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Walther et al. Vol. 22, No. 11 /November 2005 /J. Opt. Soc. Am. B 2357

Emission and detection of terahertz pulsesfrom 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 aphotoconductive switch. Enhanced terahertz pulse emission is observed with the metal tip in contact with oneof the electrodes of the photoconductive switch. Measurements of the angular dependence of the emitted THzradiation show that the metal tip acts as a highly directional antenna with radiation patterns well describedby the theory for long-wire traveling-wave antennas. Similar behavior is observed for the metal tip acting as aTHz pulse receiver, in accordance with the reciprocity principle. Effects related to the broadband nature of theTHz pulses are discussed. © 2005 Optical Society of America

OCIS codes: 180.5810, 230.7020, 230.7370, 300.6270, 350.4010.

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. INTRODUCTIONo overcome the spatial resolution limit for microscopy inhe long-wavelength region at terahertz (THz) frequen-ies, near-field methods were recently introduced that useetal tips to interact with the electric field of pulsed THz

adiation in the vicinity of the sample.1–8 In such a con-guration, the metal tip not only locally interacts with the

ncident electric field but also acts as an antenna thatouples THz radiation into or out of the region close to thepex of the tip. Similar metal wire antennas have rou-inely been used to concentrate radiation to micrometer-ized electronic elements, such as submillimeter whiskeriodes, for which the wire acts as an antenna with highlyirectional radiation characteristics.9–13 In such devices,roperties such as directional sensitivity10–12 and an-enna gain13 could be explained by long-wire antennaheory. In all these studies, however, narrowband cw ra-iation sources were used. More recently, 6 ps far-nfrared pulses from a free-electron laser with tuningrom 5 to 12 THz were coupled to a superlattice detectorhrough a metal wire antenna,14 but the correspondingandwidth of each far-infrared pulse in this case was lesshan 100 GHz. Important differences are expected, withHz sources emitting picosecond pulses with typicalandwidths extending from �100 GHz to several THz,ecause, for example, antenna efficiencies and radiationatterns of wire antennas are strongly frequency depen-ent. As a result, the broad bandwidth of THz pulses hasirect consequences for optimal coupling angles and pre-erred wire lengths, and a detailed understanding of theharacteristic radiation patterns and their frequency andire-length dependence would provide useful information

or the optimization of systems that couple THz pulses toetal tips.The properties of metal wires or tips interacting with

Hz pulses have been studied by several research groups,nd many interesting aspects of this interaction haveeen addressed, including effects on the THz pulseandwidth,3 the influence of the tip shape,4 and THz

0740-3224/05/112357-9/$15.00 © 2

ulse propagation issues.2 Further studies have demon-trated high spatial resolution in scanning near-field mi-roscopy with THz pulses and have revealed resonantrocesses between the tip and the radiation field.5–7 De-pite these achievements, angle-dependent effects associ-ted with the broadband nature of the THz pulse radia-ion used in these investigations have not yet beeneported. As a result, the coupling angles in aperturelessear-field imaging, for example, have been dictatedainly by experimental constraints rather than by opti-ization issues. Understanding how to optimize the cou-

ling angle will help in the design of more-efficient THzear-field microscopes.In this paper we demonstrate the efficient coupling of

Hz pulses out of and into a micrometer-sized photocon-uctive (PC) switch by using a metal tip. We investigatehe angular dependence of the emitted and detected ra-iation and observe effects related to the broad band-idth of the THz pulses, which can be explained by the

requency dependence of the characteristic radiation pat-erns of the metal tip acting as a highly directional an-enna. A detailed analysis of the angle dependence of themitted frequency spectra allows us to determine therequency-dependent radiation patterns, which can beuccessfully modeled by long-wire antenna theory. Owingo the reciprocity principle, the polar properties for anmitting antenna are similar to those obtained when it issed as a receiving antenna. By operating the same sys-em of PC switch and metal tip in emission and detectionode, we are able to qualitatively demonstrate reciproc-

ty. Placing the metal tip far away from the photoconduc-ive switch region allows us to spatially and, because ofdditional propagation of the electric field pulse along theetal strip transmission line, temporally delay the THz

mission from the tip with respect to the THz pulse emit-ed directly from the PC switch alone. As a result, by suc-essively changing the position of the metal tip on thetrip line, we can directly follow the propagation of thelectric field pulse on the transmission line. We point out

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2358 J. Opt. Soc. Am. B/Vol. 22, No. 11 /November 2005 Walther et al.

hat this technique represents a new approach to sam-ling voltage pulses propagating along coplanar trans-ission lines.15–18

Interestingly, various circular metallic waveguides,uch as metal tubes,19,20 submillimeter coaxial transmis-ion lines,21 and bare metal wires,22 have been shown toxhibit excellent wave-guiding properties for broadbandHz radiation. Recently, propagation of cylindrically sym-etric radial surface modes along metal wires has been

bserved.22 In light of these recent observations, we pointut that in the limit of an infinitely long, lossless wire theadiation patterns and traveling-wave description pre-ented in this paper do indeed extrapolate to these radialolarized modes. In this respect, our results help to eluci-ate the properties of short metal tips used in THz near-eld microscopy applications as well as long metal wiressed for THz pulse waveguides.

. EXPERIMENTor our investigations we used a THz time-domain spec-roscopy setup, as shown in Fig. 1. In Fig. 1(a), a PCwitch (PC1) generated pulsed THz radiation, and aetal tip in contact with one of the electrodes of PC1

cted as a transmitting antenna. Photoconductive switchC1 consisted of two gold coplanar metal strip lines withwidth of 10 �m separated by an 80 �m gap on a 500 �m

ig. 1. Experimental setup: A photoconductive switch (PC1) withmitting and receiving THz pulses. PC1 can be rotated togethernd focused by two off-axis parabolic mirrors onto a detector whhotodiodes (PD1 and PD2) are used for balanced detection. Thehe strip lines of the photoconductive switch. The z axis is in thengle of the metal tip with respect to the z axis by rotation aboutphotoconductive switch equipped with a hyperhemispheric silic

his case, PC1 is used as a THz detector.

hick semi-insulating GaAs (SI–GaAs) substrate. Theias voltage applied across the strip lines was 50 V. Theetal tip was made from platinum–iridium wire (10 mil254 �m diameter) by mechanical cutting with pliers.bservation under a microscope showed a sharplyointed, asymmetric tip. The wire was bent at a rightngle at distance L=5.1 mm from the apex, which definedhe active length of the wire antenna. The tip could beontacted either to one of the strip lines, with the angledortion of the wire acting as a spring or withdrawn byeveral millimeters with roughly 50 �m precision. Thewitch and the tip were rigidly mounted together on a me-hanical stage such that they could be rotated togetherbout the y axis by angle � with respect to the z axis, asndicated in Fig. 1. The axis of rotation intersected theoint where the tip was in contact with the strip line. Theutput of a mode-locked Ti:sapphire laser (50 fs, 800 nm,5-MHz repetition rate) was focused to a spot size of0 �m in the gap between the two coplanar strip lines byfocusing lens with a focal length of 15 mm. This focus

efined the origin of the coordinate system x=y=z=0 inig. 1(a). The excitation beam from the laser source illu-inated the gap at an angle of �25° from the z axis to

void placing a mirror in the path of the THz pulses ando minimize clipping of the excitation beam by the tip.arying the angle of incidence of the excitation beam hado apparent effect on the emitted THz radiation. In par-

al tip in contact with one of the strip lines acts as a wire antennae tip about the y axis. (a) The radiated THz pulses are collectedelectric field is electro-optically sampled in a ZnTe crystal. Two

hows a more detailed view of the metal tip in contact with one ofion of propagation toward the THz detection setup, and � is thexis. (b) In a second arrangement, THz pulses are generated froms (PC2) and focused onto the switch with the metal tip (PC1). In

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icular, no directional dependence of the emitted THz ra-iation power was observed as a function of excitation-eam illumination angle, which we note is not the case forarge aperture antennas.23 An off-axis parabolic mirror atdistance of 1 focal length �f=4 in.�=10.16 cm�� from PC1

ollected and collimated the THz radiation emitted in thedirection. A second parabolic mirror focused the pulses

o a spot at the position of the THz detector, where theHz pulses were electro-optically sampled in a 1 mmhick ZnTe crystal by use of balanced photodiodes PD1nd PD2.24,25 The 2 in. clear aperture and the 4 in. focalength of the first parabolic mirror collected THz radia-ion emitted from PC1 and the metal-tip antenna within10° of the z axis, which limited the angular resolution ofur experiment. Introducing an additional aperture to im-rove the angular resolution resulted in a dramaticallyeduced signal and was therefore not practical.

In a second experiment, the same PC switch with theetal tip shown in Fig. 1(a) was used as a THz pulse de-

ector, as described in Fig. 1(b). In this case a separate PCwitch equipped with a hyperhemispheric silicon lensPC2 in Fig. 1(b)] was placed at the position of the formerHz detector to generate free-space THz pulses.26 Thearabolic mirrors focused the THz pulses emitted fromC2 to a diffraction-limited spot at the position of PC1. Inhis case the generated photocurrent across the unbiasedhotoconductive gap of PC1 was measured and used to re-onstruct the time-dependent electric field of the incidentHz pulses. Note that, because of the long carrier lifetime

n SI–GaAs, our antenna basically detects the time inte-ral of the THz field, and we have to recover the actualHz waveform by differentiating the detector signal.27

. RESULTS AND DISCUSSIONsing the setup shown in Fig. 1(a), we examined the in-uence of the tip on the emitted THz radiation with theilt angle of the switch at �=0°. Curve (a) of Fig. 2 showshe typical bipolar THz waveform emitted from the PCwitch in the z direction when the metal tip is not in elec-rical contact with one of the electrodes (in this case at aistance of �0.2 mm). The additional weak oscillationsmmediately after the main pulse are due to water-vaporbsorption in the THz beam path, and the slightly weakerecond pulse after �12.2 ps is the THz pulse that was ra-iated into the GaAs substrate and reflected from the di-lectric interface at the back of the substrate. Contactinghe tip to one of the electrodes leads to a significantlyarger THz output and a modified waveform, as shown inurve (b) of Fig. 2. Note that, in contrast to that of theain pulse, the THz pulse reflected from the back of the

ubstrate is essentially unaltered by the presence of theip. The change in shape of the main pulse is the result ofsuperposition of the THz pulse radiated from the exci-

ation spot on the photoconductive switch and an addi-ional component radiated from the metal tip. Thus wean isolate the contribution from the tip by simply sub-racting the two waveforms with and without the tip inontact. The resultant difference waveform is shown inurve (c) of Fig. 2. Remarkably, the peak-to-peak ampli-ude of the main pulse is �1.7 times larger than the origi-al field amplitude emitted without the tip in contact,

emonstrating the radiative efficiency of the metal tip aswire antenna. As is shown below, because of the direc-

ional properties of the antenna we can further improvehe coupling efficiency by adjusting the angle � of the wireith respect to the z axis. Note that in our configuration

he wire extends somewhat out of the focal plane of therst parabolic mirror. As a result we found that, bylightly defocusing the PC switch, i.e., by a translation inhe z direction away from the mirror, we were able to pref-rentially enhance the contribution from the tip slightlyhile we reduced the signal from the switch. Contacting

he opposite electrode resulted in a sign reversal of theaveform, as expected. In our experiment we exclusively

ontacted the positive electrode, which resulted in alightly larger signal owing to the electric field enhance-ent at the anode.28

As in a conventional linear long-wire antenna, an oscil-ating current distribution along the axis of the metal tipadiates an electromagnetic field. In our case the currentn the wire is driven by the transient voltage pulseaunched by the photocurrent flowing between the stripine electrodes after switching by the excitation laserulse. The electric field from this transient partly radi-tes into free space, generating the THz waveform shownn curve (a) of Fig. 2, and partly drives a transient currentn the wire, leading to an additional THz pulse radiatedrom the metal tip acting as a wire antenna, which is thenuperimposed upon the original THz pulse [Fig. 2, curveb)]. This contribution to the THz pulse radiated from theetal tip is expected to exhibit characteristic directional

roperties.10–12

In addition to the radiation coupled into free space, anlectric field pulse also propagates along the metal stripines, which represent a coplanar transmission line,15–18

n both directions along the y axis away from the excitingaser focus at the origin. Thus moving the apex of the tipn the y direction along the strip line introduces an addi-ional path length for the voltage pulse driving the cur-ent in the wire and consequently generates an extra de-ay for the THz pulse radiated from the tip. Displacing theip from the origin therefore temporally offsets the contri-

ig. 2. THz pulses emitted by the combination of a PC switchnd a metal tip at �=0°. For (b) the tip was in contact with one ofhe strip lines of the switch. The second pulse at later times isue to internal reflection at the back surface of the substrate ofhe switch. (c) We isolated the THz pulse radiated from the metalip alone by taking the difference of the two waveforms in (a) andb). The waveforms are vertically offset for clarity.

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utions from the PC switch and the metal tip. In our ex-eriment we achieved this displacement by simply trans-ating the strip line together with the tip in the y directionith respect to the stationary laser focus. By using thisrocedure, rather than moving the tip or the laser focus,e eliminated any unwanted effects caused by changes of

he contact properties between the tip and the strip linend effects caused by changes of the laser focus. However,y doing this we also moved the tip slightly out of the fo-us of the first parabolic mirror, which limited the practi-al range of the displacement to ±250 �m. The result ofuch an experiment in which the tip and the PC switchere shifted in the positive and negative y directions with

espect to the position of the laser focus at y=0 is shownn Fig. 3(a). We observed attenuation and dispersive pulseroadening with increasing propagation length along theransmission line, as observed in studies with similarransmission line structures.15–18 In Fig. 3(b) we plot theposition of the metal tip versus the relative time delay of

he peak of the THz pulse emitted from the metal tip withespect to the peak at y=0. We obtained a linear time de-endence, from which we estimated a mean group veloc-ty of the field pulses propagating along the coplanar stripines of v= �99±4� �m/ps, which corresponds to0.330±0.013�c, where c is the speed of light in vacuum.or comparison, we calculated the group velocity through=c /��eff, using the theoretical effective dielectric con-tant �eff determined from an empirical model for copla-ar transmission lines,29,30 the geometry of our strip

ines, and a group refractive index for GaAs of �3.5 for aulse with a central frequency of 1 THz.31 As a result, weet v=98.4 �m/ps, in excellent agreement with our mea-urement. Note that our measured value is also consis-ent with previous studies of comparable coplanar waveuides on GaAs substrates.18 We point out that our metal-ip antenna method represents an alternative approach toraditional sampling techniques of picosecond electricalulses propagating along transmission lines.15–18

ig. 3. (a) Radiated THz waveforms as a function of the y posi-ion of the metal tip with respect to the position of the laser focusy=0�. The waveforms are vertically offset for clarity. (b) Relativeelay of the maximum of the THz pulses radiated from the metalip versus tip position along the y axis. The straight lines are lin-ar fits from which the mean group velocity for the propagationlong the coplanar transmission line could be extracted.
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We now investigate in more detail the radiative prop-rties of the metal tip acting as a wire antenna. As dem-nstrated, for example, in submillimeter whisker-contactiode receivers, the wire can act as a highly directionalntenna with a characteristic radiation pattern that haseen modeled by antenna theory, which considers theetal tip as a long-wire antenna supporting a traveling-ave current distribution.10–12 Theoretically, the radia-

ion patterns of linear antennas that support either a sta-ionary current distribution (standing wave) or arogressive one (traveling wave) are symmetric about theire axis and consist of lobes, which are cones of radiation

entered on the wire and tilted toward the wire axis. Theesult is a directional characteristic with a lobe in the ra-iation pattern for each half-wavelength of wire length.32

hereas the lobes of a wire with a standing-wave currentistribution are tilted in the forward and the backwardirections with respect to the middle of the wire, araveling-wave current supports only lobes in the forwardirection. Motivated by the observations for submillime-er whisker diodes,10–12 we determined the angular de-endence of the radiated THz pulse from the metal tipnd compared the results to the theory for a traveling-ave antenna. For this purpose, the emitter, including

ip, could be rotated freely about the y axis, as indicatedn Fig. 1(a), to change angle � between the axis of the

etal tip and the z direction. We excited the PC switch athe position of the metal tip (i.e., at y=0) to ensure thate did not lose the high-frequency components in the

pectrum that would have been lost if the tip had beenlaced far away from the excitation spot owing to propa-ation losses down the transmission line. This, however,imited the range of experimentally accessible angles to

�=0° –45°, because for negative angles part of the exci-ation beam was clipped by the tip and for angles largerhan 45° the laser focus on the switch became signifi-antly distorted.

The angle-dependent THz waveforms are shown in Fig.(a), and the corresponding spectral amplitudes, obtainedy Fourier transforming the time-domain signals, arehown in Fig. 4(b). The time-domain traces of the THzulses in Fig. 4(a) already reveal some of the antennaharacteristics of the radiating metal tip. As � is in-reased, the peak-to-peak amplitudes of the THz pulsesecome larger until a maximum is reached near 10°, afterhich the signal amplitudes start to decrease. This angu-

ar dependence is a direct consequence of the directionalntenna properties of the metal tip and can be explainedy the characteristic spatial radiation patterns. As a sec-nd effect, the radiated pulses temporally broaden when

gets larger. This behavior is directly related to theroadband nature of the THz pulses and leads to a spec-ral narrowing of the THz radiation emitted at large �, asllustrated in the spectra at �=40° and 45° in Fig. 4(b).

e will address these two effects and show that both cane explained by the characteristic radiation patterns ofhe antenna and their frequency dependence.

It has been shown that the metal wire of whisker-ontact diodes exhibits the antenna characteristics of araveling-wave long-wire antenna, and its radiation prop-
rties can be well described by the conventional theory for

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his type of antenna.10–12 In the far field, the electric fieldan be well described by32

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ig. 4. Angular dependence of the radiated THz pulses for theetal tip at the position of the laser focus �y=0�. (a) THz wave-

orms for different angles �, (b) corresponding frequency spectran terms of the electric field amplitude. Dashed lines, frequenciesor which the radiation patterns in Fig. 5 are determined. Theraces are vertically offset for clarity.

ig. 5. Radiation patterns of the metal-tip wire antenna for sevpectra in Fig. 4. Dotted curves, theoretical radiation patterns c10° square function to account for the angular resolution of ourccording to Eq. (2). Insets, the radiation patterns of the PC swetal tip not in contact have been subtracted from the data show

onsists of a main lobe and several weaker sidelobes, ashown in Figs. 5 and 6. Note that the electrical field re-erses its direction in each successive lobe. This effect isnalogous to the reversal of the phase of the currents inuccessive half-wavelength portions of the wire.32 Theharacteristic angles for the main lobes and the numberf lobes depend on L and �. The radiation pattern is cy-indrically symmetric about the wire axis, giving rise toadiation cones. The angle between the first (main) lobend the wire axis can be approximated by10,32

�max = cos−1�1 − 0.371��/L��. �2�

ith longer L, shorter �, or both, the lobes tilt toward thentenna axis, approaching 0° for the limit of L��. In thisimit the traveling-wave antenna is practically a wave-uide, with the dominant main lobe propagating as a ra-ial mode along the wire, as has already been demon-trated for THz pulses propagating along metal wireaveguides with lengths from a few centimeters to as

ong as 24 cm.20,22

In our case, however, the metal tip is of the order of aew wavelengths long, so the angles for the main lobes de-iate significantly from 0°, resulting in specific radiationatterns’ being formed for different wavelengths. Fromhe spectra in Fig. 4(b) we determined the electric fieldmplitude E�� ,�� at different angles at the frequenciesndicated by the dashed lines. In Fig. 5 we show the re-ultant angular dependencies of E�� ,�� as polar plots.o isolate the radiation from the metal tip, we separatelyeasured the angular radiation distribution of the PC

witch without the tip in contact, as shown in the insets of

equencies. Filled circles, experimental values extracted from theted from relation (1); solid curves, the theory convoluted with a. Dotted arrows indicate the theoretical angles of the main lobesth the metal tip not in contact. Linear fits to these data for thethe metal tip in contact in the larger plots.

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ig. 5, where the metal tip has been withdrawn from thelectrode by �0.2 mm. Note that these radiation patternsave a maximum at 0° and show no distinct features. Torst order, the angular dependence for each frequencyould be approximated by a linear relation (curves in thensets of Fig. 5), which has been subtracted from the mea-ured radiation patterns in the plots (filled circles). Foromparison, the calculated theoretical radiation patternsor the different frequencies and our antenna length of=5.1 mm are also shown in the figure (dotted curves). Asescribed in Section 2, the angular resolution of the ex-eriment is limited by the open aperture of the first off-xis parabolic mirror. As a result, the detector effectivelyverages over a range of approximately ±10°. To simulatehis property of our setup, we convoluted the theoreticalxpressions for the electric field [relation (1)] with aquare function of a corresponding width of ±10° and plot-ed the resultant electric field amplitudes in Fig. 5 (solidurves). The result of this procedure is that the mainobes become a little wider and tilt slightly towardmaller angles, with this effect being more relevant forigh frequencies. In addition, the phase reversal of suc-essive lobes leads to a reduction of the sidelobe intensityn the convoluted signal. Note that absolute radiation in-ensities cannot be determined by the model. Thereforee scaled the absolute values of the theoretical curves ar-itrarily to best fit the measured data. Our data followhe general trends of the theoretical patterns. In particu-ar, the maxima of the main lobes, as determined from Eq.2), are well reproduced as indicated by the arrows in Fig.

at theoretical angles of 27.0° for 0.2 THz, 17.0° for.5 THz, 13.4° for 0.8 THz, and 12.0° for 1.0 THz. How-ver, we generally observe wider lobes than theoreticallyxpected, which can possibly be attributed, at least partly,o the limited spatial resolution of our detector, deter-ined by the spot size of the sampling beam for the

lectro-optic detection. Such limits in the spatial resolu-ion would broaden and smear out features in the angularlots. We also measured larger signals in the sidelobe re-ion, where the radiated field amplitude should averageut owing to the phase reversals after the convolutionith the angular detector response. In this regard, note

ig. 6. Measured radiation pattern for 0.2 THz for positive andegative angles (open circles), together with the correspondingata from Fig. 5 (filled circles). The dotted curve is a theoreticalurve according to relation (1) with � and indicating the po-arity of the different lobes. The solid curve is the theory convo-uted with a ±10° square function.

hat our model assumes an infinitely thin wire. For cylin-rical antennas with finite cross section the phase of theeld varies continuously from lobe to lobe instead of hav-

ng sudden � jumps, and the minima between the side-obes are nonzero, leading to larger amplitudes in thategion.32,33 Despite these deficiencies of the model, theenerally good agreement between theory and experimenthows that the long-wire antenna theory adequately de-cribes the directional properties of a metal tip used as anntenna for THz pulses.As a consequence of the broad bandwidth of the THz

ulses, the overlap of the spatial radiation patterns leadso an angular frequency dependence, with the low fre-uencies emitted predominantly at large angles and theigh-frequency components at small angles. The result ishe spectral shift with changing �, as observed from Fig.(b). We can show that this angle-dependent frequencyhift basically follows the progression of the main lobes asredicted by theory by plotting the spectral extent of theHz pulses in Fig. 4(b) as a function of the angle �. In Fig.the bars indicate the extent of the spectra of the THz

ulses in Fig. 4(a) in terms of the FWHM bandwidth ofheir power spectra, corresponding to the 1/�2 values ofhe amplitude spectra in Fig. 4(b). Note that the solidurve in Fig. 7 is not a fit to the data but represents theheoretical dependence of the main lobe angle on the fre-uency according to Eq. (2). The data mainly follow theheoretical curve; however, there is a significant deviationt small angles, which can be at least partly explained byhe upper bandwidth limit of the generated THz pulse ra-iation.To determine the radiation pattern for negative angles

e had to offset the focus of the excitation beam slightlyrom the tip apex to avoid clipping of the THz and lasereams. In that case we lost some of the high-frequencyomponents owing to dispersion along the waveguidingtrip lines, as demonstrated above. However, we were stillble to determine the radiation characteristics for theower frequencies, for which we observed symmetric ra-iation patterns about �=0°. For example, we show inig. 6 the angle dependence of the electric field amplitude

ig. 7. Angle dependence of the spectral extent of the emittedHz pulses. Bars represent the FWHM values of the power spec-ra of the THz waveforms in Fig. 4(a). The solid curve is the the-retical curve for the frequency dependence of main lobe anglemax according to Eq. (2). Inset, a radiation pattern with the cor-esponding angle of the main lobe.

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or 0.2 THz (open circles) together with the correspondingata for positive angles taken from Fig. 5 (filled circles).he dotted curve represents the theoretical radiation pat-ern according to relation (1), and the solid curve is againhe theoretical curve convoluted with a square function of10° width to simulate the angular resolution of ouretup; � and indicate the opposite polarity of succes-ive lobes, as predicted by the theory for a long-wireraveling-wave antenna.32 Again, the magnitudes of theheoretical curves have been scaled arbitrarily to best fitur data. The observed angular distribution is symmetricbout �=0° and follows the theoretical curve. The polarityf the pulses can be deduced from the time-domain wave-orms. Figure 8 shows typical THz waveforms recordedor �= +10° ,−10°. In this case the laser focus and tip po-ition were offset by approximately 250 �m, leading to aemporal delay between the contributions from the switchnd the tip. We observed that the waveform radiated fromhe tip reverses its polarity on reversing the angle, as ex-ected from theory. Such behavior was also observed foradial waveguide modes of THz pulses propagating alongong metal wires and has been interpreted as the result ofrojecting the radial polarized modes onto the one-imensional detector, which is sensitive to linearly polar-zed radiation only.22 As our detection scheme is sensitiveo electric fields linearly polarized in the x direction, welso effectively observed the projection of the cylindricallyymmetric and radial polarized field of the THz pulseslong the x axis. As a consequence we observed a reversalf the polarity of the THz pulse emitted from the metalip, as illustrated in the inset of Fig. 8.

According to expressions (1) and (2), changing theength of the metal tip changes its radiation characteris-ics. For shorter wires, the lobes become broader and tiltway from the wire axis for a given frequency. To test thisehavior, we measured the radiation pattern for a metalip with a length of only 2.1 mm and compared it to theesult for the L=5.1 mm wire examined earlier, as shownn Fig. 9. The solid and the dashed curves are the theo-etical curves according to relation (1) for L=5.1 mm and

ig. 8. The waveforms radiated from the metal tip reverse theirolarity on changing � from positive to negative angles. As an ex-mple we show the situation in which the tip was offset from thehotoconductive region on the PC switch by y�250 �m for= +10°, −10°. Dotted lines, positions of the minima and maximaf the electric fields radiated from the metal tip. The waveformsave been vertically offset for clarity.

=2.1 mm, respectively, convoluted with a ±10° squareunction. The arrows indicate the expected maxima of theadiation patterns calculated from Eq. (2) (27.0° and 13.4°or the long and 42.7° and 20.9° for the short metal tips at.2 and 0.8 THz, respectively). As expected, the measuredobes for the shorter metal tip are at higher angles, fol-owing the theoretical patterns. Once again, our resultshow that a metal tip has characteristic radiative proper-ies for THz pulses that can be modeled by the theory forlong-wire traveling-wave antenna.According to the principle of reciprocity, the polar pat-

ern obtained for an antenna emitting radiation is theame as its receiving characteristics. In our setup weould test this by reversing the THz beam path and usinghe combination of PC switch and metal tip as a detectoror incident THz pulses. As described in Section 2 and inig. 1(b), we therefore replaced the THz detector with aC switch source (PC2) to generate THz pulses, whichere focused by the parabolic mirror optics to a spot at

he position of PC1. We measured the induced photocur-ent across the photoconductive gap of PC1 after laser ex-itation to reconstruct the time-dependent electric field ofhe incident THz pulses. Note that, owing to the long car-ier lifetime in the SI–GaAs substrate, which is of the or-er of several hundreds of picoseconds, the switch basi-ally detects the time integral of the incident electric field.herefore we differentiated and low-pass filtered the de-

ected signal according to standard procedures27 to re-over the original THz waveforms. Figure 10 shows typi-al THz pulse waveforms recorded by this method. Theop trace shows the THz pulse recorded with the metal tipot in contact with one of the strip line electrodes and un-er normal incidence. The other waveforms were recordedt different angles with the metal tip in electrical contact

ig. 9. Effect of wire length on angular radiation patterns for.2 and 0.8 THz. The data for a wire with L=5.1 mm (filledircles) and L=2.1 mm (open circles) are shown together with theorresponding theoretical radiation patterns calculated accord-ng to relation (1) and convoluted with a ±10° square function.olid and dotted arrows mark theoretical angles �max of the main

obes according to Eq. (2).

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cting as a receiving antenna. In our measurements theetal tip was slightly displaced from the photoconductive

egion on the PC switch, defined by the laser focus, whiched to a slight temporal offset of the pulse received by the

etal tip with respect to the fraction directly detected byhe PC switch. We observed a qualitatively similar behav-or to the reverse situation in which the tip was acting asn emitting antenna. In particular, angular dependenciesnd temporal broadening effects similar to those shown inig. 4(b) are observed and can be explained by the similar

requency dependence of the radiation patterns, demon-trating reciprocity of the metal-tip antenna.

Finally, we mention that in all the experiments theetal tip was either in electrical contact with one of the

trip line electrodes or withdrawn by at least 0.2 mm. Aetailed investigation of the distance dependence was notossible with the current setup but will be a subject ofurther investigation with a modified system. Preliminarytudies, however, showed that electrical pulses wereoupled between metal tip and PC switch over short dis-ances of the order of a few micrometers. We note that in-eresting configurational resonance effects between tipnd THz field have been reported in scanning near-fieldicroscopy applications,6 and similar effects can be ex-

ected to play a role in the coupling of THz radiation intohe metal tip. Likewise, we expect that, in contrast tohat we found in this study, the shape of the apex of theetal tip will affect the gap fields and hence will play aajor role in coupling over distances.

. CONCLUSIONSe investigated the antenna characteristics of a photo-

onductive switch equipped with a metal tip to coupleulsed THz radiation into free space. When we moved theetal tip, which was in contact with one of the metal strip

ines of the switch, along the strip line electrode the com-onents radiated from the metal tip and the PC switchould be temporally separated. This procedure also repre-ents an alternative method for sampling voltage tran-ients propagating along coplanar strip lines. The highly

ig. 10. THz pulses detected by the combination of the PCwitch and metal tip. Top trace, the detected THz waveform withhe metal tip not in contact with one of the strip lines for �=0°.he other waveforms were recorded with the metal tip in contactith one of the strip line electrodes. All curves are vertically off-

et for clarity.

irectional nature of the metal-tip radiation pattern wasuccessfully modeled by antenna theory, with the metalip treated as a classic long-wire traveling-wave antenna.ffects related to the broadband nature of the THz pulsesuch as pulse broadening and characteristic frequencyhifts were observed and could be understood in terms ofhe antenna properties of the metal tip. These effectshould play an important role in pulsed THz applications,or example in near-field microscopy, where similar metalips are commonly used. Because of their cylindricallyymmetric radial lobe structure our wire antenna showsotential as a radial THz pulse source. As demonstrated,igh coupling efficiencies from a PC switch to the wire cane achieved by direct contact of the tip to one of the elec-rodes. Finally, it has been shown that similar radiationatterns apply for a tip acting as an emitting or receivingntenna, in accordance with the reciprocity principle.

The authors acknowledge financial support from theatural Sciences and Engineering Research Council ofanada (NSERC), iCORE, and the NSERC Nano Innova-

ion Platform. We are grateful to Greg Popowich for assis-ance in the gold deposition. The coplanar strip line li-hography was performed at the University of Albertaicromachining and Nanofabrication Facility.

M. Walther’s e-mail address is mwaltherphys.ualberta.ca, and F. A. Hegmann’s is hegmannphys.ualberta.ca.

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