The introduction of higher-order topological insulators featuring topological corner states has been an extremely active topic for the generation of confined modes. Recent studies show that corner states are not an exclusive feature of topological insulators but can also exist as bound states in the continuum (BIC). This suggests that corner states may exist in different topological phases that exhibit a higher-order character, beyond the conventional bulk-edge correspondence. In this paper, we show that corner states can appear in a higher-order Dirac semimetal phase of a two-dimensional photonic lattice. Such a lattice displays a dispersion relationship with a fourfold degeneracy, which serves to induce a higher-order topological phase transition, leaving a Dirac point between two edge bands. Just as Dirac modes exist in regular lattice defects, the nonconventional bulk-edge-corner correspondence leads to corner states in the Dirac semimetal phase. Notably, the induced corner state exhibits an algebraic decay characteristic of long-range interactions, predicted by the massless Dirac equation. The analysis of the field profile and quality factors indicates that the state is not a BIC, but rather a corner-Dirac state. We show that if the photonic lattice does not present a higher-order phase transition the existence of the corner-Dirac state does not arise. The results obtained in this paper indicate that corner states can exist throughout the entire topological phase transition process, even in the semimetal phase, and pave the way to generate light-matter interactions with such a photonic bath.

The introduction of long-range interaction (LRI) in models that describe topological systems has unveiled previously unknown topological phases and states. Recently, in higher-order topological insulators, consideration of LRI via next-nearest-neighbor (NNN) hopping led to the discovery of unconventional confined corner states; however, their study is still limited in photonic prospects. In this paper, we bring the concept of type-III corner states into the photonic regime and reveal that their existence depends on LRI in photonic lattices, mimicking an extended two-dimensional Su-Schrieffer-Heeger (SSH) model with an asymmetric coupling. The extension of the SSH model is performed by considering a variety of NNN hopping in square lattices, and an asymmetry coupling in the intercellular NNN hopping terms of the Hamiltonian describing the system. Subsequently, we identify type-I, type-II, and type-III corner states in the analytical tight-binding model, revealing that the type-II and type-III corner states are split from the edge states. Based on the obtained results, we propose a photonic model that mimics the asymmetric coupling and find the existence of type-II and type-III corner states in the photonic model. The results presented here extend the knowledge we have about topological corner states in photonic systems and highlight the role played by LRIs in the generation of topological confined modes.

Topological photonics has attracted remarkable attention in recent years due to its ability to generate robust topological states, especially suitable for the study of cavity quantum electrodynamics. In this work, we present a theoretical study of a topological photonic crystal based on the 2D Su–Schrieffer–Heeger model, with corner states induced by a rotational operation on the axis parallel to the interface of two different topologies of a photonic crystal, forming a bowtie cavity. The studied topological photonic crystal presents inversion symmetry due to the rotation operation allowing the simultaneous existence of two non-degenerated corner states: one located in the weak coupling regime and the other in the strong coupling regime. Therefore, we present the emergence of distinctive effects from both regimes, such as the Purcell effect and Rabi splitting. We also address the study of the origin and evolution of the corner states resulting from the bulk-edge-corner correspondence. The topological bowtie cavity studied in this work combines the virtues of topological systems and the extreme confinement offered by cavities with bowtie architecture, which enriches the study of corner states in sophisticated topological structures.

In this work, we study a composite zinc oxide photonic crystal (PhC) that includes a meso-cavity coupled to a PhC L3 microcavity to obtain a double resonance effect and second-harmonic generation (SHG) conversion efficiency as high as 468 W ⁻¹ . This exceptional conversion efficiency was attributed to the high quality-factors Q found in the fundamental and second-harmonic (SH) modes whose values were of the order of 10 ⁵ and 10 ⁶ , respectively. Since the L3 microcavity plays a relevant role in the SHG of the composite PhC, we performed a calculation of its photonic band structure to observe the induced modes in its bandgap. Furthermore, we also found that the resonant mode adjusted to the frequency of the SH exhibits high Purcell factors of the order of 10 ⁵ . Hence, in a semiconductor material, it can be easily enhanced the light emission at the SH frequency using an adequate driving fundamental frequency light beam. These results can stimulate the engineering of photonic nanostructures in semiconductor materials to achieve highly efficient non-linear effects with applications in cavity quantum electrodynamics.

Topological photonics has established itself as a promising area for the development of photonic integrated circuits due to the robust properties of topological states. In recent years, different logical devices have been proposed to form the fundamental elements of an integrated topological photonic circuit. Despite the rapid theoretical growth of topological photonics, it still lacks experimental foundations concerning logical devices for on-chip integration. For this reason, in this work, we report the design and build of an all-optical photonic switch in a silicon slab working under the higher-order topological spin Hall effect. We have taken advantage of the gapped edge states due to the higher-order topology and combined this feature with changes in the dielectric permittivity of silicon by inducing transitions of free charge carriers. The transitions of charge carriers were realized through the incidence of electromagnetic radiation with a frequency close to the visible-ultraviolet region boundary, making the device operation entirely optical. The behavior of the constructed device has also been numerically simulated and compared with the experimental results obtained. This work contributes to the idea that photonic crystals are a powerful platform for studying topological states and paves the way for the experimental realization of integrated topological optical circuits.