Non-Hermitian topological effects are of crucial importance both in fundamental physics and applications. Here we discover the gain-loss-induced hybrid second-order skin-topological effect and the $\mathcal{P}\mathcal{T}$ phase transition in skin-topological modes. By studying a non-Hermitian Haldane model, we find that the topological edge modes are localized on a special type of corner, while the bulk modes remain extended. Such an effect originates from the interplay between gain, loss, and the chiral edge currents induced by the nonlocal flux, which can be characterized by considering the properties of the edge sites as a one-dimensional chain. We establish a relation between the skin-topological effect and the $\mathcal{P}\mathcal{T}$ symmetries belonging to different edges. Moreover, we discover the $\mathcal{P}\mathcal{T}$ phase transition with the emergence of exceptional points between pairs of skin-topological modes. Our results pave the way for the investigation of non-Hermitian topological physics and $\mathcal{P}\mathcal{T}$ phase transition in higher-dimensional systems.

Synthetic dimension provides a new platform for realizing topological photonic devices. Here, we propose a method to realize a rainbow concentrator of topological photonic states based on the synthetic dimension concept. The synthetic dimension is constructed using a translational degree of freedom of the nanostructures inside the unit cell of a two-dimensional photonic crystal. The translational deformation induces a nontrivial topology in the synthetic dimension, which gives rise to robust interface states at different frequencies. The topological rainbow can trap states with different frequencies, controlled by tuning the spatial modulation of interface state group velocities. The operation frequency as well as the bandwidth of the topological rainbow can be easily tuned by controlling the band gap of the photonic crystal. The topological principle can be applied to photonic crystals of any symmetry and arbitrary material composition, as long as a complete band gap exists. This Letter provides a new and general scheme for the realization of a topological rainbow concentrator and will be useful for the development of topological photonic devices.

Nanophotonic wavelength routers, which can separate and steer different incident optical wavelengths into different output ports, play a key role in many applications of integrated photonic devices. We design and experimentally demonstrate ultrasmall broadband wavelength routers using an intelligent algorithm that combines a genetic algorithm and the finite element method. The size of the device is only $1.4\mathrm{\mu m}\times 1.8\mathrm{\mu m}$, around the optical communication range, and is the smallest one demonstrated experimentally. The maximum transmission is 98% in the simulation and 71% in the experiment. Moreover, we show that various wavelength routers with different materials (both dielectric and metal), different structures, different output ports, and different operation bands can be conveniently designed using the intelligent algorithm. The average position error tolerance for each cell structure is about $\pm 20\mathrm{nm}$ for all the wavelength routers designed by our intelligent algorithm, which is possible with current nanofabrication technology. This work provides a universal platform for the realization of nanophotonic wavelength routers, and enables the design and integration of nanophotonic devices.

Optical nonreciprocity is an essential property for a wide range of applications, such as building nonreciprocal optical devices that include isolators and circulators. The realization of optical nonreciprocity relies on breaking the symmetry associated with Lorentz reciprocity, which typically requires stringent conditions such as introducing a strong magnetic field or a high-finesse cavity with nonreciprocal coupling geometry. Here we discover that the collision effect of thermal atoms, which is undesirable for most studies, can induce broadband optical nonreciprocity. By exploiting the thermal atomic collision, we experimentally observe magnet-free and cavity-free optical nonreciprocity, which possesses a high isolation ratio, ultrabroad bandwidth, and low insertion loss simultaneously. The maximum isolation ratio is close to 40 dB, while the insertion loss is less than 1 dB. The bandwidth for an isolation ratio exceeding 20 dB is over 1.2 GHz, which is 2 orders of magnitude broader than typical resonance-enhanced optical isolators. Our work paves the way for the realization of high-performance optical nonreciprocal devices and provides opportunities for applications in integrated optics and quantum networks.

Nonreciprocity is important in both optical information processing and topological photonics studies. Conventional principles for realizing nonreciprocity rely on magnetic fields, spatiotemporal modulation, or nonlinearity. Here we propose a generic principle for generating nonreciprocity by taking advantage of energy loss, which is usually regarded as harmful. The loss in a resonance mode induces a phase lag, which is independent of the energy transmission direction. When multichannel lossy resonance modes are combined, the resulting interference gives rise to nonreciprocity, with different coupling strengths for the forward and backward directions, and unidirectional energy transmission. This study opens a new avenue for the design of nonreciprocal devices without stringent requirements.