The paper investigates the influence of the electromagnetic field and standing wave structure in a quasi-optical waveguide on the dielectric measurement results and gives recommendations on the layout of measuring circuits.

Исследовано влияние структуры электромагнитного поля и стоячих волн в квазиоптическом тракте на результаты диэлектрических измерений. Даны рекомендации по организации измерительных схем.

Modern microelectronics progressively embraces high frequencies in order to process data flows faster with lower power consumption. In this context material engineering in submillimetre frequency band gains ever-greater importance. Dielectric materials synthesized for use in microelectronics shall have low losses and good insulation properties at low dielectric capacity [

One of advanced measurement methods within the submillimetre waveband is contactless method of measurement of dielectric parameters of materials. At such measurement approach a sample is arranged in a quasi-optical waveguide on the path of shaped and directed radiation beam.

Quasi-optics is the basic tool kit of measuring instruments within the submillimetre waveband (100–1000 GHz) [2–5]. At low power levels of operating radiation (up to tens of W) lateral dimensions of quasi-optical elements such as lenses, mirrors, polarisers, and attenuators do not usually exceed 50–60 mm while distances between them are about 100 mm. This is caused both by work convenience issues (in all electromagnetic radiation spectra experimenters try to find room for all measuring instruments on a worktable) and by restricted dimensions of samples under test when we speak about studying the properties of substances and materials, and dimensions of created operating devices. At high power level, in order to eliminate air gap breakdown, it is necessary to use large beam diameters or evacuated systems.

Due to commensurable lateral and longitudinal sizes of the waveguides and wavelength of the working radiation, even the simplest circuits of quasi-optic beam shaping and propagation, similar to optical systems, are augmented with strongly pronounced phenomena of diffraction and interference which drastically sophisticate the measurements. These adverse effects are eliminated with varying degrees of success and considered in empirical research [4–7], but there is no data about targeted research of their influence on the results of quasi-optical measurements.

The purpose of this research is to study on the quantitative level the spatial distribution of power density in quasi-optical waveguide, and to learn phenomena accompanying the quasi-optical measurements of transmission spectra of the samples in conditions of high monochromaticity of working radiation. The major challenges regarding the phenomena being discussed occur during measurements in the low-frequency area of submillimetre frequency band; for this reason the measurements were carried out in the band of 150–320 GHz.

With the aim of optimization of measurement diagrams, the study of transmission spectra of plane-parallel sample was for the first time carried out with deviations from normal wave incidence. Its advantages are demonstrated and specifics of spectrum calculation occurring thereat is discussed.

Backward-wave tubes (BWT) are used as sources, powered from a highly-stable source, providing the radiation monochromaticity level of Δf/f up to 10–5 and covering the range up to 1500 GHz.

Figure 1 gives insight into typical dimensions of output waveguide of a long-wave BWT. Standard dimensions of waveguide WR-6 are 1.6×0.8 mm2 , the operating band is 114.0–173.0 GHz. Usually, horn antenna is not used for measurement arrangement because at the large frequency tuning range BWT (50 %) it cannot provide a satisfactory matching.

Fig. 1. Waveguide lead of BWT-generator

For measurements of spatial power distribution in the waveguide a pyrodetector was used with the input diaphragm, 1 mm in diameter, installed on a scanner with the operating field of 110×110 mm2 . Such receiver was selected due to its small dimensions and low sensitivity to vibrations during scanning. For the purpose of transmission spectra registration a more sensitive optical-acoustic receiver OAP-5 was used.

Figure 2 shows the power distribution in the quasi-optical waveguide at two frequencies. In the near-field region, spatial power distribution has a complicated structure which at the distance of 400 mm is characterised by a bell-shaped distribution, broadening with the distance increase.

Fig. 2. Power distribution of 150 and 320 GHz quasioptical beams at different distances from the source in a diagram with a single polyethylene focusing lens 60 mm in diameter

Figure 3 shows a curve of total power of 150 and 320 GHz quasi-optical beams (50 mm in diameter) versus distance from the source in a system with a single polyethylene focusing lens 60 mm in diameter. At the distance of 1 m power loss equals to 78 and 72 %, respectively. They are entirely caused by quasi-optical beam divergence.

Flattening of power spatial distribution at the frequency of 320 GHz takes place at smaller distances than at 150 GHz.

Air absorption loss at normal humidify and temperature at the frequencies of 150 and 320 GHz do not exceed 0.05 % and 0.2 %, respectively (Fig. 4) [

Fig. 4. Signal attenuation in the air due to atmospheric oxygen and water

With the radiation focusing at the receiver (OAP-5), diffraction losses are unavoidable (Fig. 5). In this case, when a dielectric lens is used, the losses are equal to 36 and 22 % at the frequencies of 150 and 320 GHz, respectively.

Fig. 5. Shaping of submillimetre (SBMM) beam depending on distance behind the polyethylene lens with focal distance of 60 mm. Total power in the beam is preserved. Beam diameter in the focus at the level of 0.7 signal is 4 and 2.5 mm for 150 and 320 GHz, respectively. The lens is located at the distance of 920 mm from the source.

Total diffraction losses at the stages of shaping, propagation, and registration of the quasi-optical beam are rather significant and make 78 and 86 % at 320 and 150 GHz, respectively.

With reduction of the working radiation wavelength the length of quasi-optical circuit can be decreased, which is also reasonable for the purposes of absorption loss reduction in moist air.

One of the main research methods for dielectric characteristics of materials at submillimetre waveband is measurement of transmission spectra of plane-parallel samples [5–7]. An experimental transmission spectrum is obtained after considering the instrument function of the spectrometer. For each frequency of the spectrum the signal value at the receiver is measured twice – with and without the sample in the waveguide. A division result of two signals is a target value of the sample transmission at the given frequency.

Herewith, for calculation of refraction and absorption factor, plane layer formulas are used, obtained in the assumption of electromagnetic wave with plane wavefront. As demonstrated above, power distribution in quasi-optical beam acquires a nearly plane wave profile at the distances larger than 0.5 m from the radiation source.

We used a plate of high-resistance semiconductor GaAs as a test sample, with the plate thickness d = 5.896 ± 0.001 mm and the diameter 58 mm.

Figures 6a and b show transmission spectra of GaAs at two options of its installation in the quasi-optical waveguide.

Fig. 6. Transmission coefficient spectra of GaAs plane-parallel plate obtained at two configurations of the measuring path. Blue dots – experiment, red line – theory: a) the sample is arranged at the distance of 25 cm from the source; b) the sample is arranged at the distance of 80 cm from the source

At low absorption factors of material the plane-parallel sample functions as a dielectric resonator. Its transmission spectrum consists of a number of interference maximums and minimums.

As we can see, in both cases transmission spectra seem to be highly noisy with observable scatter of points but this is not due to low signal level at the receiver. This phenomenon is related to variation in standing waves which occurs after the sample installation in the waveguide. To decrease their influence it is advisable to set the sample in tilted position.

Figure 7 shows a spectrum for the case of sample tilting by 5°. Even such a small tilt of the sample dramatically changes the quality of the measured transmission spectrum.

Fig. 7. Transmission coefficient spectrum of GaAs plane-parallel plate obtained at the sample tilt relative to the optical axis by 5 degrees. Blue dots – experiment, red line – theory

In such diagram the transmission spectra are near-perfectly described by formulas for plane layer, even though the sample is installed in the near diffraction field. Here the crucial importance for improvement of the measured spectrum quality belongs to the fact that the receiver is located at a distance at which only paraxial rays remain and are registered in the quasi-optical beam.

Off-normal wave incidence on the sample exhibits unusual behaviour of maximums (and minimums) in the transmission spectra. The maximums are shifted towards high frequencies and their amplitude decreases due to absorption increase in the sample. The latter is due to the fact that geometric thickness of the sample increases in inverse proportion to cosine of the refraction angle, that results in higher energy loss of the wave. On the other hand, the phase difference which determines the wave interference period in the sample decreases in proportion to cosine of the refraction angle, and as a result the maximums drift towards high frequencies. Using the Snell’s law of refraction on the dielectric boundary with low loss, we can write a formula for the maximum of transmission coefficient:

fTmax = m/(2dn cos γ), where m – interference order (1, 2,…), d – sample thickness (cm), n – sample refraction factor, γ – refracted wave angle, fTmax – frequency for transmission maximum (cm–1).

For Tmax we can write the following proportion:

Tmax ~ exp(–4πkdfTmax /cos γ), where k – sample absorption factor, sin γ = sin α/n, α – angle of wave incidence to sample.

Accuracy of the sample refraction factor estimation from such transmission spectrum with due consideration of the off-normal wave incidence is equal to ±0.2 %. For the measured GaAs test sample these values are equal to n = 3.589, k = 3.1×10–4.

Quasi-optical technique is actually built on the basis of search of an optimal compromise between dimensions of elements and length of quasi-optical waveguides and allowable power loss, related to diffraction phenomena, especially critical at long waves, as well as absorption in the air, which is quite considerable at short waves and near the lines of water and oxygen absorption.

The optimal length of a quasi-optical waveguide in the long-wave range of submillimetre frequency band is 1 m; at this distance there are almost no phenomena in the near diffraction zone, which could distort the measurement results. With reduction of the working radiation wavelength, the length of quasi-optical circuit can be decreased, which is also reasonable for the purposes of absorption loss reduction in the air.

At high monochromaticity of working radiation typical of BWT, standing waves in the quasioptical waveguide are the factor which makes the measurements more complicated. To reduce their effect it is advisable to install a sample under study at an angle of at least 5 degrees to the plane, normal to the wave vector of the quasi-optical beam. Complication of the calculations in this case can be neglected if computer-aided processing of spectra is used.

The authors declare that there are no conflicts of interest present.