Multi-wavelength mode-locked Er/Yb Co-doped fiber laser with square nano-second pulse output

We report a multi-wavelength mode-locked Er/Yb codoped fiber laser with square nano-second pulse output, which is constructed with a “figure-of-eight” cavity structure. A section of polarization-maintaining Er/Yb co-doped double clad fiber was used as the gain medium and pumped by a fiber pigtailed multimode laser diode working at 975 nm via a multimode fiber combiner. Several megahertz repetition rate output pulses with peak power up to 9.2 W and pulse duration around several nanoseconds were obtained.     

Pivoting in Extended Rings for Computing Approximate Gr?bner Bases

It is well known that in the computation of Gr?bner bases arbitrarily small perturbations in the coefficients of polynomials may lead to a completely different staircase, even if the solutions of the polynomial system change continuously. This phenomenon is called artificial discontinuity in Kondratyev’s Ph.D. thesis. We show how such phenomenon may be detected and even “repaired” by using a new variable to rename the leading term each time we detect a “problem”. We call such strategy the TSV (Term Substitutions with Variables) strategy. For a zero-dimensional polynomial ideal, any monomial basis (containing 1) of the quotient ring can be found with the TSV strategy. Hence we can use TSV strategy to relax term order while keeping the framework of Gr?bner basis method so that we can use existing efficient algorithms (for instance the F ₅ algorithm) to compute an approximate Gr?bner basis. Our main algorithms, named TSVn and TSVh, can be used to repair artificial e{\epsilon}-discontinuities. Experiments show that these algorithms are effective for some nontrivial problems.     

Qualities of examples in learning and teaching

In this paper, we theorise about the different kinds of relationship between examples and the classes of mathematical objects that they exemplify as they arise in mathematical activity and teaching. We ground our theorising in direct experience of creating a polynomial that fits certain constraints to develop our understanding of engagement with examples. We then relate insights about exemplification arising from this experience to a sequence of lessons. Through these cases, we indicate the variety of fluent uses of examples made by mathematicians and experienced teachers. Following Thompson’s concept of “didactic object” (Symbolizing, modeling, and tool use in mathematics education. Kluwer, Dordrecht, The Netherlands, pp 191–212, 2002), we talk about “didacticising” an example and observe that the nature of students’ engagement is important, as well as the teacher’s intentions and actions (Thompson avoids using a verb with the root “didact”. We use the verb “didacticise” but without implying any connection to particular theoretical approaches which use the same verb.). The qualities of examples depend as much on human agency, such as pedagogical intent or mathematical curiosity or what is noticed, as on their mathematical relation to generalities.     

Direct mass measurements of short-lived A=2Z-1 nuclides (63)Ge, (65)As, (67)Se, and (71)Kr and their impact on nucleosynthesis in the rp process

Mass excesses of short-lived A=2Z-1 nuclei (63)Ge, (65)As, (67)Se, and (71)Kr have been directly measured to be -46,921(37), -46,937(85), -46,580(67), and -46,320(141) keV, respectively. The deduced proton separation energy of -90(85) keV for (65)As shows that this nucleus is only slightly proton unbound. X-ray burst model calculations with the new mass excess of (65)As suggest that the majority of the reaction flow passes through (64)Ge via proton capture, indicating that (64)Ge is not a significant rp-process waiting point.     

Optical characteristics of transparent PMNT ceramic and its application at high speed electro-optic switch

The optical characteristics of transparent lead magnesium niobate titanate (PMNT) electro-optic ceramic, including the electro-optic phase modulation, electric hysteresis property and thermo-optic coefficient, are investigated in detail. Based on this novel ceramic, a polarization independent electro-optic switch by using fiber Sagnac interferometer (FSI) structure is realized. An initial π-shift is introduced into the Sagnac loop to eliminate the effect of the polarization orientation of the incident light on the switch performance. Then an electrically controllable PMNT phase retarder is used to switch the optical signal between the reflection and transmission ports. Some theoretical analyses are given and the switch performances are also discussed, including the thermal characteristic and different switching frequency response.     

Deterministic quantum dense coding with cluster state in optical systems

We propose two optical schemes for implementing the deterministic single-particle and two-particle quantum dense coding using four-qubit cluster states. In the protocols, the photon is neuter particle, so it has longer decoherence time with the environment than other particles. It is easy to implement single-bit gate using the linear optical elements under certain conditions, so the transformations performed on the photons by Alice can be easily achieved. Here the cluster states can be exactly discriminated using the parity detector, PBS and FS-PBS. In addition, the success probabilities of the dense coding are both equal to 1.     

Reflection chromaticity of cholesteric liquid crystals with sandwiched periodical isotropic defect layers

We study one-dimensional photonic crystals made of cholesteric liquid crystals with sandwiched isotropic defect layers. Based on the Berreman Fast 4 × 4 matrix method, the dispersion relation of one-dimensional photonic crystals is calculated and the corresponding reflection chromaticity is obtained. It is found that the color shift could be controlled by adjusting the thickness and refractive index of the isotropic defect layers. Compared with conventional structures, the reflection chromaticity of this structure is insensitive to the incident angle, if the thickness ratio of the cholesteric liquid crystals to that of the isotropic defect layers and the refractive index of periodical isotropic defect layers are properly set. Furthermore, the common forbidden bands for both left and right circular polarizations can be obtained, and we also take the wavelength-dependent refractive indices into consideration and obtain the reflected light chromaticity with the incident angle increasing. The proposed device can be used as a reflective color filter in the display industry.     

Confinement-deconfinement interplay in quantum phases of doped Mott insulators

In the t-J model, the electron fractionalization is dictated by the phase string effect. We find that in the underdoped regime, the antiferromagnetic and superconducting phases are dual: in the former, holons are confined while spinons are deconfined, and vice?versa in the latter. These two phases are separated by a novel phase, the so-called Bose-insulating phase, where both holons and spinons are deconfined. A pair of Wilson loops was found to constitute a complete set of order parameters determining this zero-temperature phase diagram. The quantum phase transitions between these phases are suggested to be of non-Landau-Ginzburg-Wilson type.     

Linearized tensor renormalization group algorithm for the calculation of thermodynamic properties of quantum lattice models

A linearized tensor renormalization group algorithm is developed to calculate the thermodynamic properties of low-dimensional quantum lattice models. This new approach employs the infinite time-evolving block decimation technique, and allows for treating directly the transfer-matrix tensor network that makes it more scalable. To illustrate the performance, the thermodynamic quantities of the quantum XY spin chain as well as the Heisenberg antiferromagnet on a honeycomb lattice are calculated by the linearized tensor renormalization group method, showing the pronounced precision and high efficiency.     

808 nm大功率半导体激光器阵列的优化设计

 采用激射波长为808 nm的GaAs/AlGaAs梯度折射率波导分别限制单量子阱结构外延片,制备了沟道深度不同的半导体激光器阵列,并对载流子分布进行理论分析和模拟。理论和实验结果表明：引入脊形台面和隔离沟道后,激光器阵列的输出功率、电光转换效率、斜率效率和光谱特性均有显著提高。随着沟道的加深,对电流侧向扩散的限制作用增强,从而提高了阵列性能。