Details of the topological state transition induced by gradually increased disorder in photonic Chern insulators

Photonic Z_{2} Topological Anderson Insulators

That disorder can induce nontrivial topology is a surprising discovery in topological physics. As a typical example, Chern topological Anderson insulators (TAIs) have been realized in photonic systems, where the topological phases exist without symmetry protection. In this Letter, by taking transverse magnetic and transverse electric polarizations as pseudospin degrees of freedom, we theoretically propose a scheme to realize disorder-induced symmetry-protected topological phase transitions in two-dimensional photonic crystals with a combined time-reversal, mirror, and duality symmetry T_{f}=TM_{z}D. In particular, we demonstrate that the disorder-induced symmetry-protected topological phase persists even without pseudospin conservation, thereby realizing a photonic Z_{2} TAI, in contrast to a Z-classified quantum spin Hall (QSH) TAI with decoupled spins. By formulating a new scattering approach, we show that the topology of both the QSH and Z_{2} TAIs can be manifested by the accumulated spin rotations of the reflected waves from the photonic crystals. Using a transmission structure, we also illustrate the trivialization of a disordered QSH phase with an even integer topological index caused by spin coupling.

Reversible Conversion of Odd/Even One-Way Modes in Magneto-Optical Photonic Crystal Double-Channel Waveguides

We have studied the transmission properties of odd/even one-way modes and their reversible conversion in a double-channel waveguide consisting of two magneto-optical photonic crystals (MOPCs) sandwiched with Al₂O₃ PC. There exist two pairs of even and odd modes, i.e., M1(even)/M2(odd) or M3(odd)/M4(even) modes, for the double-channel waveguides with one- or two-stranded coupling layer of Al₂O₃ rods, respectively. Among them, the M1, M2, and M3 modes are caused by the weak coupling strength of two sub-waveguides, while the M4 mode results from the strong coupling effect and supports dispersionless slow-light propagation. Furthermore, we realize the reversible conversion between odd and even modes (i.e., between M1 and M2 modes, or M3 and M4 modes) in the one- or two-stranded structure, respectively, by adjusting the length and position of the perfect electric conductor (PEC) defect properly to cause the desired significant phase delay along the upper and lower equivalent transmission paths. Additionally, we find that the robustness of the M1 even mode is poor because of extra excitations of counter-propagation modes near the right Brillouin boundary, while the other three modes have extremely strong robustness against PEC defects and their one-way transmittances are nearly 100%. These results hold promise for many fields, such as slow-light modulation and the design of topological devices.

Robust topological one-way edge states in radius-fluctuated photonic Chern topological insulators

Recent developments in topological photonics have shown that the introduction of disorders can yield the innovative and striking transport phenomena. Here, we theoretically investigate topological one-way edge states in radius-fluctuated photonic Chern topological insulators (PCTIs), which are composed of two-dimensional gyromagnetic photonic crystals with cylinder site fixed but with cylinder radius fluctuated. We use a fluctuation index to characterize the degree of radius fluctuation, employ two empirical parameters to inspect the evolution of topological one-way edge states, and verify the stability of topological one-way edge states by calculating massive samples with various random numbers. We find that as the radius-fluctuation strength increases, there arises a competition between topological one-way edge state, Anderson localization state and trivial bulk state. We reveal that the Anderson localization state appears far more easily in the radius-fluctuation PCTI with even a weak strength compared with the position-perturbed PCTI with a strong randomness. We also demonstrate that the topological one-way edge states are protected against a strong fluctuation much larger than the fabrication errors in practical experiments. Our results show that the PCTIs consisting of gyromagnetic photonic crystals have a high-tolerance for the material and sample fabrication errors, and this would provide a deeper understanding of fundamental topology physics.

Topologically protected beam splitters and logic gates based on two-dimensional silicon photonic crystal slabs

The beam splitters are essential optical components that are widely used in various optical instruments. The robustness of beam splitters is very necessary to all-optical networks. Here we report the design of the topologically protected beam splitter, whose splitting ratio can change flexibly to an arbitrary ratio, such as 50:50, 33:67, 25:75, based on the two-dimensional silicon photonic crystal slab. By using the 50:50 beam splitter, all major logic gates (OR, AND, NOT, XOR, NAND, XNOR, and NOR) are suitably designed with the linear interference approach. Additionally, these devices exhibit robustness even though some disorders exist. It is expected that these robust and compact devices are potentially applicable in optical computing and signal processing.