A Note on Finitely Generated Modules over a <i>PID</i>

In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated module over a principal ideal domain.

Model Reduction by Generalized Falk Method for Efficient Dedicated to Professor Karl Stark Pister for his 95th birthday Field-Circuit Simulations

The Generalized Falk Method(GFM)for coordinate transformation,together with two model-reduction strategies based on this method,are presented for efficient coupled field-circuit simulations.Each model-reduction strategy is based on a decision to retain specific linearly-independent vectors,called trial vectors,to construct a vector basis for coordinate transformation.The reduced-order models are guaranteed to be stable and passive since the GFM is a congruence transformation of originally symmetric positive definite systems.We also show that,unlike the Pade-via-Lanczos(PVL)method,the GFM does not generate unstable positive poles while reducing the order´of circuit problems.Further,the proposed GFM is also faster when compared to methods of the type Lanczos(or Krylov)that are already widely used in circuit simulations for electrothermal and electromagnetic problems.The concept of response participation factors is introduced for the selection of the trial vectors in the proposed model-reduction methods.Further,we present methods to develop simple equivalent circuit networks for the field component of the overall field-circuit system.The implementation of these equivalent circuit networks in circuit simulators is discussed.With the proposed model-reduction strategies,significant improvement on the efficiency of the generalized Falk method is illustrated for coupled field-circuit problems.

On Countably Generated Dimension

In this article,we introduce and study the concept of countably generated dimension,which is a Krull-like dimension extension of the concept of DCC on countably generated submodules.We show that some of the basic results of Krull dimension are true for countably generated dimension.It is shown that an jR-module M has Krull dimension if and only if it has countably generated dimension,and its Krull dimension and countably generated dimension coincide.

Evaluation of the performance of linearly frequency modulated signals generated by heterodyning two free-running laser diodes

A method to evaluate the influence of the laser linewidth on the linearly frequency-modulated(LFM)signals generated by heterodyning two free-running laser diodes(LDs)is proposed.The Pearson correlation coefficient between the instantaneous frequency of the generated LFM signal and that of an ideal LFM signal is introduced to quantify the quality of the generated LFM signal.The closed-form solution of the correlation coefficient is given,which shows that the correlation coefficient is determined by the ratio of the LFM signal bandwidth to the square root of the total linewidth of the two LDs when the observation interval is fixed.Simulation results are also given,which proves the correctness of the theoretical results.

Equal-amplitude optical comb generation using multi-frequency phase modulation in optical fibers

We theoretically analyze and experimentally demonstrate a method of generating equal-amplitude optical comb exploiting multi-frequency phase modulation. The theoretical analysis shows that 4n-1 equalamplitude spectral lines can be obtained when the modulation signal comprises n frequency components including the fundamental frequency and the odd harmonic frequencies, and 2n＋1 equal-amplitude spectral lines can be obtained when the modulation signal comprises n frequency components including the fundamental frequency and the even harmonic frequencies. Then, we numerically simulate the spectra of 5, 7, 9, and 11 equal-amplitude spectral lines, respectively, which are also obtained in experiments with frequency separation of 30 MHz and flatness of better than 0.3 dB.

Frequency-doubled triangular shape lightwave generation with a flexible modulation index

An approach for full duty frequency-doubled triangle shape lightwave generation is proposed and demonstrated.It requires a dual-parallel Mach–Zehnder modulator（DP-MZM） driven by a sinusoidal signal. A stop band filter is coupled to filter out two undesired sidebands. By tuning the bias voltage applied to the DP-MZM, the output optical intensity with a full duty cycle triangle shape profile can be obtained. It is found that the required modulation index is no longer a fixed one. It can vary within a range, without degrading the target waveform. The principle is analyzed by theory and evaluated by simulation. A proof-of-concept experiment is also conducted.Good agreements between theoretical prediction and experimental results have been found. This approach might be attractive due to the feature of a variable modulation index, which insures simple operation in practice.

An optical modulation format generation scheme based on spectral filtering and frequency-to-time mapping

An optical modulation format generation scheme based on spectral filtering and frequency-to-time mapping is experimentally demonstrated. Many modulation formats with continuously adjustable duty radio and bit rate can be formed by changing the dispersion of dispersion element and the bandwidth of shaped spectrum in this scheme. In the experiment, non-return-to-zero(NRZ) signal with bit rate of 29.41 Gbit/s and 1/2 duty ratio return-to-zero(RZ) signal with bit rate of 13.51 Gbit/s are obtained. The maximum bit rate of modulation format signal is also analyzed.

Researches in microwave photonics based packages for millimeter wave system with wide bandwidth and large dynamic range

This paper presents an introduction to the researches in microwave photonics based packages and its application, a 973 project （No. 2012CB315600）, which focuses on addressing new requirements for millimeter wave （MMW） system to work with higher frequency, wider bandwidth, larger dynamic range and longer distance of signal distribution. Its key scientific problems, main research contents and objectives are briefed, and some latest achievements by the project team, including generation of linear frequency modulation wave （LFMW）, tunable optoelectronic oscillator （OEO） with lower phase noise, reconfigurable filter with higher Q value, time delay line with wider frequency range, down conversion with gain, and local oscillator （LO） transmission with stable phase, are introduced briefly.