Higher-Order Topological Insulators via Momentum-Space Nonsymmorphic Symmetries.

We theoretically construct a higher-order topological insulator (HOTI) on a Brillouin real projective plane enabled by momentum-space nonsymmorphic (k-NS) symmetries from synthetic gauge fields. Two anicommutative k-NS glide reflections appear in a checkerboard Z_{2} flux model, impose nonsymmorphic constraints on Berry curvature, and quantize bulk and Wannier-sector polarization nonlocally across different momenta. The model's bulk exhibits an isotropic quadrupole phase diagram, where the transition appears intrinsically from bulk gap closure. The model hosts the simultaneous presence of intrinsic and extrinsic HOTI features: in a ribbon geometry where one pair of boundaries gets open, the edge termination can induce boundary-obstructed topological phase within the symmetry-protected topological phase due to the breaking of k-NS symmetry. At last, we present a concrete design for the real projective plane quadrupole insulator and show how to measure the momentum glide reflection based on acoustic resonator arrays. Our results shed light on HOTIs on deformed Brillouin manifolds via k-NS symmetries.

Synthetic Non-Abelian Gauge Fields for Non-Hermitian Systems.

Non-Abelian gauge fields are versatile tools for synthesizing topological phenomena, but have so far been mostly studied in Hermitian systems, where gauge flux has to be defined from a closed loop in order for vector potentials, whether Abelian or non-Abelian, to become physically meaningful. We show that this condition can be relaxed in non-Hermitian systems by proposing and studying a generalized Hatano-Nelson model with imbalanced non-Abelian hopping. Despite lacking gauge flux in one dimension, non-Abelian gauge fields create rich non-Hermitian topological consequences. With SU(2) gauge fields, the braiding degrees that can be achieved are twice the highest hopping order of a lattice model, indicating the utility of spinful freedom to attain high-order nontrivial braiding. At both ends of an open chain, non-Abelian gauge fields lead to the simultaneous presence of non-Hermitian skin modes, whose population can be effectively tuned near the exceptional points. Generalizing to two dimensions, the gauge invariance of Wilson loops can also break down in non-Hermitian lattices dressed with non-Abelian gauge fields. Toward realization, we present a concrete experimental proposal for non-Abelian gauge fields in non-Hermitian systems via the synthetic frequency dimension of a polarization-multiplexed fiber ring resonator.

Polarization-controllable perfect vortex beam by a dielectric metasurface.

A perfect vortex beam has been attracting tremendous attention due to the fact that its ring radius is independent of the topological charge. Taking advantage of the superposition principle of phase in Fourier space, we proposed to generate perfect vortex beam using propagation-phase-based dielectric metasurface, which exhibits production efficiency larger than 83.5%. Due to the sensitivity of propagation phase to the polarization of incident beam, two sets of phase profiles can be imposed on a single dielectric metasurface, enabling the simultaneous generation of dual perfect vortex beams. Based on this property, convenient control to the radius and/or topological charge of perfect vortex beam is achieved by switching the incident polarization between two orthogonal polarizations, without redesigning metasurface or changing optical path. What's more important, the crosstalk of these two channels is low, less than 4%. Thus, the propagation-phase method of producing perfect vortex beam will find significant applications in optical communication, particle trapping, particle manipulation and holographic display.

Snell-like and Fresnel-like formulas of the dual-phase-gradient metasurface.

By patterning the metasurface of two phase gradients that are both space-orthogonal and polarization-orthogonal, we derived the three-dimensional (3D) Snell-like formula and the Fresnel-like formula of the proposed metasurface. Theoretically, the dual-phase-gradient metasurface resembles biaxial-like birefringence, i.e., decomposing any homogeneously polarized incident beam into two anomalously refracted beams whose polarizations vary as the incident beam. According to the Fresnel-like formula, the relative intensity between the two anomalously refracted beams not only depends on the incidence angle and the polarization ellipticity of the incident beam being similar to the biaxial crystals, but it also depends on the polarization ellipticity orientation even for a given incident polarization, which is an unique property absent in the biaxial crystals. All the theoretical analyses were numerically demonstrated. The 3D Snell-like and Fresnel-like formulas will make the design of functional devices based on the dual-phase-gradient metasurface much easier.

Dielectric longitudinal bifocal metalens with adjustable intensity and high focusing efficiency: erratum.

A number of erratums are presented to correct the inadvertent typing mistakes in our paper.

Monitoring algorithm of tilt angle based on sub-block plane fitting for high-resolution imaging.

The limitation of mechanical structure and misoperations can result in a small tilt angle formed by the sample and the focal plane, which will decrease the resolution of the imaging system. Moreover, the small tilt angle is difficult to be observed. In order to solve this problem, a monitoring algorithm of tilt angle based on sub-block plane fitting for high-resolution imaging systems has been proposed, which is used to measure the initial angle of most 2D samples before imaging and assist users to determine the tilt degree of the sample. Experiments demonstrate that the proposed method can measure the tilt angle with a high measurement precision of 0.007° and a low residual tilt angle of 0.004°, indicating that the algorithm has high measurement precision and stability. Further results show that the quality of the image will be improved by 20%-27% when the tilt angle is 0.3056°, which means that the small degree of tilt of the sample can seriously damage the image quality. Therefore, the study of tilt angle measurement has great significance for high-resolution imaging systems.

Dielectric longitudinal bifocal metalens with adjustable intensity and high focusing efficiency.

Metalens recently attracts enormous attention due to its microscale figure and versatile functionalities. With the combination of geometric phase and propagation phase, we first wrote the phase equation of bifocal metalens that can high efficiently focus incidence into one or two foci in tandem along longitudinal direction, depending on the polarization of incidence. More importantly, the relative intensity of the two foci can be modulated conveniently by changing the ellipticity of incidence, which is different from previous bifocal metalenses need to be repatterned for each kind of relative intensity [Opt. Express23, 29855 (2015)]. Besides, the focusing efficiency of the proposed metalens is as high as 72%, and the separate distance between those two foci can be designed at will, which may find itself significant applications in optical tomography technique, optical data storage, and so on.

Dispersion engineering in unidirectional excitation of the surface wave of photonic crystal.

The discovery of transverse spin angular momentum (SAM) of evanescent and guided modes presents a novel spin-orbit interaction (SOI), i.e., transverse SOI, to affect and control the intensity distribution and propagation path of light. In this Letter, we first theoretically verify the transverse SAM property of the surface wave of a photonic crystal (PhC) slab. Then we realize the polarization-controllable unidirectional excitation of such (forward) surface wave by means of transverse SOI. Furthermore, taking advantage of dispersion engineering of PhC, we design another PhC slab capable of sustaining a backward surface wave and find that, compared to a forward surface wave, the backward surface wave is related to inverse unidirectional excitation with incident of a circularly polarized beam. In other words, dispersion engineering of PhC provides another route to control the excitation direction of surface modes. The combination of dispersion engineering and transverse SOI will facilitate the design of functional devices based on PhC in the field of nanophotonics and nanoplasmonics.

Right- and left-handed rules on the transverse spin angular momentum of a surface wave of photonic crystal.

By investigating the surface wave of photonic crystal, we put forward two sets of rules: the right-handed screw rule, judging the transverse spin angular momentum (SAM) directions according to the propagation direction of the surface wave; and the left-handed rule, judging the excitation direction of the surface wave in accordance to the SAM direction of incident circularly polarized light and the relative position of the dipole-like scatterer with respect to the interface where the surface wave propagates. Both right- and left-handed rules apply to the interface consisting of opposite-sign-permittivity materials. With the help of these two sets of rules, it is convenient to judge the direction of the transverse SAM and the excited surface wave, which facilitate the application involving transverse SAM of the surface wave.

Parameter determination and transformation for the focusing of dielectric microspheres illuminated by optical needle.

By eliminating the spherical aberrations of microsphere we derived a simple but useful formula on the focusing of dielectric microsphere. On basis of this formula, not only can researchers determine the parameters of an optical microsphere system with super-resolution, but they can also perform parameter transformation. In order to facilitate the application, the principle of parameter transformation was summarized into three kinds of case listed in Table 1, which were all demonstrated numerically with concrete examples by finite-difference time-domain method. This formula will be conducive to the development of applications based on microsphere, such as photonic nano-jet lithography, microsphere nano-scope.

Direct measurement of the negative Goos-Hänchen shift of single reflection in a two-dimensional photonic crystal with negative refractive index.

The negative Goos-Hänchen shift (GHS) on a two-dimensional photonic crystal with an effective negative refractive index is investigated by simulation and experiment. The measured refractive index of the fabricated photonic crystal is nearly -0.44. The difference between the Goos-Hänchen shift of the transverse electric wave GTE and that of the transverse magnetic wave GTM (DGHS) in the height direction of a silicon rod is measured at three incident angles. The result shows that DGHS is always smaller than -GTM, thus GTE<0; therefore, the negative GHS does occur on the surface of the photonic crystal with a negative refractive index.

Mechanism Analysis of the Inverse Doppler Effect in Two-Dimensional Photonic Crystal based on Phase Evolution.

Although the inverse Doppler effect has been observed experimentally at optical frequencies in photonic crystal with negative effective refractive index, its explanation is based on phenomenological theory rather than a strict theory. Elucidating the physical mechanism underlying the inverse Doppler shift is necessary. In this article, the primary electrical field component in the photonic crystal that leads to negative refraction was extracted, and the phase evolution of the entire process when light travels through a moving photonic crystal was investigated using static and dynamic finite different time domain methods. The analysis demonstrates the validity of the use of np (the effective refractive index of the photonic crystal in the light path) in these calculations, and reveals the origin of the inverse Doppler effect in photonic crystals.