Distortionless Pulse Transmission in Valley Photonic Crystal Slab Waveguide

A valley photonic crystal is one type of photonic topological insulator, the realization of which needs only P-symmetry breaking. The domain wall between two valley-contrasting photonic crystals supports robust edge states, which can wrap around sharp corners without backscattering. Using the robust edge states, one can achieve pulse transmission. Here, using time-domain measurements in the microwave regime, we show distortionless pulse transmission in a sharply bended waveguide. An Ω-shaped waveguide with four 120° bends is constructed with the domain wall between two valley photonic crystal slabs. Experimental results show the progress of Gaussian pulse transmission without distortion, and the full width at half maximum of the output signal changes slightly in the Ω-shaped waveguide. By measuring the steady-state electric field distribution, we also confirm the confined edge states without out-of-plane radiation, which benefits from dispersion below the light line. Our work provides a way for high-fidelity optical pulse signal transmission and the development of high-performance optical elements, such as photonic circuits or optical delay lines.

Figure 1

Group velocity (v_g) and GVD of edge states. (a) Gapped bulk bands of two VPC slabs with the honeycomb lattice on a PEC substrate (top, VPC1 with d_A>d_B; bottom, VPC2 with d_A<d_B). Two slabs share the same bulk band gap. (b) Domain wall between two slabs. (c) Berry curvature of VPC1 and VPC2. (d) Edge dispersion of the domain wall in (b). Shaded area is the light cone. Green solid curve corresponds to the simulated edge dispersion; bright spots plot experimental results. (e) Calculated group velocity (v_g) and (f) GVD of edge states, which exhibit a uniform pulse velocity at frequencies around 5.88 GHz. This guarantees the distortionless transmission of the Gaussian pulse.

Figure 2

Distortionless pulse transmission in straight VPC slab waveguide. (a) Photograph of the straight waveguide. It consists of two VPC slabs with opposite topological indices. Blue and red stars mark positions of the detectors. Inset: measured Gaussian pulse, which is centered at 5.88 GHz with a FBHM of 40 MHz. (b) Green cross, FWHM of the measured Gaussian pulse at different distances. FWHM of the pulse at the rightmost exit changes only 3.27% compared with that of the input pulse. Purple cross, arrival time of the pulse center as a function of distance. Purple line, linear fitting relationship between arrival time and distance, indicating that the averaged group velocity of the pulse throughout the waveguide is $\overline{v_g}=0.247c$. (c) Measured pulse at different distances [marked by red stars in (a)] in the straight waveguide.

Figure 3

Distortionless pulse transmission in an Ω-shaped VPC slab waveguide. (a) Photograph of the Ω-shaped waveguide. Blue and red stars indicate positions of the detectors. Inset: measured Gaussian pulse (centered around 5.88 GHz, FBHM = 40 MHz) at the blue star. (b) Green cross, FWHM of the measured Gaussian pulse at different distances. FWHM of the pulse at the rightmost exit changes only 4.68% compared with the input pulse. Purple cross, the arrival time of the pulse center as a function of distance. Purple line, linear fitting of the arrival time, indicating that the averaged group velocity of the pulse throughout the waveguide is $\overline{v_g}=0.196c$. (c) Measured pulse at different distances [marked by red stars in (a)] in the Ω-shaped waveguide.

Figure 4

Field confinement of the measured edge states. In-plane confinement measured for E_z field distributions of the edge states in (a) straight and (b) Ω-shaped waveguides at 5.88 GHz (center of the Gaussian pulse) in the x-y plane, which confirms good confinement and robust transport of the edge states. (c)Out-of-plane confinement measured for E_z field distributions in the straight waveguide at 5.88 GHz in the x-z plane. Out-of-plane distribution shows that the edge states are confined well in the waveguide, but decay rapidly upon moving away from the top surface of the sample (denoted by white dashed line). (d) Out-of-plane field confinement of edge states for different frequencies.

Figure 5

Calculated Berry curvatures of VPC slabs of two rods with different diameters. (a) Photograph of the unit cell of VPC slab with honeycomb lattice. (b)–(d) Berry curvatures around the K point when d_A>d_B. (e)–(g) Berry curvatures around the K point when d_A<d_B.

Figure 6

Design for edge states with larger frequency bandwidth. (a) Domain wall with a transition layer between two VPC slabs. (b) Edge dispersion of the structure in (a). Frequency bandwidth of edge states for pulse transmission is 7.9% (4.73–5.12 GHz).