 N. N. Voitovich, B. Z.
Katsenelenbaum, A.N.Sivov. Method of the
surface current for construction of discrete spectrum eigen functions
in diffraction problems. Radio Engineering
and Electronic Physics, v.15, No.4, 1970
(Transl. from Radiotekhnika i Elektronika, v.15, No.4, 1970, p. 685696).
Abstract. A new method for solving the
diffraction problems on bodies with metallic or semitransparent
surfaces, as well as on dielectric bodies is proposed. The method
is based on a conception of eigen functions of discrete spectrum,
introduced into the problem for open bodies by spectral parameter
different from the frequency. These functions satisfy the radiation
condition at given real frequency termwise. The method permits to
express the solution in the form of discrete series only. Numerical
results regarding the twodimensional open resonator with plane
mirrors are presented.
 N. N. Voytovich, B. Z.
Katzenelenbaum, A. N. Sivov. The generalized
eigen function method in diffraction problems of electromagnetic wave
theory. Electromagnetic Wave Theory.
Preprints on URSI Int. Symp., Nauka Pub.,
Moscow, 1971, p. 192195.
Abstract. Bases of the generalized eigen
function method for solving diffraction problems are given. The
main property of the method is that the not only frequency can be
used as spectral parameter in the homogeneous problem giving rise
to a function set for expressing the diffraction field in closed
an open domains. The dielectric permittivity of the body, surface
impedance or transparency, etc. can be such a parameter. The main
advantages of such approach are: a) discreteness of the spectrum
in exterior problems; b) simplicity of loss describing in bodies
with lossess of only one type; c) decreasing the series dimension
in the diffraction field expresions, etc.
 N. N. Voitovich, B. Z.
Katsenelenbaum, A. N. Sivov. Stationary
functionals for the generalized method of eigen functions of diffraction
theory. Radio Engineering and Electronic
Physics, v.17, 1972, No.2 (Transl. from
Radiotekhnika i Elektronika,
v.17, 1972, No.2, p. 268275).
Abstract. The functionals stationary on
the eigen functions of homogeneous problems arising in the generalized
eigen functions method are constructed. The main property of these
problems is that the spectral parameter appears in their boundary
conditions, or in the equation describing only a part of the volume.
The boundary conditions containing spectral parameter are make natural
for constructed functionals. Some examples of usage the constructed
functionals are presented.
 N. N. Voitovich, B. Z.
Katsenelenbaum, A. N. Sivov. On the scattering
theory on a quasistationary level. Prepr.
of Inst.Radioeng. and Electr., Moscow,
No. 29(143), 1973, 23 p. (In Russian).
 N. N. Voitovich, B. Z. Katsenelenbaum,
A. N. Sivov. The smethod for diffraction
problems on bounded bodies. Prepr. of
Inst.Radioeng. and Electr., No. 30(144),
1973, 22 p. (In Russian).
 N. N. Voitovich, B. Z.
Katsenelenbaum, N. P. Santalov, A. N. Sivov.
Application of generalized eigenoscillation method to certain problems
on open and slosed resonators. Theory
of Wave Diffraction and Propagation, MoscowYerevan,
1973, part II (In Russian).
 N. N. Voitovich, B. Z.
Katzenelenbaum, N. P. Santalov, А. N. Sivov. Application
of the generalized method of proper modes in diffraction theory.
Proc.of V Colloq.on Microwave Communication,
v. IIIET, Budapest, 1974.
 N. N. Voitovich, B. Z.
Katsenelenbaum, A. N. Sivov. Generalized
method of eigenoscillations in diffraction theory. Researches
in Radio Engineering and Electronics in 19541974,
Inst. Radioeng.&Electr., Moscow, 1974.
1974 (In Russian).
 N. N. Voitovich, B. Z.
Katsenelenbaum, A. N. Sivov. The excitation
of a twodimensional metal cavity with a small opening (slotted cylinder).
Radio Engineering and Electronic Physics,
vol. 19, Dec. 1974, p. 817. (Trans. from Radiotekhnika
i Elektronika, v.19, no.12, 1974, p. 24582469).
Abstract. The generalized eigen oscillation
method is applied to a problem about resonators with small coupling.
In the first approximation, the problem of excitation of an open
resonator with small hole is solved analytically for arbitrary smooth
resonator boundary. Main characteristics of resonator (shift of
resonant frequency, Qfactor) and propagation factors of leaky waves
in waveguide with the same cross section as the resonator contour
are calculated. The coupling of resonators of some concrete forms
is investigated.
 N. N. Voitovich, N. P.
Santalov. Same applications of generalized
eigen oscillation method. Radio Engineering
and Electronic Physics, vol. 19, Dec.
1974, p. 37 (Trans. from Radiotekhnika
i Elektronika, v.19, no.12, 1974, p. 26252629).
Abstract. Two problems are solved by the
generalized eigen oscillation method. Both they are twodimensional.
The first problem concerns the close Hshaped resonator with dielectric
insertion in the passage. In the second problem an open resonator
with circular semitransparent outer surface and an elliptic dielectric
body inside one are considered. The eigen permittivities (a dielectric
permittivity values at which the resonance takes place at given
frequency) are calculated and analyzed. In the second problem, the
resonator losses can be expressedby the imaginary part of eigen
values.
 N. N. Voitovich, B. Z.
Katsenelenbaum, E. N. Korshunova, A. N. Sivov. Solution
of the external problems of diffraction and calculation of the propagation
constants of open waveguides with the aid of a real integral equation.
Radio Engineering and Electronic Physics,
vol. 20, June 1975, p. 18. (Transl. form Radiotekhnika
i Elektronika, v.20, 1975. no.6, p. 11291137).
Abstract. A new variant of the generalized
eigen oscillations method is proposed, in which the spectral parameter
is involved into asymptotical conditions at infinity. This approach
can be applied for investigation of open resonators or waveguides
with semitransparent walls. In the method, the homogeneous eigen
value problem is reduced to a real integral equation. Numerical
results for some concrete examples are presented.
 N. N. Voitovich, B. Z.
Katsenelenbaum, A. N. Sivov. The generalized
naturaloscillation method in diffraction theory. Sov.
Phys. Usp., v. 19, No. 4, 1976, p. 337352.
(Transl. from Uspechi Fizicheskikh Nauk,
v. 118, No. 4, 1976, p. 709736).
Abstract. Main properties of the generalized
eigen oscillation method (GEOM) are expounded. The main idea of
the method is stated, the comparison of the method with eigen frequency
method is made, and some problems are enumerated, to which it is
worth while to apply GEOM. Two classes of the problems are considered.
In the first class problems the spectral parameter is introduced
into the equation. The problems about homogeneous dielectric body
in the resonator (close or open), or in the free space belong to
this class. A variational approach to solving such problem is described
and numerical results concerning some concrete examples are presented.
More general problems of the class are the problem about nonhomogeneous
dielectric body as well as the quantum mechanics problem of scattering
on the quasistationary level. Numerical results regarding the last
problem are shown. In problems of the second class, the spectral
parameter is introduced into boundary conditions or into asymptotical
conditions in infinity. The problems about bodies with impedance,
metallic or semitransparent boundaries are considered. Open resonators
with plane or confocal metallic mirrors, waveguides of arbitrary
cross section with longitudinal split, close resonators connected
by small split, dielectric resonator with great permittivity value,
and open resonator with closed semitransparent wall are considered.
 N. N. Voitovich, B. Z.
Katsenelenbaum, A. N. Sivov. Investigation
of open resonators by generalized eigenoscillation method.
Mathematical Questions of the Propagation Wave
Theory, Inst.Radioeng.&Electr., Moscow,
1979, 88149.
1979, p. 88149 (In Russian).
 N. N. Voitovich.
Homogeneous problems of generalized eigen oscillation
method for bodies of revolution. Radiotekhnika
i Elektronika, v. 25, No.7, 1980, p. 15261529.
(In Russian).
Abstract. Homogeneous boundary value problems
arising in two variants of the generalized eigen oscillation method
are formulated for the case if the domain is a body of revolution
(spectral parameter is the impedance or transparency of the boundary).
The angular components of electric and magnetic fields are used
as potential function in these problems. Functionals stationary
on eigen functions of the problems are obtained.
 N. N. Voitovich, O. I.
Karashetskaya, A. I. Kidisyuk, A. I. Rovenchak. Experience
of investigation of complicateshaped resonators by generalized method
of eigenoscillations. Wave and Diffraction,
Inst.Radioeng.&Electr., Moscow, 1981, v.1,
p. 201204.
