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<jats:p>Synchronization is a phenomenon that is ubiquitous in engineering and natural ecosystems. The study of explosive synchronization on a single-layer network gives the critical transition coupling strength that causes explosive synchronization. However, no significant findings have been made on multi-layer complex networks. This paper proposes a frequency-weighted Kuramoto model on a two-layer network and the critical coupling strength of explosive synchronization is obtained by both theoretical analysis and numerical validation. It is found that the critical value is affected by the interaction strength between layers and the number of network oscillators. The explosive synchronization will be hindered by enhancing the interaction and promoted by increasing the number of network oscillators. Our results have importance across a range of engineering and biological research fields.</jats:p>

<jats:p>A Cs vapor cell-based atomic clock that uses a lin∥lin pumping scheme with dispersion detection is reported. This atomic clock shows potential for high performance because of its high contrast pumping scheme, and for miniaturization because of its simple architecture. The experimental setup and optimal operating parameters for the clock are introduced. The current fractional frequency stability is measured to be <jats:inline-formula> <jats:tex-math><?CDATA $1.3\times {10}^{-12}/\sqrt{\tau }$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>1.3</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>12</mml:mn> </mml:mrow> </mml:msup> <mml:mrow> <mml:mo stretchy="false">/</mml:mo> </mml:mrow> <mml:msqrt> <mml:mrow> <mml:mi>τ</mml:mi> </mml:mrow> </mml:msqrt> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_7_070601_ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> up to 20 s and reaches <jats:inline-formula> <jats:tex-math><?CDATA $3.1\times {10}^{-13}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>3.1</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>13</mml:mn> </mml:mrow> </mml:msup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_7_070601_ieqn2.gif" xlink:type="simple" /> </jats:inline-formula> at 200 s. We have thoroughly investigated the related noise sources that affect clock frequency stability at the 1 s and 100 s levels. The investigation shows that the laser frequency noise limits the clock frequency stability significantly. The clock performance can be further improved by technically upgrading the laser frequency stabilization setup.</jats:p>

<jats:p>We develop an integrated integrating sphere cold atom clock (ISCAC), which mainly consists of physical package, laser system, microwave source, and electronics. This compact system is more stable and reliable than the previous version. The experimental results show that the short term frequency stability of <jats:inline-formula> <jats:tex-math><?CDATA $5.4\times {10}^{-13}{\tau }^{-1/2}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>5.4</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>13</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mrow> <mml:mi>τ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo stretchy="false">/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_7_070602_ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> and 2.9 × 10<jats:sup>−15</jats:sup> at 1-day integrating time are achieved.</jats:p>

<jats:p>The DIA-type Kawai cell possesses a larger volume and a quasi-hydrostatic pressure environment and has been widely used in materials’ synthesis and x-ray diffraction experiments. However, few high-pressure <jats:italic>in situ</jats:italic> neutron diffraction experiments were performed in the DIA-type Kawai cell because there is no wide window for neutron diffraction and the second-stage anvils and guild block material attenuates the neutron signal significantly. In this work, we tentatively modified the normal DIA-type Kawai cell (MA 2-6-8) into a MA 2-8 mode by removing the six first-stage tungsten carbide anvils. As a consequence, the eight tungsten carbide anvils (Kawai cell) are directly driven by the guide blocks. The results of <jats:italic>ex situ</jats:italic> and <jats:italic>in situ</jats:italic> pressure calibration show that the cell pressure can reach 5 GPa with small truncation edge lengths (TEL) of 3 mm even at the load of 300 kN. It suggests that this MA 2-8 cell may open a new way for high-pressure and high-temperature <jats:italic>in situ</jats:italic> neutron diffraction.</jats:p>

<jats:p>The potential energy curves, spectroscopic constants, and low-lying vibration–rotation levels of ground-state O<jats:sub>2</jats:sub> and its cation <jats:inline-formula> <jats:tex-math><?CDATA ${{\rm{O}}}_{2}^{+}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_7_073101_ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> and anion <jats:inline-formula> <jats:tex-math><?CDATA ${{\rm{O}}}_{2}^{-}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_7_073101_ieqn2.gif" xlink:type="simple" /> </jats:inline-formula> were calculated with the explicitly correlated multireference configuration interaction method. The zeroth-order reference wavefunction was treated with the complete active space multiconfigurational self-consistent field method, in which the active space was carefully selected, and an additional molecular orbital <jats:inline-formula> <jats:tex-math><?CDATA ${\pi }_{{\rm{u}}}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>π</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">u</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_7_073101_ieqn3.gif" xlink:type="simple" /> </jats:inline-formula> was added into the full valence active space. The electron correlation of the 1s core in the oxygen atom was considered in the computations. The Davidson correction on molecular energy was considered to account for higher electron excitation. The relativistic effects, including the scalar relativistic effect and spin–orbit coupling, were considered in the computation of potential energy curves. These physical effects on the spectroscopic constants were examined. The low-lying levels of vibration–rotation spectra of O<jats:sub>2</jats:sub> and its ions were determined based on the computed potential energy curves. Comparisons with available experiments were made and excellent agreement was obtained for the vibrational and rotational parameters. The spectroscopic constants and vibration–rotation spectrum of <jats:inline-formula> <jats:tex-math><?CDATA ${{\rm{O}}}_{2}^{-}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_7_073101_ieqn4.gif" xlink:type="simple" /> </jats:inline-formula>, which is sparse in experiments, were provided. Our study will shed some light on further theoretical and experimental studies on these simple but important molecular systems.</jats:p>

<jats:p>We experimentally demonstrate a reliable method based on a nanofiber to optimize the number of cold atoms in a magneto–optical trap (MOT) and to monitor the MOT in real time. The atomic fluorescence is collected by a nanofiber with subwavelength diameter of about 400 nm. The MOT parameters are experimentally adjusted in order to match the maximum number of cold atoms provided by the fluorescence collected by the nanofiber. The maximum number of cold atoms is obtained when the intensities of the cooling and re-pumping beams are about 23.5 mW/cm<jats:sup>2</jats:sup> and 7.1 mW/cm<jats:sup>2</jats:sup>, respectively; the detuning of the cooling beam is −13.0 MHz, and the axial magnetic gradient is about 9.7 Gauss/cm. We observe a maximum photon counting rate of nearly (4.5±0.1) × 10<jats:sup>5</jats:sup> counts/s. The nanofiber–atom system can provide a powerful and flexible tool for sensitive atom detection and for monitoring atom–matter coupling. It can be widely used from quantum optics to quantum precision measurement.</jats:p>

<jats:p>The scattering characteristics of the periodic surface of infinite and finite media are investigated in detail. The Fourier expression of the scattering field of the periodic surface is obtained in terms of Huygens’s principle and Floquet’s theorem. Using the extended boundary condition method (EBCM) and <jats:italic>T</jats:italic>-matrix method, the scattering amplitude factor is solved, and the correctness of the algorithm is verified by use of the law of conservation of energy. The scattering cross section of the periodic surface in the infinitely long region is derived by improving the scattering cross section of the finite period surface. Furthermore, the effects of the incident wave parameters and the geometric structure parameters on the scattering of the periodic surface are analyzed and discussed. By reasonable approximation, the scattering calculation methods of infinite and finite long surfaces are unified. Besides, numerical results show that the dielectric constant of the periodic dielectric surface has a significant effect on the scattering rate and transmittance. The period and amplitude of the surface determine the number of scattering intensity peaks, and, together with the incident angle, influence the scattering intensity distribution.</jats:p>

<jats:p>Since the time step of the traditional finite-difference time-domain (FDTD) method is limited by the small grid size, it is inefficient when dealing with the electromagnetic problems of multi-scale structures. Therefore, the explicit and unconditionally stable FDTD (US-FDTD) approach has been developed to break through the limitation of Courant–Friedrich–Levy (CFL) condition. However, the eigenvalues and eigenvectors of the system matrix must be calculated before the time iteration in the explicit US-FDTD. Moreover, the eigenvalue decomposition is also time consuming, especially for complex electromagnetic problems in practical application. In addition, compared with the traditional FDTD method, the explicit US-FDTD method is more difficult to introduce the absorbing boundary and plane wave. To solve the drawbacks of the traditional FDTD and the explicit US-FDTD, a new hybrid FDTD algorithm is proposed in this paper. This combines the explicit US-FDTD with the traditional FDTD, which not only overcomes the limitation of CFL condition but also reduces the system matrix dimension, and introduces the plane wave and the perfectly matched layer (PML) absorption boundary conveniently. With the hybrid algorithm, the calculation of the eigenvalues is only required in the fine mesh region and adjacent coarse mesh region. Therefore, the calculation efficiency is greatly enhanced. Furthermore, the plane wave and the absorption boundary introduction of the traditional FDTD method can be directly utilized. Numerical results demonstrate the effectiveness, accuracy, stability, and convenience of this hybrid algorithm.</jats:p>

<jats:p>A new optical system for an augmented reality (AR) display is proposed in this paper. The optical system mainly includes a ray deflector, coupling input grating, optical waveguide, and coupling output grating. Both the ray deflector and the coupling input grating are designed based on the diffraction characteristics of the polarization grating, and the coupling output grating is the Bragg reflection grating. Compared with other AR schemes, this AR optical system not only reduces the number of projections from two to one, but also improves the efficiency of light coupling into the optical waveguides. The energy loss is reduced by utilizing the single-order diffraction characteristics of the polarization grating in its coupling input structure. The light deflector uses the polarization selectivity of the polarization grating and the characteristics of the rotating light of the twisted nematic liquid crystal layer to realize beam deflection. The working principle of the optical system is experimentally and theoretically demonstrated.</jats:p>

<jats:p>We propose a novel and efficient multi-functional optical fiber sensor system based on a dense wavelength division multiplexer (DWDM). This system consists of an optical fiber temperature sensor, an optical fiber strain sensor, and a 48-channel DWDM. This system can monitor temperature and strain changes at the same time. The ranges of these two sensors are from −20 °C to 100 °C and from −1000 <jats:inline-formula> <jats:tex-math><?CDATA $\mu \varepsilon $?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>μ</mml:mi> <mml:mi>ε</mml:mi> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_7_074202_ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> to 2000 <jats:inline-formula> <jats:tex-math><?CDATA $\mu \varepsilon $?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>μ</mml:mi> <mml:mi>ε</mml:mi> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_7_074202_ieqn2.gif" xlink:type="simple" /> </jats:inline-formula>, respectively. The sensitivities of the temperature sensor and strain sensor are 0.03572 nm/°C and 0.03808 nm/N, respectively. With the aid of a broadband source and spectrometer, different kinds and ranges of parameters in the environment can be monitored by using suitable sensors.</jats:p>