Parameters of the investigated MDS
1. Introduction
Among the open structures, which are used in millimeter and submillimeter (MSM) wave engineering, diffraction gratings (DG) made in different modifications (periodic metal and metaldielectric structures (MDS)) are of primary importance along with open cavities and open waveguides. Such systems are basic in the design of electromagnetic oscillation sources and electronic components of different instrumentation of such wavelength range. If there is a diffraction of electromagnetic fields by DG, “twoact” wave transformation usually takes place. When homogeneous plane wave falls on the plane onedimensionally periodic grating, scattered field can be considered as a spectrum of homo and heterogeneous plane waves. In this case body (incident) plane wave is transformed into body (scattered) homogeneous plane and heterogeneous (surface) waves and, thus, “twoact” transformation occurs. This type of the boundaryvalue problems has been thoroughly studied in the work [1] and partly realized in the experiment [2]. In addition, processes of surface wave transformation of distributed sources into body waves by periodic heterogeneities are of special interest. Such phenomenon can be watched when an electron beam (EB) moves uniformly near the metal DG or periodic MDS. In this case selfsurface field of the EB is scattered by DG and at least one of its harmonics is transformed into body wave of the diffraction radiation or Cherenkov radiation. It should be noted, that transformation of the surface wave of EB by DG into the diffraction radiation is also an example of the “twoact” diffraction process. In addition, phenomena, connected with the transformation of DG of the surface waves of a dielectric waveguide (DW), play a great role in MSM engineering. In this case surface waves of a DW are transformed by the DG into surface waves of the DW or into body waves separated from them.
Multilinked quasioptical systems in different modifications are very perspective in designing fundamentally new electronic devices and electronic components of instrumentation of MSM wavelength range including infrared waves. One should mentioned, that they are partly investigated by numericallyanalytic methods in the approximation of constant current [1] and using the experimental modelling. It was determined that systems with MDS included in the open cavities structure can have qualitatively new properties [3] that makes it possible to propose highfrequency filters, frequency stabilizers, energy output devices from the volume of open cavities and new types of semiconductor oscillators on its basis. A possibility of the development of a SmithParcell amplifier was considered in paper [4].
Huge number of the previously proposed systems isn’t accompanied with its complex research. This fact, therefore, makes the process of practical realization of new modifications of electronic device schemes and electronic components of MSM wavelength range on its basis very slow. So far existed numerical methods of optimization of the threedimensional superhigh frequency structures [5, 6] enable to analyze effectively electrodynamic characteristics only of some multilinked quasioptical system elements such as reflecting MDS. Meanwhile, a comprehensive solving problem of optimization of such structures requires the huge expenditure of computer time and computational power with usually ambiguous results in the end. That is why problems of development of the universal experimental facility, general technique of experimental modelling of the electromagnetic phenomena in multilinked quasioptical systems and its realization for studying electromagnetic effects in complex quasioptical systems using so far existed numericallyanalytic methods, are very topical.
In the current work general electrodynamic characteristics of the multilinked quasioptical system coupling elements have been determined on the basis of previous theoretical and experimental results in research of the simplest types of radiating system, formed by singlerow DG, and using experimental modelling of transformation of the DW surface waves into body waves by tworow DG of different modifications. Schemes of practical microwave engineering devices have been suggested on basis of these characteristics.
2. An experimental setup and measuring technique
The use of periodic MDS formed by a strip metal grating on a dielectric layer is promising for both constructing extremely highfrequency electric vacuum devices (optical coupler and diffraction radiation generator [7, 8]) and integrated forms of various functional assemblies and devices, operating in MSM ranges, including the terahertz range [9]. In contrast to reflecting metal gratings, the MDS have a number of specific features related to a possibility of exciting spatial waves of Cherenkov, normal, and abnormal diffraction radiation, when an EB moves along the MDS [1]. Therefore, it is necessary to have exhaustive information on electrodynamic characteristics of the DG and MDS, when they are used in various devices. Paper [1] presents a method for identifying properties of waves of the space charge of an EB traveling along a periodic structure, to the surface wave of the DW. This method has found a wide utility in simulating electrodynamic characteristics of various radiation modes of spatial waves on periodic MDS and on normal metal gratings. The setup for studying conversions of DW surface waves into body waves on normal metal gratings is described in [10]. However, its application for studying the MDS calls for modernization of the measuring part of the setup, taking into account special features of the analyzed object (possibility of the presence of body waves both in dielectric and outside).
Below, a universal setup that can be used for analyzing electrodynamic characteristics of both the MDS and traditional metal periodic structures is described. Results of test measurements are compared to the numerical analysis.
The complex experimental test bench for determining electrodynamic characteristics of periodic heterogeneities (MDS, strip and reflecting metal gratings), when they are excited by the DW surface wave, consists of two main modules (figure 1): (1) module for measuring waveguide characteristics (standing wave ratios (SWR), attenuation constants, etc.), and (2) module for measuring spatial characteristics of periodic structures (directional radiation patterns in the farfield zone and amplitude distributions of fields in the nearfield zone). The module for measuring spatial characteristics includes the studied object, which is generally dielectric prism 1 with the strip DG 2 imposed on its side surface. Prism 1 is attached to the special adjusting unit intended to spatially orient it in the
The module for measuring spatial characteristics of the object consists of two versatile horn antennas 6, rotation axes of which pass in the
The amplitude field distributions along the axes of the radiating system are studied in the nearfield zone (
On the whole, all indication systems of spatial characteristics and studied object were placed on a single solid laboratory platform, illuminated by special precision adjusting units. This allowed us to orient the regular part of the DW with respect to the MDS plane with an error of ~ 0.1 mm and ensure the corresponding monitoring of the coordinates of measuring elements of the setup and studied object.
The module for measuring waveguide characteristics (figure 1) is based on a standard panoramic SWR and attenuation constant measurer, consisting of the SFG, SWR and attenuation constant indicator, and DC 8 with detector sections connected to corresponding connectors of the SWR indicator. Depending on the method of bringing the couplers into the measuring line, plots of either transmission gain or SWR were determined in the specified frequency range. The obtained results were processed by the designed ADC and arrived via the USB bus at the PC for further processing. The constant power level at the input to the studied object was kept by the APR, being the part of the panoramic measurer, and the minimal reflections at the DW output were ensured by inserting matched load 5 into the measuring section (when absolute power levels were measured in the transmission line, standard wattmeters inserted directly into the measuring section instead of matched load 5 were used).
(1) The matching of DW 3 with the module for measuring waveguide characteristics, which consists in reaching 1.1 to 1.2 SWR values for the specified frequency band by optimizing parameters of matching junctions 4. (2) Determination of the relative velocity of DW surface wave β_{ w } = ν_{ ph }/c (c is the velocity of light) and stray radiation level from matching elements 4. For this purpose, the calibration reflecting DG, characteristics of which are intended for radiation in the normal direction (angle γ_{–1ν} in figure 1) in accordance with the procedure [10], and indication system of fields in the farfield zone (horn antennas 6) are used. (3) Determination according to the procedure [1] of the optimal value of the aiming parameter a from the minimal distortion of directional lobes at the central frequency. (4) Determination of MDS and DW characteristics for the specified excitation modes of body waves in accordance with relationships of [1]. (5) Replacement of the calibration reflecting grating by the studied MDS. (6) Measurements of spatial MDS characteristics with the simultaneous automatic control of its waveguide characteristics.
The described experimental setup (figure 1) is implemented for a 53 to 80GHz band, and this fact determined the selection, as a panoramic SWR and attenuation constant measurer, of a corresponding device and waveguide sections with a 3.6×1.8mm^{2} cross section. The fluoroplastic DW with a 5.2×2.6mm^{2} cross section permitted us to obtain relative phase velocities of the surface wave in interval β_{
w
} = 0.78–0.81 and to excite on the fluoroplastic MDS two main spatial radiation harmonics, namely,
MDS parameters implemented in the experiment for three main operating modes of freespace wave excitation at the central frequency are given in the Table 1.
No  Operating mode of exciting spatial waves 




β 
1  Cherenkov 
1,17  0,39  0,30  +0,5  0,788 
2  diffractionCherenkov 
3,07  1,535  0,79  0  0,788 
3  abnormal diffraction 
1,36  1,084  0,35  0,8  0,598 
The experimentally obtained data has been compared to the results of the numerical experiment based on solving Maxwell equations in a form of partial derivative using finitedifference approach and taking into account constitutive relations.
It follows from the given plots that the experiment satisfactorily correlates with the numerical analysis, and this, in turn, confirms serviceability of the described setup for studying electrodynamic characteristics of periodic structures belonging to a new class, i.e., planar MDS, which can find application in producing devices of MSM and terahertz wavelength ranges.
3. Practical devices of microwave technology and electronics
3.1. A quasioptical directional coupler
The general principle of designing DC is to use two energy transmission lines coupled to each other [11, 12], along one of which the main power ﬂow is transmitted; the auxiliary line is intended for interference and separation of forward and backward waves.
To date, depending on the imposed requirements, a great number of DC modiﬁcations are used in MSM wavelength measuring circuits.
The systems based on DW or dielectric planar waveguides [13] with distributed coupling, local coupling, and reemission into the secondary channel are the most close to the proposed DC.
In this work, the design of the DC based on two diffractioncoupled transmission lines with distributed radiation sources is studied, the sources being formed by periodic structures and DW placed along them. Figure 3 shows a general DC drawing and two possible reﬂector conﬁgurations, namely, planeparallel and planecylindrical.
The basic DC section is formed from periodic structure 1, along the longitudinal axis of which DW 2 is placed at distance a. The second section is made similarly; it also consists of periodic structure 3 and DW 4. The periodic structures are applied on surfaces of flat and cylindrical mirrors with aperture
The principle of operation of the diffractioncoupled DC is based on exciting inphase and antiphase spatial waves. As a result of the propagation of these waves along the longitudinal DC axis, the radiators exchange energies and some power is directed into the secondary channel. Results of theoretical and experimental studies of transformations of DW waves into spatial waves and of spatial waves into surface waves on periodic structures are described in detail in [1].
Let us dwell on the special features of the wave processes in the proposed quasioptical DC (figure 3). When the microwave signal is applied to input I, the delayed wave propagates in DW 2 and is scattered at periodic structure 1. In this case, a diffraction field arises, which is a superposition of plane waves. Some waves go into the DC volume at angles α as spatial waves, and the remaining ones are localized near the grating as slow harmonics propagating to the output of waveguide 2. The radiation angle of the spatial waves is determined by the relation [1]:
where β_{
w
} = ν_{
w
}/c is the relative wave velocity in the DW; ν_{
w
} is the phase velocity of the wave;
The second excitation stage of the system in figure 3 is the incidence of the spatial wave formed at angle α on structure 3. As a result of diffraction, the complete field over the periodic structure consists of the incident and spatial harmonics of the scattered field. If
When ν_{ f } ≈ ν_{ w }, the delayed wave is also excited in DW 4 and is transformed into a spatial wave on periodic structure 3. When surface waves are successively transformed into spatial ones and spatial waves are transformed into surface ones, inphase and antiphase waves are formed along the axis of reﬂectors of the DC and, as a result of their interference, part of the incident and reﬂected power is branched off to the secondary section.
The geometric sizes of the considered DC are selected from the inequalities [6] that specify the fulﬁllment of laws of ray optics in the doublemirror quasioptical systemml:
where
The fulﬁllment of the first inequality allows one to represent the field of the studied system as paraxial wave beams (figure 3), which are in many ways similar to a plane wave [14]. The second inequality minimizes the resonance phenomenon display along the longitudinal axis
When cylindrical mirrors with quadratic correction are used, the optimal values of their curvature radii,
We consider an example of selecting parameters of the DC and its components in frequency band
The experimental studies of the DC prototype were performed on the described above setup by measuring directional diagrams of the radiating systems and their nearzone fields and also by measuring waveguide characteristics of both separate DC components and the system as a whole. The mechanical part of the setup allowed one to move DC radiators in three planes with an accuracy of ±0.1 mm and, by varying over wide ranges values a and
As an example, the characteristics of the above design of the DC for two distances between the radiating mirrors are shown in figure 4.
It follows from these characteristics that, for the specified frequency interval, at distances between radiators H = 65 mm, the attenuation constant
(
It is determined that the quasioptical wave behavior of the studied system remains unchanged for
Figure 5, in particular, illustrates the relative dependences of power levels
By comparing the characteristics of the described DC with couplers on coupled DW [15], the following conclusions can be drawn. The DC characteristics in the working frequency band ∆
3.2. Quasioptical power dividers
In this subsection the results of studying the power divider (PD) design based on a tworow semitransparent periodic structure with a distributed radiation source (main section) in the form of the DW, which is placed along its longitudinal axis are presented. In this system, the surface wave of the DW is transformed on periodic grids into spatial harmonics of body waves [16]. Figure 6 shows two PD modifications with longitudinal (Δ
The PD contains DW 1, which is embedded into the main microwave section through matching junctions 2, grids made of bars 3 and 4, and radiation receivers 5. Grid 3 is fixed in position with respect to the
The principle of operation of these PD is based on transforming the DW surface wave into the spatial (body) wave, which is excited on the grids. The radiation power level of this wave can be regulated by changing phase relations of slow harmonics of waves excited on the grids of the tworow structure when its bars are shifted or when the rotation angle with respect to the DW axis is changed.
We consider general features of wave processes in the described quasioptical PD (see figure6). When the microwave signal with power
Р_{
1
} is applied to the input of DW 1, the delayed wave propagates over its surface and scatters on grids 3 and 4. In this case, the diffraction field is formed, which is the superposition of plane waves. The part of these waves goes away into the free space (powers
where γ_{
n
} is the emission angle of the harmonic with index
From equation (4), it follows that the waves with
The geometrical sizes of the considered PD are selected from equation (4) when the fundamental (
where
In the grid with the optimal profile, somewhat smaller than the integer number of halfwaves should be fitted in bar thickness 2
In addition, the intensity of the spatial waves in the considered systems can be regulated by the duty factor of the semitransparent grids made of bars
The interval of the optimal value region of parameter Δ
Hence, the surface wave mode occurs in the open structure of the DW and grid 4 at ϕ = ϕ_{
cr
}, and the further increase in ϕ results in the Bragg diffraction, for which
As an example, let us select the parameters of the PD and their main elements in the fourmillimeter wavelength range (
The experimental studies of the PD prototypes (figures 6 (a), (b)) were performed in accordance with the described above procedure.
As an example, the amplitude (relative values
The analysis of the plots in figure 7 shows that the power in the arm
From the viewpoint of regulating and calibrating the emitted power
By analyzing the characteristics of the described PD, it is possible to make the following conclusions. In contrast to the waveguide analogs and PD on DW [15], the described PD possess wider functional capabilities, allowing one to divide the power coming from the main section into equal parts between two channels and smoothly regulate it in one of the output arms of the divider. In this case, the powers arriving at the output arms of the divider can be regulated by changing the sighting distance of the DW with respect to the grid surfaces. The presented PD can be also manufactured in the planar form if periodic MDS are used [11].
3.3. Possible variants of implementation of MSM radiation sources
Nowadays MSM microwave devices (backwardwave tubes, tavelingwave tubes, klystrons) with high level of output power are widely used in transmitting equipment of communication systems, radars and radio countermeasures devices. Thus, there is the rapid development in production of travelingwave tubes with slowwave structures as a chain of coupled resonators in different geometrical modifications [8], creation amplifiers based on the multielectronbeam tubes [18] etc. Axially symmetric EB as the main working element of such devices virtually defines their basic working parameters. Therefore, special attention is given to the improvement and optimization of electronoptical systems of MSM microwave devices.
As a rule, an optimization of electronoptical system parameters bases on the information about EB characteristics. Currently, because of the rapid development in computational resources and approaches, different techniques of electromagnetic simulation based on various numerical algorithms are mostly used to get this information. Such approach allows avoiding carrying out timeconsuming and expensive experiment. Usually modelling techniques consist of two stages: computation of electromagnetic fields of the investigated system and subsequent trajectory analysis of charged particles in these fields.
In the current subsection the example of the model of the threeelectrode electron gun which is used in real microwave devices such as travellingwave tube has been presented, the optimization problems of its operating modes and axially symmetric EB characteristics have been outlined.
Axiallysymmetric EB, as a rule, is formed by threeelectrode electron gun with converging optics and introduced into slowingdown system where it is focused by periodic magnetic field. The cathode is usually produced in the form of a core made of tungstenrhenium blend with activated surface. The typical electrode configuration of axially symmetric electronoptical system is demonstrated in figure 8.
The guns of such type allow forming EB with diameter of about 0.3mm in the crossover, the beam current of 1–25 mA with accelerating voltage 2000–6000 V. For numerical simulations the finite integration technique (in literature is known as FIT [19]) was chosen as the optimal numerical algorithm for analyzing the above mentioned systems.
The combination of electrode potentials, described in [20], was taken as the initial parameters with a beam perveance
When simulation of the electronoptical system is carried out, the main parameter of optimality is the coefficient of EB passage. That is why in the first step of the optimization of the electron gun operating modes the research of a beam passage coefficient
Experimental measuring results have shown that the coefficient of the EB passage increases with increasing
Figure 9 shows that the coefficient
Besides the information about the electron deposition on the gun electrodes, which allows carrying out a preliminary analysis of its operating modes, the EB quality parameters (such as type of a particle distribution in the crosssection, laminarity, spread of the velocity transverse components etc.) are also very important. In the current work rootmeansquare emittance (statistical emittance) was used to describe such characteristics:
where
It should be noted, that formula of this type in contrast to other definitions makes it possible to express an EB emittance in a simple numerical form. In addition, we do not find it reasonable to consider a normalized beam emittance in this case because of short drift duct and low accelerating potentials of the system (EB is not relativistic) [21].
The calculated emittance with the maximal passage of the EB at a distance of 10 mm from the cathode made up ε_{
x
} = 1.71 mrad·mm and ε_{
y
} = 1.85 mrad mm in
However, as the numerical experiments to study transversal electron dynamics (figure10 (a)) has shown, value of the emittance can be decreased by variations of the potential
The analysis of twodimensional diagrams of the transversal emittance has demonstrated that the increase of the
Development of highresolution sensitive elements for terahertz frequency bandwidth is an actual problem due to a number of existing international projects of radio astronomy as well as the projects with the objective of studying the Earth atmosphere. The basic issues of arrangement of receivers in the given bandwidth are solved by application of solidstate heterodyne oscillation sources and the mixers based on the effect of electron heating in the superconductor (Hot Electron Bolometer) because such mixers have no competition analogs in this bandwidth. By now these mixers have been successfully realized at the frequencies of the order of 3 GHz. However, several research projects are related to development of the mixers optimized for higher frequencies; e.g. within the framework of the SOFIA project it is developed a heterodyne receiver for 4.8 ТHz. Principal opportunity for creation of the mixer for the given bandwidth is shown in the paper [22] where the method of electron and photo lithography is applied for its realization. As an example, figure 11 provides photos of the central part of the mixer obtained with the scanning electron microscope.
The mixers were made of NbN films with the thickness of 2 to 3.5 nm upon a silicon substrate with a MgO buffer sublayer and possessed the temperature of superconducting transition of 9 to 11 К. The best value of the noise temperature of the receiver on the basis of the electron heated mixer amounted to 1300 К and 3100 К at the heterodyne frequencies of 2.5 and 3.8 ТHz correspondingly.
In the radio astronomy devices and tools the preference is given to solid state heterodyne sources within the terahertz band due to their small dimensions, low weight and power consumption requirements, despite low output power level, which is not exceeding 1 μW at the frequency of 2 ТHz that to a significant extent complicates the problem of development of mixers for a low level of output power. Thus, there still remains actual the problem of realization of lowvoltage electrovacuum oscillation sources within the terahertz wavelength band possessing higher values of power levels as compared to those of solid state oscillators.
By the present time this problem can be solved by means of using in the vacuum electronics of planar periodic MDS [1, 11]. Block diagrams of such devices that could be realized on the basis of the above described technologies and new types of dielectrics with larger values of dielectric permeability and low loss values at high frequencies [23], are provided in figure12.
Block diagram of the oscillator in figure 12(а) suggests modulation of the EB upon a backward wave of the periodic structure (position 2) with subsequent excitation of the Cherenkov oscillation harmonic in MDS (position 3). Within the oscillator in figure 12(b) it is applied the mode of abnormal diffraction oscillation, which is realized at substantially less values of accelerating voltages of the electron flux compared to those of the Cherenkov oscillation harmonic.
At practical realization of the above block diagrams of sources of oscillation it is necessary to solve a set of problems related to the technology of manufacturing of main units of the device – the electrodynamic system, the lowvoltage source of electrons and the focusing magnetic system. The above considered technological processes – like, for instance, nano die forming – eliminate all problems related to manufacturing of both reflecting and ribbon (applied upon the dielectric layer) DG with the micron period.
Oscillator schemes presented in figure 10 are the ideological continuation of the so far developed lowvoltage backwardwave tube with multirow slowwave structures [8, 24]. A schematic view of a lowvoltage orotron based on parallel MDS and three EB are shown in figure 10 (a). The calculated MDS parameters have been determined for EB radiation at the angle of 90°. The diagram of a backwardwave tube based on an anomalous diffraction radiation for MDS is shown in figure13 (b). The arrows show the direction of wave radiation on the MDS.
The analysis of parameters of the discussed electrodynamic systems [11] and devices demonstrated in figure 13 shows that the DG/MDS or multirow systems on basis of MDS at acceleration voltages
The research conducted in [1] indicates that in order to realize the described devices in submillimeter and infrared wave ranges, an EB should be as thin as 0.04 mm. Nowadays the practical realization of such EB is possible using array type or slot type Lcathode, which allow getting uniformly distributed and stable electron emission with high current density at comparatively low field intensity.
The matrices of field emission cathodes possess the preset geometrical dimensions (diameter, step), they allow elimination of the screening effect and obtaining of homogeneous upon the surface and stable in time electron emission with the average current value of 40 μА from a separate cathode at relatively low electric field intensity values. The cathode represented in figure 14 (b) includes the cylinder container filled with a stock of the substance that decreases the output operation of the operating surface, which is represented by a continuous row of microelements forming up a “slot” Lcathode. Experimental results obtained while pilot testing of those cathodes at IRE NAS of Ukraine proved the opportunity for obtaining of such electron fluxes with highvalue current density at not high values of accelerating voltages.
4. Conclusions
In the current work the results of development of the experimental setup and procedure for measuring electrodynamic characteristics of planar periodic MDS, which can be used for manufacturing practical equipment operating in MSM and terahertz wavelength ranges are presented. Serviceability of the setup is checked by comparing the waveguide and spatial characteristics obtained experimentally and by numerical methods in a 4mm wavelength range. A circuit and principle of operation of DC based on diffractioncoupled transmission lines, the emitting apertures of which are formed from periodic structures and DW has been proposed on the basis of the conducted research.
The experimental studies of the coupler prototype in a 30 to 37GHz band have shown that the coupling on spatial waves allows one to obtain transient attenuation values in a 3 to 20dB interval at a ~ 30 dB directivity, this being roughly in conformity with similar characteristics of a coupler on DW. The main advantage of the described DC is that it is possible to correct its characteristics over wide ranges by changing the distance between the emitting apertures.
Circuits and principle of operation of quasioptical PD based on tworow periodic structures, formed by grids of metal bars and a DW placed along their longitudinal axis, have been proposed and described as the second example of realization of described above characteristics. The experimental studies of PD prototypes in a frequency range of 60–80 GHz have shown a possibility of regulating the emitted power level in the main divider arm by changing longitudinal and angular coordinates of the tworow periodic structure, which can be used for designing quasioptical attenuators.
The example of the model of the threeelectrode electron gun of travellingwave tube has been described, the optimization problems of its operating modes and axially symmetric EB characteristics have been outlined.
In addition, studied properties of electrodynamic diffraction characteristics of the surface waves on periodic heterogeneities can be realized in implementation of radiation sources on the SmithParcell effect.
Work is supported by the governmental programme No0112U001379.
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