Topological protection in photonics offers new prospects for guiding and manipulating classical and quantum information. The mechanism of spin-orbit coupling promises the emergence of edge states that are helical; exhibiting unidirectional propagation that is topologically protected against backscattering. We directly observe the topological states of a photonic analogue of electronic materials exhibiting the quantum Spin Hall effect, living at the interface between two silicon photonic crystals with different topological order. Through the far-field radiation that is inherent to the states' existence we characterize their properties, including linear dispersion and low loss. Importantly, we find that the edge state pseudospin is encoded in unique circular far-field polarization and linked to unidirectional propagation, thus revealing a signature of the underlying photonic spin-orbit coupling. We use this connection to selectively excite different edge states with polarized light, and directly visualize their routing along sharp chiral waveguide junctions.

It is well known that the quasinormal modes (or resonant states) of photonic structures can be associated with the poles of the scattering matrix of the system in the complex-frequency plane. In this work, the inverse problem, i.e., the reconstruction of the scattering matrix from the knowledge of the quasinormal modes, is addressed. We develop a general and scalable quasinormal-mode expansion of the scattering matrix, requiring only the complex eigenfrequencies and the far-field properties of the eigenmodes. The theory is validated by applying it to illustrative nanophotonic systems with multiple overlapping electromagnetic modes. The examples demonstrate that our theory provides an accurate first-principle prediction of the scattering properties, without the need for postulating ad-hoc nonresonant channels.Scattering matrices have been playing a ubiquitous role in physics since the early history of quantum field theory [1]. Nowadays, scattering-matrix techniques represent an irreplaceable tool for scientists working in nuclear physics [2], electronic transport [3], or classically chaotic systems [4], just to mention some of the several fields of application. Scattering matrices also enjoy a well deserved popularity in electromagnetic modeling, ranging from microwave devices [5] to nanophotonics applications, such as scattering and transmission from nanostructured objects [6][7][8].Most of the systems that are usually investigated with scattering-matrix techniques display a highly structured resonant response as a function of the excitation frequency (or energy), with the resonances in the spectrum being directly related to the poles of the analytical continuation of the scattering matrix in the complexfrequency plane [9,10]. For electromagnetic systems, such poles correspond to quasinormal modes (also called resonant states), i.e., complex-frequency solutions of Maxwell's equations with outgoing-wave boundary conditions [11][12][13][14][15]. In a sense, quasinormal modes represent the bare skeleton around which the frequency-dependent response of the system is built. The interplay among different electromagnetic modes has proven to be crucial for explaining several intriguing phenomena, such as Fano resonances in optical systems [16], scattering dark states [17,18], and the optical analog of electromagnetically induced transparency and superscattering [19], and for designing new optical materials, such as optical metasurfaces for wavefront shaping [20]. For these reasons, it is desirable and extremely interesting to be able to reconstruct ab initio the entire scattering matrix of a system from the knowledge of its quasinormal modes. Not only would such quasinormal-mode expansion contribute to the understanding of complicated spectral features in terms of interference and superposition of resonant states, but it would also offer practical advantages from the numerical point of view, since a full eigenmode calculation is generally faster and more comprehensive than a large number of single-frequency simulations.A...

No abstract

The introduction of topological concepts to the design of photonic crystal cavities holds great promise for applications in integrated photonics due to the prospect of topological protection. This study examines the signatures of topological light confinement in the leakage radiation of 2D topological photonic crystal cavities. The cavities are implemented in an all-dielectric platform that features the photonic quantum spin Hall effect at telecom wavelengths and supports helical edge states that are weakly coupled to the radiation continuum. The modes of resonators scaling down to single point defects in the surrounding bulk lattice are characterized via spectral position and multipolar nature of the eigenstates. The mode profiles in real and momentum space are mapped using far-field imaging and Fourier-spectropolarimetry, revealing how certain properties of the cavity modes reflect on their origin in the topological bandstructure. This includes band-inversion-induced confinement and inverted scaling of mode spectra for trivial and topological defect cavities. Furthermore, hallmarks of topological protection in the loss rates are demonstrated, which are largely unaffected by cavity shape and size. The results constitute an important step toward the use of radiative topological cavities for on-chip confinement of light, control of emitted wave fronts, and enhancement of light-matter interactions.

No abstract