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This paper explores the detection capability of space-borne detectors to the anisotropic stochastic gravitational-wave background (SGWB) without relying on the low-frequency approximation. To assess the detection performance, we calculate the power-law integrated sensitivity (PLIS) curve. Our results demonstrate that a single detector has limited capabilities in detecting multipole moments beyond the monopole ($l=0$), quadrupole ($l=2$), and hexadecapole ($l=4$). However, when multiple detectors are combined, the presence of multiple pointing directions and the separation between detectors significantly enhance the detection capabilities for the other multipole moments. For instance, when considering the dipole ($l=1$), combining TianQin with TianQin II and LISA with TianQin significantly improves the detection sensitivity by 2-3 orders of magnitude, compared with using a single TianQin and a single LISA, respectively., Comment: 12 pages, 8 figures

Raman spectroscopy is a powerful tool to detect, analyze and identify molecules. It has been a long-history pursuit to push the detection limit of Raman spectroscopy down to the fundamental single-molecule (SM) level. Due to the tiny cross section of intrinsic Raman scattering of molecule, some enhancement mechanisms of light-matter interaction must be implemented to levitate the Raman scattering intensity by a huge number of ~14-15 orders of magnitude, to the level comparable with the molecule fluorescence intensity. In this work we report unambiguous observation of single-molecule Raman spectroscopy via synergic action of electromagnetic and chemical enhancement for rhodamine B (RhB) molecule absorbed within the plasmonic nanogap formed by gold nanoparticle sitting on the two-dimensional (2D) monolayer WS2 and 2 nm SiO2 coated gold thin film. Raman spectroscopy down to an extremely dilute value of 10-18 mol/L can still be clearly visible, and the statistical enhancement factor could reach 16 orders of magnitude compared with the reference detection sample of silicon plate with a detection limit of 10-2 mol/L. The electromagnetic enhancement comes from local surface plasmon resonance induced at the nanogap, which could reach ~10-11 orders of magnitude, while the chemical enhancement comes from monolayer WS2 2D material, which could reach 4-5 orders of magnitudes. The synergic implementation and action of these two prestigious Raman scattering enhancement mechanisms in this specially designed 2D material-plasmon nanogap composite nanoscale system enables unambiguous experimental observation of single-molecule Raman spectroscopy of RhB molecule. This route of Raman enhancement devices could open up a new frontier of single molecule science, allowing detection, identification, and monitor of single molecules and their spatial-temporal evolution under various internal and external stimuli.

Metastasis is the main fatal cause of colorectal cancer (CRC). Although enormous efforts have been made to date to identify biomarkers associated with metastasis, there is still a huge gap to translate these efforts into effective clinical applications due to the poor consistency of biomarkers in dealing with the genetic heterogeneity of CRCs. In this study, a small cohort of eight CRC patients was recruited, from whom we collected cancer, paracancer, and normal tissues simultaneously and performed whole-exome sequencing. Given the exomes, a novel statistical parameter LIP was introduced to quantitatively measure the local invasion power for every somatic and germline mutation, whereby we affirmed that the innate germline mutations instead of somatic mutations might serve as the major driving force in promoting local invasion. Furthermore, via bioinformatic analyses of big data derived from the public zone, we identified ten potential driver variants that likely urged the local invasion of tumor cells into nearby tissue. Of them, six corresponding genes were new to CRC metastasis. In addition, a metastasis resister variant was also identified. Based on these eleven variants, we constructed a logistic regression model for rapid risk assessment of early metastasis, which was also deployed as an online server, AmetaRisk (http://www.bio-add.org/AmetaRisk). In summary, we made a valuable attempt in this study to exome-wide explore the genetic driving force to local invasion, which provides new insights into the mechanistic understanding of metastasis. Furthermore, the risk assessment model can assist in prioritizing therapeutic regimens in clinics and discovering new drug targets, and thus substantially increase the survival rate of CRC patients.

The recombination rate of markers far away from the candidate gene in the F2 and BC1P1 population. (DOCX 13 kb)

Supplementary 1. Sequences of W1827 and P1835. (DOC 29 kb)

Surface plasmon polaritons (SPPs) have been widely investigated in the past decades. Due to their unique feature of field localization, optical energy can be strongly confined in the subwavelength and even nanoscale space. This strong confinement gives rise to dramatically increased electromagnetic field strength, leading to greatly enhanced light-matter interactions. The properties of SPP are strongly dependent on material, morphology and structure. The wavelength of surface plasmon resonance can be readily manipulated over broadband optical spectra, covering ultraviolet, visible, near infrared to far infrared. In this review article, both working principle and applications of surface plasmon enhanced light-matter interactions, such as fluorescence, Raman scattering, nonlinear optics, heat effects, photoacoustic effects, photo-catalysis, and photovoltaic conversion, are comprehensively reviewed. Besides, the current problems and future research directions of surface plasmons are discussed. Our paper provides valuable reference for future high-performance plasmonic device and technology applications.

High-quality three-dimensional polystyrene opal photonic crystals are fabricated by vertical deposition method. The transmission properties with different incident angles and different composite refractive index contrasts are experimentally and theoretically studied. Good agreement between the experiment and theory is achieved. We find that with the increasing incident angle, the gap position shifts to the short wavelength (blue shift) and the gap becomes shallower; and with the increase of refractive index of the opal void materials and decrease the contrast of refractive index, the gap position shifts to the long wavelength (red shift). At the same time, we observe the swelling effects when the sample is immerged in the solutions with different refractive indices, which make the microsphere diameter in solution become larger than that in air. The understanding of band gap shift behaviour may be helpful in designing optical sensors and tunable photonic crystal ultrafast optical switches.

We numerically investigate the quality factors of two-dimensional (2D) photonic crystal (PC) microcavities using an auxiliary differential equations (ADE) technique in the context of finite-difference time-domain (FDTD) method. The microcavities are formed by point defects in the air hole lattice hexagonally patterned in ZnO (zinc oxide) matrix. The quality factors of these microcavities are limited primarily by the absorption of the background dielectric. We show that the ratio between the quality factors of microcavities in lossy and lossless background dielectric depends on the overlap between the field of cavity modes and the absorbing background dielectric in addition to the magnitude of absorption. These results will be helpful when designing and optimizing photonic crystal microcavities formed in lossy medium.

We numerically investigate the coupling of TE-like modes and TM-like modes in a two-dimensional (2D) photonic crystal (PC) slab composed of truncated cone silicon rods. In such structures, the classification of TE-like modes and TM-like modes is generally impossible and the coupling occurs due to vertical structural asymmetries. The frequency and wavevector dependences of the mode coupling are discussed by investigating the photonic band structures, and the coupling efficiency is studied by examining the transmittance. The results show that the efficiency of mode conversion is strengthened by the vertical asymmetry and weakened by the clear small gap. These structures could be used as polarization conversion devices in integrated optics.

A highly efficient W3 Y-branch filter in a two-dimensional photonic crystal slab with triangular lattice of air holes is designed and fabricated, and its transmission properties are measured. By accurately adjusting the size of the resonant cavities, the minimum wavelength spacing of 7 nm between two channels is realized. The corresponding resonant wavelengths of the two cavities agree well with the calculated ones. This implies that this kind of filter may be promising in integrated wavelength division multiplexing system.

We report the imaging properties of a two-dimensional rectangular-lattice photonic crystal (PC) slab consisting of rectangular metallic rods immersed in a dielectric background. By simulating the electromagnetic wave propagation through such a PC slab with the finite-difference time-domain method, we find that a point source placed in the vicinity of the PC slab can form a good-quality image through the slab. The frequency region where a good-quality image is formed can be controlled by choosing the direction along which the PC slab surface normal is placed.

We demonstrate a high-performance apertureless near-field probe made of a tapered metal tip with a set of periodic shallow grooves near the apex. The spontaneous emission from a single emitter near the tip is investigated systematically for the side-illumination tip enhanced spectroscopy (TES). In contrast with the bare tapered metal tip in conventional side-illumination TES, the corrugated probe not only enhances strongly local excitation field but also concentrates the emission directivity, which leads to high collection efficiency and signal-to-noise ratio. In particular, we propose an asymmetric TES tip based on two coupling nanorods with different length at the apex to realize unidirectional enhanced emission rate from a single emitter. Interestingly, we find that the radiation pattern is sensitive to the emission wavelength and the emitter positions respective to the apex, which can result in an increase of signal-to-noise ratio by suppressing undesired signal. The proposed asymmetrical corrugated probe opens up a broad range of practical applications, e.g. increasing the detection efficiency of tip enhanced spectroscopy at the single-molecule level.

The extraordinary light transmission through a 200-nm thick gold film when passing through different subwavelength hole arrays is observed experimentally. The sample is fabricated by electron beam lithography and reactive ion etching system. A comparison between light transmissions shows that the hole shape changing from rectangular to diamond strongly affects the transmission intensity although both structures possess the same lattice constant of 600 nm. Moreover, the position of the transmission maximum undergoes a spectral red-shift of about 63 nm. Numerical simulations by using a transfer matrix method reproduce the observed transmission spectrum quite well.

Imaging properties of a two-dimensional photonic crystal (PC) slab consisting of a triangular lattice of metallic cylinders immersed in a dielectric background are investigated by the finite-difference time-domain technique. With the calculated field patterns of a point source placed in the vicinity of the PC slab and the corresponding equifrequency-surface contours, we find that a high-quality image can form in the opposite side of the slab in the lowest TM-polarized photonic band, and this near-field image is formed mainly by the self-collimation effect.

Scalar diffraction theory, although simple and efficient, is too rough for analysing diffractive micro-optical elements. Rigorous vectorial diffraction theory requires extensive numerical efforts and is not a convenient design tool. In this paper we employ a simple approximate vectorial diffraction model which combines the principle of the scalar diffraction theory with an approximate local field model to analyse the diffraction of optical waves by some typical two-dimensional diffractive micro-optical elements. The TE and TM polarization modes are both considered. We have found that the approximate vectorial diffraction model can agree much better with the rigorous electromagnetic simulation results than the scalar diffraction theory for these micro-optical elements.

Defect modes in one-dimensional photonic crystals (PCs) can be readily detected from the solution of the transmission spectra via the standard transfer-matrix method. We adopt an analytic Bloch-mode approach to examine this problem in terms of eigenmode solutions and investigate the dispersion behaviour of localized defect modes supported by a defect layer sandwiched within two symmetric semi-infinite PCs that are made from multiple constituents. The results show that the number of defect modes grows when the dielectric constant and width of the defect layer increase.

Silicon photonics is considered as a promising technology to realize high-performance photonic integrated circuits, owing to its complementary metal oxide semiconductor-compatibility which is applicable for large-scale integration at low cost. However, due to the limitation of optoelectronic properties of silicon, the challenge to the realization of high-performance active device on the silicon integrated platform still exists. The recent development of graphene-silicon hybrid photonic integrated circuit provides a practical solution to this problem, because graphene, as a superior two-dimensional material, possesses many advantageous optoelectronic properties, such as high mobility, high electro-optical coefficient, and broadband absorption, which can be fully exploited to break through the material limitation of silicon. Moreover, compared with other active integrated materials such as germanium and compound semiconductors, graphene is cost-effective and can be conveniently integrated with silicon photonic device. Here, we review some important research progress of graphene-silicon hybrid photonic integrated circuits that include optical sources, optical waveguides, optical modulators, and photodetectors. The challenges and prospects of these devices are also analyzed, which are expected to be beneficial to the relevant research communities.

Negative refraction and imaging properties of the electromagnetic wave through a two-dimensional photonic crystal (PC) slab, which consists of a square lattice of elliptical dielectric rods immersed in the air background, is studied by the plane-wave expansion method and the finite-difference time-domain method. A point source placed in the vicinity of the PC slab can form a good-quality image spot through the PC slab for the incident frequencies within the second photonic band. The calculated result also shows that negative refraction occurs in this kind of PC slab.

Two kinds of subwavelength hole arrays in metallic films are designed to verify the important role of the periodicity in enhanced transmission of light. The measured optical spectra show that the quasiperiodic hole arrays exhibit an enhanced transmission peak centred at 707 nm with a transmission intensity of about 20%, while no plasmon resonance peak is found for the amorphous hole arrays. When the hole diameter decreases in the quasiperiodic structure, the position of the transmission peak shifts slightly, and the transmittance drops. These phenomena indicate the important role of the long-range structural order (particularly the periodicity) in assisting the coupling of incident light wave with the surface plasmon modes of the metallic structures.

We fabricated two-dimensional photonic crystal slab Y-branch waveguides with different intervals between the two output ports and measured their light guiding characteristics. The field intensity distributions of the TE polarized wave modes are also calculated by means of a transfer matrix method. Both the theoretical and experimental results show that the minimum interval between the two output ports is about 1.4 times the transport wavelength of 1.55 μm. If the interval becomes smaller, light waves in the two branches will couple each other seriously. The result will be helpful for designs of ultracompact wave demultiplexers and all-optical integrated circuits.

The transmission properties of quasiperiodic photonic crystals (QPCs) based on the random square-triangle tiling system are investigated by the multiple scattering method. The hollow cylinders are introduced in our calculation. It is found that QPCs with hollow cylinders also possess a complete band gap common to s- and p-polarized waves when the inner radius of hollow cylinders is larger than a certain value. The QPCs possessing the complete band gap can be applied to the fields of light emitting, wave-guides, optical filters, high-Q resonators and antennas.

On-chip optical isolators play a key role in optical communications and computing based on silicon integrated photonic structures. Recently there have raised great attentions and hot controversies upon isolation of light via linear and passive photonic structures. Here we analyze the optical isolation properties of a silicon photonic crystal slab heterojunction diode by comparing the forward transmissivity and round-trip reflectivity of in-plane infrared light across the structure. The round-trip reflectivity is much smaller than the forward transmissivity, justifying good isolation. The considerable effective nonreciprocal transport of in-plane signal light in the linear and passive silicon optical diode is attributed to the information dissipation and selective modal conversion in the multiple-channel structure and has no conflict with reciprocal principle., Comment: 14 pages, 4 figures

All-optical integrated circuits for computing and information processing have been pursued for decades as a potential strategy to overcome the speed limitations intrinsic to electronics. However feasible on-chip integrated logic units and devices still have been limited by its size, quality, scalability, and reliability. Here we demonstrate all-passive on-chip optical AND and NAND logic gates made from a directional emitting cavity connecting two ultrasmall photonic crystal heterojunction diodes. The measured transmission spectra show more than 10dB contrast of the logic transport with a high phase tolerance, agreeing well with numerical simulations. The building of linear, passive, and ultracompact silicon optical logic gates might pave the way to construct novel nanophotonic on-chip processor architectures for future optical computing technologies., Comment: 19 pages, 5 figures

Based on the concept of quasi-phase matching nonlinear interaction, and successful fabrication of nonlinear photonic crystal using high voltage electric field in 90's, studies on nonlinear photonic crystal were made by different research teams. The related works sharply developed from single one-dimensional superlattice to various structures. On the other hand, further fabrications were made in these crystals, for example, the fabrication of optical waveguides etc. Fabrications of multiple optical waveguides in one two-dimensional photonic crystal were suggested in this paper. This will be helpful to the extension of laser wavelengths, compact optical elements and all-optical switches.

A material with the formula ZrMgMo3O12 having negative thermal expansion is presented and characterized. It is shown that ZrMgMo3O12 crystallizes in an orthorhombic symmetry with space group Pnma(62) or Pna21(33) and exhibits negative thermal expansion in a large temperature range (αl = −3.8 × 10−6 K−1 from 300K to 1000K by x-ray diffraction and αl = −3.73 × 10−6 K−1 from 295K to 775K by dilatometer). ZrMgMo3O12 remains the orthorhombic structure without phase transition or decomposition at least from 123K to 1200K and is not hygroscopic. These properties make it an excellent material with negative thermal expansion for a variety of applications.

We present a systematic experimental investigation on visible light collimation by a nanostructured slit flanked with a pair of periodic array of grooves in gold thin film. A wide variety of aspects are considered, such as the polarization state, the transport path of incident light, the groove—groove spacing, the groove width and depth. Our results clearly show that the relationship between the collimation wavelength and the periodicity of the slit-groove structure accords well with the surface plasmon dispersion model proposed by previous researchers. Furthermore, the surface plasmon wave phase retardation effect induced by the surface structure is also verified via the measurement for samples with different groove widths and depths. These results indicate that the detailed geometry of the groove structure has obvious impacts on the collimation effect and the angular distribution of the diffraction light in the subwavelength plasmonic system.

Second harmonic generation (SHG) in one-dimensional nonlinear photonic crystals made from periodically alternating ferroelectric and dielectric layers is investigated by means of the transfer matrix method. When tuned at the photonic band gap (PBG) edges, the fundamental wave and second harmonic wave slow down, and the filed enhancement takes place within the nonlinear photonic crystal. The phase mismatching can be compensated for to some extent and the second harmonic process will be enhanced. Numerical results show that the enhancement of SHG in the PBG structure can be up to four orders of magnitude compared with the traditional quasi-phase-matching structure.

We design and realize a 90° waveguide bend in two-dimensional triangular lattice silicon photonic crystal slabs by connecting linear waveguides along the orthogonal Γ – K and Γ – M directions. A pass band of 70 nm is realized by optimizing the geometry of the Γ – M waveguide. The connection region of the waveguide bend is optimized to improve the transmission efficiency of infrared light through the two different kinds of waveguides. The transmission efficiency of an optimized single bend is about 75% in simulation and 45% in measurement.

We design high quality factor (Q) photonic crystal microcavities in diamond films for applications in quantum information based on color centers. A photonic microcavity made from a waveguide heterostructure with a mode gap is demonstrated to have a high Q factor over 1051400 and a modal volume V of 2.24 cubic wavelengths by modifying the mode gap width and the tapered region geometry. Besides its ultrahigh Q factor, the waveguide-like geometry of the cavity allows for easy on-chip transportation of quantum information between different cavities.

The translational symmetric associated with photonic crystal is absent in the rotationally symmetric quasiperiodic photonic crystal （QPCs）, and the quasiperiodic photonic crystal has more defect modes than photonic crystal because of it. In this paper, we investigate the defect modes in the 12-fold quasiperiodic photonic crystal by the multiple scattering method. We find that there is a directional defect mode in quasiperiodic photonic crystal. When the defect rotates against the centre of the symmetry, there emerges a new defect mode.

Using focused ion beam lithograph, we fabricated W3 straight waveguide in two-dimensional photonic crystal slab on SOI (silicon on insulator) wafer. The light propagation was observed on top and from the end of the sample. The transmission dip and mode distribution at the outlet of ridged waveguide were measured. The results show that light can propagate in the photonic crystal waveguide.

Photoluminescence (PL) spectra of annealed a-SixC1-x:H films were studied. The-widths of the exponential bandtails were determined by means of the temperature dependences of PL peak energy positions. The experimental results shows that PL peak energy positions shift towards the lower energy with annealing temperature increasing. The bandtail widths have been calculated according to the exponential bandtail model, the calculation shows that the bandtails contract with increase of annealing temperature. A discussion about the results has been given.