waveforms for different angles, (b) corresponding frequency spectra in terms of the electric field amplitude. Dashed lines, frequencies for which the radiation patterns in Fig. 5 are determined. The traces are vertically offset for clarity. With longer L, shorter, or both, the lobes tilt toward the antenna axis, approaching 0 for the limit of L. In this limit the traveling-wave antenna is practically a waveguide, with the dominant main lobe propagating as a radial mode along the wire, as has already been demonstrated for THz pulses propagating along metal wire waveguides with lengths from a few centimeters to as long as 24 cm. 20,22 In our case, however, the metal tip is of the order of a few wavelengths long, so the angles for the main lobes deviate significantly from 0, resulting in specific radiation patterns being formed for different wavelengths. From the spectra in Fig. 4(b) we determined the electric field amplitude E, at different angles at the frequencies indicated by the dashed lines. In Fig. 5 we show the resultant angular dependencies of E, as polar plots. To isolate the radiation from the metal tip, we separately measured the angular radiation distribution of the PC switch without the tip in contact, as shown in the insets of Fig. 5. Radiation patterns of the metal-tip wire antenna for several frequencies. Filled circles, experimental values extracted from the spectra in Fig. 4. Dotted curves, theoretical radiation patterns calculated from relation (1); solid curves, the theory convoluted with a ±10 square function to account for the angular resolution of our setup. Dotted arrows indicate the theoretical angles of the main lobes according to Eq. (2). Insets, the radiation patterns of the PC switch with the metal tip not in contact. Linear fits to these data for the metal tip not in contact have been subtracted from the data shown for the metal tip in contact in the larger plots.

2362 J. Opt. Soc. Am. B/ Vol. 22, No. 11/ November 2005 Walther et al. Fig. 5, where the metal tip has been withdrawn from the electrode by 0.2 mm. Note that these radiation patterns have a maximum at 0 and show no distinct features. To first order, the angular dependence for each frequency could be approximated by a linear relation (curves in the insets of Fig. 5), which has been subtracted from the measured radiation patterns in the plots (filled circles). For comparison, the calculated theoretical radiation patterns for the different frequencies and our antenna length of L=5.1 mm are also shown in the figure (dotted curves). As described in Section 2, the angular resolution of the experiment is limited by the open aperture of the first offaxis parabolic mirror. As a result, the detector effectively averages over a range of approximately ±10. To simulate this property of our setup, we convoluted the theoretical expressions for the electric field [relation (1)] with a square function of a corresponding width of ±10 and plotted the resultant electric field amplitudes in Fig. 5 (solid curves). The result of this procedure is that the main lobes become a little wider and tilt slightly toward smaller angles, with this effect being more relevant for high frequencies. In addition, the phase reversal of successive lobes leads to a reduction of the sidelobe intensity in the convoluted signal. Note that absolute radiation intensities cannot be determined by the model. Therefore we scaled the absolute values of the theoretical curves arbitrarily to best fit the measured data. Our data follow the general trends of the theoretical patterns. In particular, the maxima of the main lobes, as determined from Eq. (2), are well reproduced as indicated by the arrows in Fig. 5 at theoretical angles of 27.0 for 0.2 THz, 17.0 for 0.5 THz, 13.4 for 0.8 THz, and 12.0 for 1.0 THz. However, we generally observe wider lobes than theoretically expected, which can possibly be attributed, at least partly, to the limited spatial resolution of our detector, determined by the spot size of the sampling beam for the electro-optic detection. Such limits in the spatial resolution would broaden and smear out features in the angular plots. We also measured larger signals in the sidelobe region, where the radiated field amplitude should average out owing to the phase reversals after the convolution with the angular detector response. In this regard, note Fig. 6. Measured radiation pattern for 0.2 THz for positive and negative angles (open circles), together with the corresponding data from Fig. 5 (filled circles). The dotted curve is a theoretical curve according to relation (1) with and indicating the polarity of the different lobes. The solid curve is the theory convoluted with a ±10 square function. Fig. 7. Angle dependence of the spectral extent of the emitted THz pulses. Bars represent the FWHM values of the power spectra of the THz waveforms in Fig. 4(a). The solid curve is the theoretical curve for the frequency dependence of main lobe angle max according to Eq. (2). Inset, a radiation pattern with the corresponding angle of the main lobe. that our model assumes an infinitely thin wire. For cylindrical antennas with finite cross section the phase of the field varies continuously from lobe to lobe instead of having sudden jumps, and the minima between the sidelobes are nonzero, leading to larger amplitudes in that region. 32,33 Despite these deficiencies of the model, the generally good agreement between theory and experiment shows that the long-wire antenna theory adequately describes the directional properties of a metal tip used as an antenna for THz pulses. As a consequence of the broad bandwidth of the THz pulses, the overlap of the spatial radiation patterns leads to an angular frequency dependence, with the low frequencies emitted predominantly at large angles and the high-frequency components at small angles. The result is the spectral shift with changing, as observed from Fig. 4(b). We can show that this angle-dependent frequency shift basically follows the progression of the main lobes as predicted by theory by plotting the spectral extent of the THz pulses in Fig. 4(b) as a function of the angle. In Fig. 7 the bars indicate the extent of the spectra of the THz pulses in Fig. 4(a) in terms of the FWHM bandwidth of their power spectra, corresponding to the 1/ 2 values of the amplitude spectra in Fig. 4(b). Note that the solid curve in Fig. 7 is not a fit to the data but represents the theoretical dependence of the main lobe angle on the frequency according to Eq. (2). The data mainly follow the theoretical curve; however, there is a significant deviation at small angles, which can be at least partly explained by the upper bandwidth limit of the generated THz pulse radiation. To determine the radiation pattern for negative angles we had to offset the focus of the excitation beam slightly from the tip apex to avoid clipping of the THz and laser beams. In that case we lost some of the high-frequency components owing to dispersion along the waveguiding strip lines, as demonstrated above. However, we were still able to determine the radiation characteristics for the lower frequencies, for which we observed symmetric radiation patterns about =0. For example, we show in Fig. 6 the angle dependence of the electric field amplitude

Walther et al. Vol. 22, No. 11/November 2005 / J. Opt. Soc. Am. B 2363 for 0.2 THz (open circles) together with the corresponding data for positive angles taken from Fig. 5 (filled circles). The dotted curve represents the theoretical radiation pattern according to relation (1), and the solid curve is again the theoretical curve convoluted with a square function of ±10 width to simulate the angular resolution of our setup; and indicate the opposite polarity of successive lobes, as predicted by the theory for a long-wire traveling-wave antenna. 32 Again, the magnitudes of the theoretical curves have been scaled arbitrarily to best fit our data. The observed angular distribution is symmetric about =0 and follows the theoretical curve. The polarity of the pulses can be deduced from the time-domain waveforms. Figure 8 shows typical THz waveforms recorded for = +10, 10. In this case the laser focus and tip position were offset by approximately 250 m, leading to a temporal delay between the contributions from the switch and the tip. We observed that the waveform radiated from the tip reverses its polarity on reversing the angle, as expected from theory. Such behavior was also observed for radial waveguide modes of THz pulses propagating along long metal wires and has been interpreted as the result of projecting the radial polarized modes onto the onedimensional detector, which is sensitive to linearly polarized radiation only. 22 As our detection scheme is sensitive to electric fields linearly polarized in the x direction, we also effectively observed the projection of the cylindrically symmetric and radial polarized field of the THz pulses along the x axis. As a consequence we observed a reversal of the polarity of the THz pulse emitted from the metal tip, as illustrated in the inset of Fig. 8. According to expressions (1) and (2), changing the length of the metal tip changes its radiation characteristics. For shorter wires, the lobes become broader and tilt away from the wire axis for a given frequency. To test this behavior, we measured the radiation pattern for a metal tip with a length of only 2.1 mm and compared it to the result for the L=5.1 mm wire examined earlier, as shown in Fig. 9. The solid and the dashed curves are the theoretical curves according to relation (1) for L=5.1 mm and Fig. 8. The waveforms radiated from the metal tip reverse their polarity on changing from positive to negative angles. As an example we show the situation in which the tip was offset from the photoconductive region on the PC switch by y 250 m for = +10, 10. Dotted lines, positions of the minima and maxima of the electric fields radiated from the metal tip. The waveforms have been vertically offset for clarity. Fig. 9. Effect of wire length on angular radiation patterns for 0.2 and 0.8 THz. The data for a wire with L=5.1 mm (filled circles) and L=2.1 mm (open circles) are shown together with the corresponding theoretical radiation patterns calculated according to relation (1) and convoluted with a ±10 square function. Solid and dotted arrows mark theoretical angles max of the main lobes according to Eq. (2). L=2.1 mm, respectively, convoluted with a ±10 square function. The arrows indicate the expected maxima of the radiation patterns calculated from Eq. (2) (27.0 and 13.4 for the long and 42.7 and 20.9 for the short metal tips at 0.2 and 0.8 THz, respectively). As expected, the measured lobes for the shorter metal tip are at higher angles, following the theoretical patterns. Once again, our results show that a metal tip has characteristic radiative properties for THz pulses that can be modeled by the theory for a long-wire traveling-wave antenna. According to the principle of reciprocity, the polar pattern obtained for an antenna emitting radiation is the same as its receiving characteristics. In our setup we could test this by reversing the THz beam path and using the combination of PC switch and metal tip as a detector for incident THz pulses. As described in Section 2 and in Fig. 1(b), we therefore replaced the THz detector with a PC switch source (PC2) to generate THz pulses, which were focused by the parabolic mirror optics to a spot at the position of PC1. We measured the induced photocurrent across the photoconductive gap of PC1 after laser excitation to reconstruct the time-dependent electric field of the incident THz pulses. Note that, owing to the long carrier lifetime in the SI GaAs substrate, which is of the order of several hundreds of picoseconds, the switch basically detects the time integral of the incident electric field. Therefore we differentiated and low-pass filtered the detected signal according to standard procedures 27 to recover the original THz waveforms. Figure 10 shows typical THz pulse waveforms recorded by this method. The top trace shows the THz pulse recorded with the metal tip not in contact with one of the strip line electrodes and under normal incidence. The other waveforms were recorded at different angles with the metal tip in electrical contact

2364 J. Opt. Soc. Am. B/ Vol. 22, No. 11/ November 2005 Walther et al. Fig. 10. THz pulses detected by the combination of the PC switch and metal tip. Top trace, the detected THz waveform with the metal tip not in contact with one of the strip lines for =0. The other waveforms were recorded with the metal tip in contact with one of the strip line electrodes. All curves are vertically offset for clarity. acting as a receiving antenna. In our measurements the metal tip was slightly displaced from the photoconductive region on the PC switch, defined by the laser focus, which led to a slight temporal offset of the pulse received by the metal tip with respect to the fraction directly detected by the PC switch. We observed a qualitatively similar behavior to the reverse situation in which the tip was acting as an emitting antenna. In particular, angular dependencies and temporal broadening effects similar to those shown in Fig. 4(b) are observed and can be explained by the similar frequency dependence of the radiation patterns, demonstrating reciprocity of the metal-tip antenna. Finally, we mention that in all the experiments the metal tip was either in electrical contact with one of the strip line electrodes or withdrawn by at least 0.2 mm. A detailed investigation of the distance dependence was not possible with the current setup but will be a subject of further investigation with a modified system. Preliminary studies, however, showed that electrical pulses were coupled between metal tip and PC switch over short distances of the order of a few micrometers. We note that interesting configurational resonance effects between tip and THz field have been reported in scanning near-field microscopy applications, 6 and similar effects can be expected to play a role in the coupling of THz radiation into the metal tip. Likewise, we expect that, in contrast to what we found in this study, the shape of the apex of the metal tip will affect the gap fields and hence will play a major role in coupling over distances. 4. CONCLUSIONS We investigated the antenna characteristics of a photoconductive switch equipped with a metal tip to couple pulsed THz radiation into free space. When we moved the metal tip, which was in contact with one of the metal strip lines of the switch, along the strip line electrode the components radiated from the metal tip and the PC switch could be temporally separated. This procedure also represents an alternative method for sampling voltage transients propagating along coplanar strip lines. The highly directional nature of the metal-tip radiation pattern was successfully modeled by antenna theory, with the metal tip treated as a classic long-wire traveling-wave antenna. Effects related to the broadband nature of the THz pulses such as pulse broadening and characteristic frequency shifts were observed and could be understood in terms of the antenna properties of the metal tip. These effects should play an important role in pulsed THz applications, for example in near-field microscopy, where similar metal tips are commonly used. Because of their cylindrically symmetric radial lobe structure our wire antenna shows potential as a radial THz pulse source. As demonstrated, high coupling efficiencies from a PC switch to the wire can be achieved by direct contact of the tip to one of the electrodes. Finally, it has been shown that similar radiation patterns apply for a tip acting as an emitting or receiving antenna, in accordance with the reciprocity principle. 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