Numerical simulation and temporal characterization of dual-pumped microringresonator-based optical frequency combs

Dual-pumped microring-resonator-based optical frequency combs(OFCs) and their temporal characteristics are numerically investigated and experimentally explored. The calculation results obtained by solving the driven and damped nonlinear Schr?dinger equation indicate that an ultralow coupled pump power is required to excite the primary comb modes through a non-degenerate four-wave-mixing(FWM) process and, when the pump power is boosted, both the comb mode intensities and spectral bandwidths increase. At low pump powers, the field intensity profile exhibits a cosine variation manner with frequency equal to the separation of the two pumps, while a roll Turing pattern is formed resulting from the increased comb mode intensities and spectral bandwidths at high pump powers. Meanwhile, we found that the power difference between the two pump fields can be transferred to the newly generated comb modes, which are located on both sides of the pump modes, through a cascaded FWM process. Experimentally, the dual-pumped OFCs were realized by coupling two self-oscillating pump fields into a microring resonator. The numerically calculated comb spectrum is verified by generating an OFC with 2.0 THz mode spacing over 160 nm bandwidth. In addition, the formation of a roll Turing pattern at high pump powers is inferred from the measured autocorrelation trace of a 10 free spectral range(FSR) OFC. The experimental observations accord well with the numerical predictions. Due to their large and tunable mode spacing, robustness,and flexibility, the proposed dual-pumped OFCs could find potential applications in a wide range of fields,including arbitrary optical waveform generation, high-capacity optical communications, and signal-processing systems.

MATHEMATIC DESCRIPTION ABOUT RANDOM VARIABLE WITH FUZZY DENSITY FUNCTION (RVFDF)

The random variable with fuzzy probability caused by fuzziness of probability density function was studied. The basic concepts/definitions and calculating methods of the interval/fuzzy probability density function, the random variable with fuzzy density function (RVFDF) and its distribution function, mathematical expectation and variance are given and same theorems related to the RVFDF are proved.

Distribution and morphometric characters of the Mediterranean longnosed skate,Dipturus oxyrinchus(Chondrichthyans:Rajidae)in the Gulf of Gabes(Tunisia,Central Mediterranean)

Objective:To investigate biometrics of Dipturus oxyrinchus(D.oxyrinchus),including length-weight relationships,total length(TL),disc width(DW),distance measured of snout tip to eye,width of the mouth,distance from snout tip to first dorsal,and the numeric characters in the Gulf of Gabes.Methods:Monthly sampling was conducted commercial bottom-trawl during December 2006 and January 2007,operating at a depth of 80-185 m.The TL,DW,distance of snout tip to eye,width of the mouth,distance from snout tip to first dorsal were measured to the nearest 0.1 cm and the weight was measured to the nearest 0.1 g.The parameters a and b were estimated by the least squares regression method.Results:A total of 520 D.oxyrinchus was ranged from 16.5 to 105.0 cm in TL and 30-5300 g in total mass were analyzed during this study.The overall sex ratio was significantly different from the expected value of 1:16(df=1,χ^(2)=3.38,P<0.05),and there was significant difference in the TL(t-test=16.53,df=520,P<0.05).There was significant difference in the regression slopes between sexes for the TL and DW relationship(t-test=17.53,df=520,P<0.05).The b value for the TL/weight relationship for males D.oxyrinchus sampled in this study(3.01)was lower than that for female(3.23).Morphometric characters were strongly positively correlated for TL.Conclusions:This study reported the first description of biometric relationships for D.oxyrinchus,which would be useful for the sustainable conservation of this rear fishery in the Gulf of Gabes and also form the basis for their inclusion in a regional security programme.