Topological bulk laser and method based on band inversion and reflection of optical field

A topological bulk laser based on reflection of optical field induced by band inversion, comprising:

• an N-type contact layer;
• an N-type confinement layer;
• an active layer;
• a P-type confinement layer;
• and a P-type contact layer, wherein the N-type contact layer, the N-type confinement layer, the active layer, the P-type confinement layer, and the P-type contact layer are configured to form an electrically injected laser;
• an N-type substrate;
• a topological bulk laser cavity constructed by two-dimensional photonic crystals with distinct topology including a topological photonic crystal and a topologically trivial photonic crystal,
• a ring-shaped N-type electrode on the N-type contact layer, wherein the ring-shaped N-type electrode is surrounding the two-dimensional photonic crystals;
• and
• a P-type electrode on the P-type contact layer,
• wherein the topological bulk laser is electrically injected, wherein for the electrically injected laser, the photonic crystals are formed on the P-type contact layer and partial P-type confinement layer,
• wherein the topological photonic crystal and trivial photonic crystal include multiple unit cells periodically arranged into different honeycomb-type lattice with a same lattice period, wherein an outer edge of each unit cell is a regular hexagon comprising six nanoholes, forming two bulk bands of a dipole and a quadrupole mode, wherein when a distance between centers of the six nanoholes and a center of the hexagon is equal to one third of a lattice period, the dipole and quadrupole modes are degenerate at a center region of a Brillouin zone since the inter-cell and intra-cell coupling strength are equal, forming a double-degenerate Dirac-cone type band structure at the F point,
• wherein the double-degenerate Dirac-cone type band structure is opened when the six nanoholes are shrunk or expanded with the center of hexagon unit cell as the center, wherein when the distance between the center of each nanoholes and the center of the hexagon unit cell is less than one third of the lattice period, there is no band inversion between the dipole and quadrupole modes of the photonic crystal, forming a trivial photonic crystal having the double-degenerate Dirac-cone type band structure in a topologically trivial state,
• wherein a distance between a center of each of the nanoholes and the center of the hexagon unit cell is more than one third of the lattice period, a band inversion between the dipole mode and the quadrupole mode occurs in the center region of the Brillouin zone, forming the topological photonic crystal having the double-degenerate Dirac-cone type band structure in a topological state,
• wherein the trivial photonic crystal and the topological photonic crystal are combined to form an interface, which produces a new reflection and confinement mechanism which is effective for photon states with frequency in the center region of the Brillouin zone, since states in the trivial photonic crystal are prohibited from propagating into the topological photonic crystal due to the opposite parities of wavefunctions, and vice versa, wherein the interface is bent to form a closed contour, photons with a frequency in the center region of the Brillouin zone is reflected along the internal interface, leading to simulated emission, thereby forming the topological bulk laser cavity inside the interface,
• wherein for the electrically injected laser, the voltage is applied across the active layer, carriers are injected and confined into the active layer, generating optical radiation, wherein a band-inversion-induced reflection at the interface only occurs in a small range of wave vector in the center region of the Brillouin zone, which produces an optical mode with efficient confinement only exists in the center region of the Brillouin zone, which limits the number of laser cavity modes to receive feedback, resulting in single-mode lasing,
• wherein the band-inversion-induced reflection only occurs in the center region of the Brillouin zone, which produces an optical mode with efficient confinement only exists in the center region of the Brillouin zone, wherein the modes have a large momentum component perpendicular to the interface of the topological bulk laser cavity, and thus have vertical emission characteristics.