applied sciences

Article Beam Profile Characterisation of an Optoelectronic Silicon -Integrated PIN-PD Emitter between 100 GHz and 1 THz

Jessica Smith 1,2, Mira Naftaly 2,* , Simon Nellen 3 and Björn Globisch 3,4

1 ATI, University of Surrey, Guildford GU2 7XH, UK; [email protected] 2 National Physical Laboratory, Teddington TW11 0LW, UK 3 Fraunhofer Institute for Telecommunication, Heinrich Hertz Institute, Einsteinufer 37, 10587 Berlin, Germany; [email protected] (S.N.); [email protected] (B.G.) 4 Institute of Solid State Physics, Technical University Berlin, Hardenbergstr. 36, 10623 Berlin, Germany * Correspondence: [email protected]

Featured Application: This paper can be an important starting point for establishing beam profile measurements as an essential characterization tool for terahertz emitters.

Abstract: Knowledge of the beam profiles of terahertz emitters is required for the design of tera- hertz instruments and applications, and in particular for designing terahertz communications links. We report measurements of beam profiles of an optoelectronic silicon lens-integrated PIN-PD emitter at frequencies between 100 GHz and 1 THz and observe significant deviations from a profile. The beam profiles were found to differ between the H-plane and the E-plane, and to vary strongly with the emitted frequency. Skewed profiles and irregular side-lobes were observed. Metrological aspects of beam profile measurements are discussed and addressed.

 Keywords: terahertz; emitters; beam profile 

Citation: Smith, J.; Naftaly, M.; Nellen, S.; Globisch, B. Beam Profile Characterisation of an Optoelectronic 1. Introduction Silicon Lens-Integrated PIN-PD In recent years, continuous-wave (CW) Terahertz (THz) radiation has become a promis- Emitter between 100 GHz and 1 THz. ing candidate for short range communication links bridging between fibre-optical networks Appl. Sci. 2021, 11, 465. and wireless transmission, the so-called “THz bridge”. Besides this latest field of applica- https://doi.org/10.3390/ tions, THz technology is employed in a wide range of applications such as: [1], app11020465 bio-medical imaging [2,3], reflection imaging [4], security [5,6], non-destructive testing [7], non-contact imaging for art and archaeological conservation [8,9], and wireless communica- Received: 24 December 2020 Accepted: 30 December 2020 tion links [10,11]. CW THz spectroscopy with photomixing emitters and receivers enables Published: 6 January 2021 compact sensor heads that cover a broad frequency range of more than 3 THz combined with high sensitivity [1,12–17]. In particular, photomixers based on indium phosphide

Publisher’s Note: MDPI stays neu- (InP) make it possible to build CW THz systems using off-the-shelf components originally tral with regard to jurisdictional clai- developed for fibre-based telecommunications [13,18,19]. The mature telecom technology ms in published maps and institutio- enables the development of compact and robust THz systems and even photonic integrated nal affiliations. circuits [14,20]. Wireless communication benefits from fibre-coupled THz transceivers since they can be integrated seamlessly into optical communication networks, because they use the same infrastructure, e.g., amplifiers or modulators [10,21,22]. High-speed photodiodes (PD), originally developed as photodetectors for optical Copyright: © 2021 by the authors. Li- communications [23,24], serve as an optoelectronic converter in THz emitters [25–31]. censee MDPI, Basel, Switzerland. To produce an optical signal modulated at the desired THz frequency fTHz, two single- This article is an open access article mode signals (f 1, f 2) are superposed. The envelope frequency of the resulting beat note distributed under the terms and con- is the difference frequency of the laser signals. As long as the PD is capable of following ditions of the Creative Commons At- that envelope frequency, a photocurrent is generated equal to f = |f − f |. For efficient tribution (CC BY) license (https:// THZ 1 2 creativecommons.org/licenses/by/ radiation into free space, a broadband antenna is attached to the diode and the diode is 4.0/). mounted onto a substrate lens [32]. In this work, a waveguide-integrated PIN photodiode

Appl. Sci. 2021, 11, 465. https://doi.org/10.3390/app11020465 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 465 2 of 12

with attached bow-tie antenna is employed, which is mounted on a hyper-hemispheric silicon lens and packaged into a fibre-pigtailed housing. A detailed description of this emitter and its THz performance can be found elsewhere [33]. While many aspects of PD devices and THz systems as a whole have been inten- sively studied, the emitter radiation pattern in the THz domain is generally assumed to be Gaussian. Since mirrors or are commonly employed in spectroscopic and sensing applications, the beam profile of THz emitters remains widely unknown. However, in THz communication links, no beam forming elements can be placed in the free space between the emitter and the receiver. For all applications, but particularly for those involving medium and long-range free-space propagation such as communications, it is important to have a good understanding of the spatial profile of the THz beam. Therefore, an investiga- tion of the beam profile is urgently required to develop transmitters, i.e., antenna structures, dedicated to THz communication links. In microwave and millimetre wave communication systems, the characterization of emitter (transmitter) beam profiles has long since been accepted as an essential tool. In this field, the techniques for antenna characterisation are extensively developed and well understood [34]. Furthermore, specialized facilities are available to perform the required measurements. None of these as yet exist for THz devices. THz radiation is often assumed to propagate as a perfect Gaussian beam, which the present study shows to be inaccurate. There is very little published literature on measurements of beam profiles of CW THz emitters, with the vast majority of beam profile data describing pulsed systems [35–38]. This is primarily due to the widespread use of pulsed THz systems for spectroscopy, where beam profile properties may give rise to errors in spectroscopic data. Moreover, pulsed THz emitters have peak powers that are 3–4 orders of magnitude higher than CW devices, facilitating beam characterisation. Of the existing literature on CW beam profiles, most are for high power laser sources with a narrow tuning range such as quantum cascade (QCLs) [39,40] and gas lasers [41]. In this study we performed detailed measurements of the beam profile of a commercial THz emitter based on a PIN photodiode at frequencies between 100 GHz and 1 THz, and for both E-plane and H-plane.

2. Materials and Methods The PIN diode emitter was fabricated at Fraunhofer HHI in Germany [33]. A diagram of the emitter antenna is shown in Figure1 with the E- and H- planes indicated. The emitter is mounted onto a hyper-hemispherical high-resistivity silicon (Si) lens with a diameter of 10 mm to reduce both [32] and coupling losses (due to Fresnel reflections) from the InP substrate to air. The beam profiles were obtained using an angular mapping method, applied in two orthogonal orientations to yield beam profiles in the E-plane and H-plane. The frequency of the emitter was tuned from 100 GHz to 1 THz. The beam profile of an emitter can be described by adopting two different approaches: (i) lateral displacement or (ii) angular displacement of the emitter with respect to the re- ceiver. For a where lateral dimensions and profile are preserved with distance from the source, lateral mapping is appropriate to describe the beam profile. For a divergent source, angular mapping is more appropriate, because angular spread and variation is preserved with distance from the source. Since the PIN diode emitter examined here is a divergent source, its beam profiles were measured using an angular mapping method. Appl. Sci. 2021, 11, x FOR PEER REVIEW 3 of 12

Appl.Appl. Sci. Sci. 20212021, ,1111, ,x 465 FOR PEER REVIEW 3 of3 of 12 12

Figure 1. (a) Photograph of the fibre‐coupled PIN‐PD emitter module. Optical fibre (blue cable) and SMB cable (black cable) for the electrical bias can be seen. (b) The H‐ and E‐plane orientations are marked on the housing of the module. (c) Schematic structure of the PIN‐PD emitter chip. The waveguide integrated PD is connected to an extended bow‐tie antenna with a bracket‐like electronic structure (inset). H‐ and E‐field orientations are highlighted.

The beam profile of an emitter can be described by adopting two different approaches: (i) lateral displacement or (ii) angular displacement of the emitter with FigureFigurerespect 1. 1. (a ()toa Photograph) Photographthe receiver. of ofthe For the fibre fibre-coupleda ‐collimatedcoupled PIN PIN-PDbeam‐PD emitter where emitter module. lateral module. Optical dimensions Optical fibre fibre (blue and (blue cable) profile cable) are andandpreserved SMB SMB cable cable with(black (black distance cable) cable) for for from the the electrical electricalthe source, bias bias canlateral can be be seen. mapping seen. (b ()b The) The is H appropriate H-‐ and and E‐ E-planeplane toorientations orientationsdescribe the areare beammarked marked profile. on on the the housingFor housing a divergent of the of the module. module. source, (c) Schematic (angularc) Schematic structuremapping structure of isthe more of PIN the‐PD PIN-PDappropriate, emitter emitter chip. because The chip. waveguideTheangular waveguide integrated spread integrated and PD variationis connected PD is connected is topreserved an extended to an with extended bow distance‐tie antenna bow-tie from with antenna the a source.bracket with‐ alikeSince bracket-like the PIN electronic structure (inset). H‐ and E‐field orientations are highlighted. electronicdiode emitter structure examined (inset). H- here and is E-field a divergent orientations source, are highlighted.its beam profiles were measured using an angular mapping method. The beam profile of an emitter can be described by adopting two different TheThe angular angular profiles profiles of bothof both orientations orientations of the of emitter the emitter were measuredwere measured using the using setup the approaches: (i) lateral displacement or (ii) angular displacement of the emitter with shownsetup inshown Figure in2 Figure. The emitter 2. The emitter was placed was placed on a rotary on a rotary stage andstage rotated and rotated with respectwith respect to respect to the receiver. ◦For a collimated◦ ◦ beam where lateral dimensions and profile are theto detectorthe detector from from−45 −45°to +45 to +45°in 0.2in 0.2°steps. steps. The The detector detector was was a Tydexa Tydex GC-1T GC‐1T Golay Golay cell cell preserved with distance from the source, lateral mapping is appropriate to describe the withwith an an 11-mm 11‐mm aperture. aperture. The The emitter emitter was was powered powered and and controlled controlled by by a a Toptica Toptica TeraScan TeraScan beam profile. For a divergent source, angular mapping is more appropriate, because system.system. The The bias bias modulation modulation frequency frequency was was set set to to 11.242 11.242 Hz, Hz, since since this this was was the the optimum optimum angular spread and variation is preserved with distance from the source. Since the PIN modulationmodulation frequency frequency to to maximise maximise the the responsivity responsivity of of the the Golay Golay detector. detector. The The output output of of diode emitter examined here is a divergent source, its beam profiles were measured using thethe detector detector was was read read by by a lock-ina lock‐in amplifier amplifier (Signal (Signal Recovery Recovery 7265 7265 DSP). DSP). an angular mapping method. The angular profiles of both orientations of the emitter were measured using the setup shown in Figure 2. The emitter was placed on a rotary stage and rotated with respect to the detector from −45° to +45° in 0.2° steps. The detector was a Tydex GC‐1T Golay cell with an 11‐mm aperture. The emitter was powered and controlled by a Toptica TeraScan system. The bias modulation frequency was set to 11.242 Hz, since this was the optimum modulation frequency to maximise the responsivity of the Golay detector. The output of the detector was read by a lock‐in amplifier (Signal Recovery 7265 DSP).

FigureFigure 2. 2.Experimental Experimental set-up set‐up for for mapping mapping angular angular beam beam profiles. profiles. The The source, source, mounted mounted on on a rotary a ◦ ◦ stage,rotary is rotatedstage, is between rotated −between45 and − 4545° withand 45° respect with to respect the detector. to the detector. The detector The isdetector placed onis placed a linear on translationa linear translation stage to allow stage variation to allow ofvariation the distance of the between distance the between emitter the and emitter detector. and detector. 3. Results

3.1. Power Measurements The power output of the emitter, shown in Figure3a, was measured for frequencies between 50 GHz and 1000 GHz using both a pyroelectric detector (Sensor- und Lasertechnik FigureTHZ 2. 10) Experimental and a Golay set cell‐up for (Tydex mapping GC-1T). angular THz beam radiation profiles. from The source, the emitter mounted was on collected a rotaryand re-focused stage, is rotated by two between parabolic −45° and mirrors, 45° with as shownrespect into the Figure detector.3b. The The pyroelectric detector is placed detector on awas linear calibrated translation by stage the to national allow variation institute of the for distance metrology between of Germany the emitter (PTB) and detector. and was used to measure the emitter power at frequencies between 50 GHz and 500 GHz. Frequencies between 200 GHz and 1000 GHz were measured using the more sensitive Golay cell, and the overlapping measurements between 200 GHz and 500 GHz were used to calibrate the Golay cell responsivity. Measurements were taken in 10 GHz steps. Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 of 12

3. Results 3.1. Power Measurements The power output of the emitter, shown in Figure 3a, was measured for frequencies between 50 GHz and 1000 GHz using both a pyroelectric detector (Sensor‐ und Lasertechnik THZ 10) and a Golay cell (Tydex GC‐1T). THz radiation from the emitter was collected and re‐focused by two parabolic mirrors, as shown in Figure 3b. The pyroelectric detector was calibrated by the national institute for metrology of Germany (PTB) and was used to measure the emitter power at frequencies between 50 GHz and 500 GHz. Frequencies between 200 GHz and 1000 GHz were measured using the more sensitive Golay cell, and the overlapping measurements between 200 GHz and 500 GHz Appl. Sci. 2021, 11, 465 4 of 12 were used to calibrate the Golay cell responsivity. Measurements were taken in 10 GHz steps.

FigureFigure 3. 3.( a(a)) Power Power output output of of the the PIN PIN diode diode as as a a function function of of frequency. frequency. Power Power was was measured measured with with a calibrateda calibrated pyroelectric pyroelectric detector detector for for frequencies frequencies below below 500 500 GHz GHz and and with with a Golay a Golay cell cell for 200for 200 GHz GHz to 1000to 1000 GHz. GHz. (b) ( Opticalb) Optical setup setup for powerfor power measurement. measurement.

3.2.3.2. Beam Beam Profiles Profiles AngularAngular beam beam profile profile measurements measurements for for both both orientations orientations of of the the PIN PIN diode diode emitter emitter werewere performed performed with with the the Golay Golay cell cell for for a frequency a frequency range range of 100 of GHz100 GHz to 1000 to GHz1000 atGHz 50 GHz at 50 intervals.GHz intervals. The resulting The resulting profiles areprofiles shown are in Figureshown4a,b. in AllFigure profiles 4a,b. were All normalised profiles were to allownormalised for ease to of allow comparison, for ease since of comparison, the power ratiosince between the power the ratio low andbetween high frequenciesthe low and ishigh over frequencies two orders is of over magnitude two orders (see of Figure magnitude3). (see Figure 3). TheThe H-plane H‐plane profiles profiles in in Figure Figure4 a,4a, while while not not perfectly perfectly Gaussian, Gaussian, show show a a single single peak peak ◦ centredcentred around around 0 0°for for frequencies frequencies below below 400 400 GHz. GHz. Between Between 400 400 GHz GHz and and 600 GHz,600 GHz, the sin- the glesingle peak peak becomes becomes significantly significantly broader broader and shows and significant shows significant small features small throughout features thethroughout profile. Above the profile. 600 GHz, Above the centre600 GHz, of the the peak centre skews of tothe the peak negative skews angles. to the negative angles.In Figure 4b, the E-plane profiles for frequencies below 250 GHz also show a peak ◦ centredIn atFigure 0 ; however, 4b, the E unlike‐plane theprofiles H-plane for frequencies profiles, there below are 250 also GHz significant also show side a lobes peak eithercentred side at of0°; the however, centre. unlike Above the 300 H GHz,‐plane these profiles, side lobesthere disappear,are also significant but the main side peaklobes becomeseither side heavily of the skewed centre. to Above the positive 300 GHz, angles these and side highly lobes asymmetrical. disappear, but the main peak becomesWhile heavily the bow-tie skewed antenna to the itself positive is symmetric, angles and the highly feeding asymmetrical. lines and the InP substrate are not.While When the the bow ‐tie antenna is itself of a similar is symmetric, order as the the feeding dimensions lines and of the the feeding InP substrate point structuresare not. When or the the substrate, wavelength those is structures of a similar start order to radiate as the or dimensions cause refraction. of the The feeding influence point ofstructures the feeding or pointthe substrate, geometry those on the structures beam profile start is studiedto radiate in a or separate cause publication.refraction. The influence of the feeding point geometry on the beam profile is studied in a separate publication. Appl. Sci. 2021, 11, 465 5 of 12 Appl. Sci. 2021, 11, x FOR PEER REVIEW 5 of 12

Figure 4. NormalizedNormalized angular angular beam beam profiles profiles of of the the PIN PIN diode diode emitter emitter for for frequencies frequencies between between 100 100 GHz GHz and and 1 THz 1 THz at 50 at 50GHz GHz intervals, intervals, measured measured at ata distance a distance of of 60 60 mm mm from from the the emitter emitter for: for: (a ()a )H H-plane‐plane orientation orientation and and ( (bb)) E E-plane‐plane orientation. orientation. All profilesprofiles areare normalisednormalised forfor easeease ofof comparison.comparison.

3.3. Experimental Considerations 3.3.1. Near Field vs. Far Far Field The electromagnetic electromagnetic field field of of an an antenna antenna is iscommonly commonly described described as evolving as evolving from from the nearthe near field field region, region, where where the theangular angular distribution distribution of the of thefield field varies varies with with distance distance from from the antenna,the antenna, to the to thefar farfield field region, region, where where the the angular angular distribution distribution is is distance distance-independent.‐independent. The near-field region may be further divided into the reactive and radiative regions. The re- The near‐field region may be further divided into the reactive and radiative regions. The active near field region decays rapidly with distance from the antenna, and becomes reactive near field region decays rapidly with distance from the antenna, and becomes negligible compared with the radiative component within one wavelength distance from negligible compared with the radiative component within one wavelength distance from Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 12 Appl. Sci. 2021, 11, 465 6 of 12

the antenna. Within the radiative near field region, the distances from an observation the antenna. Within the radiative near field region, the distances from an observation point point to two arbitrary antenna elements will generally be different, so that the relative to two arbitrary antenna elements will generally be different, so that the relative phase phase and amplitude of their contributions to the field will be different. As the observation and amplitude of their contributions to the field will be different. As the observation point point moves further away from the antenna, the relative differences in distances between moves further away from the antenna, the relative differences in distances between an- antenna elements to the observation point will decrease, and so the contributions of tenna elements to the observation point will decrease, and so the contributions of separate separate antenna elements will become more equal. Hence, in the far field, the antenna antenna elements will become more equal. Hence, in the far field, the antenna appears appears as a point source, and the angular distribution of the emitted field becomes as a point source, and the angular distribution of the emitted field becomes independent independentof the distance of the from distance the antenna. from the Therefore, antenna. itTherefore, is necessary it is to necessary ensure that to antennaensure that beam antennaprofiles beam are measuredprofiles are in measured the far field. in the far field. TheThe commonly commonly used used criterion criterion for for the the distance distance from from the the antenna antenna at which at which its itsradiation radiation is considered to be far‐field, Lfar, may be calculated from [42]: is considered to be far-field, Lfar, may be calculated from [42]: For 𝐷 , 𝐿 2𝜆 , λ 2c (1) For D < , L f ar > 2λ = , (1) 2 f For 𝐷 , 𝐿 , (2) λ 2D2 2D2 f where D is the emitter apertureFor D and> λ, Lis the> radiation= wavelength., Equation (2) is (2) 2 f ar λ c sometimes referred to as the Fraunhofer distance. This is defined as the distance between a radiatingwhere D ispoint the emitter source aperture and a receiving and λ is theantenna radiation of aperture wavelength. D such Equation that the (2) isspherical sometimes wavefrontreferred of to asthe the source Fraunhofer varies distance.by no more This than is defined π/8 radians as the distance over the between entire aantenna radiating aperture.point source These andlimits a receiving for the far antenna field ofdistance aperture areD somewhatsuch that the arbitrary, spherical and wavefront so it is of π preferablethe source to variesmeasure by no the more beam than profiles/8 radians at a distance over the entiregreater antenna than that aperture. suggested These limitsby Equationsfor the far (1) field and distance(2). Figure are 5 somewhat shows this arbitrary, distance and for sofrequencies it is preferable between to measure 100 GHz the and beam 1 THzprofiles for radiation at a distance travelling greater through than that both suggested air and by silicon, Equations as calculated (1) and (2). from Figure Equation5 shows this distance for frequencies between 100 GHz and 1 THz for radiation travelling through (2). both air and silicon, as calculated from Equation (2). In the case of the PIN diode THz emitter, the aperture is the size of the bow‐tie In the case of the PIN diode THz emitter, the aperture is the size of the bow-tie antenna, antenna, which is 1 mm. The emitter is mounted on a hyper‐hemispherical Si lens having which is 1 mm. The emitter is mounted on a hyper-hemispherical Si lens having a diameter a diameter of 10 mm. The overall combined thickness of the silicon lens and InP chip is of 10 mm. The overall combined thickness of the silicon lens and InP chip is approximately approximately 6.5 mm [32]. As the wavelength of the radiation is shorter in silicon (λSi = 6.5 mm [32]. As the wavelength of the radiation is shorter in silicon (λSi = λ0/nSi where λ0/nSi where nSi = 3.42 is the of silicon), the far field distance in silicon is n = 3.42 is the refractive index of silicon), the far field distance in silicon is longer. It can longer.Si It can be seen from Figure 5 that at frequencies above 300 GHz, the near‐field be seen from Figure5 that at frequencies above 300 GHz, the near-field region extends region extends beyond the silicon lens boundary. Figure 4a,b shows peak broadening and beyond the silicon lens boundary. Figure4a,b shows peak broadening and an increase in an increase in small features in both the E‐ and H‐ plane profiles beginning at 300 GHz to small features in both the E- and H- plane profiles beginning at 300 GHz to 400 GHz and 400 GHz and continuing up to 1 THz. This could indicate that the near‐field extending continuing up to 1 THz. This could indicate that the near-field extending beyond the lens beyondhas a the significant lens has effect a significant on the profile. effect As on stated the profile. previously, As stated all profile previously, measurements all profile shown measurementsin this paper shown were recorded in this paper at a distance were recorded of 60 mm at from a distance the antenna; of 60 thus, mm they from are the well antenna;within thus, the far they field are region well within for all the frequencies far field measured.region for all frequencies measured.

25 in air in Si 20

15

10 Si lens boundary

Far field distance (mm) distance Far field 5

0 200 400 600 800 1000 Frequency (GHz)

Figure 5. Figure 5. TheThe far farfield field distance, distance, as asgiven given by by Equation Equation (2), (2), for for frequencies frequencies between between 100 100 GHz GHz and and 1 1 THz THzfor for radiation radiation travelling travelling through through air air and and silicon. silicon. Appl. Sci. 2021, 11, x FOR PEER REVIEW 7 of 12

Appl. Sci. 2021, 11, 465 7 of 12

3.3.2. Dependence of Beam Profile on Distance from Detector The validity of the angular profile measurements in this study is based on the 3.3.2. Dependence of Beam Profile on Distance from Detector assumption that the emitter produces a divergent beam, such that the angular profiles are distanceThe invariant. validity In of order the angular to verify profile this measurements assumption, angular in this study profiles is based at 600 on GHz the assump-were recordedtion that at the different emitter producesdistances a from divergent the beam,emitter such for that both the emitter angular orientations. profiles are distance The frequencyinvariant. of In600 order GHz to was verify chosen this for assumption, this test and angular those profiles in the following at 600 GHz sections were recorded because at at 600different GHz distancesthere is a fromsingle the peak emitter in both for E both‐plane emitter and orientations.H‐plane, and The there frequency is sufficient of 600 THz GHz powerwas chosento provide for this good test SNR and (signal those in‐to the‐noise following ratio). sectionsThe profiles because shown at 600 in GHzFigure there 6a,b is a confirmsingle good peak inconsistency, both E-plane apart and from H-plane, minor and variations there is sufficient in the width THz power and height. to provide These good smallSNR features (signal-to-noise can be explained ratio). The by the profiles differences shown in in angular Figure 6resolutiona,b confirm caused good by consistency, varying theapart distance from between minor variations the emitter in and the width detector. and The height. angular These resolution small features will be can discussed be explained in detailby the in the differences next section. in angular resolution caused by varying the distance between the emitter and detector. The angular resolution will be discussed in detail in the next section.

b 1.0 a 1.0 1.5 cm 2 cm 1.5 cm 0.8 2.5 cm 2 cm 3 cm 0.8 2.5 cm 3.5 cm 3 cm 3.5 cm 0.6 4 cm 0.6 4 cm 4.5 cm 4.5 cm 5 cm 5 cm 0.4 5.5 cm 0.4 5.5 cm Normalised Power

Normalised Power Normalised 0.2 0.2

0.0 0.0 -45 -30 -15 0 15 30 45 -45 -30 -15 0 15 30 45 Angle (deg) Angle (deg)

Figure 6. Beam profiles measured at varying distance between the emitter and the detector, at 600 GHz for: (a) E-plane Figure 6. Beam profiles measured at varying distance between the emitter and the detector, at 600 GHz for: (a) E‐plane orientation and (b) H-plane orientation. orientation and (b) H‐plane orientation. 3.3.3. Angular Resolution 3.3.3. Angular Resolution The step size of the rotary stage used in these measurements was 0.2◦. However, as seenThe in step Figure size2, theof the angular rotary resolution stage usedθ resin ofthese the measurements waswas limited 0.2°. However, by the diame- as seenter in of theFigure detector 2, the aperture angular and resolution the distance θres between of the measurements the emitter and was detector. limited The by aperture the diameterof the Golayof the detector aperture was 11 mm and and the distance its distance between from the emitter and was detector. 60 mm. The Using aperturethese values, of the Golay the acceptance detector anglewas 11 of mm the detectorand its distance is calculated from tothe be emitter 10.4◦. Towas confirm 60 mm. this Usingestimate, these additionalvalues, the measurements acceptance angle were of made the detector at distances is calculated of 35 mm to and be 70 10.4°. mm To from confirmthe emitter, this estimate, where theadditional data at measurements 35 mm should were have made an acceptance at distances angle of 35 approximately mm and 70 mmdouble from thatthe atemitter, 70 mm. where An extrapolation the data at procedure 35 mm should was then have applied an acceptance to the 70 mm angle data approximatelyto obtain an estimateddouble that profile at 70 mm. for 35 An mm, extrapolation which allows procedure to compare was it then with applied the experimen- to the 70 talmm data data measured to obtain an at 35estimated mm distance. profile for The 35 results mm, which of this allows test at to 600 compare GHz are it with shown the in experimentalFigure7a,b datafor both measured orientations. at 35 mm Both distance. extrapolated The profilesresults agreeof this quite test wellat 600 with GHz the are mea- shownsured in data. Figure Small 7a,b differences for both orientations. in the profiles Both may extrapolated be attributed profiles to the aperture agree quite of the well Golay withbeing the circular,measured whereas data. Small a square differences aperture in was the assumedprofiles may in order be attributed to simplify to the aperture calculation. of the GolaySimulations being circular, of the effect whereas of angular a square resolution aperture on was the observed assumed beam in order profile to simplify are shown thein calculation. Figure8a–f. A variety of model beam profiles were generated with a resolution of 0.2 ◦, includingSimulations a single of the Gaussian, effect of a angular skewed Gaussian,resolution andon the Gaussians observed with beam additional profile are lobes. shownThese in profiles Figure 8a–f. were A then variety extrapolated of model beam to show profiles their were appearance generated with with a coarser a resolution angular of resolution.0.2°, including The a following single Gaussian, can be concluded a skewed from Gaussian, these simulations:and Gaussians with additional lobes. These profiles were then extrapolated to show their appearance with a coarser 1. In the case of a single central peak (FWHM > θres), whether a perfect (Figure8a) or a angular resolution.skewed (Figure The following8b) Gaussian, can be coarser concluded resolution from willthese cause simulations: negligible distortion or 1. In thenone, case even of a single when resolutioncentral peakθres (FWHMis reduced > θres by), awhether factor of a 10.perfect (Figure 8a) or a 2. skewedWhen (Figure narrow 8b) features Gaussian, are addedcoarser to resolution the curve (Figurewill cause8c–f), negligible then angular distortion resolutions or none,greater even when than the resolution width of θ theres is feature reduced (FWHM by a factor < θres )of cause 10. broadening and flattening of the feature. Appl.Appl. Sci. Sci. 2021 2021, ,11 11, ,x x FOR FOR PEER PEER REVIEW REVIEW 88 ofof 1212

2.2. WhenWhen narrow narrow features features are are added added to to the the curve curve (Figure (Figure 8c–f), 8c–f), then then angular angular resolutions resolutions Appl. Sci. 2021, 11, 465 8 of 12 greatergreater than than the the width width of of the the feature feature (FWHM (FWHM < < θ θresres)) cause cause broadening broadening and and flattening flattening ofof the the feature. feature.

Figure 7. Comparison of the profile at 600 GHz measured at 35 mm from the emitter with an acceptance angle of 17.9◦ FigureFigure 7 7. .Comparison Comparison of of the the profile profile at at 600 600 GHz GHz measured measured at at 35 35 mm mm from from the the emitter emitter with with an an acceptance acceptance angle angle of of 17.9° 17.9° with the profile extrapolated from a measurement at 70 mm from the emitter with an acceptance angle of 9.0◦:(a) E-plane withwith the the profile profile extrapolated extrapolated from from a a measurement measurement at at 70 70 mm mm from from the the emitter emitter with with an an acceptance acceptance angle angle of of 9.0°: 9.0°: ( a(a) )E E‐plane‐plane orientationorientationorientation andand and (( bb(b)) ) H-planeH H‐plane‐plane orientation.orientation. orientation.

FigureFigureFigure 8.8 8. .SimulationsSimulations Simulations ofof of modelmodel model beambeam beam profilesprofiles profiles asas as theythey they wouldwould would appearappear appear atat at variousvarious various acceptanceacceptance acceptance angles,angles, angles, revealingrevealing revealing thethe the effectseffects effects ofof of angularangularangular resolution. resolution.resolution. The The initialinitial profile profileprofile has hashas 0.2 0.2°0.2°◦ resolution. resolution.resolution. (a(a) ) single single Gaussian, Gaussian, ( (b(b)) ) skewed skewedskewed Gaussian, Gaussian,Gaussian, ( (cc()c) ) Gaussian GaussianGaussian with withwith shoulders,shoulders,shoulders, (( dd(d––f–f)f) ) GaussianGaussian Gaussian withwith with additionaladditional additional 33° ◦3° widewide wide featurefeature feature ofof of differingdiffering differing amplitudesamplitudes amplitudes and and and separation. separation. separation.

3.3.4. Standing Waves 3.3.4. Standing Waves Standing waves are an important consideration in measurements of beam profiles, Standing waves are an importantimportant consideration in measurements of beam profiles,profiles, because they may cause errors and artefacts in the data. Standing waves are formed because they maymay causecause errorserrors andand artefactsartefacts inin thethe data.data. StandingStanding waveswaves areare formedformed betweenbetween the thethe emitter emitteremitter and andand detector detectordetector when whenwhen their their surfacestheir surfacessurfaces act as aactact resonator, asas aa resonator,resonator, supporting supportingsupporting multiple reflections.multiplemultiple reflections.reflections. The presence TheThe presence ofpresence standing ofof standing wavesstanding causes waveswaves significant causes causes significantsignificant variations variationsvariations in the detected inin thethe signaldetecteddetected arising signalsignal from arisingarising wavelength-scale fromfrom wavelengthwavelength changes‐‐scalescale in changes thechanges relative inin thethe distance relativerelative between distancedistance the betweenbetween emitter andthethe emitter detector.emitter andand In detector.detector. order to In understandIn orderorder toto understandunderstand the effect of thethe standing effecteffect ofof waves, standingstanding the waves,waves, beam profile thethe beambeam at 600profileprofile GHz atat was 600600 mapped GHzGHz waswas for mappedmapped both orientations forfor bothboth orientationsorientations over the distance overover thethe equal distancedistance to half-wavelength equalequal toto halfhalf‐‐ (0.25 mm). The results are shown in Figure9a,b below. It is seen that standing waves have a negligible effect on the observed beam profile. Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 12

Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 12

wavelength (0.25 mm). The results are shown in Figure 9a,b below. It is seen that standing Appl. Sci. 2021, 11, 465wavelengthwaves (0.25 havemm). a The negligible results areeffect shown on the in observedFigure 9a,b beam below. profile. It is seen that standing 9 of 12 waves have a negligible effect on the observed beam profile.

Figure 9. Comparison of beam profiles at 600 GHz measured at various positions on a standing Figure 9. ComparisonFigure 9. ofComparison beamwave. profiles (a) E of‐plane beam at 600 orientation profiles GHz measured at where 600 GHz at 35.6 various measured mm positionsand at35.9 various mm on a are standing positions at the wave. wave on a (maximum.standinga) E-plane orientation (b) H‐plane where 35.6 mmwave. and (a 35.9) E‐orientationplane mm areorientation at where the wave where35.5 maximum. mm 35.6 and mm 35.75 and (b) mm H-plane35.9 are mm at orientationare the at wave the wave maximum. where maximum. 35.5 mm (b) and H‐ 35.75plane mm are at the wave maximum.orientation where 35.5 mm and 35.75 mm are at the wave maximum. 3.3.5. Repeatability of Measurements 3.3.5. Repeatability3.3.5.The Repeatabilityoffinal Measurements experimental of Measurements issue to be considered is measurement repeatability. Figure The final10 shows experimentalThe the final mean experimental issue and tostandard be considered issue deviation to be is considered measurementof five scans is measurement of repeatability. the emitter repeatability. at Figure 600 GHz Figure in the 10 10 shows theH‐plane. showsmean theItand is mean seenstandard andthat standard thedeviation noise deviation in of the five data scans of fiveis negligible,of scans the emitter of the and emitter at the 600 error at GHz 600 bars GHzin the are in thetoo H-planesmall . H‐plane. Itto is be Itseen isdistinguishable seen that thatthe noise the noisein in the the inplot. data the is data negligible, is negligible, and the and error the bars error are bars too are small too small to be to be distinguishabledistinguishable in the plot. in the plot.

25 25 20 20 15 15 10 Power (a.u.) 10 Power (a.u.) 5 5 0 -45 -30 -15 0 15 30 45 0 -45 -30 -15 0Angle 15 (deg) 30 45 Angle (deg) Figure 10. The mean and standard deviation of 5 beam profile scans at 600 GHz in the H-plane Figure 10. The mean and standard deviation of 5 beam profile scans at 600 GHz in the H‐plane orientation. The error bars are shown in pink. Figure 10. Theorientation. mean and The standard error bars deviation are shown of 5 beamin pink. profile scans at 600 GHz in the H‐plane orientation. The4. error Discussion bars are shown in pink. 4. Discussion The observed deviations in the beam profiles from a Gaussian beam may come from 4. Discussion theThe coupling observed of deviations the THz antenna in the beam and the profiles Si lens from [43 –a45 Gaussian]. It has beam been previouslymay come from shown The observedthethat coupling small deviations of differences the THzin the antenna inbeam the profiles positionand the from Si of lens the a Gaussian[43–45]. lens with It beam has respect been may previously to come the antennafrom shown can that have the couplingsmall ofsignificant the differences THz antenna effects in the on and position the the profiles Si of lens the of [43–45]. lens the emitted with It hasrespect radiation been to previously the [43 antenna,44]. However,shown can have that the significant antenna is small differenceseffectspositioned inon the the position atprofiles the centre ofof thethe of lensemitted the with lens radiation with respect an automatedto [43,44]. the antenna However, pick can and have the place antenna significant tool and is positioned the deviation effects on theat the fromprofiles centre the of central of the the emitted lens position with radiation isan smaller automated [43,44]. than pickHowever, 20 µ m.and Hence, place the antenna tool the effectand is the positioned of deviation incorrect positioningfrom the at the centrecentral ofof the the position lens chip with on is thesmalleran automated lens than should 20 pick μ bem. ofand Hence, minor place the importance. tool effect and of the incorrect deviation In addition, positioning from numerical the of the models chip central positionon ofthe theis lenssmaller beam should profiles,than be 20 μof whichm. minor Hence, will importance. the be discussedeffect ofIn incorrect addition, in detail positioning numerical elsewhere, ofmodels show the chip that of the the beam emitted on the lens shouldbeam profilebe of minor is expected importance. to have In a addition, circular symmetry numerical when models the of lens the is beam perfectly centred on the emitter. However, when a small off-axis displacement (<100 µm) is present in the alignment of the lens with the centre of the emitter, both the main peak and side lobes can become asymmetrical and the main peak may become skewed. Filipovic et al. [45] showed Appl. Sci. 2021, 11, 465 10 of 12

that such a displacement can cause the peak of the radiation profile to be shifted from the centre by >10◦. This type of behaviour is particularly apparent in the high frequency profiles in both orientations, as seen in Figure4. Internal reflections and refractions in the lens can give rise to side lobes in the beam. Although the dimensions of the silicon lens, especially the height of the hyper-hemisphere, are designed for minimal internal reflections, fabrication tolerances, which are as high as ± 50 µm, may influence the observed beam profile. Furthermore, the features in the beam profile differ significantly between the E-plane and the H-plane, with the E-plane having more regular profiles. At lower frequencies, the features appear more pronounced. This effect is attributed to the design of the antenna structure and the feeding point geometry, which connects the diode with the bowtie antenna (see Figure1c). The influence of the feeding point and the antenna geometry on the beam profile of PIN diode emitters is currently under further investigation.

5. Conclusions The angular beam profiles of a THz emitter based on a PIN photodiode with attached bow-tie antenna were measured in both the E-plane and H-plane orientations at frequencies between 100 GHz and 1 THz using a Golay cell power detector. Beam profiles were recorded in the far-field of the antenna, and were found to be distance-invariant. The effects of angular resolution were examined, and it was concluded that the employed setup is capable of resolving features within 10◦ angular width. For frequencies above 600 GHz, the beam profiles in the H-plane orientation were found to be significantly asymmetrical and skewed away from the centre. This may be attributed to a slight misalignment between the antenna and the centre of the lens. Moreover, the small feeding point structure that connects the photodiode and the antenna might act as a contributing radiating element and thus distort the beam profile when the wavelength becomes sufficiently small. At frequencies below 250 GHz, side lobes in the beam profiles were observed in the E-plane, and these may be attributed to internal reflections within the silicon lens. Although some of the lower frequency profiles consist of a single peak centred around 0◦, none of the measured profiles are perfectly Gaussian. This indicates the importance of acquiring accurate measurements of the radiation profiles of such emitters before consider- ing them for use in free-space transmission systems such as those used for communications. Accurate profiles will allow for better link budget estimations in communication links. Moreover, reliable methods for beam profile measurements are essential for efficient com- ponent design. It is also important to consider the beam profile in designing optics for spectroscopy systems in order to ensure artefact-free measurements with maximum sensi- tivity. In addition, accurate beam profile measurements are essential for the development of broadband terahertz emitters. Hence, this paper can be an important starting point for establishing beam profile measurements as a characterization tool for terahertz emitters.

Author Contributions: Conceptualization, J.S. and M.N.; methodology, J.S., M.N., and S.N.; formal analysis, J.S. and M.N.; investigation, J.S. and M.N.; writing—original draft preparation, J.S. and S.N.; writing—review and editing, M.N., S.N., and B.G.; visualization, J.S. and M.N. All authors have read and agreed to the published version of the manuscript. Funding: The work of J. Smith was funded by the iCASE programme of the Engineering and Physical Sciences Research Council (EPSRC), UK. The work of M. Naftaly was funded by the Horizon 2020 project “TERAPOD”, under grant agreement No. 761579. The work of S. Nellen and B. Globisch were funded by the Horizon 2020 project “TERAWAY” under grant agreement No. 871668. Data Availability Statement: Data is contained within the article. Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results. Appl. Sci. 2021, 11, 465 11 of 12

References 1. Preu, S.; Döhler, G.H.; Malzer, S.; Wang, L.J.; Gossard, A.C. Tunable, continuous-wave Terahertz photomixer sources and applications. J. Appl. Phys. 2011, 109, 061301. [CrossRef] 2. Wei, L.; Yu, L.; Jiaoqi, H.; GuoRong, H.; Zhang, Y.; Fu, W. Application of terahertz spectroscopy in biomolecule detection. Front. Lab. Med. 2018, 2, 127–133. [CrossRef] 3. Yang, X.; Zhao, X.; Yang, K.; Liu, Y.; Liu, Y.; Fu, W.; Luo, Y. Biomedical Applications of Terahertz Spectroscopy and Imaging. Trends Biotechnol. 2016, 34, 810–824. [CrossRef][PubMed] 4. Zimdars, D.; White, J.S. Terahertz reflection imaging for package and personnel inspection. Def. Secur. 2004, 5411, 78–83. [CrossRef] 5. Tsydynzhapov, G.E.; Gusikhin, P.A.; Muravev, V.M.; Andreev, I.V.; Kukushkin, I.V. New terahertz security body scanner. In Proceedings of the 2018 43rd International Conference on , Millimeter, and Terahertz Waves (IRMMW-THz), Nagoya, Japan, 9–14 September 2018; p. 1. [CrossRef] 6. Trontelj, J.; Sešek, A. Electronic terahertz imaging for security applications. In Proceedings of the SPIE 9747, Terahertz, RF, Millimeter, and Submillimeter-Wave Technology and Applications IX, San Francisco, CA, USA, 13–18 February 2016; p. 974713. [CrossRef] 7. Zhong, S. Progress in terahertz nondestructive testing: A review. Front. Mech. Eng. 2019, 14, 273–281. [CrossRef] 8. Cosentino, A. Terahertz and Cultural Heritage Science: Examination of Art and Archaeology. Technology 2016, 4, 6. [CrossRef] 9. Stuebling, E.-M.; Staats, N.-A.; Globisch, B.; Schell, M.; Portsteffen, H.D.; Koch, M. Investigating the layer structure and insect tunneling on a wooden putto using robotic-based THz . IEEE Trans. Terahertz Sci. Technologies 2020, 10, 1. [CrossRef] 10. Castro, C.; Nellen, S.; Elschner, R.; Sackey, I.; Emmerich, R.; Merkle, T.; Globisch, B.; De Felipe, D.; Schubert, C. 32 GBd 16QAM Wireless Transmission in the 300 GHz Band Using a PIN Diode for THz Upconversion. OFC 2019, M4F.5.[CrossRef] 11. Ali, M.; Guzmán, R.C.; Cojocari, O.; Nellen, S.; Santamaría, G.; García-Muñoz, L.E.; Segovia-Vargas, D.; Globisch, B.; Carpintero, G. Quasi-Optic Transmitter and Receiver Modules Enabling Next-Generation Ultra-Broadband Wireless Links at Carrier-Wave Frequencies Ranging from 60 to 180 GHz. J. Infrared Millim. Terahertz Waves 2019, 40, 688–695. [CrossRef] 12. Globisch, B.; Kohlhaas, R.B.; Liebermeister, L.; Schell, M.; Nellen, S. Recent progress of continuous-wave terahertz systems for spectroscopy, non-destructive testing, and telecommunication. In Proceedings of the Terahertz, RF, Millimeter, and Submillimeter- Wave Technology and Applications XI, San Francisco, CA, USA, 27 January–1 February 2018; Volume 10531, p. 105310C. [CrossRef] 13. Liebermeister, L.; Nellen, S.; Kohlhaas, R.; Breuer, S.; Schell, M.; Globisch, B. Ultra-fast, High-Bandwidth Coherent cw THz Spectrometer for Non-destructive Testing. J. Infrared Millim. Terahertz Waves 2019, 40, 288–296. [CrossRef] 14. Göbel, T.; Stanze, D.; Globisch, B.; Dietz, R.J.B.; Roehle, H.; Schell, M. Telecom technology based terahertz photomixing system with 105 decibel signal-to-noise ratio and 35 terahertz bandwidth. Opt. Lett. 2013, 38, 4197–4199. [CrossRef] [PubMed] 15. Nellen, S.; Globisch, B.; O’Gorman, J.; Anthur, A.; Vujicic, V.; Barry, L.P.; Schell, M. Fiber-coupled, photoconductive receiver for heterodyne detection up to 1 THz stabilized by an optical frequency comb. In Proceedings of the International Conference on Infrared, Millimeter, and Terahertz Waves, IRMMW-THz, Cancun, Mexico, 27 August–1 September 2017. [CrossRef] 16. Olvera, A.F.; Lu, H.; Gossard, A.C.; Preu, S. Continuous-wave 1550 nm operated terahertz system using ErAs:In(Al)GaAs photo-conductors with 52 dB dynamic range at 1 THz. Opt. Express 2017, 25, 29492–29500. [CrossRef] 17. Deninger, A.; Roggenbuck, A.; Schindler, S.; Preu, S. 2.75 THz tuning with a triple-DFB laser system at 1550 nm and InGaAs photomixers. J. Infrared Millim. Terahertz Waves 2014, 36, 269–277. [CrossRef] 18. Stanze, D.; Deninger, A.; Roggenbuck, A.; Schindler, S.; Schlak, M.; Sartorius, B. Compact cw Terahertz Spectrometer Pumped at 1.5 µm Wavelength. J. Infrared Millim. Terahertz Waves 2010, 32, 225–232. [CrossRef] 19. Stanze, D.; Göbel, T.; Dietz, R.; Sartorius, B.; Schell, M. High-speed coherent CW terahertz spectrometer. Electron. Lett. 2011, 47, 1292–1294. [CrossRef] 20. Theurer, M.A.D.; Göbel, T.; Stanze, D.; Troppenz, U.; Soares, F.; Grote, N.; Schell, M. Photonic-integrated circuit for continuous- wave THz generation. Opt. Lett. 2013, 38, 3724–3726. [CrossRef] 21. Koenig, S.C.; Lopezdiaz, D.; Antes, J.; Boes, F.; Henneberger, R.; Leuther, A.; Tessmann, A.; Schmogrow, R.; Hillerkuss, D.; A Palmer, R.; et al. Wireless sub-THz communication system with high data rate. Nat. Photon. 2013, 7, 977–981. [CrossRef] 22. Nagatsuma, T.; Ducournau, G.; Renaud, C.C. Advances in terahertz communications accelerated by photonics. Nat. Photon. 2016, 10, 371–379. [CrossRef] 23. Ishibashi, T.; Shimizu, N.; Kodama, S.; Ito, H.; Nagatsuma, T.; Furuta, T. Uni-Traveling-Carrier Photodiodes. In Ultrafast Electronics and Optoelectronics; The Optical Society: Washington, DC, USA, 1997; p. UC3. 24. Bach, H.-G.; Umbach, A.; Van Waasen, S.; Bertenburg, R.; Unterborsch, G. Ultrafast monolithically integrated InP-based photoreceiver: OEIC-design, fabrication, and system application. IEEE J. Sel. Top. Quantum Electron. 1996, 2, 418–424. [CrossRef] 25. Stanze, D.; Bach, H.-G.; Kunkel, R.; Schmidt, D.; Roehle, H.; Schlak, M.; Schell, M.; Sartorius, B. Coherent CW terahertz systems employing photodiode emitters. In Proceedings of the International Conference on Infrared, Millimeter, and Terahertz Waves, Busan, Korea, 21–25 September 2009. [CrossRef] 26. Ishibashi, T.; Muramoto, Y.; Yoshimatsu, T.; Ito, H. Unitraveling-Carrier Photodiodes for Terahertz Applications. IEEE J. Sel. Top. Quantum Electron. 2014, 20, 79–88. [CrossRef] Appl. Sci. 2021, 11, 465 12 of 12

27. Nakajima, F.; Furuta, T.; Ito, H. High-power continuous-terahertz-wave generation using resonant-antenna-integrated uni- travelling-carrier photodiode. Electron. Lett. 2004, 40, 1297. [CrossRef] 28. Renaud, C.C.; Natrella, M.; Graham, C.; Seddon, J.; Van Dijk, F.; Seeds, A.J. Antenna Integrated THz Uni-Traveling Carrier Photodiodes. IEEE J. Sel. Top. Quantum Electron. 2018, 24, 1–11. [CrossRef] 29. Hisatake, S.; Kim, J.-Y.; Ajito, K.; Nagatsuma, T. Self-Heterodyne Spectrometer Using Uni-Traveling-Carrier Photodiodes for Terahertz-Wave Generators and Optoelectronic Mixers. J. . Technol. 2014, 32, 3683–3689. [CrossRef] 30. Rouvalis, E.; Fice, M.J.; Renaud, C.C.; Seeds, A.J. Optoelectronic detection of millimetre-wave signals with travelling-wave uni-travelling carrier photodiodes. Opt. Express 2011, 19, 2079–2084. [CrossRef][PubMed] 31. Rouvalis, E.; Renaud, C.C.; Moodie, D.G.; Robertson, M.J.; Seeds, A.J. Continuous Wave Terahertz Generation From Ultra-Fast InP-Based Photodiodes. IEEE Trans. Microw. Theory Tech. 2012, 60, 509–517. [CrossRef] 32. Van Rudd, J.; Mittleman, D.M. Influence of substrate-lens design in terahertz time-domain spectroscopy. J. Opt. Soc. Am. B 2002, 19, 319–329. [CrossRef] 33. Nellen, S.; Ishibashi, T.; Deninger, A.; Kohlhaas, R.B.; Liebermeister, L.; Schell, M.; Globisch, B. Experimental Comparison of UTC- and PIN-Photodiodes for Continuous-Wave Terahertz Generation. J. Infrared Millim. Terahertz Waves 2019, 41, 343–354. [CrossRef] 34. Balanis, C.A. Modern Antenna Handbook, 4th ed.; John Wiley & Sons: Hoboken, NJ, USA, 2011. 35. Han, J.W.; Choi, Y.G.; Lee, J.S. Radiating pattern of surge-current-induced THz light in near-field and far-field zone. Sci. Rep. 2018, 8, 6513. [CrossRef] 36. Damian, V.; Vasile, T. Techniques for THz Beams Evaluations; CAS: Sinaia, Prahova, 2017; pp. 227–230. [CrossRef] 37. Logofătu, P.C.; Damian, V. Super resolution terahertz imaging by subpixel estimation: Application to hyperspectral beam profiling. J. Opt. 2018, 20, 055701. [CrossRef] 38. Bitzer, A.; Helm, H.; Walther, M. Beam-Profiling and Wavefront-Sensing of THz Pulses at the Focus of a Substrate-Lens. IEEE J. Sel. Top. Quantum Electron. 2008, 14, 476–481. [CrossRef] 39. Richter, H.; Greiner-Bär, M.; Pavlov, S.G.; Semenov, A.D.; Wienold, M.; Schrottke, L.; Giehler, M.; Hey, R.; Grahn, H.T.; Hübers, H.-W. A compact, continuous-wave terahertz source based on a quantum-cascade laser and a miniature cryocooler. Opt. Express 2010, 18, 10177–10187. [CrossRef] 40. Steiger, A.; Gutschwager, B.; Kehrt, M.; Monte, C.; Müller, R.; Hollandt, J. Optical methods for power measurement of terahertz radiation. Opt. Express 2010, 18, 21804–21814. [CrossRef][PubMed] 41. Vasile, T.; Damian, V.; Coltuc, D.; Petrovici, M. Single pixel sensing for THz laser beam profiler based on Hadamard Transform. Opt. Laser Technol. 2016, 79, 173–178. [CrossRef] 42. Balanis, C.A. Antenna Theory: Analysis and Design; John Wiley & Sons: Hoboken, NJ, USA, 2016. 43. Ozbey, B.; Sertel, K. Distinct Gaussian Properties of Multiple Reflections in Extended Hemispherical Lenses. J. Infrared Millim. Terahertz Waves 2019, 40, 1053–1073. [CrossRef] 44. Jepsen, P.U.; Keiding, S.R. Radiation patterns from lens-coupled terahertz antennas. Opt. Lett. 1995, 20, 807–809. [CrossRef] 45. Filipovic, D.; Gauthier, G.; Raman, S.; Rebeiz, G. Off-axis properties of silicon and quartz dielectric lens antennas. IEEE Trans. Antennas Propag. 1997, 45, 760–766. [CrossRef]