Topological insulator laser: Theory

Abstract

Topological insulators are phases of matter characterized by topological edge states that propagate in a unidirectional manner that is robust to imperfections and disorder. These attributes make topological insulator systems ideal candidates for enabling applications in quantum computation and spintronics. We propose a concept that exploits topological effects in a unique way: the topological insulator laser. These are lasers whose lasing mode exhibits topologically protected transport without magnetic fields. The underlying topological properties lead to a highly efficient laser, robust to defects and disorder, with single-mode lasing even at very high gain values. The topological insulator laser alters current understanding of the interplay between disorder and lasing, and at the same time opens exciting possibilities in topological physics, such as topologically protected transport in systems with gain. On the technological side, the topological insulator laser provides a route to arrays of semiconductor lasers that operate as one single-mode high-power laser coupled efficiently into an output port.

Perspective on topological states of non-Hermitian lattices

“…The interest in non-Hermitian Hamiltonians was originally focused in  -symmetric Hamiltonians [23] as a generalization of quantum mechanics where the Hermiticity constraint could be removed while keeping a real spectra. Today, this has shifted to non-Hermitian Hamiltonians regarded as an effective description of, for example, open quantum systems [24,25], where the finite lifetime introduced by electronelectron or electron-phonon interactions [26][27][28], or disorder [29], is modeled through a non-Hermitian term, or in the physics of lasing [30][31][32][33][34]. An additional source of momentum in this field comes from the study of systems where the quantum mechanical description is used after mapping to a Schrödinger-like equation, as in systems with gain and loss (as found in optics and photonics [35][36][37][38]), surface Maxwell waves [39], and topoelectrical circuits [40,41].…”

Active topological photonics

“…Such chiral edge mode is robust in a sense that backscattering is prohibited in the presence of local disorder due to timereversal symmetry breaking of the system. The unprecedented properties of the topological edge mode bring the interest of making it as a light source, especially a laser [28,29,71]. In general, defects and disorders in the laser cavity lead to scattering loss, which degrades the performance of laser by reducing the quality factor and lowering the output efficiency.…”

“…There is another class of two-dimensional topological lasers, which do not break the time reversal symmetry [29,71]. The structure is based on the construction of the Harper-Hofstadter model using ring resonators originally realized by [5,6] where we have set the lattice spacing to be unity and assumed that the hopping strength is isotropic.…”

Topological Photonic Integrated Circuits Based on Valley Kink States

“…Despite early studies in nonreciprocal systems, photonic topological edge states without breaking time‐reversal symmetry (TRS) can be realized in systems that allow an analog of quantum spin‐Hall effect with a pseudospin degree of freedom of photons. Various optical degrees of freedom have been used as pseudospin, such as polarizations in bianisotropic metamaterials, TE and TM modes in photonic crystals, chiralities of whispering‐gallery modes in ring resonators, and more recently p ‐ and d ‐orbitals in artificial photonic atoms . However, these schemes are either incompatible with integrated photonic platforms or suffer from bulky footprints and large out‐of‐plane radiation loss …”