Simultaneously Suppressing Low-Frequency and Relaxation Oscillation Intensity Noise in a DBR Single-Frequency Phosphate Fiber Laser

Effective multiple optoelectronic feedback circuits for simultaneously suppressing low-frequency and relaxation oscillation intensity noise in a single-frequency phosphate fiber laser are demonstrated. The forward transfer function, which relates the laser output intensity to the pump modulations, is measured and analyzed. A custom two-path feedback system operating at different frequency bands is designed to adjust the pump current directly. The relative intensity noise is decreased by 20dB from 0.2 to 5kHz and over lOdB from 5 to lOkHz. The relaxation oscillation peak is suppressed by 22dB. In addition, a long term （24h） laser instability of less than 0.05% is achieved.

Numerical simulation of four-wave mixing efficiency and its induced relative intensity noise

Four-wave mixing, as well as its induced intensity noise, is harmful to wavelength division multiplexing systems. The efficiency and the relative intensity noise of four-wave mixing are numerically simulated for the two-wave and the three-wave fiber transmissions. It is found that the efficiency decreases with the increase of both the frequency spacing and the fiber length, which can be explained using the quasi-phase-matching condition. Furthermore, the relative intensity noise decreases with the increase of frequency spacing, while it increases with the increase of fiber length, which is due to the considerable power loss of the pump light. This investigation presents a good reference for the practical application of wavelength division multiplexing systems.

Investigation on the intensity noise characteristics of the semiconductor ring laser

Based on the frequency-domain multimode theoretical model, detailed investigations on the noise characteristic of the semiconductor ring laser （SRL） are first performed in this paper. The comprehensive nonlinear terms related to the third order nonlinear susceptibility Z3 are included in this model; the Langevin noise sources for electric field and carrier density fluctuations are also taken into account. As the injection current increases, the SRL may present several operation regimes. Remarkable and unusual low frequency noise enhancement in the form of a broad low frequency tail extending all the way to the relaxation oscillation peak is observed in any of the operation regimes of SRLs. The influences of the backscattering coefficient on the relative intensity noise （RIN） spectrum in typical operation regimes are investigated in detail.

Stimulated Brillouin scattering-induced phase noise in an interferometric fiber sensing system

Stimulated Brillouin scattering-induced phase noise is harmful to interferometric fiber sensing systems. The localized fluctuating model is used to study the intensity noise caused by the stimulated Brillouin scattering in a single-mode fiber. The phase noise structure is analyzed for an interferometric fiber sensing system, and an unbalanced Michelson interferometer with an optical path difference of 1 m, as well as the phase-generated carrier technique, is used to measure the phase noise. It is found that the phase noise is small when the input power is below the stimulated Brillouin scattering threshold, increases dramatically at first and then gradually becomes flat when the input power is above the threshold, which is similar to the variation in relative intensity noise. It can be inferred that the increase in phase noise is mainly due to the broadening of the laser linewidth caused by stimulated Brillouin scattering, which is verified through linewidth measurements in the absence and presence of the stimulated Brillouin scattering.

Intensity Noise Suppression of an FP Laser by External Injection Locking

The optimal intensity noise suppression of a Fabry-Perot （FP） laser is experimentally acquired by relatively strong external optical injection locking technology. The maximum suppression is up to 9dB around the relaxation oscillation peak of the free running FP laser. We demonstrate how the injection light power and detuning frequency influence the intensity noise suppression effects. Additionally, the relationship between the optimal suppression range and the stable locking range is experimentally studied：both ranges enlarge as the injection light power increases, but the stable locking range permits larger detuning frequency at identical injection light power.

Relative intensity noise in high-speed hybrid square-rectangular lasers

Relative intensity noise(RIN) and high-speed modulation characteristics are investigated for an Al Ga In As/In P hybrid square-rectangular laser(HSRL) with square side length, rectangular length, and width of 15,300, and 2 μm, respectively. Single-mode operation with side-mode suppression larger than 40 dB has been realized for the HSRL over wide variation of the injection currents. In addition, the HSRL exhibits a 3 dB modulation bandwidth of 15.5 GHz, and an RIN nearly approaches standard quantum shot-noise limit 2 hv∕P=-164 dB∕Hz at high bias currents due to the strong mode selection of the square microcavity. With the increase of the DC bias current of the Fabry–Perot section, significantly enhanced modulation bandwidth and decreased RIN are observed.Furthermore, intrinsic parameters such as resonance frequency, damping factor, and modified Schawlow–Townes linewidth are extracted from the noise spectra.

Stochastic resonance in an over-damped linear oscillator

For an over-damped linear system subjected to both parametric excitation of colored noise and external excitation of periodically modulated noise, and in the case that the cross-correlation intensity between noises is a time-periodic function, we study the stochastic resonance （SR） in this paper. Using the Shapiro-Loginov formula, we acquire the exact expressions of the first-order and the second-order moments. By the stochastic averaging method, we obtain the analytical expression of the output signal-to-noise ratio （SNR）. Meanwhile, we discuss the evolutions of the SNR with the signal frequency, noise intensity, correlation rate of noise, time period, and modulation frequency. We find a new bona fide SR. The evolution of the SNR with the signal frequency presents periodic oscillation, which is not observed in a conventional linear system. We obtain the conventional SR of the SNR with the noise intensity and the correlation rate of noise. We also obtain the SR in a wide sense, in which the evolution of the SNR with time period modulation frequency presents periodic oscillation. We find that the time-periodic modulation of the cross-correlation intensity between noises diversifies the stochastic resonance phenomena and makes this system possess richer dynamic behaviors.

Scanning paths for estimating sound power of noise sources by sound intensity scanning method

A mathematical model of deterndulng sound power by using the scanning method is developed. It is assumed that the scanning speed is constant and the noise source is stationary The accuracy of estimating sound power along some simple paths on the surfaces such as rectangle, disc and hemisphere is analyzed. It is argued that the accuracy of estimating sound power is strongly depended on a suitable selection of scan path. The accurate estdriation of sound power can be made by scanning along some simple paths.

Two-Mode Biomedical Sensor Build-up:Characterization of Optical Amplifier

Intracavity absorption spectroscopy is a strikingly sensitive technique that has been integrated with a two-wavelength setup to develop a sensor for human breath.Various factors are considered in such a scenario,out of which Relative Intensity Noise(RIN)has been exploited as an important parameter to characterize and calibrate the said setup.During the performance of an electrical based assessment arrangement which has been developed in the laboratory as an alternative to the expensive Agilent setup,the optical amplifier plays a pivotal role in its development and operation,along with other components and their significance.Therefore,the investigation and technical analysis of the amplifier in the system has been explored in detail.The algorithm developed for the automatic measurements of the system has been effectively deployed in terms of the laser’s performance.With this in perspective,a frequency dependent calibration has been pursued in depth with this scheme which enhances the sensor’s efficiency in terms of its sensitivity.In this way,our investigation helps us in a better understanding and implementation perspective of the proposed system,as the outcomes of our analysis adds to the precision and accuracy of the entire system.

The stationary distribution and stochastic persistence for a class of disease models:Case study of malarial

This paper presents a nonlinear family of stochastic SEIRS models for diseases such as malaria in a highly random environment with noises from the disease transmission and natural death rates,and also from the random delays of the incubation and immunity periods.Improved analytical methods and local martingale characterizations are applied to find conditions for the disease to persist near an endemic steady state,and also for the disease to remain permanently in the system over time.Moreover,the ergodic stationary distribution for the stochastic process describing the disease dynamics is defined,and the statistical characteristics of the distribution are given mumerically.The results of this study show that the disease will persist and become permanent in the system,regardless of(1)whether the noises are from the discase transmission rate and/or from the natural death rates or(2)whether the delays in the system are constant or random for individuals in the system.Furthermore,it is shown that"weak"noise is associated with the existence of an endemic stationary distribution for the disease,while"strong"noise is associated with extinction of the population over time.Numerical simulation examples for Plasnodiurr vitar malaria are given.

STABILITY OF SOME KIND OF STOCHASTIC DIFFERENTIAL EQUATION

In this paper,a kind of stochastic differential equation is investigated and the almost sure exponential stability of the equation is obtained using Gronwall’s inequality.Further,we also give other noise intensity function to keep the stability of the system.

A Four-Element Sensor Array Consisting of Asymmetric Distributed-Feedback Fiber Lasers

A sensor array system formed by arranging four asymmetric distributed-feedback fiber lasers （DFB-FL） in ascending order according to their slope efficiencies was proposed. The output flatness could be effectively improved with the application of asymmetric DFB-FLs. The last element had almost the same output with the others although it obtained the smallest pump power. The relative intensity noise （RIN） and relaxation oscillation frequency of the sensor array were also analyzed. It is found that the relaxation oscillation frequency of a certain DFB-FL was relevant to its relative position in the array. And the RIN of a certain DFB-FL was always affected by the other elements in the array, which was not dependent on the order of their arrangement.

Cascaded Random Raman Fiber Laser With Low RIN and Wide Wavelength Tunability

Cascaded random Raman fiber lasers(CRRFLs)have been used as a new platform for designing high power and wavelength-agile laser sources.Recently,CRRFL pumped by ytterbium-doped random fiber laser(YRFL)has shown both high power output and low relative intensity noise(RIN).Here,by using a wavelength-and bandwidth-tunable point reflector in YRFL,we experimentally investigate the impacts of YRFL on the spectral and RIN properties of the CRRFL.We verify that the bandwidth of the point reflector in YRFL determines the bandwidth and temporal stability of YRFL.It is found that with an increase in the bandwidth of the point reflector in YRFL from 0.2 nm to 1.4 nm,CRRFL with higher spectral purity and lower RIN can be achieved due to better temporal stability of YRFL pump.By broadening the point reflector’s bandwidth to 1.4 nm,the lasing power,spectral purity,and RIN of the 4th-order random lasing at 1349 nm can reach 3.03 W,96.34%,and–115.19 dB/Hz,respectively.For comparison,the spectral purity and RIN of the 4th-order random lasing with the point reflector’s bandwidth of 0.2 nm are only 91.20%and–107.99 dB/Hz,respectively.Also,we realize a wavelength widely tunable CRRFL pumped by a wavelength-tunable YRFL.This work provides a new platform for the development of ideal distributed Raman amplification pump sources based on CRRFLs with both good temporal stability and wide wavelength tunability,which is of great importance in applications of optical fiber communication and distributed sensing.