INSTITUTE OF PHYSICS PUBLISHING SEMICONDUCTOR SCIENCE AND TECHNOLOGY

Semicond. Sci. Technol. 20 (2005) S164–S177 doi:10.1088/0268-1242/20/7/006

Travelling-wave photonic mixers forincreased continuous-wave power beyond1 THzErnest A Michael

Physics Institute, University of Cologne, Germany

Received 21 January 2005Published 8 June 2005Online at stacks.iop.org/SST/20/S164

AbstractTravelling-wave designs for terahertz photonic mixers have been shown tosurpass limitations of small-area designs and therefore have the potential togenerate greatly increased continuous-wave (CW) powers at frequencieswell above 1 THz and towards 2 THz. Still a lot of optimization process hasto be done and new materials tested. Results with different geometries andmaterials made to date are compared.

1. Introduction

Materials with extremely short photocarrier trapping timesdown to 100 fs combined with electrode structures with transittimes below some tens of picoseconds, or high-electron-mobility materials with electrode structures in the ballisticlimit, are interesting for terahertz (THz) continuous-wave(CW) photonic mixer radiation sources. They can be regardedas fast photoconductive switches continuously modulated bythe beat of two near-infrared (NIR = 780–1550 nm) lasers inthe THz frequency range. Compared to other THz sources, theasset of photomixers is their unbeatable tuning range limitedin principle only by the overall speed of these photodetectors,as is given by the carrier relaxation speed of the photo-mixingmaterial as well as the transit and RC time of the electrodestructures used.

In recent years, distributive absorbing travelling-wave (TW) designs of photodetectors underwent hugeimprovements of operating bandwidth far beyond 100 GHz.The central idea of a TW mixer is to bypass the parasitic RCconstant of the corresponding lumped-element capacity bydistribution of the beat-signal generation along a transmissionline. While the TW idea is old, a first proposal to use it togenerate mm-waves with mid-IR gas lasers on a HgCdTe-Schottky-contact stripline integrated into a waveguide wasmade in 1981 [1]. From this, it took a while until edge-coupled photodiodes such as TW devices were proposed andinvestigated [2, 3].

TW photomixer designs can be divided into two classesdepending on the effective infrared absorption of the devicestructure. Low effective absorption αIR � 1 µm−1 leads toedge-coupled (fibre-illuminated) and waveguide-integrated

designs, whereas high absorption leads to verticallyilluminated designs (free-space or fibre). Biased byapplication perspectives in communication technology andwithin the ALMA project (see below), edge-coupled solutionsfor the 1300–1550 nm fibre window were preferred so thatthe class of waveguide-integrated designs has drawn mostattention in the recent years. Consequently, huge progresstowards combined higher bandwidths and efficiencies hasbeen made for these devices while mostly using pulsedmeasurement techniques to investigate and optimize them, dueto the dominating pulsed-mode application perspective. Whileone record for ultrahigh bandwidth and efficiency of pulsedTW detectors chased the next one, basically no effort has beenmade to investigate the continuous-wave performance of thesame devices. This is probably due to low commercial interestin the application of the same devices such as CW sub-mm andTHz sources for communication purposes, originating from theopaqueness of the atmosphere. But the situation may changeas various ‘near range’ commercial applications are beginningto draw interest for very frequency-agile and highly coherentradiation sources, because the improving photonic technique iscurrently enabling a cheaper, smaller, simpler, non-cryogenicand low power consumption approach. Another indicator forthis might be that antennae have recently been integrated withfast (TW) photodetectors to directly measure the radiated THzpower, but still, however, only under pulsed conditions to date[4, 5].

On the other hand, there has always been greatscientific interest in more powerful broadly tunable CWTHz sources. There are currently two development-pushingplatforms for terahertz technologies for the application as localoscillators (LO) in heterodyne terahertz receivers based on

0268-1242/05/070164+14$30.00 © 2005 IOP Publishing Ltd Printed in the UK S164

Travelling-wave photonic mixers for increased continuous-wave power beyond 1 THz

superconductor–insulator–superconductor junctions (SIS) orhot-electron bolometers (HEB).

The Stratospheric Observatory for Infrared Astronomy(SOFIA) removes the atmospheric restrictions above 1 THzto a large degree and lets terahertz astronomy techniquesprogress rapidly towards higher frequencies. The pump powernecessary for SIS and HEB mixers scales with the mixer areaand is a challenge above 1 THz but within the reach of thecurrent development of LT-GaAs-based photomixers: the latestand best report for smallest area SIS junctions is ppump ≈0.1 µW at 1 THz at the mixer [6] (with a theoretical frequencydependence of ppump ∼ f 2), and for HEB it is ppump ≈0.4 µW at 1.9 THz at the mixer [7] (with an expected frequencydependence of ppump ∼ f ). It is generally symptomatic thatpower requirements increase with frequency. Power in excessof 1 µW towards 2 THz is needed taking into account lossesin the optics, and even multiples of that are needed for arrayreceivers, which are strongly desired due to precious observingtime.

The Atacama Large Millimeter Array (ALMA) is thedevelopment-pushing platform for the sub-THz range needinga photonic LO technology based on a long-distance opticalfibre distribution network to obtain in-phase heterodyne-mixing at all antennae. Therefore, the interest is set to developCW devices for 1.55 µm, where fibre losses are low and Er-doped fibre amplifiers can be used. First, it was plannedto generate a base frequency range around 100 GHz at eachantenna efficient enough to drive multipliers to access thehigher bands up to 500 GHz [8]. Therefore, groups wereconcentrating on developing efficient waveguide-integrateddevices for the 100 GHz range. These sources are basedon the InGaAs material system [9, 10], which obtains muchhigher efficiencies at 100 GHz than the LT-GaAs systemowing to a ten times larger electron mobility–lifetime product,but which is comparable at 500 GHz and inferior at higherfrequencies. Meanwhile, due to the progress in photomixingefficiency for higher frequencies, it is rather preferred todirectly access the higher bands with photomixers [8]. Onepiece of good news causing this change came from groupsdeveloping devices based on the powerful principle of uni-travelling carrier (UTC) photodiodes [54]; the other came fromrecent advancements in designing waveguide-integrated TWphotomixers with increased bandwidth–efficiency products.

Motivated by the application of highest NIR-powerlevels, TW mixers for the range above 1 THz were realizedwith a free-space vertically illuminated coplanar stripline onLT-GaAs based on angle-tuned phase matching [11, 12].The latest developments within this principle [13, 14] openup the perspective that continuous-wave photonic TW mixersproduce power comparable to that of multiplier or laser-sideband sources above 1.5 THz. Although they willprobably never be in a position to compete with THz quantumcascade lasers concerning output power, they clearly have theadvantage of full tunability determined only by the responsetime of the mixer, besides non-cryogenic operation. Therefore,they will stay interesting in all cases where microwatt powerlevels are sufficient.

In this paper, both types of TW mixers, edge-coupled andvertically illuminated, will be discussed comparatively.

2. Fundamental considerations

Before practical devices are reported, basic parametersdetermining the physical performance of a TW mixer maybe presented, so that based on this, the concepts and practicalsolutions of different groups addressing different goals withinthe optimization of these basic parameters can be outlined andmore easily understood.

Generally, the power from a distributed photomixer resultsfrom a (constructive) interference of differential photocurrentcontributions along a stripline waveguide with impedance Z ata discrete port z2:

PTHz(ω) = ηrZ

2

∣∣∣∣∣∫ z2

z1

iTHz(ω, z) exp[−[0.5αFIR(ω)

+ i�k(ω)](z2 − z)]dz

∣∣∣∣∣2

. (1)

An antenna with a radiation efficiency ηr is located at the portz2, impedance-matched to the waveguide. No reflections areassumed at z2 and z1. The device is regarded to be quasi one-dimensional because in the two transversal directions (x, y)the dimensions are very small compared to the interferencewavelength 1/λTHz = 1/λNIR,1 − l/λNIR,2. The device lengthL = z2 − z1 is assumed to be larger than λTHz. This is oftennot the case for practical devices as we will see later where wealso discuss other possible definitions for a TW device.

Equation (1) takes into account the terahertz lossesαFIR(ω) on the stripline waveguide and the phase mismatch�k(ω) between the THz wave and the optical beat signaltravelling at the group velocity of the two laser frequencieswith powers PNIR,j , which will be described later. Theinterference is constructive if �k(ω) = 0.

The one-dimensional RF-photocurrent density iTHz :=δITHz/δz is then described phase-independently and splits upinto contributions from electrons (i = e) and holes (i = h),iTHz = iTHz,e + iTHz,h:

iTHz,i (ω, z) = i0,i (z)

1 + iτiω(2)

where τ i is the effective electrode response time and i0,i isthe interference part of the one-dimensional dc-photocurrentdensity.

In a simplified approach, the photocarrier density ni isgiven by assuming a localized equilibrium between generationand recombination, αNIR · cρNIR(t)/hνNIR = ni(t)/τ rec,i, withthe photocarrier recombination time τ rec,i. An advancedapproach would also include the delocalizing effect ofdiffusion and mobility of the carriers, and of inhomogeneousillumination. αNIR is the NIR-absorption coefficient whichmay be saturated, and ρNIR is the interference part of the NIRenergy density for the general case of a confined (standingwave) NIR radiation field inside the mixer. In order to accountfor higher modes in the NIR beams ρNIR is a complex field alsocontaining the x-dependence of the phase difference �ϕ(x)between the two beams:

ρNIR(x, y) = 2√

ρNIR,1(x, y)ρNIR,2(x, y) exp(i�ϕ(x)).

As an example of the geometry, we consider a verticallyilluminated MSM configuration in which the electrodes areat (x,y) = (−s/2,0) and (+s/2,0). We leave it to the reader to

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substitute the axis orientations for other geometries (e.g. edge-coupled mixers) and to reverse some simplifying assumptionsin the following which specialize on vertically illuminateddevices. The local current density is given by ji = enivdr(Eb)with �j || �Eb. In the following, we restrict our discussion to highE-fields: because vdr(Eb) saturates already at rather low biasfields of approx. 1 V µm−1, it is almost constant throughout thexy cross-section, so that we can assume in good approximationji ∼ ni and photocurrent reducing space charges are avoided(i.e. �∇ · �j = 0) if the NIR intensity follows the bias E-fieldstrength. In praxis, we normally have the contrary case: theintensity has a maximum in the middle between the electrodesor at least a flat profile, rather than maxima near the electrodes.From this example, we can see that the efficiency of a mixergenerally depends on the overlap between the bias E-field andthe NIR field. However, within the scope of this paper, wecan only consider the space charge free case in which the totalphotocurrent can be obtained from integration over an arbitraryiso-potential surface like the symmetry plane between the twoelectrodes at x = 0:

i0,i = eτrec,i

hνNIR

∣∣∣∣∫ 0

−d

αNIR(ρNIR)cρNIR(y)vdr,i (Eb,x(y)) dy

∣∣∣∣ (3)

where d is the absorption layer thickness in the propagationdirection of the optical waves.

The transit time τ trans,i can be introduced τtrans,i (Eb) =s∗/vdr,i (Eb), where s∗ is the effective transit distance ofcharge carriers along the (curved) E-field lines and is largerthan the electrode spacing s in the case of surface electrodes.Equation (3) can be written in summary as

i0,i (z) = e

hνNIR

τrec,i (Vb)

τtrans,i (Vb)mNIRηNIR2

√pNIR,1(z)pNIR,2(z)

(4a)

where pNIR,j (z)(z) := ∂PNIR(z)/∂z = ∫ a/2−a/2 INIR,j (x, z) dx are

the incident (external) one-dimensional NIR-power densitiesresulting from integration over the transversal aperture, a, ofthe mixer structure. With the assumption of a saturated driftvelocity over the whole integration region of equation (3), weroughly restrict the geometry to d < s in the case of verticallyilluminated MSM structures.

According to equations (3) and (4a), we define the factorsmNIR and ηNIR, which describe the horizontal and verticalparts of the THz-relevant efficiency of NIR absorption, whichfactorize due to the assumption of a saturated constant driftvelocity.

(1) The external absorption efficiency ηNIR is defined as

ηNIR =∫ 0−d

αNIR(ρNIR(x))cρNIR(x, y)dy

INIR(x)� 1, (4b)

where INIR = 2√

INIR,1INIR,2 is the (external) incidentintensity. Usually, the resulting number should be independentof the x-position and therefore can be taken outside the integralof equation (3). It describes the reflection losses at theNIR coupling surface (about 30% without AR-coating) orenhancement in a resonant cavity formed by a top partialreflector and a buried Bragg reflector.

In the case of vertically illuminated devices, ηNIR canalso contain the shielding of a top metal electrode structurealthough this is xz-dependent and is then taken into account

as an averaged surface reflectivity. For edge-coupled NIR-waveguide-integrated structures ηNIR also depends on themode confinement within the waveguide [15], once modematch from a fibre is given.

(2) The horizontal part of the efficiency, mNIR, needs alittle more discussion. Above, we considered the simple caseof homogeneous illumination with a localized balance betweengeneration and recombination of photocarriers. An advancedapproach also includes a smearing-out of photocarriers dueto a recombination length lrec = vdr · τ rec in the order of20–100 nm for materials with electron traps or even the wholeelectrode gap for materials without electron traps. Diffusionwithin τ rec would also have to be taken into account. As aconsequence, an integration has to be introduced over sometransversal extension over the transversal aperture a of themixer structure, so that mNIR goes over to

mNIR =

∣∣∣∫ a/2−a/2

√INIR,1(x)INIR,2(x) exp(i�ϕ(x))dx

∣∣∣2√

pNIR,1pNIR,2� 1.

(4c)

This expression has the meaning of a transversal mode overlapfactor over the transversal optical aperture a of the mixerstructure, including the phase difference of the two laser beams(see e.g. figure 14(a)). It is assumed to be constant in thez-direction. The longitudinal (z-direction) overlap factorwould result from the integration of equation (4a) inequation (1) over z.

For most materials, velocity saturation is observed atrather low bias fields, e.g. at 1–2 V µm−1 in LT-GaAs,far below the optimum operation voltages observed forvertically illuminated surface electrodes with small-areainterdigitated finger [24] and TW [11] structures, calledMSM structures. A simplified expression for voltagesaturation of the charge carrier drift velocity may be given asvdr,i (Eb) = µiEb/

(1+Eb

/Esat

b

) = vsatdr,i

/(1+vsat

dr,i

/µiEb

). µe

is the mobility of the photoelectrons in the conduction band,and µh is the mobility of the holes which is usually one to twoorders of magnitude smaller than that of the electrons.

We ignore an overshoot for vdr at lower field strengths,as observed for many semiconductors at electrode spacings�1 µm. The correct description of the overshoot is importantin p–i–n devices with very thin i-layers in the order of 100–200 nm, helping us to increase the efficiency and bandwidth(see also [55]), whereas it is unimportant in MSM devices ofgap widths in the order of 1 µm.

In equations (2) and (4), we have to distinguish threedifferent time constants, which, in turn, all have to bedistinguished between electrons and holes. τ i is the effectiveresponse time to absorbed light in the middle of the electrodesseen locally at the negative and positive electrode, respectively.In general, the electrode response time is a function of therecombination time τ rec, the transit time τ trans, the bias fieldin the photoconductive gap s∗ and the carrier mobility anddiffusion constants. It is observed that τ rec < τ i < τ trans,which can be understood theoretically for a time-periodicexcitation involving diffusion. To illustrate the frequency-limiting contribution of the transit time, we might recall thepicture of a charge cloud which is diffusing out rapidly intoall directions from the point of photo-generation, while the

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Travelling-wave photonic mixers for increased continuous-wave power beyond 1 THz

Table 1. Intrinsic parameters (at 300 K) of materials interesting for photonic THz generation. Some constants are not known to date.LT-GaAs shows increase of lifetime with voltage. This effect influences the device performance a lot (see the text) and therefore needs to beinvestigated for the other materials as well, as it is expected to vary considerably. On the other hand, the saturation velocities are found to bevery similar.

αIR(λ) µe (cm2 (V s)−1) vsatdr el. µh (cm2 (V s)−1)

λ (nm) (µm−1) τ e (ps) (cm s−1) τ h (ps)

Established materials for sub-mm and THz devicesLT-GaAs [17] 780–850 1–2 <2500 <107 200

0.2–0.3 >6LT-GaAs 1300–1550 0.1–0.2 <2500 <107 200

>0.3InGaAs 1300–1550 1–2 10 000 1.3 × 107 200

‘long’ ‘long’

New materials, currently being investigatedErAs:InGaAs [20] 1300–1550 1–2 ? ? ?ErAs:GaAs [21] 780–850 1–2 >3000 ? ?N-implant. GaAs [22] 780–850 1–2 >3000 ? ?

0.2–0.3 ?

Suggested materials not used yetIon-impl. InGaAs [23] 1300–1550 1–2 ? ? ?InP 950–1000 1 5400 1 × 107 200

‘long’ ‘long’

centre of charge is drifting only relatively slowly into thedirection of the E-field. For this complicated situation, noexplicit equations are available (1/τ = 1/τ rec + 1/τ trans is justwrong for our case), while some numerical results have beenobtained by Monte Carlo simulations [16].

A compilation of material parameters of photonic THzmaterials is given in table 1. Two cases have to be consideredregarding the lifetime of the photocarriers τ rec in equation (4a),which have strong implications on the device design.

2.1. Material without electron traps (e.g. InGaAs)

In trap-free materials, the photocarrier lifetime is in the rangeof tens of picoseconds. Therefore, the speed of devicesbased on trap-free materials is dominated by the transit time(τtrans � τrec) and relies on a high carrier mobility and a verythin photo-active intrinsic layer (∼200 nm) so that the structureof choice is a p–i–n structure for these materials. In edge-coupled devices, cladding layers are needed for the opticalwaveguide which reduce the NIR absorption to levels matchedto the device length (small filling factor). The claddinglayers need to be highly n- and p-doped to establish electricalcontact with the absorbing i-layer. Therefore, absorptionof the travelling THz wave is much higher than that of theplanar surface waveguides on intrinsic material (see section2.3). Due to this, peak efficiency is always traded off againstbandwidth in practical designs [15]. Due to the very thini-layer, a one-component model with an effective mobility andrecombination/transit time of electrons and holes is assumed.The recombination times of both carriers are given by theirtransit times to the electrodes: τ rec,i = τ trans,i, for which itis assumed that recombination takes place at the i–n- andi–p-layer interfaces; otherwise, the transit time would beeffectively increased and device speed reduced. The powerin transit-time-dominated devices is expected to behave likePTHz ∼ (PIRVb)

2/s∗4 up to a breakdown field Vb/s∗ which,according to the avalanche mechanism, is expected to be higherthan that for large-gap devices. Vb is the bias voltage.

2.2. Material with electron traps (e.g. LT-GaAs)

In the case of LT-GaAs, electrons are trapped in As-anti-site mid-gap states at time scales of τ rec,e = τ trap,e ∼200 fs,and these charged anti-sites subsequently trap the holes atmuch longer time scales of τ rec,h > 6 ps, so that a two-component model is needed to describe the mixers adequately.As discussed above, the transit time is given by the saturationdrift velocity and is in the order of 10–20 ps µm−1 gap width. Itis characteristic of mixers based on electron-trapping materialsthat their high speed is traded off against low efficiency dueto τrec � τtrans. The electronic part of the dc photocurrenttherefore behaves like

iph,e(0) ∼ τrec,e

τtrans→ τrec,ev

satdr,e

s∗ (5)

and the THz-power scales on the photoconductive gap widthlike PTHz ∼ 1/s∗2. This velocity saturation voltage would resultin a corresponding low THz power if there were no degradationof the trap time at higher voltages [18], and therefore also ofthe electrode response time:

τe(Vb) = τe(0) + a2V2

b + a3V3

b + · · · (6)

with a2, a3 > 0. By virtue of iph,i ∼ µi · τ rec,i, a correspondingincrease of the observed dc photocurrent occurs, enhanced bythe Ohmic and Schottky characteristic of the contacts:

iph,e(Vb) = isatph,e + b1Vb + b2V

2b + · · · for Vb > V sat

b (7)

with b1, b2 > 0. Increase of (effective) electron lifetimeand quadratic increase of photocurrent are consistent withthe picture of electron avalanches taking place. For manyLT-GaAs mixers, the photocurrent is observed to be purelyquadratic above the bias field at which saturation of the driftvelocity occurs (∼1 V µm−1) up to the breakdown field(>15 V µm−1) with a saturation current offset isat

e .The observed voltage dependence of the THz power canconsequently be described by [14]

PTHz(Vb) =(c0 + c1Vb + c2V

2b

)2

1 +(c3 + c4V

2b + c5V

3b

)2 (8)

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E A Michael

which bears a super-quadratic increase of the THz power above∼1 V µm−1 with a strong second saturation above 15 V µm−1.This behaviour complicates the search for the best materials.

Because the contribution of holes is negligible at THzfrequencies, due to their much longer lifetime of severalpicoseconds and their much lower mobility than that of theelectrons in the conduction band, equation (8) represents theelectronic part of a two-component model at THz frequencies.Towards ‘near-dc’ frequencies (<10 GHz) the rf-power isgoverned to 95% by the holes, because µhτ h ≈ 5µeτ e [14].

Although it is still not fully understood, LT-GaAs iscurrently the most successful and best studied [19, 25–27]THz material used in a whole variety of devices. It is theonly high-resistivity and high-breakdown-field material withsub-ps photoelectron trap times known yet which retains thisproperty fairly well at high bias fields.

While it has its band edge at 800 nm (αIR ∼1 µm−1),it luckily also absorbs not too weakly in the range ofλ = 1300–1550 nm (αIR ∼ 0.1 µm−1) by virtue of two-photonabsorption [28] and/or absorption from the mid-gap arsenicantisite traps. It is therefore also applicable for edge-coupledgeometry at these wavelengths [29].

While ultra-short-lifetime materials with high NIRabsorption at the pump wavelength of 1500 nm are searched forto realize vertically illuminated devices operating at this pumpwavelength (e.g. the hetero-structure ErAs:InGaAs [20]),edge-coupled p–i–n devices on the basis of highly 780 nm-absorbing LT-GaAs have also been investigated at 780 nm [4]and demonstrated a benefit of the usage of electron-trappingmaterial versus non-electron-trapping material.

2.3. Terahertz losses

2.3.1. MSM structures. At lower frequencies, losses in themetallization are governed by Ohmic losses in the skin layer(∼f 1/2); at higher frequencies, the stimulation of substratemodes and Cherenkow radiation plays the dominant role,because of the shock waves induced by the effective refractionindex of the stripline being smaller than that of the substrate(∼f 3). Therefore, THz losses are well described by [13]

αTHz = αc

√f + αrf

3. (9)

Typical values for THz absorption for 500–1500 GHz are in therange 3–6 mm−1. For a plain CPS on LT-GaAs, the calculatedand measured losses can be inferred from figure 1. Losses forother stripline geometries, such as CPW or microstrip, are verysimilar. A comprehensive collection of formulae for the CPStransmission line is contained in [30], and for CPW line in [31].A full-wave analysis of CPS and microstrip lines is containedin [32]. Losses at high frequencies should be substantiallyreduced by (backward) substrate removal [4, 5], but a directcomparison for THz frequencies has not been made to date.

Terahertz absorption complicates the design of edge-coupled TW mixers, because it biases the device lengthtowards shorter values through an adjustment of the infraredabsorption constant towards higher values. This leads tohigher power densities in the mixers and therefore thedestruction power is lower, a problem for the design of highinfrared power accepting devices.

In the case of vertically illuminated mixers it is easier:the line-focus length can be optimized during operation by

50

40

30

20

10

00.0 0.5 1.0

Frequency [THz]

Atte

nuat

ion

Coe

ffici

ent [

dB/m

m]

1.5 2.0 2.5 3.0

Theory

αC (dB/mm): 11.2 13.5αR (dB/mm): 0.63 0.78

Measured

Figure 1. Measured and calculated losses of a CPS stripline witha = 2 µm gap and b = 4 µm outer width, from [12]. © 1999 IEEE.

1010-5

0.0001

0.001

0.01

0.1

100 1000Frequency [GHz]

Fiel

d at

tenu

atio

n co

effi

cien

cy [

µm-1

]

Figure 2. p–i–n-CPW stripline losses: example for losses extractedexperimentally from the comparison of two p–i–n devices of lengths10 µm and 25 µm, from [33]. Dimensions of the CPW: width ofcentral stripline 1 µm (i-layer = 170 nm, n- and p-layer both600 nm), inner distance of outer CPW striplines about 15 µm.© 1998 IEEE.

adjusting the optics until the illumination intensity is as closeas possible to, but still well below, the destruction limit of thedevice for a given illumination power.

2.3.2. p–i–n structures. As can be seen from figure 2, theincrease of absorption is ∼f 2 and is about an order ofmagnitude higher in the THz range compared to MSM devices,which is a serious problem for their performance above 1 THz:very short lengths have to be used and therefore NIR power islimited even more than in small-area MSM devices.

2.4. Infrared absorption and device saturation

The infrared absorption of photonic materials is mostly in theorder of 1 µm−1 at their band edge (see table 1). Therefore, allphotoconductive materials used at 780 and 1500 nm, exceptLT-GaAs and InP at 1500 nm, are in principle suited for verticalillumination. In edge-coupled designs, the effective absorptionis lowered by geometrical means (filling factor) by additionaltransparent (larger gap) waveguide cladding layers (often InP)needed for confinement of the travelling NIR radiation [9]. Onthe other hand, the absorptive core layer has to be chosen asthin as possible for the smallest transit times. Typical lengths

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Travelling-wave photonic mixers for increased continuous-wave power beyond 1 THz

of waveguide-integrated TW mixers range from 10 µm [33](not yet in the TW range) to 700 µm [34], depending on thematerial, structure, desired bandwidth and efficiency.

A useful expression defined in the literature is theresponsivity R := Iph/PIR, used with both the dc and thetransient photocurrent in a pulsed measurement. The goalfor photonic mixers is to reach high responsivities at low biasvoltages, because then the burden for high infrared poweris relieved, given the problem of lower device breakdownvoltages at higher intensities and associated thermal burnout.For edge-coupled devices, this goal is even more imperative,because infrared power is even more limited especially at theinput-coupling facet (located at z1) due to the necessary smallwaveguide cross-sections for single-mode operation. Highintensities at the input of an edge-coupled TW mixer leadalso to saturation effects and response time degradation due tospace-charge screening at the electrodes [35]. As a solutionto this dilemma, TW amplification photodetectors (TAP) arecurrently being investigated [36] to circumvent high facetillumination, resulting saturation and associated degradationof response time. Enormous efficiency–bandwidth productsare expected for this type of mixer.

2.5. Velocity match

Equation (1) may be rewritten as

PTHz(ω, Vb, PIR) = ηrRaI0,e(Vb, PIR)2

2

F(ω)

1 + (τe(Vb)ω)2(10)

where F(ω) summarizes the details of generation andabsorption of the THz signal along the transmission line aswell as a reduction of bandwidth given by non-perfect velocitymatch of THz and NIR waves. It is F(ω) = 1 for no THzabsorption and perfect velocity match. Ra is the real part ofthe antenna impedance and I0,e is the electronic part of the totaldc photocurrent, integrated over the device length.

The phase mismatch �k(ω) between the THz wave withthe phase velocity VTHz and the optical beat signal travellingat the group velocity Vgroup,opt of the two laser frequencies isgiven by

�k(ω) = ω

(1

Vgroup,opt(ω)− 1

VTHz

). (11)

In good approximation, a dispersion-free terahertz waveguidecan be assumed: typical microwave transmission line velocitiesfor coplanar striplines (CPS) or coplanar waveguides (CPW)are given by VTHz = c/

√(1 + εTHz)/2 (= 0.38c in the case of

ε = 12.8 for GaAs), so that in the case of an edge-coupleddevice with embedded optical waveguide in the substrate(Vopt = c/

√εopt = 0.28c for ε = 12.8), we obtain a

considerable velocity mismatch:

�k(ω) = ω/c(√

εopt −√

(εTHz + 1)/2) ≈ 0.95ω/c.

The simplified but unrealistic case with a constant intensity∼1/L over a length L and no losses may be imagined first.Then the velocity mismatch factor for PTHz can be expressedas

Fc(ω) = sin2[�k(ω)L/2]

[�k(ω)L/2]2(12)

True TW behaviour is given with Vopt = VTHz (�k = 0).Otherwise, for �k = 0, the dependence on ω introduces an

additional frequency roll-off, which is equivalent to a lumped-element RC constant. In order to determine a 3 dB frequencyfor the velocity mismatch, the following approximation isuseful:

Fc(ω) ≈ 1 − 1

15

(ωL

(1

Vopt− 1

VTHz

))2

⇒ fTW,3 dB

≈ 2.74VTHzVopt

2πL(VTHz − Vopt). (13)

2.5.1. Edge-coupled mixers. Ignoring NIR saturation(iTHz(z) ∼ αNIRe−αIRz), the integral (1) can be explicitly solvedfor an edge-coupled device as a function of infrared absorption,terahertz absorption and phase mismatch to give the THzpower

PTHz(ω) ∼ α2NIR

∣∣∣∣e−0.5αTHzL − e−(αNIR+i�k(ω))L

αNIR − 0.5αTHz + i�k(ω)

∣∣∣∣2

(14)

if the infrared input facet and the antenna are located at 0 andL > 1/αIR, respectively. This expression is valid if the inputend at z = 0 is terminated by a matched shunt resistance.Otherwise, reflections from the backward waves introduce aspectral modulation which results, in the case of short devices,in a reduction of the bandwidth and 3 dB greater near-dcresponsivity. No shunt resistance is necessary in the caseof phase match �k(ω) = 0.

For most materials usable for wafer-integratedwaveguides and their claddings, εopt and εTHz are similar sothat it is notoriously VTHz > Vopt for MSM structures. Onetechnique to bypass this is to use a slow-wave structure for theMSM THz waveguide [37] or to use a periodic arrangementof identical lumped-element photomixers along an integratedwaveguide [9].

In p–i–n structures, the situation is different and morecomplicated: for the desired case of a broad waveguide(better optical confinement) with the thinnest possible i-layer(smallest transit times), the electrical wave velocity is muchslower than the optical, so that a trade-off between efficiencyand bandwidth has to be made [15].

However, as can be seen from figure 3, for edge-coupleddevices of length below about 100 µm, the bandpass isnot limited primarily due to velocity mismatch but moredue to other parameters, such as trapping and transit timeand carrier diffusion [33]. However, pulsed response-timemeasurements are made by using electro-optical (EO) on-waveguide sampling, and therefore may not be free of pulsedistortions, so that the true bandwidth may be larger thanreported. Rather than using EO on-waveguide sampling,broadband measurements could be performed using integratedbow-tie antennae with external EO sampling or time-integratedFourier-transform spectroscopy. A first step into this directionwas made using integrated slot antennae to couple out a THzsignal from a pulsed waveguide-integrated TW mixer into freespace [4, 5].

2.5.2. Vertically coupled mixers. It is an advantagefor vertically coupled TW devices that pump power canbe distributed relatively uniformly over a large area andthe mixing length can be varied in situ in order to find

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0.51011

1012

1013

1 1.5 2

Vm/Vo : Velocity mismatch factor

Ideal TWPD

Loss and dispersion

No reflectionReflection

tlifetime=300 fs

*actual device

No loss and dispersion

3dB

ban

dwid

th (

Hz)

Figure 3. Example for a theoretical velocity mismatch bandwidthand practical limitations due to the material for a device of 25 µmlength, which shows that the device is not in TW mode, from [33].© 1998 IEEE.

Figure 4. TW mixer with angle-tuned phase match, from [11].Depicted is the special case of k2 perpendicular to the surface. Theterahertz wave travels in the direction in which the projection of thelarger optical frequency wave vector is pointing. Reprinted withpermission from Shuji Matsuura, Applied Physics Letters, 74, 2872(1999). Copyright 1997, American Institute of Physics.

the best compromise between the least THz absorptionand a power density sufficiently far away from thermalburnout. Additionally, free-space-illuminated mixers have theimportant advantage that the group velocity of the optical beatsignal (moving fringes) can be matched perfectly to that ofthe THz wave, which enables long line-foci biased, however,towards small values in practice by the THz absorption αTHz

on the stripline. For higher NIR powers, the device lengthcan be increased L ∼ PNIR and the obtainable THz power isexpected to scale approximately with L2 exp(−αTHzL/2). Thefirst free-space pumped TW THz mixer was demonstrated in[11] as depicted in figure 4. The velocity of the optical beatfringes is given by

Vopt = Cgroup = �ω

�k||= c(f1 − f2)

f1 sin �1 − f2 sin �2. (15)

�1 and �2 are the angles of the NIR wavefronts with respectto the surface. Solving for �k = 0 for small angles givesd(�1 − �2)/d(f1 − f2) ≈ 0.4◦/THz.

Going back to equation (1), we have with a Gaussian beamwith waist wNIR in the z-direction

PTHz(ω) ∼ 2

πw2NIR

∣∣∣∣∫ z2

z1

exp

(−2

(z

wNIR

)2)

× exp([−0.5αTHz − i�k(ω)](z2 − z)) dz

∣∣∣∣2

. (16)

The position with respect to the antenna has to be optimizedin dependence on w and αTHz. For not too high absorption(αTHz < 4 mm−1), the highest THz powers are obtained withz2 = 1w, . . . , 1.5w, if we centre the beam axis at z = 0.Different cases for this are depicted in figure 5 as functions ofthe mixing angle in comparison to the simplified expression inequation (12).

An example of an angle-self-tuning optics setup isshown in figure 6, while other more compact optics arepossible. The idea is to exploit the grating dispersion todesign a frequency-independent optical setup which generatesthe proper transformation from the grating dispersion to thevelocity-match angle frequency dependence on the mixer.

2.6. Definition for TW mode

While criteria for the design of TW devices are reported in[15, 16], we deduce from the above discussion a usefuldefinition for a velocity-matched device actually being in TWmode or not. Looking at equation (13), a possible criterionwhether a specific device might be called a TW device isfTW,3 dB > fRC,3 dB. For this, we assume that the transmissionline of the TW mixer consists of a lumped element (total)capacity proportional to its length which determinates fRC,3 dB.Provided the width of the structure is sufficiently narrow, wesee that L is of no importance from this viewpoint and we justneed to be close to a velocity match. From this standpoint, alldevices discussed in this review are indeed TW devices.

But for a true TW device, there should be an additionalcondition: constructive interference in the backward directionshould be suppressed. In figure 5(b) the backward poweris plotted for the case of a perfect forward velocity matchfor which the backward direction has a phase mismatchof �kback(ω) = 2ω/Vgroup,opt(ω) = 2ω/VTHz according toequation (11). We see that for all geometries, backward poweris no more than 10% at device lengths of L > λTHz/2, and forvertically pumped devices, this suppression is generally moreeffective than for edge-coupled devices.

For edge-coupled devices, we have the additionaldifficulty of an abrupt termination of the transmission lineat z1 (input port), so that the backward wave is totally reflectedthere. This gives an interference modulation at z2 (outputport), which is equivalent to a bandwidth reduction in thecase of L < λTHz. Therefore, edge-coupled devices are muchharder to operate in the TW regime than vertically coupled:at short device lengths interference with the backward wavespoils potential large bandwidths. For sufficient lengths, theeffective NIR-absorption constant is hard to reduce sufficientlyby cladding layers, the THz absorption is too high and velocitymatch is not well enough given. From these reasons, mostpractical edge-coupled devices described in the following arehardly in TW mode.

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Travelling-wave photonic mixers for increased continuous-wave power beyond 1 THz

1 0.5 0 0.5 11 10 5

1 10 4

0.001

0.01

0.1

1

[degree]

Fc for L = 150 µm (Eq. 12) FWHM = 75 µm FWHM = 150 µm (Eq. 16) FWHM = 300 µm

0 0.2 0.4 0.6 0.8 11 10 5

1 10 4

0.001

0.01

0.1

1

10

backward THz-power

edge-coupled

vertically coupled

NIR absorption length or intensity width w [l], L=2w

(a)

(b)

Figure 5. (a) Normalized THz power PTHz(�) at 1 THz as a function of phase-match angle (according to equation (16)) for Gaussianillumination with line-foci of FWHM = 75 µm, 150 µm and 300 µm, with z1 = −1.2w and z2 = +1.2w, in comparison to the simplifiedexpression of equation (12) for L = 150 µm (dots). The backward signal is represented by the corresponding negative angle. The THzstripline absorption in this example is 4 mm−1. (b) Normalized backward power as a function of device length L for velocity match given inthe forward direction. The NIR intensity is INIR ∼ exp(−z/w) for edge-coupled and INIR ∼ exp(−2(z/w)2) for vertically coupled devicesover L = 2w.

3. Practical devices

As is clear from the beginning, all possible geometries fallinto two classes, namely edge-coupled designs and verticallycoupled designs. Fundamental aspects with regard to thisclassification have been discussed in the previous section.THz-suited materials turn out to be highly absorbing at theirband edge (αIR ∼ 1 µm−1) so that it is only a questionof operation wavelength, whether the material is suited forvertical designs or not. For long-distance fibre applicationssuch as ALMA, materials for 1550 nm are desired [8].

Most edge-coupled TW mixers have been characterizedexclusively from the standpoint of fast pulse signal detectionfor telecommunications. Therefore, most edge-coupled TWdevices have been investigated only by on-waveguide EOsampling. While this technique is very useful to characterizespeed, stripline absorption and responsivity, no direct infrared-to-THz conversion efficiencies are obtained. Such data aresuited to select good candidate devices for follow-up CW-THzstudies in which the devices additionally have to withstand

a much higher average optical and electric power dissipationcompared to the pulsed mode.

Some edge-coupled devices have been integrated withplanar antennae and were characterized by their pulsed THzemission above 500 GHz [4, 5]. Others were exclusivelydesigned for CW purposes [9], but have only been testedbelow 500 GHz so far. Within the scope of this paper,which is focused on the CW THz-output capabilities of TWmixers, THz efficiencies obtained from pulsed measurementsare reported side-by-side with CW efficiencies obtained fromvertically coupled devices designed and optimized for CWterahertz power, which have been experimentally investigatedwith coherent dual-colour CW diode laser systems.

3.1. Edge-coupled devices

Two designs are possible: (1) planar electrode (MSM)structures and (2) vertical electrode structures (p–i–n). Thisdifferentiation is made with respect to the local contactgeometry: because no epitaxial growth can take place on metalin a vertical electrode configuration, the lower electrode is a

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blazed grating2400 L/mm

diffraction-limitedfocusing lensf=6.5mm

Mixer onSi-Hyper-

cylinder lensf=80mm

cylinder lensf=30mm

cyl. lensf=100mm

(R=5mm)hemisphere

course adjustment of angle

mod

e fi

l ter

NIR fromSOA

(pin

hole

opt

iona

l )

M1M2

M3 M4

M5THzto detector

Coarse adjustment of mixing angle

Figure 6. Self-tuning optics setup for vertically coupled TWmixers [38].

highly p-doped layer with metal-like properties connecting thephotoactive i-layer to the outer stripline of a CPW waveguide.Vertical MSM structures have been fabricated for small areasusing a flip-chip technique [51], but not for waveguidestructures to date.

3.1.1. p–i–n structures. Very fast devices have been createdwith edge-coupled designs by using the thinnest photoactivelayers. An example is shown in figure 7. This device has onlybeen characterized by electro-optic sampling to date.

Even at the thinnest i-layers, edge-coupled p–i–nstructures have been shown experimentally not to be purelytransit-time-dominated devices, because they ultimately

Figure 7. Left: edge-coupled p–i–n design of an LT-GaAs-based device [39]. TW length is L = 25 µm. Reprinted with permission fromYi-Jen Chiu, Applied Physics Letters, 71, 2508 (1997). Copyright 1997, American Institute of Physics. Right: performance of such a device[33]. © 1998 IEEE.

perform better with a photoactive layer from LT-GaAscompared to a trap-free material such as InGaAs [39].

3.1.2. Multi-quantum-well (MQW) p–i–n structure CW design.Edge-coupled CW devices of L = 50 µm and 6 µm width weredesigned for λ = 1.55 µm with a 400 nm thick photoactivelayer from InGaAs or InGaAs/InGaAsP multi-layers of thesame total thickness [9] (figure 8). A model for gain and losswas developed and fitted to the experimental results in orderto optimize future devices. A power of 1 mW at 100 GHz wasobtained with 100 mW optical power and it was demonstratedto pump an SIS receiver at 460 GHz, which estimates thepower to more than 1 µW. Above 100 GHz the frequencyroll-off was found to be f −3.

3.1.3. MSM structures. The complementary approachto build up an edge-coupled waveguide mixer is to useplanar surface electrodes on top of an LT-GaAs layer (MSMstructure). In figure 9, a cross-section of a CPW MSMstructure using LT-GaAs at 780 nm is shown, resulting in avery short device no longer in the TW regime [42]. Becausethe contact area is illuminated from inside the dielectric, muchsmaller contact separations (0.2–0.3 µm) than possible forvertically surface-illuminated devices, together with a largesurface metallization fraction, can be used. These ultra-narrowgaps are realized with a self-aligning undercut etch techniquewhich produces two different surface levels for both electrodes,so that a CPW stripline geometry is naturally chosen to supportthe optical waveguide confinement underneath. Photonictransmitters were fabricated using this layer structure, shownin figures 10 and 11. The devices were illuminated at 780 nmwith 1 ps long trains consisting of 100 fs pulses, generatedby an etalon with a free spectral range tuned to the antennaresonance frequency, at a duty cycle of 12 000 at 80 MHzrepetition rate.

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Travelling-wave photonic mixers for increased continuous-wave power beyond 1 THz

TW-PD

InGaAs:C(Contact Layer)

InAlAs:C(Upper Clanding)

InGaAs nid(Absorber)

InGaAsP:S(Core)

InP:S(Lower Cladding)InGaAs(Each Stop)

InP:nid(Buffer Layer)

InP:Fe(Substrate)

frequency (THz)0.001

20

10

-20

-30

-40

-10

0

0.01 0.1 1

outp

ut p

ower

(dB

)

1.55µm opticalheterodync input

generated (sub)mm-wave power

1

Figure 8. p–i–n structure tested for CW application. Below are themeasured and calculated output spectra for 200 mW combinedinfrared power at 1.55 µm, from [40, 41]. © 2003 IEEE.

CPW Metal

wcw

LTG GaAsAIAs

Undoped AI0.35Ga0.65As

Undoped AI0.5Ga0.5As

S.I. GaAs substrate

Figure 9. Layer structure of a photonic transmitter with MSMstructure based on LT-GaAs and cladding layers, pumped at 780 nm.The air gap width is 0.3 µm, from [42]. © 2001 IEEE.

To compare the results between pulsed and CWmeasurements, a definition such as ηTHz := PTHz/PIR [4, 5]is not useful because it depends on the infrared power appliedto the mixer. It is also not meaningful in the sense ofquantum efficiency, because the mixer generates the terahertzpower also from the dc bias. To define a THz efficiency, weshould recall that the THz power generated by photomixingfollows a quadratic law: PTHz ∼ P 2

IR at least for small powers.Therefore, a more appropriate definition is

ηpeakTHz := P

peakTHz

/P

peak2

IR = 1

dcP av

THz

/P av2

IR = 1

dcηav

THz (17)

for peak and average signals, taking into account the duty cycledc of the pulsed operation. Very high peak powers up to 40 Ware applied in pulsed measurements, huge values compared to

Figure 10. Photonic transmitter resonant for 645 GHz. The lengthof the device is 20 µm. Reprinted with permission from Jin-Wei Shi,Applied Physics Letters, 81, 5108 (2002). Copyright 2002,American Institute of Physics.

(a)

(b)

Figure 11. Saturation effects in edge-coupled MSM mixers underpulsed operation: (a) the pump power saturation reduces withincreasing bias (here measured at 645 GHz), which points tospace-charge screening (from [5]), © 2004 IEEE; (b) voltagesaturation (here measured at 1600 GHz with 0.66 mW averagedpump power) is due to increasing carrier lifetime. Reprinted withpermission from Jin-Wei Shi, Applied Physics Letters, 81, 5108(2002). Copyright 2002, American Institute of Physics.

CW intensities of (currently) below 500 mW. About 104 timesmore THz peak power is produced under pulsed conditions,but the average infrared power applied is only a couple ofmilliwatts. Therefore, thermal effects can be neglected, whichplay a large role in CW operation of vertically illuminateddevices already at 300 mW—a value which would probablybe problematic for an edge-coupled mixer, due to the smallcross-section of the optical waveguide.

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Figure 12. Response times for different illumination intensities.The increase for higher intensities is explained by field screeningeffects due to high charge carrier densities. Illumination intensities:A–F: 79, 45, 17, 9, 4.1 and 0.49 pJ/pulse, from [43]. Reprinted withpermission from Kian-Giap Gan, Applied Physics Letters, 80, 4054(2002). Copyright 2002, American Institute of Physics.

It is plausible that the THz efficiency defined asηTHz:=PTHz

/P 2

IR of the same device is always larger underpulse excitation than under CW excitation: the photomixermaterial is excited very quickly during a 100 fs pulse sothat a part of the power spectrum towards higher frequenciesis due to this transient increase of the photocurrent, whichalso happens for very slow relaxing materials such as SIGaAs. Secondly, the material has plenty of time betweenthe pulses (∼12 ns) to relax electronically (electron trapsare emptied) while the lattice is only marginally heatedby the low average NIR power. On the other hand,saturation with respect to the NIR intensity [4] degradesTHz power at the very high intensities occurring in thetransient pulses (figure 11), which is caused by degradationof transit time due to space-charge-screening effects(figure 12) [43], whereas voltage saturation [5] is also observedat the low intensities in CW devices [18]. For saturation in aclassical sense (through depletion of electrons at the valenceband edge), infrared intensities are still not high enough evenunder pulsed conditions.

3.2. Vertically coupled CW devices

Historically, the interest in vertically illuminated TWphotomixers originated more from work with small-areavertically coupled devices [44] than it was stimulated fromsome direct comparison with edge-coupled TW mixers: atthe time the vertically illuminated CPS TW mixer wasdemonstrated [11, 12], the only CW THz results were achievedwith vertically illuminated small-area structures [45]. Small-area vertically illuminated interdigitated MSM structures(figure 14(a), left) based on low-temperature-grown GaAs(LT-GaAs) were historically the first devices to generatesubstantial power (∼1 µW) at 1 THz, but they were not ableto surpass this level due to design difficulties above 1 THz:in small-area mixers used with broadband antennae ofload resistance Ra, the uncompensated mixer capacitance Cintroduces a roll-off ∼1/[1 + (RaCω)2], setting in around orbelow 1 THz. This roll-off can be avoided in principle, butis difficult for practical devices: if small-area photomixers arelocated at the foot-point of resonant antennae, capacitance up

0.01

2

4

0.1

2

4

1

2

4

10

Bol

omet

er s

igna

l [V

]

3.02.52.01.51.00.5

Frequency [THz]

))(())2(1(

1~)(

220

2 Γ+. ..+ ννντπν

el

f−

Figure 13. Measured power spectrum of a TW mixer with a 47 µmlong dipole antenna with resonance frequency 1.5 THz [11] and ourfit to it (see the text). The peak signal corresponds to a terahertzpower of 200 nW.

to a certain value can be tuned out by the antenna inductance,and the envelope of the resonance peak THz powers is givenby the roll-off ∼1/[1 + (τ eωres)2],where τ e is the effectiveelectrode response time. This procedure needs a very precisedesign by simulating the interplay between mixer, antenna andrf-stop-filter and is deteriorated by the THz absorption towardshigher frequencies [46]. The restriction of the capacitanceimposes upper limits on the area (and thus NIR power becauseof destruction intensity) and lower limits on the finger spacing(conversion efficiency), and therefore limits the ultimate THzpower with a given photoconductive material [47]. BecauseNIR power is close to the destruction limit, improved thermalsinking is especially essential for small-area mixers: 2 µW at1 THz is reported for such structures at 90 mW infrared powerwith λ-double-dipole antennae of 210 � impedance [46].100 mW seems to be a limit for infrared power on small-areastructures, unless they are cooled, e.g. to LiN2 temperature, asthe low thermal conductivity of LT-GaAs is a major problemfor these devices [48].

The vertically illuminated CPS TW setup, alreadyoutlined in the theory part, was shown to avoid these NIRpower and THz resonance restrictions [11, 12]: a power of300 mW was found to be deployable on the mixer withoutproblems, the power being rather limited by the semiconductoroptical amplifier (SOA), and was generating 200 nW of powerat 1 THz. While a factor of 5–10 increase is expected from thedeployed NIR power compared to the results with the small-area structures of [46], this has to be divided by 3 again dueto a CPS-waveguide impedance of 70 �. Additional lossesdue to the extended dimensions also have to be taken intoaccount, as well as the sensitivity to only the fundamentalNIR mode.

The observed behaviour obtained with a resonantλ/2-dipole antenna for 1.5 THz is shown in figure 13, andthe measured bandpass can be very well fitted by a one-time-constant expression (τ el ≈ 0.28 ps) and a resonant antennapart (fres = 1.5 THz), showing that the device RC constant isbypassed by establishing a distribution of the mixing process.The deviation at higher frequencies can be understood withincreasing THz losses on the strip line and the antenna.

Both edge-coupled TW mixers and vertically coupledCPS-based TW mixers have the same problem of focusing

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Travelling-wave photonic mixers for increased continuous-wave power beyond 1 THz

the power diffraction-limited into the aperture of the CPS oroptical waveguide, respectively. However, it is easier to obtaina diffraction-limited focus in one dimension: simple mathsshows that a one-dimensional 2w-wide aperture (a slit) cancollect 95%, while a two-dimensional 2w-diameter aperture,the situation for an edge-coupled mixer, can accept only 86.5%of a Gaussian mode.

While mode purity is a requirement for CPS waveguidemixers, commercial SOAs have a fundamental mode contentof only about 50%. The higher modes cannot be coupledinto a diffraction-limited aperture and just lead to decreasedTHz power due to heating of the substrate on the left andright of the stripline. Thus, they need to be filtered out byintroducing a pinhole mode filter after the amplifier. Uponreducing the gap width below the diffraction limit, nothing canbe gained using a CPS by using vertically illuminated mixers,as PNIR,gap/s → const. As for the vertically illuminated TWmixer the line-focus length is biased by the relative high THzabsorption towards small values and the focus width is biasedtowards small gaps, the TW-mixer area is to be minimized,again arriving quickly at some power limitation like earlierwith the vertically illuminated small-area mixers.

To even more efficiently bypass NIR power-bandwidth limitations, we used a structure which combinesthe advantages of a conventional interdigitated small-area structure (wider transversal aperture and higherphotoconductive gain) with that of a waveguide (intrinsicbypass of RC time constant, larger area due to extendedlength); an interdigitated finger coplanar stripline structurewas used as depicted in figure 14 [14]. Such a structure alsohas a slow-wave behaviour and therefore was proposed earlierfor phase-matched longitudinally pumped TW photodetectors[37]. In addition to this aspect, which is only important foredge-coupled designs, it opens up the domain of smallestphotoconductive gap widths for TW devices. In figure 14(b),the measured performance of such a device is compared tothat of a plain CPS using the same LT-GaAs material. Thesame optical setup is used for both, except that the CPS isoperated with a pinhole filter, which cuts out about 50% of theSOA power in higher modes, while the TW-MSM structureaccepts all higher modes and thus produces four times moreTHz power.

In comparison to the whole field of TW devices, firstresults on using interdigitated finger CPS structures forimproved THz power from vertically illuminated TW mixersare very promising for the future development of TWmixers beyond 1 THz. We found that theoretically possibleimprovements compared to a plain CPS are deterioratedby increased voltage saturation due to a fringing E-fieldat the interdigitated finger tips, limiting bias voltages to<12 V µm−1, and we could explain this within a bias modelusing a voltage-increased carrier trapping time [18]. Here, wecan see that the role of the LT-GaAs material and the layerstructure needs additional investigation: while similar strongvoltage saturation has been observed and studied previouslyfor small-area structures [24], other groups could use biasvoltages up to 20 V µm−1 [11]. Therefore, voltage saturationis probably a question of the LT-GaAs material [19], electrodecontact quality and layer structure [49]. The observed largescatter of THz efficiencies obtained with LT-GaAs of the samemanufacturing parameters (see table 2) makes this material

s

ba

w

s

102

2

3

4

56

103

2

3

4

56

104

2

PF

IR [nW

]

1600140012001000800600400200

frequency [GHz]

TW-MSM: s = 1.4 µm20V, 320mW, no mode filter

CPS: gap width = 2.0 µm28V, 100mW, with mode filter

(a)

(b)

Figure 14. (a) Left: geometry of a small-area MSM structure orsection of a TW-MSM. Right: example of a TW-MSM structurewith inner part of bow-tie antenna (scanning electron microscopepicture), from [14]. (b) Total power spectrum of TW-MSM and CPSwith bow-tie antenna L = 300 µm on 1.5 µm LT-GaAs/0.3 µmAlAs/SI GaAs. The power is corrected for calculated bow-tiereflection efficiency, but not for reflection losses of the Sihemispherical lens (30%), from [14]. Reprinted with permissionfrom E A Michael, Applied Physics Letters, 86, 111120 (2005).Copyright 2005, American Institute of Physics.

very difficult and increases demand for the investigation ofalternative materials, such as ErAs:GaAs [21] or ion-implantedGaAs [22].

4. Outlook

The THz efficiencies of LT-GaAs-based edge-coupled deviceswith gaps of about 0.3 µm and vertically coupled devicesalready with gaps of about 1.5 µm give the impressionthey are approximately the same, but this remains to bechecked by the respective CW measurements. The efficienciescompared in table 2 scatter exceeding the usual THz calibrationerror of ±30%. These as yet unexplained differences pointto irreproducibility difficulties within the LT-GaAs materialsystem. On the other hand, the high efficiency demonstratedwith a tuned resonant small-area structure [46] outlines theimprovement potential for the unchanged TW structures of[11, 14].

Edge-coupled devices may not be able to cope withthe highest CW-infrared powers, unless large cross-sectionand large absorption-volume concepts are also employed,e.g. an interdigitated-finger CPS [37] combined with a widemultimode optical waveguide. However, longitudinal beatingeffects of the modes would complicate such a concept [50]and the problem of extremely high intensities at the input facet

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Table 2. Experimental results for responsivity := Iph/PNIR and THz efficiency := PTHz/P2NIR. In spite of the lack of CW data for the

edge-coupled waveguide-integrated devices, they are compared with CW data of vertically illuminated devices. For comparison, the bestresult ever obtained for a small-area mixer is reported here, too (see the text for discussion).

Effective gap Responsivity THz efficiency Max. NIR-width/ thickness Bias R := Iph/PNIR λIR, ηTHz := PTHz/ power applied

Reference Material Geometry of i-layer (µm) (V) (A W−1) frequency P 2NIR (W−1) (mW)

[9, 41] InGaAs/ p–i–n-CPW 0.4 7 0.2 1.55 µm,InGaAsP L = 50 µm 160 GHz 0.1 CW 100MQW 460 GHz 4 × 10−4 CW 200

[9] InGaAs/ MSM 0.2 7 0.25 1.55 µm,InAlAs P-TWPD 100 GHz 1.2 × 10−3 CW 200MQW L = 650 µm

[4] LT-GaAs, MSM-CPW 0.3 15 0.012 pulsed 0.78 µm, 2.7 × 10−5 ∼4 × 104

rem. substr slot ant. 645 GHz pulsed over ∼1 ps[5] LT-GaAs, MSM-CPW 0.3 15 0.012 pulsed 0.78 µm, 1.8 × 10−5 ∼4 × 104

rem. substr slot ant. 1600 GHz pulsed over ∼1 ps[11] LT-GaAs Planar CPS 2.0 35 0.010 0.85 µm,

dipole 1200 GHz 2.2 × 10−6 CW 300[13] LT-GaAs Planar CPS 2.0 40 0.010? 0.85 µm,

log-period 1800 GHz 9 × 10−6 CW 180[14] LT-GaAs TW-MSM 1.4 20 0.017 0.78 µm,

bowtie 1000 GHz 1.2 × 10−5 CW 320[46] LT-GaAs Small-area 0.8 15 0.005? 0.8 µm

MSM, dipole 1000 GHz 2.4 × 10−4 100

remains. MSM-based concepts have to be preferred to keepthe THz losses as low as possible.

Therefore, vertically illuminated TW devices are probablymaking the jump towards higher CW THz power due tosuperior pump power capabilities; as available powers fromoptical amplifiers or power diodes will exceed 1 W in thenear future, the increase of area will be a crucial feature forphotonic mixers even in the possible case of high Gaussicitybeams provided from external cavity power-diode lasers orthrough fibres; assuming a burnout intensity of 1 mW µm−2

for LT-GaAs, this corresponds to a few 100 µm focus length inthe described large-area design. The potential might be evenhigher if passive cooling techniques are employed. Gratingefficiencies up to 95% can be achieved with holographicgratings, while antireflection coatings of the LT-GaAs andthe silicon lens will together lead to almost a factor of 2improvement.

Power increase exceeding ∼1/s2 is expected by reducingthe electrode spacing s down to the transit time dominatedregion of 200 nm [17]. However, the production of thesefine structures might prove to be difficult, as the fingers haveto be very narrow to obtain a reasonable optical throughputso that stabilization with an antireflection coating will beobligatory. Vertical electrode structures for MSM devicesare also an interesting alternative from this viewpoint, asfirst results on these for small-area structures demonstrateda smaller electrode response time [51] than found with planarmixers [19, 14]. Semi-transparent top-electrode material suchas TiO [52] or 10 nm thick gold [51] could be employed hereto form a resonant cavity for the NIR radiation, so that thethickness of the photoconductive material can be reduced fortransient-time-limited or even overshoot-velocity-dominatedoperation which would result in much higher 3 dB frequencies.

In vertical MSM or p–i–n electrode designs, it may bestraightforward to introduce an electron diffusion blockinglayer to overcome diffusion limitation of the transit time.This UTC concept may be the next to be implemented with

TW devices, as a first step with a few lumped-elementdiodes along an edge-coupled optical waveguide has beenperformed already for an edge-coupled device [53], andvertically illuminated structures with this principle may bemanufactured more easily.

Substrate removal should give a large improvement athigh frequencies, as a steep increase of losses ∼f 3 towards3 THz is expected from shock radiation and substrate modes[13], but this has not yet been compared experimentally.

If future development of TW mixers includes all thediscussed improvements, microwatt power levels at 2 THz willnot be unrealistic. Accordingly, there is great potential thatTW approaches with large mixing areas will deliver enoughpower to pump hot-electron bolometers and SIS mixers up to2 THz and perhaps higher.

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