An Equivalent Condition on the Switching Construction of Differentially 44-uniform Permutations on \gf_{2^{2k}} from the Inverse Function

Differentially $4$-uniform permutations on \gf_{2^{2k}} with high nonlinearity are often chosen as substitution boxes in block ciphers. Recently, Qu et al. used the powerful switching method to construct permutations with low differential uniformity from the inverse function \cite{QTTL, QTLG} and proposed a sufficient but not necessary condition for these permutations to be differentially $4$-uniform. In this paper, a sufficient and necessary condition is presented. We also give a compact estimation for the number of constructed differentially $4$-uniform permutations. Comparing with those constructions in \cite{QTTL, QTLG}, the number of functions constructed here is much bigger. As an application, a new class of differentially $4$-uniform permutations is constructed. The obtained functions in this paper may provide more choices for the design of substitution boxes

Monolithic integration of broadband optical isolators for polarization-diverse silicon photonics

Integrated optical isolators have been a longstanding challenge for photonic integrated circuits (PIC). An ideal integrated optical isolator for PIC should be made by a monolithic process, have a small footprint, exhibit broadband and polarization-diverse operation, and be compatible with multiple materials platforms. Despite significant progress, the optical isolators reported so far do not meet all these requirements. In this article we present monolithically integrated broadband magneto-optical isolators on silicon and silicon nitride (SiN) platforms operating for both TE and TM modes with record high performances, fulfilling all the essential characteristics for PIC applications. In particular, we demonstrate fully-TE broadband isolators by depositing high quality magneto-optical garnet thin films on the sidewalls of Si and SiN waveguides, a critical result for applications in TE-polarized on-chip lasers and amplifiers. This work demonstrates monolithic integration of high performance optical isolators on chip for polarization-diverse silicon photonic systems, enabling new pathways to impart nonreciprocal photonic functionality to a variety of integrated photonic devices

Amorphous photonic topological insulator

Photonic topological insulators (PTIs) exhibit robust photonic edge states protected by band topology, similar to electronic edge states in topological band insulators. Standard band theory does not apply to amorphous phases of matter, which are formed by non-crystalline lattices with no long-range positional order but only short-range order. Among other interesting properties, amorphous media exhibit transitions between glassy and liquid phases, accompanied by dramatic changes in short-range order. Here, we experimentally investigate amorphous variants of a Chern-number-based PTI. By tuning the disorder strength in the lattice, we demonstrate that photonic topological edge states can persist into the amorphous regime, prior to the glass-to-liquid transition. After the transition to a liquid-like lattice configuration, the signatures of topological edge states disappear. This interplay between topology and short-range order in amorphous lattices paves the way for new classes of non-crystalline topological photonic materials.Comment: 13 pages, 4 figure

Observation of photonic antichiral edge states

Chiral edge states are a hallmark feature of two-dimensional topological materials. Such states must propagate along the edges of the bulk either clockwise or counterclockwise, and thus produce oppositely propagating edge states along the two parallel edges of a strip sample. However, recent theories have predicted a counterintuitive picture, where the two edge states at the two parallel strip edges can propagate in the same direction; these anomalous topological edge states are named as antichiral edge states. Here we report the experimental observation of antichiral edge states in a gyromagnetic photonic crystal. The crystal consists of gyromagnetic cylinders in a honeycomb lattice, with the two triangular sublattices magnetically biased in opposite directions. With microwave measurement, unique properties of antichiral edge states have been observed directly, which include the titled dispersion, the chiral-like robust propagation in samples with certain shapes, and the scattering into backward bulk states at certain terminations. These results extend and supplement the current understanding of chiral edge states

Observation of unconventional van der Waals multiferroics near room temperature

The search for two-dimensional (2D) van der Waals (vdW) multiferroics is an exciting yet challenging endeavor. Room-temperature 2D vdW few-layer multiferroic is a much bigger insurmountable obstacle. Here we report the discovery of an unconventional 2D vdW multiferroic with out-of-plane ferroelectric polarization and long-range magnetic orders in trilayer NiI2 device from 10 K to 295 K. The evolutions of magnetic domains with magnetic field, and the evolutions between ferroelectric and antiferroelectric phase have been unambiguously observed. More significantly, we realize a robust mutual control of magnetism and ferroelectricity at room temperature. The magnetic domains are manipulated by a small voltage ranging from 1 V to 6 V at 0 T and 295 K. This work opens opportunities for exploring multiferroic physics at the limit of few atomic layers.Comment: 4 figure

Epitaxial growth of high quality Mn3SnMn_3Sn thin films by pulsed laser deposition

Non-collinear antiferromagnet Weyl semimetal $Mn_3Sn$ have attracted great research interest recently. Although large anomalous Hall effect, anomalous Nernst effect and magneto-optical effect have been observed in $Mn_3Sn$, most studies are based on single crystals. So far, it is still challenging to grow high quality epitaxial $Mn_3Sn$ thin films with transport and optical properties comparable to their single crystal counterparts. Here, we report the structure, magneto-optical and transport properties of epitaxial $Mn_3Sn$ thin films fabricated by pulsed laser deposition (PLD). Highly oriented $Mn_{3+x}Sn_{1-x}$ (0001) and (11$\bar2$0) epitaxial films are successfully growth on single crystalline $Al_2O_3$ and MgO substrates. Large anomalous Hall effect (AHE) up to $\left| \Delta R_H\right|$=3.02 $\mu\Omega\cdot cm$, and longitudinal magneto-optical Kerr effect (LMOKE) with $\theta_K$ = 38.1 mdeg at 633 nm wavelength are measured at 300 K temperature, which are comparable to $Mn_3Sn$ single crystals. Our work demonstrates that high quality $Mn_3Sn$ epitaxial thin films can be fabricated by PLD, paving the way for future device applications