Electrodynamic modeling of slot gratings by the generalized scattering matrix method – spherical wave decomposition

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Abstract

An algorithm is presented for the electrodynamic analysis of a two-dimensional waveguide slot array of finite dimensions. To solve the boundary value problem, the generalized scattering matrix method is used. The complex problem for a structure with large electrical dimensions is divided into two subproblems: wave scattering on one lattice element and the interaction of waves within the lattice. In accordance with this method, the electromagnetic field of a solitary lattice element is represented in the form of an expansion in incident and scattered spherical waves. The solution to the first subproblem is given by the scattering operator, which relates the amplitudes of the incident and scattered waves. The solution to the second subproblem yields an interaction matrix that relates the amplitudes of waves incident on the mth array element with the amplitudes of waves scattered by the nth element. Application of the scattering operator and interaction matrix to the analysed lattice leads to a system of linear algebraic equations for the amplitudes of the scattered waves. A non-periodic slot grating, focused in the Fresnel zone, containing up to a thousand elements is analysed. The obtained numerical results are in good agreement with the known behaviour of focused leaky wave gratings. Possible areas of application of the method are discussed.

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About the authors

S. E. Bankov

Kotel’nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences

Author for correspondence.
Email: sbankov@yandex.ru
Russian Federation, Moscow, 125009

M. D. Duplenkova

Kotel’nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences

Email: sbankov@yandex.ru
Russian Federation, Moscow, 125009

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Supplementary files

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2. Fig. 1. Elementary radiator and waveguide-slot grating.

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3. Fig. 2. Dependence of the variation of the transmission coefficient ∆T on the number of basis functions Nb.

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4. Fig. 3. Dependence of the variation of the reflection coefficient ∆R on the parameter Nθ.

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5. Fig. 4. Model 1 with end screen; 1–10 – ports.

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6. Fig. 5. Model 2 with an infinite plane.

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7. Fig. 6. Frequency dependences of the scattering parameters of the grating calculated by the OMR-RSV method (solid curves) and HFSS (dots); the reflection (1) and transmission (2) coefficients were determined for ports 3, 8.

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8. Fig. 7. Normalized radiation patterns in the elevation plane for models 1 (a) and 2 (b), calculated using the OMR-RSV method (solid curves) and HFSS (dots).

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9. Fig. 8. Normalized RP as a function of azimuth angle: according to the OMR-RSV method (solid curves) and HFSS (dots).

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10. Fig. 9. The main beam of the pattern at frequencies f = 10 (1), 10.2 (2), 10.4 (3), 10.6 (4), 10.8 (5) and 11 GHz (6); according to the OMR-RSV method (solid curves) and HFSS (dots).

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11. Fig. 10. Focused waveguide grating.

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12. Fig. 11. Configuration of the focused grating.

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13. Fig. 12. Frequency dependences of scattering parameters: reflection coefficient (1) and waveguide transmission coefficient (2).

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14. Fig. 13. Normalized distributions of the electric field in the XOZ plane at frequencies of 9 (a), 10 (b), 11 GHz (c). The electric field is normalized to the maximum electric field strength at a frequency of 10 GHz.

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15. Fig. 14. Frequency dependence of angle θₘ.

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16. Fig. 15. Focal curve.

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17. Fig. 16. Normalized distribution of the electric field at a frequency of 10 GHz in the YOZ plane for angles α₀= 20° (a), 10° (b), 0° (c).

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