Numerical study of dispersion characteristics of cylindrical spiral lines and periodic gratings based on them

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Abstract

Numerical studies of the dispersion characteristics of cylindrical spiral lines have been carried out. One-dimensional and two-dimensional periodic lattices formed by such lines are also considered. The eigenvalue method was used in combination with periodic boundary conditions. The dispersion characteristics are calculated in the range of parameters for which the conditions of applicability of the known approximate numerical-analytical methods for analyzing spiral lines are not met. The dispersion characteristics of the first two eigen-waves in one-dimensional and two-dimensional periodic lattices of spirals are obtained for different values of phase shifts between lattice periods. It is shown that the main type of wave in them is a wave slowed down relative to the axes of the lines with the direction of rotation of the field vector determined by the direction of winding of the spiral.

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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

V. I. Kalinichev

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

Email: sbankov@yandex.ru
Russian Federation, Moscow

References

  1. Силин Р.А., Сазонов В.П. Замедляющие системы. М.: Сов. радио, 1966.
  2. Юрцев О.А., Рунов А.В., Казарин А.Н. Спиральные антенны. М.: Сов. радио, 1974.
  3. Силин Р.А. Периодические волноводы. М.: Фазис, 2002.
  4. Bankov S.E., Bugrova T.I. // Microwave Optical Technol. Lett. 1993. V. 6. № 13. P. 782.
  5. Банков С.Е., Фролова Е.В.// РЭ. 2023. T. 68. № 9. С. 835.
  6. Вайнштейн Л.А. Электромагнитные волны. М.: Радио и связь. 1988.

Supplementary files

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2. Fig. 1. Model of a three-dimensional cylindrical spiral line.

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3. Fig. 2. Model of a single line cell (PML layers not shown).

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4. Fig. 3. Dispersion characteristics of a spiral line at Ds = 4 mm, Dw = 1 mm, p = 1 (1), 2 (2), 5 (3), 10 mm (4).

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5. Fig. 4. Dispersion characteristics of a spiral line at p = 5 mm, Dw = 1 mm, Ds = 10 (1), 8 (2), 6 (3), 4 mm (4).

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6. Fig. 5. Dispersion characteristics of a spiral line at p = 5 mm, Ds = 4 mm, Dw = 0.5 (1), 1 (2), 2 mm (3).

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7. Fig. 6. Instantaneous distribution of the amplitude of the electric field strength of the surface wave of the spiral in the transverse plane XOY at a frequency of 9.633 GHz.

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8. Fig. 7. Dispersion characteristic of a spiral line in a wide frequency range (a) and in a narrow vicinity of the forbidden zone (b) at p = 5 mm, Ds = 4 mm, Dw = 1 mm: forward (1) and backward waves (3) and the corresponding counter-propagating waves (2) and (4).

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9. Fig. 8. Fragment of a linear periodic lattice of spiral lines.

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10. Fig. 9. Model of a single cell for a linear periodic lattice of spiral lines.

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11. Fig. 10. Dispersion curves for the first eigenwave in a linear lattice of spiral lines at δφy = 0° (1), 45° (2), 90° (3) and 180° (4): a – deceleration relative to the line axes, b – total deceleration; dashed curve – dispersion of a single line.

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12. Fig. 11. Dispersion curves for the second eigenwave in a linear lattice of spiral lines at δφy = 0° (1), 45° (2), 90° (3), 180° (4): a – deceleration relative to the line axes, b – complete deceleration; light circles in Fig. (a) – inflection points.

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13. Fig. 12. Dependences of the total slowdown of the first (solid curves) and second (dashed lines) natural waves of a linear array on the frequency at δφy = 0° (a) and 180° (b). Light circles in Fig. (a) and (b) are inflection points.

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14. Fig. 13. Dependence of the propagation angle of the fundamental wave relative to the line axes in a linear array on the frequency at δφy= 0° (1), 45° (2), 90° (3), 180° (4).

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15. Fig. 14. Dependences of the slowdown of the fundamental wave of a linear array along the line axes on the phase shift between them at f = 5 (1), 6 (2) and 7 GHz (3); the dots on the curves indicate the slowdown values ​​at δφy = 0°, 15°, 30°, 45°, 90°, 135° and 180° (from left to right).

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16. Fig. 15. Fragment of a two-dimensional periodic lattice of spiral lines.

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17. Fig. 16. Model of a single cell of a two-dimensional periodic lattice of spiral lines.

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18. Fig. 17. Dispersion curves of the first eigenwave in a two-dimensional lattice for δφ = 0° (1), 45° (2), 90° (3) and 180° (4): a – deceleration relative to the line axes, b – total deceleration; the dotted curve is the dispersion of a single line.

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19. Fig. 18. Dispersion characteristics of the second eigenwave in a two-dimensional lattice of spiral lines at δφ = 0° (1), 45° (2), 90° (3), 180° (4): a – slowdown relative to the line axes, b – total slowdown; light circles in Fig. (a) – inflection points.

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20. Fig. 19. Dependences of the total slowdown of the first (solid curves) and second (dashed) eigenwaves of a two-dimensional lattice on the frequency at δφ = 0° (a) and 180° (b); the light circle in Fig. (a) is the inflection point.

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21. Fig. 20. The propagation angle of the fundamental wave relative to the line axes depending on the frequency in a two-dimensional array for δφ= 0° (1), 45° (2), 90° (3) and 180° (4).

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22. Fig. 21. Dependences of the slowdown of the fundamental wave of a two-dimensional array along the axes of the lines on the phase shift between them at f = 6 (1), 7 (2) and 8 GHz (3); the dots on the curves indicate the slowdown values ​​at δφy = 0°, 15°, 30°, 45°, 90°, 135° and 180° (from left to right).

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