Fig. 1. The schematic diagram of the structure of the comb-shaped space-filling curve. (a) The schematic diagram of the comb-shaped space-filled meta-structure and the simulation domain. The period w and duty cycle of the comb-shaped space-filling metallic curve structure are 10 mm and 0.5, respectively. The metal wire width a is 2.5 mm, half cycle

width d is 5 mm, the total length of the structure is L, the width of the structure is W= 7.5 cm, the metal structure fills the air waveguide

forming the gray part, and its effective length is S; (b) The schematic of double-open comb-shaped space-filling metallic

curve structure; (c) The schematic of single-open comb-shaped space-filling metallic curve structure

Fig. 2. 2D simulation of single-opening and double-opening comb structures with different number of periods. (a) The magnetic field distribution of fundamental mode in the double-opening comb-shaped space-filled meta-structure. (b) The magnetic

field distribution of fundamental mode in the single-opening comb-shaped space-filled meta-structure; (c) The theoretical and

simulated structure compression ratios, and the Q factors of the double-opening and single-opening comb-shaped

space-filled meta-structures as functions of period number N, respectively

Fig. 3. Higher-order eigenmode calculations for double-open comb structures. (a) The scattering cross-section of the eigenmodes (M₀~M₉) of the double-opening space-filling metal curve structure; (b) The magnetic field distributions of the M₀~M₄ order eigenmodes of the double-opening-space-filling metal curve structure in the Z direction and the pole mode of each order corresponding to the eigenmode

Fig. 4. 2D simulation of various types of space-filling curvilinear structures. (a) The schematic diagram of Hilbert-type space-filling meta-structure and the magnetic field distributions at different eigenmode orders (M₀~M₄); (b) The schematic diagram of rectangular spiral structure and the magnetic field distributions at different eigenmode orders (M₀~M₄); (c) The schematic diagram of combined structure and the magnetic field distributions at different eigenmode orders(M₀~M₄); (d) The scattering cross-section of the corresponding eigenmodes (M₀~M₄) of the preceding meta-structures

Fig. 5. 3D simulation of a double-opening comb structure. (a) The schematic diagram of the three-dimensional double-opening comb-shaped space-filling metal curvilinear structure with a period number of 15; (b)The electric field distributions on X~Z section of the three-dimensional simulated eigenmodes of the double-opening comb-shaped space-filled meta-structure