How do we understand mathematical practices in non-mathematical fields? Reflections inspired by cases from 12th and 13th century China

Recent studies of the history of mathematics have shed light on the diversity of mathematical practices in the ancient world. In this article, I address this issue from two perspectives. First, I analyze different mathematical instruments used in different domains in 12^th and 13^th century China. Second, by analyzing how the text is related to the problems written down in the same period, I argue that there existed two categories of mathematical problems. As a result, I suggest that problems, textual procedures, and material operations should be considered together when regarding various mathematical practices in mathematical and non-mathematical fields.     

A Mid-IR 14.1W ZnGeP2 Optical Parametric Oscillator Pumped by a Tm,Ho:GdVO4 Laser

We report a high power and high efficiency double resonant ZnGeP2 （ZGP） optical parametric oscillator （OPO） pumped by a Tm,Ho：GdVO4 laser. We employ a Tm,Ho：GdVO4 laser as the pump source operated at 2.049 μm with M^2 = 1.1. The ZGP OPO can generate a total combined output power of 14.1 W at 3.80μm signal and 4.45 μm idler under pumping power of 28. 7 W. The slope efficiency reaches 61.8%, and M^2 = 3.6 for OPO output is obtained.     

Comparison of Nd:YAG Ceramic Laser Pumped at 885nm and 808nm

Laser performance of 1064 nm domestic Nd：YAG ceramic lasers for 885 nm direct pumping and 808 nm traditional pumping are compared. Higher slope efficiency of 34% and maximum output power of 16.5 W are obtained for the 885nm pump with a 6ram length 1 at.% Nd：YAG ceramic. The advantages for 885nm direct pumping are discussed in detail. This pumping scheme for highly doping a Nd：YAG ceramic laser is considered as an available way to generate high power and good beam quality simultaneously.     

End-Pumped Tm:YAG Ceramic Slab Lasers

Lasers from a Tm：YAG slab is end-pumped by continuous-wave output of the Tm：YAG ceramic ceramic am~e reported for the t~rst time to our best knowledge. The Tm：YAG ceramic a laser diode with central wavelength 792nm. At room temperature, the maximum power is 4.5 W, and the sloping efficiency is obtained to be 20.5%. The laser spectrum is centered at 2015nm.     

Simulation of thin disk laser pumping process for temperature dependent Yb:YAG property

A novel model of Cw diode pumped Yb:YAG thin disk laser has been presented to simulate absorption pump power distribution by Monte-Carlo ray tracing. Comparing obtained results with the common distribution function indicate the offered model is quite trustful. So these findings help to evaluate temperature distribution due to the 3D finite element analyses (FEA) based on heat conduction equation. To improve our simulation the temperature dependent of crystal property such as the absorption coefficient, thermal conductivity, stimulated emission cross section and Boltzman population factors are considered by a numerical iterative approach.     

Q-switched Nd lasers pumped directly into the F3/2 emitting level

The influence of the direct pumping into the ⁴F_3/2 emitting level on the output characteristics of continuous-wave (CW) pumped, passively or actively (acoustooptic, AO) Q-switched Nd lasers is discussed. In case of passive Q-switching by Cr⁴⁺:YAG saturable absorber (SA) crystal, the change of pumping wavelength from 0.81 μm into the highly-absorbing ⁴F_5/2 level to 0.88 μm into the ⁴F_3/2 level of Nd does not modify the energy of the Q-switch pulse, but increases the pulse repetition rate and the laser average power for the same absorbed pump power. This is demonstrated with 0.81 and 0.88 μm CW laser diode-pumped Nd:YAG and Nd-vanadate lasers with average output power in the watt-level range at 1.06 μm. The effect is explained by the control of passive Q-switching by the intracavity photon flux that is influenced by the pump wavelength and by the initial transmission of the SA crystal. On the other hand, it is discussed and experimentally proved that due to the possibility to control externally the frequency of switching, in case of the AO Q-switched Nd laser the change of the pump wavelength from 0.81 to 0.88 μm increases the pulse energy for a fixed frequency, leading to a corresponding increase of the average laser power.     

Phonon relaxation and heat conduction in one-dimensional Fermi-Pasta-Ulam β lattices by molecular dynamics simulations

The phonon relaxation and heat conduction in one-dimensional Fermi-Pasta-Ulam (FPU) β lattices are studied by using molecular dynamics simulations.The phonon relaxation rate,which dominates the length dependence of the FPU β lattice,is first calculated from the energy autocorrelation function for different modes at various temperatures through equilibrium molecular dynamics simulations.We find that the relaxation rate as a function of wave number k is proportional to k 1.688,which leads to a N 0.41 divergence of the thermal conductivity in the framework of Green-Kubo relation.This is also in good agreement with the data obtained by non-equilibrium molecular dynamics simulations which estimate the length dependence exponent of the thermal conductivity as 0.415.Our results confirm the N 2/5 divergence in one-dimensional FPU β lattices.The effects of the heat flux on the thermal conductivity are also studied by imposing different temperature differences on the two ends of the lattices.We find that the thermal conductivity is insensitive to the heat flux under our simulation conditions.It implies that the linear response theory is applicable towards the heat conduction in one-dimensional FPU β lattices.     

Comparison of Laser Performances of 5at.% Yb:Gd2xY2(1-x)SiO5 Crystals between Different Cutting Directions

We investigate the laser actions of 5at.% Yb:Gd_2xY_2(1-x)SiO₅ (Yb:GYSO; x=0.1) crystals with different cutting directions, parallel and vertical to the growth axis. Our results show that the cutting direction of the sample plays an astonished role in the laser operation. The sample cut vertically to the growth axis possesses the favourable lasing characteristics. Its output power reaches 3.13W at 1060nm with a slope efficiency of 44.68% when the absorbed pump power is 8.9,W. In contrast, the sample cut parallel reaches only 1.65W at 1044nm with a slope efficiency of 33.76% with absorbed pump power of 7.99W. The absorption and emission spectra of the two samples are examined and the merit factor M is calculated. Our analysis is in agreement well with the experimental results. The wavelength tuning range of the superior sample covers from 1013.68nm to 1084.82nm.     

High Power Continuous-Wave and Acousto-Optic Q-Switched Nd：GdVO4 Laser Operated at 912 nm

We present a high power and efficient operation of the ^4F3/2 → ^4I9/2 transition in Nd：GdVO4 at 912nm. In the cw mode, the maximum output power of 8.6 W is achieved when the incident pump power is 40.3 W, leading to a slope efficiency of 33.3% and an optical-optical efficiency of 21.3%. To the best of our knowledge, this is the highest cw laser power at 912nm obtained with the conventional Nd：GdVO4 crystal. Pulsed operation of 912nm laser has also been realized by inserting a small aeousto-optie （A-O） Q-Switch inside the resonator. As a result, the minimal pulse width of 20ns and the average laser power 1.43 W at the repetition rate of lOkHz are obtained, corresponding to 7.1 kW peak power. We believe that this is the highest laser peak power at 912nm. Furthermore, duration of 65ns has also been acquired when the repetition rate is 100 kHz.     

Passively Q-Switched Quasi-Continuous-Wave Diode-Pumped Intracavity Optical Parametric Oscillator at 1.57

We report on a passively Q-switched quasi-cw diode-pumped Nd:YAG including an intracavity optical parametric oscillator. The dynamics of this system is described by solving the coupled equations. The effect of the initial transmission of Cr⁴⁺:YAG saturable absorber on the signal wave operation is studied. Under optimum conditions, we achieve 2.3mJ energy at 1.57μm wavelength for 40Hz repetition rate. The peak power of the pulses amounts to 0.88MW with the pulse width of 2.6ns. When the Fresnel reflection losses of the filters are taken into account, the pulse energy would be higher than 2.3mJ. To the best of our knowledge, this is the highest pulse energy and peak power for such a type of single resonant quasi-cw diode pumped Nd:YAG/Cr⁴⁺:YAG IOPO laser.