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 a...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.展开更多
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, th...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.展开更多
基金Strategic Priority Research Program of the Chinese Academy of Sciences(CAS)(XDB 24030600)National Key Research and Development Program of China(2016YFF0200702)+1 种基金National Natural Science Foundation of China(NSFC)(61690222,61308037,61635013)CASSAFEA International Partnership Program for Creative Research Teams
文摘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.
文摘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.
