- Email: [email protected]
Low-loss single-mode waveguide for submillimetre and millimetre wavelengths
LOW-LOSS WAVEGUIDF. FOR MILLIMETRE
SINGLE-MODE SUBMILLIMETRE WAVELENGTHS
AND
D. J. HARRIS, K. W. LEE and R. J. BATT’ University of Wales Institute
I
Portsmouth
of Science and Technology, Department of Physics, Electronics and Electrical Engineering, King Edward VII Avenue. CardifT CFI 3NU. U.K. and Polytechnic Department of Electrical and Electronic Engineering. Portsmouth. I1.K.
Abstract--Groove
guide is potentially attractwe as a low-loss low-mode guide for the 10lS1000GHz frequency range. The theoretical characteristics, including the ability to reject higher order modes, are discussed. Experimental measurements of performance at 100 and 890 GHz are presented.
INTRODUCTION
Conventional microwave techniques, using TE, o mode propagation in rectangular waveguide, may be readily applied at frequencies up to 1OOGHz. The problems associated with shorter wavelengths are shown in Fig. 1. The theoretical and experimental attenuations are 5 and IOdBm-’ at a wavelength of 2 mm, for dominant mode propagation. and are increasing rapidly as the wavelength is decreased further. Moreover. for only single mode propagation the guide cross-section dimensions must be less than the wavelength, leading to minute tube size and associated difficulties in constructing waveguide and components. The power handling capability of such guide is also very low. It
-
WC(29) I 65x0.83mmz
WG (26) 3.10xl.55mmz
100 -
_ . .
8 .N
Nz
---a_
__-_---WCC221 7 12x3.57m-n
-
Operating rouge 8
10-1 I
Ewzwnental
result
I
I
I
I
2
3
4
5
I 6 b.
I
I
I
7
8
9
mm
Fig. I. Standard rectangular TE 1o wavcguidc attenuation. 741
IO
D. J. HARKIS. K. W. Lm. and R. J. BATT
742
Fig. 2. Basic configuration
and field distribution of TE,, mode E-field. dotted line. H-field.
in groove
guide.
Solid
line
is clear from Fig. 1 that the attenuation is much less if oversize guide is used, but this leads to the possibility of multimode propagation. which may not be important for short guides or non-coherent operation. but for coherent situations many wavelengths in length the presence of many modes leads to confusion of the signal. The recent development of high power sources at these short wavelengths emphasizes the need for a suitahie low-loss guide. Groove guide has been previously investigitted” 4’ and many of its ch~~r~~cteristics enL~merated. Further investigations are being carried out with the objective of developing a wavcguide system to match the new sources and detectors now available at short-millimetric and submillimetric wavelengths. BASIC
PROPERTIES
OF
GROOVE-GUIDE
The configuration and field distribution of the TE,, mode in groove guide is shown in Fig. 2. The field is a modified form of the TElo low loss mode that can exist between in the parallel conducting planes. For the TE, 1 mode there is a field concentration region of the groove which can be considered to act as a ‘lower phase velocity region’. The field decays exponentially in the outer region. and the transverse dimension can therefore be limited. A precise sotution to the field distribLltion is comptic~~ted because of the abrupt change in boundaries. but convergent series solutions can be obtained by equating appropriate conditions at the boundary between the groove and outer regions. For normal groove dimensions simple approximations using only the first term of the series solution suffice. The attenuation of groove guide can be readily computed, and the theoretical loss of guide in copper for a groove depth rl of a yuarter of the plane separation 7c (the reason for this is given later) and for a groove width 2tr equal to the plane separation or to half the plane separation. is shown in Fig. 3. From this figure it is clear that for low loss propagation the plane separation must be much greater than the wavelength.
Low-loss single-mode
waveguide
for submillimetre
and millimetre
wavelengths
743
20/2c=O,5 20/2c=
1.0
-
-
t
’
1o-2 0
I
I
I
I
2
3
1
x0. mm
Fig. 3. Theoretical attenuation of
TE,, mode in groove guide. Groove ation. (i = 5.8 x IO’ Sm-'.
depth = i plane separ-
but that the theoretical loss can be very low, e.g. 0.1 dBm-’ even at a wavelength of 1 mm. Such a condition for other guides would normally lead to multimode propagation however. The special characteristic of groove guide in rejecting higher order modes was disof a single order mode in the cussed by Nakahara and Kurauchi. “) The combination groove region with a single order mode in the outer region, or combinations of other equal-order modes, leads to an exponential decay in the transverse direction and therefore confinement. However, if a mode of higher order in the groove region is coupled to one of lower order in the outer region, e.g. a third order mode in the groove to a first order mode in the outer region, then the outer region transverse distribution exponent becomes imaginary, i.e. the energy is propagated out of the central region and the higher order mode energy is lost from the system. This can be shown by consideration of the wave equation in the two regions. Thus any mode. apart from those of first order, will be rejected provided that it can be radiated or absorbed in the outer region. The effectiveness of this rejection depends upon the coupling between appropriate field distributions in the groove and outer regions, which in turn is affected by the ratio of groove depth to plane separation. This characteristic of groove guide allows it to propagate as a low-mode guide even for large plane separations.
ON
THE EFFECT OF HIGHER ORDER
GROOVE DEPTH MODE REJECTION
A series of measurements(‘) was made at a wavelength of 8 mm on groove guide of variable groove depth. A resonance technique was used whereby a IOcm length of guide, short-circuited at each end by conducting planes with coupling apertures,
D. J. HARKIS. K. W. Ltk and R. J. BATT
744
0
O-
TE z mode
0
0
0
0 0 0
l-L 1 cl*h, JIllI 0
0
0
0
0
0
0
0
(a)
27 GHz
Fig.
4. Resonance
spectra from depth =
u
i
i,
40
27
to
1Smm,
d
JI
4.n 1
GHz
40 GHI. Plant separation (b) groove depth = 7.5 mm.
= 30mm.
(ai
Ciroow
could be excited as a resonator over a frequency range of 27.--40 GHz to give a resonance spectrum. This technique allows the dispersion, the attenuation and the moding characteristic to be obtained. Resonance spectra for two groove depths are shown in Fig. 4, for a plane separation of 30mm. The order of the higher order modes could be determined by a perturbation technique, and the variation of higher order mode magnitudes with groove depth is shown in Fig. 5. It is seen that when the groove depth is about a quarter of the plane separation the higher order mode contributions are negligible. Consideration of coupling between modes in the two regions of the guide confirms that such a groove-depth/plane-separation relationship does give good coupling between
0
TE
2
4
6 d, mm
8
mode
IO
0
12
Los-loss
single-mode waveguide for submillimetre
and millimetre
wavelengtha
I l-
745
LJ
416mm
I= 389mm
Fig. 6. Resonance spectrum
at 96.5 GNz. Plane separation = Iffmm. Groove width = Smm.
Groove
depth = 2.5 mm
relevant modes, but is not critical. It is important to note that the groove depth does not depend on the wavelength and does not require fabrication with an accuracy which is a small fraction of a wavelength. The relationship L&?c.= l/4 has been used for all further measurements on groove guide. Cross-sections of guides used at wavelengths of 3 mm and 3.17 jlrn have included Iossy expanded potystyrene and aquadag, respectivefy, to absorb higher order modes. EXPERIMENTAL ME~~~~~~~~~S 3 mm WAVELENGTH
AT
Rosonancc measurements’“’ at 96.5 GHz, using an Impart source (Piessey ATU 27f) have been made on lengths of guide 12 and 42 cm in length. In each case the length of short-circuited guide could be continuously varied over a few centimetres to give a resonance spectrum. By combining the results of the two lengths of guide the endplatc and coupling aperture losses coulll be eliminated to obtain the loss of the guide itself. A spectrum for a plane separation of 10 mm. a groove depth of 2.5 mm and a groove width of 5 mm is shown in Fig. 6. The higher order mode contribution is negligible even though the plane separation is more than 32. Evaluation of the guide ~~tten~~~~t~ol~ from the resonance widths for the two lerrgths of‘ i~l~im~~~um guide gave 0.7dBm ‘~ The theoretical loss for this guide is 0.1 dBm_‘. The agreement is considered good. A factor of 2-4 is normally found between theoretical and experimental attenuation figures for carefully drawn waveguide in the millimetric region and our guide was made by conventional workshop techniques. The very small difference between the guide wavelength of 3.13 mm and the fret space wavelength of 3.1 1 mm shows that the groove guide used has very low dispersion. EXPERIMENTAL 337 /em
MEASUREMENTS
AT
WAVELENGTH
Preli~~~i~ary measurements on groove guide using an HCN laser as source have been made. The experimental system is shown in Fig. 7. Since the laser is a constant frequency source the resonator length must be varied. and this was accomplished” by varying the temperature over a 75-C range. For the 25cm tength of guide this gives a length change in excess of a half wavelength, i.e. sufficient to display two resonance peaks.
746
D. .I. HARRIS. K. W. L.FI, and R .I. BAI I
Reference
slgnoi
Coupling apertures of 0.25 mm diameter were needed to give adequate detector rusponsc. Plane separations of 2 and 4 mm, and groove widths of 0.5. I.0 and 2.0 mm have been used, the groove depth in each case being ;I quarter of the plant separation. A rcsonancc curve for II separation of 4 mm and groove width of 2.0 mm is shown in Fig. X. The distance between peaks converted to length variation using the thermal coeflicicnt of expansion corresponds well with the wavelength. The Q-factor of the main IXSOI~;~IICC gives an attenuation of 14dBm-‘. compared with a theoretical value of 1 dBtn ‘. No estimate of the contribution due to the endplates and coupling apertures to this figtlrc
Low-loss
single-mode
waveguide
for submillimetre
and millimetre
747
wavelengths
has been possible, but the experience at 3 mm wavelength suggests that these end tosses will be appreciable. The presence of a minor peak indicates the existence of an additional mode. With a decrease of plane separation and groove width this minor peak is not present, but the attenuation is greater. We are still investigating guide behaviour at this wavelength. SUMMARY
OF
GROOVE
GUIDE
CHARACTERISTICS
Groove guide has the advantage that it is large in dimension compared with the wavelength and simple to construct, since no dimension is criticai to a small fraction of a wavelength. The special characteristic of the guide in rejecting most higher order modes can result in single mode propagation even though the dimensions are large. The large dimensions give a low attenuation to the guide, i.e. more than an order of magnitude less than dominant mode rectangular guide, and a high power transmission capability. The field configuration of groove guide should enable components such as detectors, couplers, attenuators and phase shifters to be constructed. Indeed, it may well be possible to develop oscillators also in the guide, leading to an entire groove guide system. Ackflowlr,c/yc,,i~ltrlt- We are glad to acknowledge the assistance and valuable J. M. Reeves of Portsmouth Polytechnic in the development of this work.
REFERENCES I. 2. 3. 4. 5. 6. 7.
TISCHER.F. J., IEEE
Trans. MTT-11, 291 (1963). YIE. H. Y. & N. F. AVDEH,Pm. Nur. Ektrott. Cot@: 21. 18 (1965). GRIEMSMANN,J. W. E.. Proc. Symp. Quasi-Optics, 565 (1964). NAKAHARA, J. & N. KLJRACICHI. Suwitottzo Elrc. Tech. Rev. 5. 65 (1965). HARRIS, D. J. & K. W. Ltx, Electron. La 13, 775 (1977). HARRIS. D. J. & K. W. LEE. Electrons. Lrrt. 14, 101 (197X). BATT. R. J., A. DOSWELL& D. J. HARRIS. Electro~~. Letr. 10, 145 (1974).
discussion
provided
by Mr
SINGLE-MODE SUBMILLIMETRE WAVELENGTHS
AND
D. J. HARRIS, K. W. LEE and R. J. BATT’ University of Wales Institute
I
Portsmouth
of Science and Technology, Department of Physics, Electronics and Electrical Engineering, King Edward VII Avenue. CardifT CFI 3NU. U.K. and Polytechnic Department of Electrical and Electronic Engineering. Portsmouth. I1.K.
Abstract--Groove
guide is potentially attractwe as a low-loss low-mode guide for the 10lS1000GHz frequency range. The theoretical characteristics, including the ability to reject higher order modes, are discussed. Experimental measurements of performance at 100 and 890 GHz are presented.
INTRODUCTION
Conventional microwave techniques, using TE, o mode propagation in rectangular waveguide, may be readily applied at frequencies up to 1OOGHz. The problems associated with shorter wavelengths are shown in Fig. 1. The theoretical and experimental attenuations are 5 and IOdBm-’ at a wavelength of 2 mm, for dominant mode propagation. and are increasing rapidly as the wavelength is decreased further. Moreover. for only single mode propagation the guide cross-section dimensions must be less than the wavelength, leading to minute tube size and associated difficulties in constructing waveguide and components. The power handling capability of such guide is also very low. It
-
WC(29) I 65x0.83mmz
WG (26) 3.10xl.55mmz
100 -
_ . .
8 .N
Nz
---a_
__-_---WCC221 7 12x3.57m-n
-
Operating rouge 8
10-1 I
Ewzwnental
result
I
I
I
I
2
3
4
5
I 6 b.
I
I
I
7
8
9
mm
Fig. I. Standard rectangular TE 1o wavcguidc attenuation. 741
IO
D. J. HARKIS. K. W. Lm. and R. J. BATT
742
Fig. 2. Basic configuration
and field distribution of TE,, mode E-field. dotted line. H-field.
in groove
guide.
Solid
line
is clear from Fig. 1 that the attenuation is much less if oversize guide is used, but this leads to the possibility of multimode propagation. which may not be important for short guides or non-coherent operation. but for coherent situations many wavelengths in length the presence of many modes leads to confusion of the signal. The recent development of high power sources at these short wavelengths emphasizes the need for a suitahie low-loss guide. Groove guide has been previously investigitted” 4’ and many of its ch~~r~~cteristics enL~merated. Further investigations are being carried out with the objective of developing a wavcguide system to match the new sources and detectors now available at short-millimetric and submillimetric wavelengths. BASIC
PROPERTIES
OF
GROOVE-GUIDE
The configuration and field distribution of the TE,, mode in groove guide is shown in Fig. 2. The field is a modified form of the TElo low loss mode that can exist between in the parallel conducting planes. For the TE, 1 mode there is a field concentration region of the groove which can be considered to act as a ‘lower phase velocity region’. The field decays exponentially in the outer region. and the transverse dimension can therefore be limited. A precise sotution to the field distribLltion is comptic~~ted because of the abrupt change in boundaries. but convergent series solutions can be obtained by equating appropriate conditions at the boundary between the groove and outer regions. For normal groove dimensions simple approximations using only the first term of the series solution suffice. The attenuation of groove guide can be readily computed, and the theoretical loss of guide in copper for a groove depth rl of a yuarter of the plane separation 7c (the reason for this is given later) and for a groove width 2tr equal to the plane separation or to half the plane separation. is shown in Fig. 3. From this figure it is clear that for low loss propagation the plane separation must be much greater than the wavelength.
Low-loss single-mode
waveguide
for submillimetre
and millimetre
wavelengths
743
20/2c=O,5 20/2c=
1.0
-
-
t
’
1o-2 0
I
I
I
I
2
3
1
x0. mm
Fig. 3. Theoretical attenuation of
TE,, mode in groove guide. Groove ation. (i = 5.8 x IO’ Sm-'.
depth = i plane separ-
but that the theoretical loss can be very low, e.g. 0.1 dBm-’ even at a wavelength of 1 mm. Such a condition for other guides would normally lead to multimode propagation however. The special characteristic of groove guide in rejecting higher order modes was disof a single order mode in the cussed by Nakahara and Kurauchi. “) The combination groove region with a single order mode in the outer region, or combinations of other equal-order modes, leads to an exponential decay in the transverse direction and therefore confinement. However, if a mode of higher order in the groove region is coupled to one of lower order in the outer region, e.g. a third order mode in the groove to a first order mode in the outer region, then the outer region transverse distribution exponent becomes imaginary, i.e. the energy is propagated out of the central region and the higher order mode energy is lost from the system. This can be shown by consideration of the wave equation in the two regions. Thus any mode. apart from those of first order, will be rejected provided that it can be radiated or absorbed in the outer region. The effectiveness of this rejection depends upon the coupling between appropriate field distributions in the groove and outer regions, which in turn is affected by the ratio of groove depth to plane separation. This characteristic of groove guide allows it to propagate as a low-mode guide even for large plane separations.
ON
THE EFFECT OF HIGHER ORDER
GROOVE DEPTH MODE REJECTION
A series of measurements(‘) was made at a wavelength of 8 mm on groove guide of variable groove depth. A resonance technique was used whereby a IOcm length of guide, short-circuited at each end by conducting planes with coupling apertures,
D. J. HARKIS. K. W. Ltk and R. J. BATT
744
0
O-
TE z mode
0
0
0
0 0 0
l-L 1 cl*h, JIllI 0
0
0
0
0
0
0
0
(a)
27 GHz
Fig.
4. Resonance
spectra from depth =
u
i
i,
40
27
to
1Smm,
d
JI
4.n 1
GHz
40 GHI. Plant separation (b) groove depth = 7.5 mm.
= 30mm.
(ai
Ciroow
could be excited as a resonator over a frequency range of 27.--40 GHz to give a resonance spectrum. This technique allows the dispersion, the attenuation and the moding characteristic to be obtained. Resonance spectra for two groove depths are shown in Fig. 4, for a plane separation of 30mm. The order of the higher order modes could be determined by a perturbation technique, and the variation of higher order mode magnitudes with groove depth is shown in Fig. 5. It is seen that when the groove depth is about a quarter of the plane separation the higher order mode contributions are negligible. Consideration of coupling between modes in the two regions of the guide confirms that such a groove-depth/plane-separation relationship does give good coupling between
0
TE
2
4
6 d, mm
8
mode
IO
0
12
Los-loss
single-mode waveguide for submillimetre
and millimetre
wavelengtha
I l-
745
LJ
416mm
I= 389mm
Fig. 6. Resonance spectrum
at 96.5 GNz. Plane separation = Iffmm. Groove width = Smm.
Groove
depth = 2.5 mm
relevant modes, but is not critical. It is important to note that the groove depth does not depend on the wavelength and does not require fabrication with an accuracy which is a small fraction of a wavelength. The relationship L&?c.= l/4 has been used for all further measurements on groove guide. Cross-sections of guides used at wavelengths of 3 mm and 3.17 jlrn have included Iossy expanded potystyrene and aquadag, respectivefy, to absorb higher order modes. EXPERIMENTAL ME~~~~~~~~~S 3 mm WAVELENGTH
AT
Rosonancc measurements’“’ at 96.5 GHz, using an Impart source (Piessey ATU 27f) have been made on lengths of guide 12 and 42 cm in length. In each case the length of short-circuited guide could be continuously varied over a few centimetres to give a resonance spectrum. By combining the results of the two lengths of guide the endplatc and coupling aperture losses coulll be eliminated to obtain the loss of the guide itself. A spectrum for a plane separation of 10 mm. a groove depth of 2.5 mm and a groove width of 5 mm is shown in Fig. 6. The higher order mode contribution is negligible even though the plane separation is more than 32. Evaluation of the guide ~~tten~~~~t~ol~ from the resonance widths for the two lerrgths of‘ i~l~im~~~um guide gave 0.7dBm ‘~ The theoretical loss for this guide is 0.1 dBm_‘. The agreement is considered good. A factor of 2-4 is normally found between theoretical and experimental attenuation figures for carefully drawn waveguide in the millimetric region and our guide was made by conventional workshop techniques. The very small difference between the guide wavelength of 3.13 mm and the fret space wavelength of 3.1 1 mm shows that the groove guide used has very low dispersion. EXPERIMENTAL 337 /em
MEASUREMENTS
AT
WAVELENGTH
Preli~~~i~ary measurements on groove guide using an HCN laser as source have been made. The experimental system is shown in Fig. 7. Since the laser is a constant frequency source the resonator length must be varied. and this was accomplished” by varying the temperature over a 75-C range. For the 25cm tength of guide this gives a length change in excess of a half wavelength, i.e. sufficient to display two resonance peaks.
746
D. .I. HARRIS. K. W. L.FI, and R .I. BAI I
Reference
slgnoi
Coupling apertures of 0.25 mm diameter were needed to give adequate detector rusponsc. Plane separations of 2 and 4 mm, and groove widths of 0.5. I.0 and 2.0 mm have been used, the groove depth in each case being ;I quarter of the plant separation. A rcsonancc curve for II separation of 4 mm and groove width of 2.0 mm is shown in Fig. X. The distance between peaks converted to length variation using the thermal coeflicicnt of expansion corresponds well with the wavelength. The Q-factor of the main IXSOI~;~IICC gives an attenuation of 14dBm-‘. compared with a theoretical value of 1 dBtn ‘. No estimate of the contribution due to the endplates and coupling apertures to this figtlrc
Low-loss
single-mode
waveguide
for submillimetre
and millimetre
747
wavelengths
has been possible, but the experience at 3 mm wavelength suggests that these end tosses will be appreciable. The presence of a minor peak indicates the existence of an additional mode. With a decrease of plane separation and groove width this minor peak is not present, but the attenuation is greater. We are still investigating guide behaviour at this wavelength. SUMMARY
OF
GROOVE
GUIDE
CHARACTERISTICS
Groove guide has the advantage that it is large in dimension compared with the wavelength and simple to construct, since no dimension is criticai to a small fraction of a wavelength. The special characteristic of the guide in rejecting most higher order modes can result in single mode propagation even though the dimensions are large. The large dimensions give a low attenuation to the guide, i.e. more than an order of magnitude less than dominant mode rectangular guide, and a high power transmission capability. The field configuration of groove guide should enable components such as detectors, couplers, attenuators and phase shifters to be constructed. Indeed, it may well be possible to develop oscillators also in the guide, leading to an entire groove guide system. Ackflowlr,c/yc,,i~ltrlt- We are glad to acknowledge the assistance and valuable J. M. Reeves of Portsmouth Polytechnic in the development of this work.
REFERENCES I. 2. 3. 4. 5. 6. 7.
TISCHER.F. J., IEEE
Trans. MTT-11, 291 (1963). YIE. H. Y. & N. F. AVDEH,Pm. Nur. Ektrott. Cot@: 21. 18 (1965). GRIEMSMANN,J. W. E.. Proc. Symp. Quasi-Optics, 565 (1964). NAKAHARA, J. & N. KLJRACICHI. Suwitottzo Elrc. Tech. Rev. 5. 65 (1965). HARRIS, D. J. & K. W. Ltx, Electron. La 13, 775 (1977). HARRIS. D. J. & K. W. LEE. Electrons. Lrrt. 14, 101 (197X). BATT. R. J., A. DOSWELL& D. J. HARRIS. Electro~~. Letr. 10, 145 (1974).
discussion
provided
by Mr