In this article,we study the limit behavior of solutions to an energy-critical complex Ginzburg–Landau equation.Via energy method,we establish a rigorous theory of the zero-dispersion limit from energy-critical compl...In this article,we study the limit behavior of solutions to an energy-critical complex Ginzburg–Landau equation.Via energy method,we establish a rigorous theory of the zero-dispersion limit from energy-critical complex Ginzburg–Landau equation to energy-critical nonlinear heat equation in dimensions three and four for both the defocusing and focusing cases.Furthermore,we derive the inviscid limit of energy-critical complex Ginzburg–Landau equation from energy-critical nonlinear Schrödinger equation in dimension four for the focusing case.展开更多
Due to triangular photonic crystal fiber （PCF） high nonlinearity and low dispersion slope, using the condition that the different linear phase shift combination must satisfy the phase match, the expressions of gain ...Due to triangular photonic crystal fiber （PCF） high nonlinearity and low dispersion slope, using the condition that the different linear phase shift combination must satisfy the phase match, the expressions of gain and bandwidth for one-pump fiber-optic parametric amplifiers （1P-FOPA） based on PCF in the normal and abnormal dispersion regimes are derived respectively. Then, 1P-FOPAs performance comparison among PCF, dispersion-shifted fiber （DSF） and highly nonlinear fibers （HNLF） are carried out by numerical simulations. It is shown that the 1P-FOPA based on triangular PCF can provide higher peak gain over wider bandwidth. When the pump wavelength is at the zero-dispersion wavelength （ZDWL）, about 108.7 nm single-pass gain bandwidth and 91.4 dB peak gain can be obtained; when in the normal dispersion regime and near zero-dispersion wavelength, not less than 46 nm single-pass gain bandwidth 77.1 nm away from pump can be achieved. Finally the influence of dispersion fluctuation is analyzed, and the result shows that the tolerance of the 1P-FOPA based on photonic crystal fiber is better.展开更多
基金supported by the NSF of Jiangsu Province(Grant Nos.BK20221497 and BK20230036)the NSF of China(Grant No.U2340221)and National Key R&D Program of China(Grant No.2022YFC3202602)+4 种基金supported by the Young Scientist Program of the Ministry of Science and Technology of China(Grant No.2021YFA1002200)the NSF of China(Grant No.123115300372)the Taishan Scholar Project and the NSF of Shandong Province(Grant No.ZR2022YQ01)supported by NSFC(Grant Nos.11901350 and 12371172)the Fundamental Research Funds of Shandong University。
文摘In this article,we study the limit behavior of solutions to an energy-critical complex Ginzburg–Landau equation.Via energy method,we establish a rigorous theory of the zero-dispersion limit from energy-critical complex Ginzburg–Landau equation to energy-critical nonlinear heat equation in dimensions three and four for both the defocusing and focusing cases.Furthermore,we derive the inviscid limit of energy-critical complex Ginzburg–Landau equation from energy-critical nonlinear Schrödinger equation in dimension four for the focusing case.
文摘Due to triangular photonic crystal fiber （PCF） high nonlinearity and low dispersion slope, using the condition that the different linear phase shift combination must satisfy the phase match, the expressions of gain and bandwidth for one-pump fiber-optic parametric amplifiers （1P-FOPA） based on PCF in the normal and abnormal dispersion regimes are derived respectively. Then, 1P-FOPAs performance comparison among PCF, dispersion-shifted fiber （DSF） and highly nonlinear fibers （HNLF） are carried out by numerical simulations. It is shown that the 1P-FOPA based on triangular PCF can provide higher peak gain over wider bandwidth. When the pump wavelength is at the zero-dispersion wavelength （ZDWL）, about 108.7 nm single-pass gain bandwidth and 91.4 dB peak gain can be obtained; when in the normal dispersion regime and near zero-dispersion wavelength, not less than 46 nm single-pass gain bandwidth 77.1 nm away from pump can be achieved. Finally the influence of dispersion fluctuation is analyzed, and the result shows that the tolerance of the 1P-FOPA based on photonic crystal fiber is better.
