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In a periodic system with parity-time (PT) symmetry, spontaneous breaking of PT symmetry occurs when non-Hermiticity exceeds a critical value, thereby dividing the Bloch bands into PT-exact phase and PT-broken phase in two momentum regimes.From another perspective, PT-broken momentum regime can be deemed as a momentum gap if we consider Bloch k as eigenvalue of the problem instead.The topological aspects of such a type of momentum gap (PT-broken regime) remain unexplored. Here, we study the topological properties of momentum bandgap in one-dimensional (1D) PT-symmetric photonic crystals (PCs).k*p analysis shows that reversing the system's non-Hermiticity would lead to a topological phase transition, which is manifested as a local geometric phase along the momentum band.As a consequence of such geometric phase, a temporal boundary state (TBS) exists in the middle of momentum gap. Its robustness against perturbations and disorders is numerically verified by temporal simulations.

Refractive index is a fundamental electromagnetic (EM) parameter that can describe photonic continuous media (PCM) traditionally as either transparency or opacity. Recently, topological theory offers a new set of phases to characterize PCM as either trivial or nontrivial, by using topological invariant which are not direct to EM parameters. As all of optical properties in PCM should be related to EM parameters, we formulate a topological index based on EM parameters and establish its phase map in this work. The map can analytically describe the deterministic condition for a topologically nontrivial phase. Our findings indicate that the topology of 2D bi-anisotropic PCM is determined by the sign of the topological index. Another EM parameter of pseudo surface impedance is also introduced for the opaque regions of PCM, showing that the topological opacity has a full range of impedance values ranging from negative to positive, while the trivial case only has either negative or positive impedance. The simulation results show that an interface between two opacities with differing index signs can support robustly optical propagation of topological edge states. As the index only depends on EM parameters, it will pave an insightful way to further understand the intrinsic properties of photonic topology.

Topological photonics provide a novel platform to robustly manipulate the flow of light and design high-performance nanophotonic devices. To do this, a fundamental mechanism is the flexible control of optical transport based on topological boundary states on edges or corners. In this work, we design a multiport device to route the topologically optical transport by using both valley-dependent edge states (VDESs) and second-order corner states (SOCSs). The VDESs are derived from sublattice symmetry breaking in a honeycomb lattice, while SOCSs are induced by the lattice deformation of Kagome lattice. In terms of unit cell, we find that both configurations can be reconsidered as the same triangular-lattice photonic crystal, which consists of a hexagon-profile air hole array in silicon background. Therefore, a four-port device is designed based on the two configurations. In simulation, we observe the frequency-dependent routing effect of the topologically optical transport by merging of VDESs and SOCSs. This work not only shows a novel platform to explore various topological phases in the photonic system but also provides guidance in the development of topological photonic integrated circuits with mode division multiplexing.

Valley photonic crystal is one type of photonic topological insulator, whose realization only needs P-symmetry breaking. The domain wall between two valley-contrasting photonic crystals support robust edge states which can wrap around sharp corners without backscattering. Using the robust edge states, one can achieve the pulse transmission. Here, using time-domain measurement in the microwave regime, we show distortionless pulse transmission in a sharply bended waveguide. An Omega-shaped waveguide with four 120-degree bends is constructed with the domain wall between two valley photonic crystal slabs. Experimental results show the progress of Gaussian pulse transmission without distortion, and the full width at half maximum of the output signal was changed slightly in the Omega-shaped waveguide. By measuring steady state electric field distribution, we also confirmed the confined edge states without out-of-plane radiation which benefits from the dispersion below the light line. Our work provides a way for high-fidelity optical pulse signal transmission and develop high-performance optical elements such as photonic circuits or optical delay lines., 21 pages, 6 figures

Topological states, first known as quantum Hall effect or Chern insulating crystal, have been generalized to many classical wave systems where potential applications such as robust waveguiding, quantum computing and high-performance lasers are expected. However, a crystal can be either topologically trivial or nontrivial, depending on its detailed configuration, and one needs to carefully design the structure and calculate its topological invariant before the actual applications. Here, we theoretically study and experimentally demonstrate the second Chern crystal in a four-dimensional space by introducing two extra synthetic translation dimensions. Due to the inherently nontrivial topology of the synthetic translation space, this abstract four-dimensional crystal is guaranteed to be topologically nontrivial regardless of the detailed configuration. The dimensional hierarchy of gapless boundary modes can be deduced by dimension reduction. Remarkably, one-dimensional gapless dislocation modes are observed and their robustness is confirmed in our experiments. This ubiquitous phenomenon in synthetic translation space provides perspectives on the findings of topologically nontrivial crystals and inspires the designs of classical wave devices., Comment: 10 pages, 4 figures

Three-dimensional (3D) artificial metacrystals host rich topological phases, such as Weyl points, nodal rings and 3D photonic topological insulators. These topological states enable a wide range of applications, including 3D robust waveguide, one-way fiber and negative refraction of surface wave. However, these carefully designed metacrystals are usually very complex, hindering their extension to nanoscale photonic systems. Here, we theoretically proposed and experimentally realized an ideal nodal ring in visible region using a simple 1D photonic crystal. The pi Berry phase around the ring is manifested by a 2pi reflection phase's winding and the resultant drumhead surface states. By breaking the inversion symmetry, the nodal ring can be gapped and the pi-Berry phase would diffuse into a toroidal shaped Berry flux, resulting in photonic ridge states (the 3D extension of quantum valley Hall states). Our results provide a simple and feasible platform for exploring 3D topological physics and their potential applications in nanophotonics., Comment: 15 pages, 5 figures

Metagratings have been shown to form an agile and efficient platform for extreme wavefront manipulation, going beyond the limitations of gradient metasurfaces. Previous approaches for transmissive metagratings have resorted on compound asymmetric inclusions to achieve single-channel near-perfect diffraction. However, such complex inclusions are sensitive to geometric parameters and lack the flexibility for arbitrary phase modulation, restricting applications to beam deflection. Here, we show perfect unitary diffraction in all-dielectric transmissive metagratings using rectangular inclusions by tailoring their multipole interferences. Using this principle, we experimentally demonstrate analog phase profile encoding of a hologram through displacement modulation of CMOS-compatible silicon nitride nanobars, manifesting broadband and wide-angle high diffraction efficiencies for both polarizations and across the entire visible range. Featured with extreme angle/wavelength/polarization tolerance and alleviated structural complexity for both design and fabrication, our demonstration unlocks the full potential of metagrating-based wavefront manipulation for a variety of practical applications.

The recent realization of photonic topological insulators has brought the discovery of fundamentally new states of light and revolutionary applications such as non-reciprocal devices for photonic diodes and robust waveguides for light routing. The spatially distinguished layer pseudospin has attracted attention in two-dimensional electronic materials. Here we report layered photonic topological insulators based on all-dielectric bilayer photonic crystal slabs. The introduction of layer pseudospin offers more dispersion engineering capability, leading to the layer-polarized and layer-mixed photonic topological insulators. Their phase transition is demonstrated with a model Hamiltonian by considering the nonzero interlayer coupling. Layer-direction locking behavior is found in layer-polarized photonic topological insulators. High transmission is preserved in the bilayer domain wall between two layer-mixed photonic topological insulators, even when a large defect is introduced. Layered photonic topological insulators not only offer a route towards the observation of richer nontrivial phases, but also open a way for device applications in integrated photonics and information processing by using the additional layer pseudospin., Comment: 16 pages, 5 figures

As one of nanoscale planar structures, metasurface has shown excellent superiorities on manipulating light intensity, phase and/or polarization with specially designed nanoposts pattern. It allows to miniature a bulky optical lens into the chip-size metalens with wavelength-order thickness, playing an unprecedented role in visible imaging systems (e.g. ultrawide-angle lens and telephoto). However, a CMOS-compatible metalens has yet to be achieved in the visible region due to the limitation on material properties such as transmission and compatibility. Here, we experimentally demonstrate a divergent metalens based on silicon nitride platform with large numerical aperture (NA~0.98) and high transmission (~0.8) for unpolarized visible light, fabricated by a 695-nm-thick hexagonal silicon nitride array with a minimum space of 42 nm between adjacent nanoposts. Nearly diffraction-limit virtual focus spots are achieved within the visible region. Such metalens enables to shrink objects into a micro-scale size field of view as small as a single-mode fiber core. Furthermore, a macroscopic metalens with 1-cm-diameter is also realized including over half billion nanoposts, showing a potential application of wide viewing-angle functionality. Thanks to the high-transmission and CMOS-compatibility of silicon nitride, our findings may open a new door for the miniaturization of optical lenses in the fields of optical fibers, microendoscopes, smart phones, aerial cameras, beam shaping, and other integrated on-chip devices., 16 pages, 7 figures

The microstructure was fabricated on LED surface with a picosecond laser. The measurement of far field light distribution from processed LED agrees with the simulation. Such fabrication may have potential application for LED light distribution.

In this paper, we study valley degree of freedom in all dielectric silicon photonic graphene. Photonic band gap opening physics under inversion symmetry breaking is revisited by the viewpoint of nonzero valley Chern number. Bulk valley modes with opposite orbital angular momentum are unveiled by inspecting time-varying electric fields. Topological transition is well illustrated through photonic Dirac Hamiltonian. Valley dependent edge states and the associated valley-protected backscattering suppression around Z-shape bend waveguide have been demonstrated., 12 pages, 4 figures

Objective: To evaluate short-term and medium-term outcomes of microendoscopy-assisted minimally invasive transforaminal lumbar interbody fusion (MIS-TLIF) and open TLIF for lumbar degenerative disease. Methods: In this prospective, randomized control study, 50 cases received microendoscopy-assisted MIS-TLIF (MIS group), while another well-matched 50 cases accepted open TLIF (open group). Parameters between both groups, including surgical duration, intraoperative blood loss and radiologic exposure, postoperative analgesic usage and ambulatory time, visual analogue scale (VAS) for back and leg, functional scores, self-evaluation of surgical outcome (modified MacNab criteria), interbody fusion rate, adjacent segment degeneration (ASD) rate, as well as complication incidence were compared at 1 month and 24 months postoperatively. Results: Intraoperative blood loss and postoperative analgesic usage were significantly reduced in MIS group (P0.05). Excellent and perfect scale rating by modified MacNab criteria, interbody fusion rate, ASD rate and complication incidence between both groups were nearly the same (P>0.05). Conclusions: Microendoscopy-assisted MIS-TLIF owns advantages of less iatrogenic injury, decreased blood loss, reduced analgesic usage and earlier rehabilitation, while it has drawbacks of more surgical duration and radiologic exposure. It is superior than open TLIF in terms of short-term clinical outcomes and has similar medium-term clinical outcomes.

We proposed a group-theory method to calculate topological invariant in bi-isotropic photonic crystals invariant under crystallographic point group symmetries. Spin Chern number has been evaluated by the eigenvalues of rotation operators at high symmetry k-points after the pseudo-spin polarized fields are retrieved. Topological characters of photonic edge states and photonic band gaps can be well predicted by total spin Chern number. Nontrivial phase transition is found in large magnetoelectric coupling due to the jump of total spin Chern number. Light transport is also issued at the {\epsilon}/{\mu} mismatching boundary between air and the bi-isotropic photonic crystal. This finding presents the relationship between group symmetry and photonic topological systems, which enables the design of photonic nontrivial states in a rational manner., Comment: 5 pages, 4 figures

We demonstrate a single-exposure holographic fabrication of two-dimensional photonic crystal with round-cornered triangular `atoms' arranged in a triangular lattice. Simulation results show that double absolute photonic band gaps exist in this structure. Our experimental results show that holographic lithography can be used to fabricate photonic crystals not only with various lattice structures but also with various kinds of structures of the atoms, to obtain absolute band gaps or a particular band gap structure. Furthermore, the single-exposure holographic method not only makes the fabrication process simple and convenient but also makes the structures of the atoms more perfect.

An optical Fano resonance, which is caused by birefringence control rather than frequency selection, is discovered. Such birefringence-induced Fano resonance comes with fast-switching radiation. The resonance condition $\varepsilon_t< 1/\varepsilon_r$ is revealed and a tiny perturbation in birefringence is found to result in a giant switch in the principal light pole induced near surface plasmon resonance. The loss and size effects upon the Fano resonance have been studied Fano resonance is still pronounced, even if the loss and size of the object increase. The evolutions of the radiation patterns and energy singularities illustrate clearly the sensitive dependence of Fano resonance upon the birefringence.

A quantitative condition is derived to evaluate the monocular accommodation in holographic stereograms. We find that the reconstruction can be viewed as true-3D image when the whole scene is located in the monocular cues area, with compatible monocular cues and binocular cues. In contrast, it reveals incorrect monocular cues in the visible multi-imaging area and the lacking information area. To demonstrate our theoretical predictions, a pupil-function integral imaging algorithm is developed to simulate the mono-eye observation, and a holographic printing system is set up to fabricate the full-parallax holographic stereogram. Both simulation and experimental results match our theoretical predictions., Comment: 16 pages, 4 figures

We investigated the plasmonic modes in a two-dimensional quasicrystalline array of metal nanoparticles. The polarization of the modes is in the array plane. A simplified eigen-decomposition method is presented with the help of rotational symmetry. Two kinds of anti-phase ring modes with radial and tangential polarizations are of highest spatial localizations among all of plasmonic modes. For the leaky characteristic of the anti-phase ring modes, the highest fidelity mode is found to be tangential polarized mode in the quasicrystal array, whereas normal-to-plane polarized mode in the solo ring. The leaky characteristics and spatial localizations of other plasmonic modes are also studied, for example, collective vortex mode that may be potentially useful to form negative responses in plasmonic device, and collective radial mode that may be used to generate light sources with radial polarizations., Comment: 20 pages, 4 figures

We show that a metamaterial slab with arbitrary values of epsilon and mu behaves as a cloak at a finite frequency for a small object located sufficiently close to it due to the suppression of the object's optical excitations by enhanced reflections. Reflections due to propagating components can partially suppress the excitation while evanescent components can cloak the object completely. In particular, a Veselago slab with epsilon = mu = -1 + i delta, as well as a class of anisotropic negative refractive index slabs, can completely cloak the small object placed within a finite distance from the slab when delta -> 0., 28 pages, 4 figures, including a paper and its auxiliary material

It is revealed in the present paper that the reflectance around the defect mode of one-dimensional defective photonic crystal (PC) in an asymmetric structure approaches to 1, while the phase-shift depends on the number of the coupled-defect layers, i.e., the phase shift is 2π for every sub-peak of the defect mode. When the defect layer is a temperature sensitive material, very small change of temperature will cause a significant phase change. Secondly, it is demonstrated that the relationship of phase and temperature has a linear range. According to the above characteristics, a highly sensitive temperature sensor is designed based on the phase property of photonic crystal. Moreover, this principle of PC phase sensing can be extended to study other sensors, such as the two-dimensional PC, which is suitable for optical integration.

It is revealed that the reflectance in the whole stop band of a heterostructure, including the defect mode, approaches 1; while the phase-shift depends on the sub-photonic crystal (PC) that faces the incident direction. For every sub-peak in the defect mode or every pass band of the sub-PC facing the incident direction, the phase shift is 2π. These properties are useful for designing optical phase devices several orders more sensitive than those using amplitude-signal. In this paper, a sensitive optical phase logic gate (NAND) is described as an example of optical phase devices. Moreover, these properties are also useful for the study of related physical phenomena.

The expressions of the dispersion relationship and space localization in the one-dimensional photonic crystal (1DPC) with symmetric semi-infinite period number and a central defect layer are deduced, which are valid for the defect 1DPC consisting of materials with arbitrary frequency-dependence. Based upon them, we found that the eigenfrequency of defect state is red-shifted with the increasing geometry thickness of defect layer in right-handed materials. On the contrary, the frequency is blue-shifted when the defect layer is a left-handed material. Moreover, the defect state is more localized for symmetric semi-infinite period structures consisting of metamaterials than those of conventional right-handed materials.

Our numerical simulation results show that if a compound structure is composed of a lattice with a larger periodic constant and a lattice with a small periodic constant, the lattice with larger periodic constant will play the role of defects. The frequencies of defect modes are dependent on the rod radius (r2) of square lattice with a larger periodic constant, and the relationship of the defect modes and r2 is almost independent of a2. The defect mode is dependent on incidence angle when a22. Furthermore, by optimizing the size of the rods (r2) of the larger periodic lattice, single defect mode, multiple defect modes with equal or different frequency spacing, including single polarization or TE and TM overlap defect mode, can be gotten respectively. The transmissivity of the defect modes are inversely proportional to a2.

It is theoretically demonstrated that the omnidirectional reflection band in one-dimensional disordered photonic crystals (1D DPCs) can have a width as broad as that in one-dimensional periodic photonic crystals (1D PPCs) with the same layer number. In the band gap, the electric field intensity distributions in a 1D DPC are almost the same as in 1D PPCs. However, near the band edges, the electric field intensity distribution in the 1D PPC is symmetric, remarkably different from the asymmetric field patterns in the 1D DPCs that are designable and controllable. This characteristic in the 1D DPCs should open a new way to design photonic-crystal-based devices.

This paper has theoretically studied the characteristic frequencies of band structures in two-dimensional metallic-dielectric photonic crystals. It is demonstrated that a large filling fraction benefits the existence of absolute photonic band gap, while a smaller filling fraction benefits an absolute negative refraction band. In addition, it also finds that the relation between the cut-off frequency of E-polarized wave and the filling fraction exceeding 10% is content with a linear increasing function, whose coefficients are exponential to the normalized lattice constant. These investigations have significant implications for tuning the operational frequencies to desired applications and manufacturing photonic crystals.

By combining two Fibonacci quasi-periodic structures and a periodic structure to form a heterostructure, a broad omnidirectional reflection band is obtained. From the numerical results performed by the transfer matrix method, it is found that the reflection bands of the two Fibonacci quasi-periodic sub-structures and the periodic sub-structure can be compensated for each other. This method is expected to be useful in constructing a one-dimensional quasi-periodic photonic crystal structure with a broad omnidirectional reflection band.