Cylindrical periodic surface lattice as a metadielectric: Concept of a surface-field Cherenkov source of coherent radiation

A two-dimensional (2D), cylindrical, periodic surface lattice (PSL) forming a surface field cavity is considered. The lattice is created by introducing 2D periodic perturbations on the inner surface of a cylindrical waveguide. The PSL facilitates a resonant coupling of the surface and near cutoff volume fields, leading to the formation of a high-$Q$ cavity eigenmode. The cavity eigenmode is described and investigated using a modal approach, considering the model of a cylindrical waveguide partially loaded with a metadielectric. By using a PSL-based cavity, the concept of a high-power, 0.2-THz Cherenkov source is developed. It is shown that if the PSL satisfies certain defined conditions, single-mode operation is observed.

Figure 1

(a) Photograph of the 2D periodic lattice of length $L$ $=$ 48 mm machined on the inner surface of copper cylindrical waveguide of mean diameter 80 mm. The lattice has longitudinal period $d_{\mathrm{z}}$ $=$ 8 mm and number of azimuthal variations $\mathrm{m̄}=$ 28 azimuthal. (b) The chessboard model [5, 7], of the 2D cylindrical lattice studied via numerical simulations and illustrated using 3D code MAGIC. (c) The excitation of surface currents on the lattice fundamental cell boundaries observed using 3D code CST MICROWAVE STUDIO.

Figure 2

The schematics of the (a) r-z and (b) r-φ cross sections of partially loaded cylindrical waveguide.

Figure 3

The comparison of the transverse structures of the (a) electric $E_{\mathrm{z},\mathrm{r},\mathrm{\varphi }}$ and (b) magnetic $B_{\mathrm{z},\mathrm{r},\mathrm{\varphi }}$ fields observed (3D code MAGIC) inside the SF cavity (solid lines) and smooth cylindrical waveguide (SCW) cavity (broken lines). The SCW cavity eigenmode's transverse structure coincides with the structure of the near cutoff TM${}_{0,10}$ wave. The inserts (contour diagrams) illustrate (a) electric and (b) magnetic fields inside the SF cavity (the 1/28th section of the structure).

Figure 4

The contour plots of (a,b) electric ($E$) field's components and (c,d) magnetic ($B$) field's components in (a,d) r-z and (b,d) r-φ cross sections. The contours indicate the field strength and polarity. The figures observed using full 3D code MAGIC when the structure is irradiated by the narrow-band (35–40 GHz), flat-top-spectrum pulse.

Figure 5

The unperturbed dispersions of the fundamental volume and ±1 harmonics surface partial fields observed inside the 2D cylindrical PSL of 80 mm mean diameter, $\mathrm{m̄}=$28, and amplitude of the perturbations tending to zero. The volume field is associated with the TM${}_{0,10}$ mode of the cylindrical waveguide, while the second partial field is associated with (a) whispering-gallery mode (TM${}_{28,1}$-TE${}_{28,1}$) and (b,c,d,e,f) surface field having an imaginary transverse wave number. The crossing between volume and surface field at exact cutoff frequency (${\mathrm{k̄}}_z^2=k_{\perp s}^2+k_{\perp v}^2$) is shown in (a) and (d). The figures (b) and (c) are observed if ${\mathrm{k̄}}_z^2<k_{\perp s}^2+k_{\perp v}^2$, while (e) and (f) if ${\mathrm{k̄}}_z^2>k_{\perp s}^2+k_{\perp v}^2$. The arrows indicate the displacement of the surface field dispersions with increase of ${\mathrm{k̄}}_z$. The dashed lines indicate schematically the splitting of the dispersions with increase of the lattice contrast.

Figure 6

The spectra of the structure's eigenmodes excited (solid lines) if the input signal used to irradiate the lattice has a flat-top spectrum in the frequency ranges (a) 30–40 GHz and (b) 35–40 GHz.

Figure 7

The contour plots of (a,b) electric ($E$) field's components and (c,d) magnetic ($B$) field's components in (a,d) r-z and (b,d) r-φ cross sections. The contours indicate the field strength and polarity. The figures were observed using full 3D code MAGIC when the structure was irradiated by the narrow-band (65–70 GHz), flat-top-spectrum pulse. The dotted line shows schematically the boundary of the imaginary metadielectric, whose radius coincides with caustic radius.

Figure 8

The spectrum of the output radiation (first column) and output power (second column) from Cherenkov oscillator driven by a 20-A, thin, annular electron beam with interaction region formed by cylindrical 2D PSL of 11 mm diameter with $\mathrm{m̄}$ $=$ 20 and 30 longitudinal periods. The lattice's longitudinal period and beam accelerating voltage was (a) $d_{\mathrm{z}}$ $=$ 1.32 mm, $U$ $=$ 300 kV; (b) $d_{\mathrm{z}}$ $=$ 1.26 mm, $U$ $=$ 250 kV; and (c) $d_{\mathrm{z}}$ $=$ 0.82 mm, $U$ $=$ 100 kV.

Figure 9

(a) The output power and (b) the spectrum of the output radiation observed from the Cherenkov maser driven by a thin, annular, 40-A, 50-kV electron beam and based on a 2D PSL of 11 mm mean diameter and 17.4 mm length (30 longitudinal periods) and having $\mathrm{m̄}$ $=$ [18;21].