Fig. 1. Schematic diagram of SLRT in the MOPC waveguide.

Fig. 2. (a) Schematics of the MOPC waveguide involving strongly coupling TPSs. RTPS and LTPS indicate whether the TPSs are propagating rightwards or leftwards, respectively. (b) Band structure of the MOPC waveguide. (c)–(e) Electric field profiles at different frequencies: (c) f1=4.25  GHz, (d) f2=4.292  GHz, (e) f3=4.35  GHz. The area marked by the blue dashed box in (c) is the supercell used in the calculation of the photonic band.

Fig. 3. (a) Flat band with different H0 in the half-Brillouin zone. (b) Group velocities of different flat bands. (c) Electric field profiles at three frequencies: frd=4.292  GHz, fpl=4.346  GHz, and fbu=4.393  GHz. (d) Electric field amplitudes along the upper boundary as shown in (c).

Fig. 4. Electric field distributions with a local designed gradient magnetic field. (a) frd=4.292  GHz, (b) fpl=4.346  GHz, (c) fbu=4.393  GHz.

Fig. 5. Illustration of broadband large-length SLRT in the MOPC waveguide with a gradient magnetic field.

Fig. 6. Electric field amplitudes of the wave packet along the upper boundary at different times: (a) 10 ns, (b) 40 ns, (c) 70 ns, and (d) 100 ns. The magnetic field strengths applied to the regions 1, 2, and 3 are H1=1700  G, H2=1800  G, and H3=1900  G, respectively. (e) Fourier transformation spectrum normalized to each amplitude at x0=0, x1=3.5a, x2=10.5a, and x3=17.5a along the upper boundary of the waveguide. (f) The partial enlargement of the area marked by the black dashed box in (e).