Low-loss Transmission Lines for High-power Terahertz Radiation

Applications of high-power Terahertz (THz) sources require low-loss transmission lines to minimize loss, prevent overheating and preserve the purity of the transmission mode. Concepts for THz transmission lines are reviewed with special emphasis on overmoded, metallic, corrugated transmission lines. Using the fundamental HE₁₁ mode, these transmission lines have been successfully implemented with very low-loss at high average power levels on plasma heating experiments and THz dynamic nuclear polarization (DNP) nuclear magnetic resonance (NMR) experiments. Loss in these lines occurs directly, due to ohmic loss in the fundamental mode, and indirectly, due to mode conversion into high order modes whose ohmic loss increases as the square of the mode index. An analytic expression is derived for ohmic loss in the modes of a corrugated, metallic waveguide, including loss on both the waveguide inner surfaces and grooves. Simulations of loss with the numerical code HFSS are in good agreement with the analytic expression. Experimental tests were conducted to determine the loss of the HE₁₁ mode in a 19 mm diameter, helically-tapped, three meter long brass waveguide with a design frequency of 330 GHz. The measured loss at 250 GHz was 0.029 ± 0.009 dB/m using a vector network analyzer approach and 0.047 ± 0.01 dB/m using a radiometer. The experimental results are in reasonable agreement with theory. These values of loss, amounting to about 1% or less per meter, are acceptable for the DNP NMR application. Loss in a practical transmission line may be much higher than the loss calculated for the HE₁₁ mode due to mode conversion to higher order modes caused by waveguide imperfections or miter bends.     

Transmission of horizontally polarized waves and trapped waveguide modes in inhomogeneous media

A generalized Wentzel-Kramer-Brillouin (WKB) approach is used to obtain full wave solutions for horizontally polarized waves in inhomogeneous media when no closed form analytic solutions are known. This approach is suitable for complex permittivity profiles with critical coupling regions even when the permittivity gradient approaches zero. The transmission and reflection coefficients and the characteristic surface impedance for inhomogeneous layers of finite thickness are computed for several permittivity profiles. Excitation of propagating and evanescent waves is considered and the results are shown to satisfy the realizability and reciprocity relationships in electromagnetic theory. Sinusoidal permittivity profiles for which closed form analytical solutions are known are also considered to provide an additonal check on the generalized WKB solutions. For permittivity profiles with several spatial periods, transmission windows with very narrow beamwidths are found to exist. When conditions for total internal reflection in the inhomogeneous dielectric layer are satisfied, the reciprocal of the reflection coefficient vanishes and propagating waves are trapped in the layer. For these trapped waveguide modes the inhomogeneous dielectric is characterized by a surface reactance.     

Measurement of RF Transmission Mode in ITER Relevant EC H&;CD Transmission Line

The preliminary results of mode measurement in the ITER relevant 40 m long transmission test line composed from 63.5 mm diameter corrugated waveguides and miter bends are presented. The field patterns were measured by taking temperature profiles on a paper screen placed in front of the waveguide end using an infrared imaging camera. The complex electric field at the waveguide end was retrieved from the measured temperature profiles. As a result, the transmission power includes 87% of HE₁₁ mode and 6% of LP₁₁ odd (HE₂₁+TE₀₁) mode and small ratios of other modes. The mode content had small dependence on length of the transmission line. This result indicated that the higher order mode content generated at the input of the transmission line is conserved and propagated through the transmission line. This suggests that the initial RF coupling to the waveguide is critical since it affects the launcher efficiency.     

A dielectric rod waveguide coupled with metal rectangular waveguide

Measurements have been done in the millimeter wave region on a composite waveguide which comprises a dielectric rod waveguide connecting two metal rectangular waveguides. Such a waveguide has been used by us in a Josephson harmonic mixer installed in a small metal cryostat, to prevent the thermal invasion from outside environment and to transmit both signal and LO waves with small losses. The measured transmission loss, that is caused mainly by the coupling loss between metal rectangular waveguides (TE₁₀ mode) and a dielectric rod waveguide (HE₁₁ mode), has been less than 2dB in the frequency range of 52–104 GHz.     

Calculation of a Hyperbolic Corrugated Horn Converting the TEM<Subscript>00</Subscript> Mode to the HE<Subscript>11</Subscript> Mode

Corrugated waveguide transmission lines are in use to transmit high power mm-wave radiation from gyrotrons to the plasma for electron cyclotron plasma heating in tokamaks such as ITER. The coupling efficiency of the gyrotron output radiation formed as a quasi-Gaussian beam to the waveguide mode is a critical issue. A hyperbolic corrugated horn serves as a converter of the TEM₀₀ Gaussian mode to the HE₁₁ mode of a corrugated waveguide. We report the design of a hyperbolic horn for application in the ITER transmission line at 170 GHz. The theoretical conversion efficiency of the horn is higher than 0.995.     

Atténuation dans un guide d’onde circulaire à cannelure hélicoïdale

Experimental results of attenuation properties for a circular waveguide with helical corrugation propagating the HE ₁₁ mode is presented. Dispersion curve and attenuation values are obtained using classical cavity measurements. First results show a low attenuation and then such a structure would be convenient for antenna feeder applications.     

Hybrid mode trasmission in 62-m corrugated waveguide

Experimental measurements by wavepacket reflectometry are carried out to verify the low transmission loss of hybrid mode on HE₁₁ in the corrugated waveguide with 88.9 mm in diameter. The HE₁₁ mode is injected into the 62-m straight circular corrugated waveguide and the beat between the HE₁₁ and HE₂₁ (including degenerated TE₀₁ and TM₀₂) modes is observed. The loss is too small to measure and inferred to be less than 2 db/km. The result shows that the use of HE₁₁ mode for electron cyclotron heating system is suitable.     

Guided-Wave Experiments with Dielectric Waveguides Having Finite Periodic Corrugation

A planar dielectric waveguide having finite periodic rectangular corrugation is investigated analytically and experimentally, in case of surface waves propagating at an angle to the corrugation. In analytical considerations, a finitely corrugated guide is regarded as consisting of many step discontinuities connected by a length of uniform slab waveguide, and its propagation characteristics in the Bragg interaction region are derived from a cascaded connection of the transmission matrix expressing a step discontinuity. Although the present method takes only surface wave modes into account and neglects the wave with continuous spectrum, the calculated results show an excellent agreement with experimental ones which are performed for art H-guide in the microwave region.     

Surface emitting characteristics of silicon waveguides

This paper concerns the surface emitting characteristics of silicon waveguides in the millimeter-wave frequency band. The waveguides used in the experiment are rectangular slabs of high resistivity silicon (30,000 ohm-cm). A series of periodic perturbations on the waveguide surface provide a radiating antenna. A rectangular grating with a period of Λ=1.8 mm, a height of 0.35 mm, and a duty cycle of 0.46 was sawn into the top surface of a silicon waveguide with a width of 3 mm and a height of 1.41 mm. Experiments were performed to measure the attenuation, dispersion and the radiation characteristics of the waveguides. The test setup was used to monitor the frequency, radiation angle, and the radiated power. Measurements are made over a band of frequencies around the second Bragg frequency. The detector was scanned from 88–95 GHz and changes were observed in the attenuation constant, dispersion relation and the far field radiation pattern. From these results we were able to verify the grating theory.     

Circular groove shaped resonator for millimeter waves

In millimeter wave lengths region semiconductor generators, amplifiers, mixers and other solid state UHF devices find a wide application. In our work, we suggested to use aCircular Through-Shaped Resonator for obtaining power combination using active elements at frequency region Δf≈20–40 GHz. The resonator is formed by two plane aluminum reflectors. The first reflector has a circular groove. The second reflector has coupling elements. The first and the second reflectors are considered as a ring groove shaped waveguide. A resonator spectrum was calculated and analyzed in the frequency range Δf ≈20–40 GHz. It is showed that, in the given frequency range the resonator spectrum has a complicated structure and is formed by a series of spectrum lines; a frequency range between the series increases with the frequency increasing. We studied on transmission coefficient of the resonator, frequency shifts of spectrum lines when inserting a thin (t/λ≈0.003) dielectric substrates into the resonator, and also attenuation constants of waves propagating in circular groove (due to losses in metal).     

Acousto-optic diffraction of optical guided waves in crystal quartz

A waveguide supporting a single propagating mode has been fabricated by ion beam modification of X-cut crystal quartz. The gas ion implantation reduced the index of a subsurface layer, and guiding occurred in the surface region. The acoustic properties of the quartz are little affected. Bragg diffraction of guided light by surface acoustic waves was observed with efficiencies of approximately 0.25% per milliwatt acoustic power.     

Bragg Interaction of Electromagnetic Waves in a Ferrite Slab Periodically Loaded with Metal Strips

The waveguiding characteristics of electromagnetic TE waves in a ferrite slab periodically loaded with metal strips are investigated. Theoretical formulation by means of the spectral domain approach is employed to obtain the Brillouin diagrams of two types of volume modes and a surface mode. It is found that the nonreciprocal properties of waves depend on the metal strip profile and bias magnetic field strength. Experiments on the magnetic-field dependence of the Bragg frequency and the stop bandwidth are carried out in the millimeter-wave frequencies. Typical results obtained from a polycrystalline YIG slab with periodic gold strips deposited on one surface are stop bandwidth about 2.14 GHz, with return loss about 2 dB at the Bragg frequency of 47.5 GHz, for the bias magnetic-field strength of 5.7 kG. The Bragg frequency can be tuned over the range of 1.39 GHz by varying the bias magnetic field from 0 to 8.2 kG. Experimental results show good agreement with theoretical predictions.     

Study of the loss of the H 11 mode in a modified circular waveguide in a wide frequency range

The specific attenuation coefficient of the hybrid HE ₁₁ mode in a modified circular waveguide is calculated using a method developed earlier. Calculations are performed in a wide frequency range for a number of waveguide diameters. Combinations of the parameters of modified waveguides providing a substantial decrease in the specific attenuation as compared to that in an empty waveguide are determined.     

Optical propagation of the HE11 mode and Gaussian beams in hollow circular waveguides

The propagation of the HE₁₁ mode and Gaussian beams in hollow oversized circular waveguides is analyzed using optical theories. Different types of waveguides are considered : hollow dielectric or conducting waveguides, dielectric-lined waveguides, corrugated waveguides. General formulas are derived which give the power transmission through these different guides. The best wall materials and structures are determined from a comparison of the waveguide transmissions, at the infrared and millimeter wavelengths. The question of the coupling between the HE₁₁ mode and Gaussian beams is discussed and from a review of coupling coefficients derived before, an optimum value is pointed out. The problem of matching a Gaussian beam into circular waveguides in order to achieve the maximum power transmission is analyzed. These results are of interest for infrared lasers or waveguide applications and for Electron Cyclotron Wave (ECW) systems at the millimeter wavelength.     

Attenuation Characteristics of Corrugated Circular Groove Waveguide

When neglecting space harmonics and higher-order slot modes, the attenuation characteristic of corrugated circular groove waveguide has been investigated. It is shown that under certain conditions, the attenuation coefficient of HE ₁₁ mode will be lower than that of dominant TE ⁽¹⁾ ₁₁ mode of circular groove waveguide with same radius.     

Experimental analysis of metal coated dielectric waveguides

This paper concerns the experimental characteristics of metal coated dielectric waveguides with a rectangular surface corrugation. Waveguide are designed to operate at a second Bragg frequency of 90 GHz. The period, height and the duty cycle of a rectangular grating were calculated using the chosen frequency. A metallic layer of aluminum is sputtered on one side of the slab waveguide. The purpose of the metallic layer is to simulate a layer of high density plasma on the surface of the waveguide similar to that obtained by optical excitation of semiconductor structures. Experiments were performed to examine the far field radiation pattern, attenuation constant and the dispersion relation. Due to the presence of the plasma layer there will be an angular shift in the far field radiation pattern. We have observed angular shifts of about 20? in the radiation pattern of the waveguide before and after coating. Measurements are made in the frequency range of 88–95 GHz. This waveguide structure can be used to design an electronically steerable antenna and an electronic phase shifter operating in the millimeter-wave frequency band.     

A Method for Determination of Alcohol Content in Dielectric Liquids by a Longitudinal-Slot Waveguide

A new method is proposed to determine the content of alcohol in dielectric liquids. The method is based on measuring the attenuation of a wave propagating in a rectangular waveguide with a longitudinal slot in its narrow wall, immersed in a liquid under test. The propagation constant of the H ₁₀ mode in such a waveguide is calculated numerically for various parameters of the medium and the waveguide. It is shown that the attenuation of the wave depends on the parameters of the dielectric medium outside the waveguide. Experiment is carried out on two different types of waveguide at frequencies from 29 to 37 GHz with a solution of ethyl alcohol in water as the external medium. The results of the measurements show that the method can be used for the on-line measurement of alcohol concentration during fermentation.     

Out-of-Band Response of a Coax-to-Waveguide Adapter

The input impedance and transmission coefficients of a coax-to-waveguide adapter are analyzed for out-of-band frequencies. Numerical results are shown for an S-band adapter for frequencies from 2 to 10 GHz. The above-band response is frequency sensitive because of the presence of higher order propagating modes in the waveguide.     

Radio Communication in Tunnels

The attenuation constant of radio waves in tunnels was obtained experimentally and theoretically. According to this study, the tunnel is a transmission channel of high-pass type. It is found that the higher the frequency, the smaller the attenuation constant. The experimental values of attenuation constants are similar to the theoretical values of the the TE/sub 01/ and EH/sub 11/ and modes when the tunnel is regarded as a circular waveguide with the same cross-sectional area as the tunnel. Radio communication using the tunnel was proven to be fully possible in spite of the standing wave effects due to the interference of the propagation modes.     

Radiation patterns of the HE11 mode and Gaussian approximations

The problem of the approximation of the HE₁₁ radiation pattern by a Gaussian distribution is discussed. A numerical comparison between the HE₁₁ far-field theoretical pattern, and the Gaussian approximations derived by Abrams and by Crenn, permits and evaluation of the precision of these approximations. A new optimized HE₁₁ Gaussian approximation is calculated: the value of r_o=0.421a (or w_o=0.596a) for the beam radius at the waist is demonstrated to give the best HE₁₁ Gaussian approximation in the far-field and is very close to the result given by Crenn, while the Abrams value is less precise. The calculations are extended to the near-field. Universal curves for intensity, amplitude and power distribution are given for the HE₁₁ radiated mode. These results are of interest for laser waveguide applications and for plasma ECRH transmission systems.