Numerical and experimental investigation of a 5-portmitre-bend directional coupler for mode analysisin corrugated waveguides

Juan Ruiz & Walter Kasparek & Carsten Lechte & Burkhard Plaum & Hiroshi Idei

Received: 21 December 2011 /Accepted: 24 February 2012 /Published online: 14 March 2012# Springer Science+Business Media, LLC 2012

Abstract A directional coupler array with 5 ports integrated into a mitre bend for corrugatedwaveguide transmission lines at 140 GHz has been manufactured. The design is reviewed,and calculations on the performance for in-situ power measurement and mode discriminationare shown. Emphasis is given on detection of errors in alignment of the transmission system.Experimental tests are performed to benchmark the calculations. The results confirm thepredictions and show that such a coupler is a viable tool for power measurement and basicmode analysis in high-power transmission systems.

Keywords Directional coupler . Corrugated waveguides . Hybrid modes . Mode analysis .

Electron cyclotron heating

1 Introduction

In Electron Cyclotron Resonance Heating (ECRH) systems for thermo-nuclear fusionexperiments, high-power millimetre waves have to be transmitted from the gyrotrons tothe plasma. Oversized corrugated waveguides carrying the HE11 mode or beam waveguidesconducting a gaussian beam are used [1]. Owing to the large diameter of the waveguides andthe beams, a high-precision alignment of the systems is necessary. This is especiallynecessary in high-power long-pulse or cw systems like the 170 GHz HE11 waveguidesystem for ITER, where higher-order modes can cause severe damage to fragile components,like the vacuum barrier window or non-cooled parts of the launchers.

For simple power measurement in corrugated waveguides, directional couplers in mitrebend mirrors can be used. The most compact solution for a bi-directional coupler employs afundamental waveguide integrated below the mirror surface (with about 1 mm remaining

J Infrared Milli Terahz Waves (2012) 33:491–504DOI 10.1007/s10762-012-9883-0

J. Ruiz :W. Kasparek (*) : C. Lechte : B. PlaumInstitut für Plasmaforschung der Universität Stuttgart, Pfaffenwaldring 31, 70569 Stuttgart, Germanye-mail: kasparek@ipf.uni-stuttgart.de

H. IdeiResearch Institute for Fusion Science (RIAM), Kyushu University, Fukuoka, Japan

wall thickness) and coupled to free space via a tapered hole array [2]. The width of thewaveguide is matched to the angle of incidence by choosing the Brillouin angle of thewaveguide equal to the angle of incidence; its orientation determines the polarizationdirection. Complete in-situ field analysis is possible with full-surface couplers, using beamsplitters integrated into (mitre bend) mirrors [3, 4]. However, such devices are very difficultand expensive to manufacture, especially for cw designs. A simpler alternative is a multi-port directional coupler, which is relatively easy to manufacture and compatible with coolingstructures. A 4-port directional coupler developed for alignment control in beam waveguidesshowed high performance [5].

In this paper, the design and investigations of a 5-port coupler for use in corrugated HE11

transmission lines as used in the ASDEX upgrade ECRH systems [6] are presented. The goalof the development for these couplers is (i), to obtain signals for the power detection in themain (HE11) mode and (ii), the level of spurious modes caused by tilt misalignments and bybeam diameter mismatch.

Note that modes in balanced, strongly oversized corrugated waveguides – as is the casefor high-power millimetre wave systems – can be described by two different modesystems, by hybrid (HEmn and EHmn) and by linearly polarized (LPmn) modes. Therelationship between these mode systems is described in Ref. [7]. For the present work,the description of the waveguide fields by LPmn modes seems more appropriate, andtherefore is used throughout this paper. In the following, the mode structure of the LPmn

modes is shortly reviewed, the design of the 5-port mitre bend coupler is described, andbasic calculations on coupler signals are presented. Model experiments are performed tobenchmark the results. Finally, an outlook is given discussing the use of these couplers forhigh-power cw systems.

2 Linearly polarized modes in corrugated waveguides

2.1 Electromagnetic fields of LPmn modes

For polarization in the y-direction, the dominant fields of an LPmn mode are given by [7]

Ey;mn r; fð Þ ¼ A JmXmnr

a

� �� e j wt�kzzð Þ � cos mfð Þ

sin mfð Þ

( ); ð1Þ

Hx;mn r; fð Þ ¼ � A kzw μ0

JmXmnr

a

� �� e j wt�kzzð Þ � cos mfð Þ

sin mfð Þ:

( ): ð2Þ

All other fields are negligible by a factor l /a, where l is the wavelength and a is thewaveguide radius. In (1) and (2), the cos-term corresponds to odd modes LPmn

(o), the sin-term to even modes LPmn

(e). Xmn is the nth zero of the Bessel function of order m, and thepropagation constant kz of the mode is

kz;mn ¼ k0 �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� X 2

mn

k0að Þ2s

; ð3Þ

492 J Infrared Milli Terahz Waves (2012) 33:491–504

k0 being the propagation constant in vacuum. The (power) normalization factors to create anorthonormal mode set are given by

N0n ¼ A2pa2J 21 X0nð Þfor LP0n modes m ¼ 0ð Þ ð4Þ

Nmn ¼ 0:5 � A2pa2J 2m�1 Xmnð Þfor all other LPmn modes: ð5Þ

2.2 Excitation of linearly polarized modes in corrugated waveguides

Corrugated waveguide transmission systems usually are fed by the output beam of agyrotron, where the beam parameters are matched by a mirror system to optimize theexcitation of the main transmission mode, the HE11 or LP01. As shown e. g. in Ref. [8],the alignment at the entrance to the waveguide is very critical: a tilt of few tenths of a degreewill excite several percent of higher-order modes, predominantly the LP11

(o), (hybrid modesHE21 + TE01), or LP11

(e) (HE21 + TM02), depending on the polarization with respect to theplane of the tilt.

The same modes are excited by a radial displacement of the beam. A mismatch of thediameter of the input beam will excite axially symmetric modes, predominantly the LP02 mode.Even for perfectly aligned input beams, typical manufacturing tolerances of the transmissioncomponents and alignment errors cause a few percent of higher-order modes [9].

In Fig. 1, the profiles of these essential modes, LP01, the LP02, the LP11(e), and the LP11

(o) areshown. One can see that in a single-mode system, there is always an appropriate position wherea probe could be situated for measurement of the mode power. However, in a typical transmis-sion line with mainly LP01 and several percent of spurious modes, the fields in the waveguideswill interfere, and the power distribution across the waveguide will be a function of the relativephase between the modes. For any two modes present in the waveguide, the local power willvary strongly according to the beating of the modes with the beat wavelength

Λmn;m0n0 ¼ 2pkz;mn � kz;m0n0

: ð6Þ

This behaviour is shown in Fig. 2, where the power distribution in the waveguide isplotted at various positions along the waveguide for a mode mixture of LP01 and LP02(Fig. 2a), and LP01 and LP11

(o) (Fig. 2b). If more modes were present in the waveguide, amuch more complicated behaviour would be expected.

2.3 Detection of LPmn modes with a 5-port coupler

In principle, the beating makes it impossible to measure the mode power with a probesituated at a single position. Only if the relative mode spectrum (including the relative modephases) stays constant, a power measurement is possible, when the coupler is calibrated to acalorimetric power reference.

A way to improve the measurement performance is the use of a 5-port coupler andappropriate signal processing. The couplers are situated in the centre (r00) and at identicalradial positions (r/a00.63 in the present case) forming a cross, as sketched in Fig. 3.

The coupler outputs (amplitudes!) are added with appropriate weighting factors such thatthe interfering modes cancel, and the mode signal to be measured is summed up construc-tively, finally squared in the detector to get a power-proportional output signal.

J Infrared Milli Terahz Waves (2012) 33:491–504 493

For clarification, Fig. 4 shows again the main mode fields plotted along the radius, withthe coupler positions marked by vertical lines.

2.4 Calculation of the mode powers from the coupler signals

In the general case the number of modes, which can be detected, is equal to the number ofcouplers, if the coupler positions are chosen properly.

Assuming a mode mixture, which consists only of the modes LP01, LP02, LP11(e), and

LP11(o), it is possible to unambiguously obtain the mode powers from the coupler signals L,

R, T, B and C.In addition, the relative phases of the modes have no influence on the calculation, which

means that the results are independent from the actual position of the coupler in the transmissionline. This is done by multiplying the coupler signals, which are assumed (e.g. adjusted withphase shifters) to have identical phases, with real weighting factors (e.g. adjusted by attenu-ators) and summing them up. The sums are then proportional to the mode amplitudes. Thegeneral formula for the calculation for one mode is of the form:

Am ¼ cLLþ cRRþ cTT þ cBBþ cCC ð7Þ

a)

x (m) x (m)

y (m

)

y (m

)

x (m) x (m)

y (m

)

y (m

)

b)

x (m) x (m)

y (m

)

y (m

)

x (m) x (m)

y (m

)

y (m

)

Fig. 1 Linearly polarized modes in a corrugated waveguide with radius a043.5 mm. The colours show theamplitude of the modes, the arrows depict the polarisation direction. a) LP01 (left), LP02 (right); b) LP11

(e)

(left), LP11(o) (right).

494 J Infrared Milli Terahz Waves (2012) 33:491–504

a)

x (m)x (m) x (m)

y (m

)

x (m)x (m) x (m)

y (m

)

b)

x (m) x (m)x (m)

y (m

)

x (m) x (m)x (m)

y (m

)

z = 0.0 m z = 0.71 m z = 1.41 m

z = 0.0 m z = 1.96 m z = 3.92 m

Fig. 2 Power distribution for a mixture of two modes showing the beating along the waveguide withradius a043.5 mm at a frequency f0140 GHz. a) 88% LP01 and 12% LP02, with beat wavelengthΛ01,0202.82 m; b) 90% LP01 and 10% LP11

(o) with beat wavelength Λ01,0207.84 m (percentagevalues relate to mode power).

43.5 mm

27.6 mm

T

B

L RC

Fig. 3 Positions and names ofcouplers signals.

J Infrared Milli Terahz Waves (2012) 33:491–504 495

Here, L, R, T, B and C are the amplitudes of the coupler signals, cL, cR, cT, cB and cC are theweighting factors. The weighting factors are normalized such that the mode power becomesPm ¼ A2

m.For the case of simultaneous detection of 5 modes from 5 signals, we get a matrix

equation:

A!¼ ðMÞ

LRTBC

0BBBB@

1CCCCA ð8Þ

The mode amplitudes are contained in the vector A!, the rows of the matrix (M) contain

the weighting factors for each mode. In order to calculate the coefficients of (M), we assumea pure mode (denoted 1) with the power of 1. For obtaining the mode amplitude from thecoupling signals independently of the position, the matrix (M) must fulfil:

ðMÞ

L1R1

T1B1

C1

0BBBB@

1CCCCA ¼

10000

0BBBB@

1CCCCA ð9Þ

L1, R1, T1, B1 and C1 are the coupling signals for the described case, which are identical tothe field values of the pure mode 1 sampled at the coupler positions. By writing theanalogous expressions for the other modes (denoted 2 – 5), we get the inverse matrix of (M):

ðMÞ�1 ¼

L1 L2 L3 L4 L5R1 R2 R3 R4 R5

T1 T2 T3 T4 T5B1 B2 B3 B4 B5

C1 C2 C3 C4 C5

0BBBB@

1CCCCA ð10Þ

This general formalism can be extended to n coupler channels. It allows the detection of nmodes, if the coupler positions are chosen such, that the inverse of (M) according to (10) is

Fig. 4 Field amplitude of LP01, LP02 and LP11(o) as function of the waveguide radius, with coupler positions

at r00, and r/a00.63 marked by vertical lines. The amplitudes are normalized for identical mode power.

496 J Infrared Milli Terahz Waves (2012) 33:491–504

non-singular. Another criterion for choosing the coupler position would be a high signal forthe modes, which should be detected, to increase the dynamic range of the system.

With the present coupler positions, we can detect the LP01, LP02, LP11(e) and LP11

(o)

modes. The next important mode, the LP03 cannot be detected because the couplers are onlyat 2 different radial positions, which means that only 2 rotational symmetric modes can bedistinguished. It was, however, possible to obtain weighting factors for getting the ampli-tudes of the 4 modes (see Table 1).

The coefficients for extracting the LP11(e,o) content are obvious, here we subtract the

upper and lower (or left and right) signals cancelling the fields of rotational symmetric LP0mmodes.

Thus, a tilt in the waveguide or a misaligned input beam can be easily detected by such acoupler anywhere in the waveguide. The LP01 and LP02 modes are extracted by doing alinear combination of all 5 coupler signals. The weighing factors for the centre and the outersignals are chosen such that a pure LP01 mode results in a zero signal for the LP02 detectionand vice versa. Note that the LP02 signal can be a tracer for a possible diameter mismatch ofthe beam injected into the waveguide.

In principle, it would be sufficient to use just 2 opposite outer signals (T and B or L andR) to detect the LP0m modes. Using all 4 signals, however, has the advantage that the higher-order LP21 modes have no influence on the LP0m results.

Figure 5 shows the simulated mode powers generated from a synthetic mode mixtureusing the coefficients in Table 1. The mode powers are reproduced perfectly at any positionalong the waveguide.

2.5 Sensitivity to higher-order modes

As already mentioned, the LP21(e,o) modes will not disturb the results because their contri-

bution to the coupler signals is cancelled if the coefficients of Table 1 are used. Anotherimportant mode however is the LP03 (HE13) mode. It is rotationally symmetric and willinfluence the detected powers of the LP01 and LP02 modes. Figure 6 shows the detectedpowers according to Fig. 5 for the case of an additional content of 0.2% LP03. We observe aspurious modulation of the detected powers of the LP01 and LP02 modes, while the detectedpowers of the LP11

(e,o) modes are unaffected.It might be possible to decrease the modulation by the LP03 mode by optimizing the

positions of the outer holes. For a complete suppression (or separate detection) of the LP03mode, one would, however, need holes at three different radial positions (see section 2.6).On the other hand, the LP02 and LP03 modes are excited by the same type of misalignment.In a practical application it might be sufficient to adjust the coupling into the transmissionline such that the detected LP02 power becomes minimal.

Other types of spurious modes, which are for example excited by astigmatism of thegyrotron beam injected into the waveguide, require more coupling channels to be detected.

Table 1 Amplitude coefficients for extracting the mode powers from the coupler signals.

Mode cL cR cT cB cC

LP01 0.5869 0.5869 0.5869 0.5869 0.895

LP02 -0.3847 -0. 3847 -0. 3847 -0. 3847 0.766

LP11(e) 0.0 0.0 1.102 -1.102 0.0

LP11(o) 1.102 -1.102 0.0 0.0 0.0

J Infrared Milli Terahz Waves (2012) 33:491–504 497

For the case that the axes of the astigmatic beam are parallel to the axes of the coupler(defined by the positions of T - B and L - R), at least the signals of LP11

(e,o) are notinfluenced. Generally, if other than these 5 modes exist in the waveguide, the detectionbecomes disturbed and is no longer independent of the position of the couplers. For themaximum acceptable level of spurious modes it is difficult to make a general estimationbecause it strongly depends on the mode type and the relative phase with the other modes.

2.6 Optimised coupler positions

An optimised version of the couplers would have the vertical holes (T and B) at differentradial positions, than the horizontal holes (See Fig. 7). This would allow detection of theLP03 mode in addition to the other modes. In the formalism presented in 2.4, the matrix (M)would be invertible for n05.

Fig. 5 Calculated outputs of the mode power from a synthetic mode mixture (94% LP01, 1% LP02, 2%LP11

(e), 3% LP11(o) ) over axial positions from 0 m to 8.0 m.

Fig. 6 Calculated outputs of the mode power from a synthetic mode mixture (93.8% LP01, 1% LP02, 2%LP11

(e), 3% LP11(o), 0.2% LP03) over axial positions from 0 m to 8.0 m.

498 J Infrared Milli Terahz Waves (2012) 33:491–504

3 The prototype 5-port coupler

3.1 Design of the couplers

The 5-port coupler is integrated into the mirror of a mitre bend as used in the 140 GHzECRH systems at ASDEX Upgrade. Figure 8 shows the reflecting side as well as the backside. Five leaky wave antennas form the individual couplers; they consist of fundamentalwaveguides below the mirror surface, which are coupled to free space via a hole array. Theuse of a short antenna array instead of single holes reduces the sensitivity against strayradiation (very high-order modes) in the waveguide and allows to separate between forwardand backward power. Such couplers [2] are widely used in ECH experiments like W7-AS,ASDEX Upgrade [6], and LHD [10] to measure the transmitted power on (mitre-bend)mirrors in corrugated waveguides and beam waveguides.

The width of the waveguide is matched to the angle of incidence α by choosing theproper Brillouin angle Θ of the waveguide:

Θ ¼ arccosffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� l

2a

� �2q� �; Θ ¼ 90� � a ð11Þ

L R

T

C

B

Fig. 7 Optimized hole positionsfor detecting 3 different LP0mmodes.

Fig. 8 Mitre bend mirror with integrated 5-port coupler. Left: mirror surface; the insert shows a sketch of asingle waveguide coupler (cross-section). Right: Coupler mirror mounted on the mitre bend casing showingthe waveguide connections.

J Infrared Milli Terahz Waves (2012) 33:491–504 499

Thus this coupler produces a (half-) conical antenna beam with an opening angle of 2Θ; it isespecially sensitive to radiation incident at the angle α, with a beam width (FWHM) of theorder of λ/ 2LAcosα, where LA is the length of the array (see details e. g. in [5]). For the mitrebend application with α045°, the waveguide width at 140 GHz is a01.51 mm.

The waveguide couplers are integrated into the mirror by standard milling of thewaveguide channels with subsequent closing of the waveguide by electroforming (seeFig. 8, including the inset) and final machining of the mirror surface. Within the waveguiderun, a taper is integrated to get standard D-Band waveguide output with flanges UG-387/Uat the rear side of the mirror.

In the present coupler mirror, the coupling waveguides are oriented upright, i.e. the holearray can excite only currents, which are perpendicular to the waveguide. This means thatthe couplers are sensitive for the polarization perpendicular to the plane of incidence. In caseof polarization which is not oriented along this plane, or in case of elliptical polarization,only the polarization component in the perpendicular plane is measured; this does onlychange the absolute signals, but not the relations between the signals. For application in atransmission line, the coupler would usually be installed after the polarisers, which areadjusted such that maximum output with best signal-to-noise ratio is obtained. If thetransmission line contains mitre bends, which are oriented in planes perpendicular to eachother and which are equipped with couplers, both polarisations could be analyzed simulta-neously. Note that couplers for universal polarisation can be made by using square wave-guides (width a) with subsequent ortho-mode transducers to separate the polarisation signalsat the outputs; alternatively, pairs of waveguides with perpendicular orientation with respectto each other can be used.

The present prototype is not cooled as it is intended for maximum pulses of 1 MW for10 s. Note, however, that the electroforming technique easily allows the integration of a layerof cooling channels below the waveguides, to get a cw design. Cooled mirrors withwaveguide couplers are used in the matching optics of the ECRH system in W7-X [11],and have been tested at 900 kW for 30 min pulse length. At Kyushu University, a prototypeof a similar 5-port mitre-bend directional coupler has been designed for cw 1 MWoperationof the 170 GHz ITER application. The coupler mirror with cooling channels is going to befabricated with a brazing technique.

The array antenna is produced by drilling holes into the mirror surface, where the holediameter is tapered to achieve an antenna pattern with low sidelobes. For the couplers undertest, 19.8 mm long arrays with 19 holes each at a distance of 1.1 mm were used. The holediameter was chosen in the range of 0.82 mm – 0.55 mm to approximate a raised-cosinetapered coupling as

E / 0:9 � cos px2 � 9:1

� �þ 0:1; ð12Þ

yielding a coupling factor for the centre coupler in case of an LP01 mode of typ. –60 dB.Note that this relatively high coupling factor was used to get sufficient SNR for the low-power test; couplers for high-power use [6] typically are designed with coupling factors inthe range of -70 to -80 dB.

3.2 Radiation pattern of the couplers

The antenna pattern of the couplers was checked in a compact range; results are shown inFig. 9. The main lobes agree well with the calculations; a small, but negligible deviation ofthe 45°-orientation can be explained by a slight increase of the waveguide width of

500 J Infrared Milli Terahz Waves (2012) 33:491–504

(effectively) 40 μm. As this value is higher than the typical mechanical tolerance, (part of)this increase might be caused by the relatively large coupling holes. The measured sidelobelevel is somewhat higher than calculated, probably due to small deviations of the holediameters from the specified values. Nevertheless, a coupling directivity of about 30 dB isobtained except for the central one, where probably a defect flange produces some reflec-tions within the coupler waveguide. Variations of the coupling strength (cf. the R-port inFig. 9) must be included in the calibration of the detectors, or have to be corrected withattenuators.

4 Experimental test of the 5-port coupler

For the experimental test of the 5-port coupler, defined mode mixtures of LP01 and a higher-order mode were injected in to the waveguide. The LP01 mode was generated by a matchedlens horn (combination of Gaussian beam horn [12] and a Teflon lens) with mode purity of>96%. To excite an LP02 mode, the distance between horn and lens was varied in a definedway to obtain a beam which was mismatched in diameter; additionally, a horn producing asmaller beam waist was used. From mode analysis of the output field, the LP02 content wascalculated. Higher symmetric modes are excited only with negligible power as shown in Ref.[8]. For the experimental investigation of asymmetric modes, a defined tilt in the angle ofincidence of the injected beam was introduced to excite mainly the LP11

(e) asymmetric mode[8]. Again, the relation between tilt angle and LP11

(e) contents was obtained from modeanalysis. The mitre-bend coupler signals were measured at different positions along thewaveguide, i.e. with different relative phases between the modes, and the effect of spuriousmodes was studied.

In Fig. 10, the power measured from the 5 ports in the mitre-bend with a 12% LP02 modecontent is plotted against position in the waveguide. The interference between modes LP01and LP02 creates a beat pattern along the waveguide with a period of approx 2.8 m; the totalpower injected is now distributed between the fundamental mode and the higher ordermodes.

From the figure it can be seen that the beating pattern increases or reduces the power levelin the outer ports as a function of position, it is like as if the beam was being focused or

0 30 60 90 120 150 180

-40

-30

-20

-10

0

pow

er (

dB)

Radiation angle Θ (deg)

RCBLTcalc.

Fig. 9 Radiation pattern of the coupling arrays in the plane defined by the normal on themirror and the line of holes.

J Infrared Milli Terahz Waves (2012) 33:491–504 501

defocused with a lens system, so much that the power in the outer ports overrun the power ofthe centre port at approx 1.4 m.

It is obvious that for the practical case, where onemeasurement position only is used, and thephase relations between the modes are not known there, a quantitative result cannot be obtainedfrom these power signals. However, as shown in chapter 2.4, the use of the amplitudeinformation allows the extraction of mode compositions. For the experimental demonstration,only two of the coupler outputs were used for simplicity. To detect the LP02 contents, couplersignals from ports C and L were added according to the coefficients in Table 1 using adirectional coupler and an adjustable attenuator and phase shifter in the waveguide from theC-port. Calibration of this interferometer was performed with a “pure” LP01 mode by using thesignal from C only (the waveguide from port L was opened for this case).

Figure 11 (left) shows the output of the interferometer C –L, when the contents of theLP02 mode is varied by changing the position of the feed horn in the LP01 generator. When

0 1 2 30

5

10

15

20

25

30 C B L T R

Pow

er (

dB)

Position of coupler (m)

Fig. 10 Coupled power from the 5 ports for an LP01 with an admixture of 12% LP02 mode, measured with themitre bend installed at various positions in the waveguide line (symbols). The beat wavelength between thesetwo modes is 2.84 m as can be seen from the calculated curves (solid line: expected signal from C; dashedline: expected signals from B, L, R, T).

1E-3 0,01 0,1 1 10

-12

-6

0

6

12

18

24

30

MeasurementCalculation

Inte

rfer

omet

er s

igna

l (dB

)

additional LP02 contents (%)

Fig. 11 Output of interferometer C – L at position 0 m as function of the horn position (left) and thepercentage of LP02 (right): Note that the position “50 mm” is the nominal horn position where mode purity ofLP01 is maximum.

502 J Infrared Milli Terahz Waves (2012) 33:491–504

the data are plotted against the resulting LP02 contents (Fig. 11, right), a very goodagreement with the calculated curve is obtained. The results show a high sensitivity forthe spurious mode, with the lower limit practically given by the mode purity used in thecalibration procedure. For the present case, an error of <0.1% LP02 would be derived fromthe data in Fig. 11 (right).

For the experimental investigation of asymmetric modes, a defined tilt δ in the angle ofincidence of the injected beam was introduced to excite the LP11

(e). For detection of thismode, an interferometer between the ports T and B was implemented using the appropriateweighting factors in Table 1. Once the interferometer was balanced (at z00.1 m), the outputpower as function of the tilt angle δ was recorded. With identical settings of the interfer-ometer, the experiment was repeated at three different positions along the waveguide,especially selected (cf. Fig. 2) to measure the content of the LP11

(e) where the power levelfrom the ports could not allow its proper detection. As seen from Fig. 12, the minimum ofthe output occurs always at the same angular position δ, i.e. with nominally 0% of LP11

(e).This clearly shows that such a coupler can be used for alignment of a transmission system atarbitrary positions. An angular resolution of δ≤0.1° was obtained. From the mode analysiswe can now relate the interferometer output to the LP11

(e) mode content. The results arefairly independent of the measurement position; deviations can be mostly explained by theprecision when setting the angle δ, the finite mode purity for balancing the interferometer,and variations in alignment when moving the mitre bend between the measurement posi-tions. For the present case, an error of <0.4% LP11

(e) would be derived from the data inFig. 12 (right).

5 Conclusions and outlook

The present work shows that a 5-port coupler integrated into a mitre bend is a valuable toolfor mode analysis and alignment in LP01 transmission lines. Depending on the signalanalysis, the power of the main mode and several higher-order modes can be measured.The device is especially sensitive to the LP02 mode, which is excited when the line is fedwith a beam with diameter mismatch, and to the even and odd LP11 modes, which are tracersfor angular misalignment. Proof-of-principle measurements clearly confirm the calculations.

The present design using short line arrays for the couplers reduces the interference fromvery high-order modes, and allows the discrimination of forward and backward modes. The

0

6

12

18

24

30

36

tilt angle (deg)

pow

er (

dB)

0.1 m 2.1 m 4.1 mcalc.

-0,8 -0,4 0,0 0,4 0,8 0,1 1 100

6

12

18

24

30

36

0.1 m + 4.1 m - 2.1 m - 0.1 m - 4.1 m + 2.1 m +

pow

er (

dB)

LP11 contents (%)

Fig. 12 Output of interferometer T – B at positions z00.1 m, 2.1 m and 4.1 m as function of the tilt angle δ ofthe input beam (left) and the percentage of LP11

(e) (right). Symbols: measurement data (see legend), solid line:calculated output.

J Infrared Milli Terahz Waves (2012) 33:491–504 503

fabrication by electroforming avoids any contact problems within the coupler waveguides:This makes the design robust with respect to heating in high-power applications. Moreover,a second layer of channels for water-cooling for CW operation can be easily embedded intothe copper mirror.

A general formalism was developed to calculate the weighting factors for detecting themode amplitudes independently of the coupler position within the transmission line. Thepositions of the holes must be chosen such, that the matrix of the sampled field amplitudes isnon-singular. Further optimization should result in high signal levels from the couplers toimprove the robustness against noise.

With classical microwave techniques, the summation of 5 ports needs many components.Therefore, several options are under investigation for a simple and robust system for modeanalysis. This includes (i) optimisation of the benefit from 2 or 3 ports only, (ii) integratingof necessary couplers and phase shifters into the copper mirror, and (iii) using amplitude andphase information detected by heterodyne or homodyne receivers at the various ports andprocessing the data numerically. Work for these options as well as fabrication of cooledcoupler mirrors is underway.

Acknowledgement This work was supported in part by the Collaborative Research Program of the ResearchInstitute for Applied Mechanics, Kyushu University.

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