Statistical Properties of the Output Light Intensity in a Single-Mode Laser Driven by Correlated Noises

By using linear approximation we derive expressions for the correlation function,power spectrum and correlation time of the output light intensity in a single-mode laser driven by additive white noise and multiplicative colored noise with an exponential correlation form.The effects of correlation strength and correlation time of the noises on the above quantities are discussed and compared with the case of a delta function correlation form for the noises.

Correlation Function and Time-Dependent Moments of the Intensity for Gain-Noise Model of a Single-Mode Laser with Exponential Function Correlation Noise

The gain-noise model of a single-mode laser driven by correlated additive and multiplicative white noises is investigated theoretically.The analytical expressions of the time-dependent moments and correlation function of the laser intensity are derived by means of linear approximation method.Some novel phenomena are found.In certain cases,instead of monotonic evolution,the evolution curves of the intensity correlation function versus time exhibit the negative minimum value,whereas a peak for the evolution of the normalized variance of the laser intensity with time emerges.

Influence of Noise on Time Evolution of Intensity Correlation Function

Using the linear approximation method, we have studied how the correlation function C（t） of the laser intensity changes with time in the loss-noise model of the single-mode laser driven by the colored pump noise with signal modulation and the quantum noise with cross-correlation between the real and imaginary parts. We have found that when the pump noise self-correlation time T changes, （i） in the case of r 〈〈 1, the C（t） vs. t curve experiences a changing process from the monotonous descending to monotonous rise, and finally to the appearance of a maximum; （ii） in the case of r 〉〉 1, the curve only exhibits periodically surging with descending envelope. When r 〈〈 i and T does not change, with the increase of the pump noise intensity P, the curve experiences a repeated changing process, that is, from the monotonous descending to the appearance of a maximum, then to monotonous rise, and finally to the appearance of a maximum again. With the increase of the quantum noise intensity O,, the curve experiences a changing process from the monotonous rise to the appearance of a maximum, and finally to the monotonous descending. The increase of the quantum noise with cross-correlation between the real and imaginary parts will lead to the fall of the whole curve, but not affect the form of the time evolution of C（t）.

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.

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.

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.

Relative Intensity Noise in the Single Quantum Well Diode

Based on the mathematical model of quantum well laser diode(QW LDs) developed, the paper presents a relative intensity noise(RIN) model, which employs Gaussian form random noise with its average being to zero. It can be straightforwardly used to describe the effect of the noise on the performance of QW LDs. The RIN becomes notable in the frequency range of interests and therefore affects the device modulation property. The results are in good agreement of the published data. The RIN model proposed and the results can be used for purpose of device technique improvement and performance simulation of optical communication systems and networks.

Investigation on Major Noise Sources of Vehicle Diesel Engine Based on Sound Intensity Measurement

In order to reduce the noise and vibration of the diesel engine,it is crucial to exactly identify the engine noise source character.Based on "two-microphone" method,the sound intensity measurement of a vehicle four-stroke diesel engine was carried out in a hemi-anechoic chamber.Then the sound intensity contour maps were obtained from the measurement results and the main noise components of different frequencies on all the measurement surfaces were picked out to construct contour maps.By analysizing the relationship between the characteristics of contour maps and the space distribution of the engine compartment,the major sources of the exterior radiation noise of the diesel engine were identified.The results provided a creditable basis for improving the noise performance of the engine in the next phase.

MUL TIPLICATIVE NOISE IN TRANSIENT LASER INTENSITY

Effects of multiplicative noise in transient laser intensity are investigated theoretically. Analytic solutions are calculated through a reduced Fokker-Planch equation and the results with different pump parameters are discussed.

Enhancement of the Neuronal Dynamic Range by Proper Intensities of Channel Noise

The capability of a biological neuron to discriminate the intensity of external stimulus is measured in its dynamic range.In previous studies,a few factors have been reported to be able to enhance the dynamic range,e.g.,electrical coupling and active dendrites.Here we numerically show that intrinsic channel noise within neurons has a subtle effect in neuronal dynamic range modulation.Our simulation results indicate that for relatively weak noise intensity,the dynamic range of the neuron is enhanced significantly.However,as the noise intensity becomes stronger,the dynamic range of the neuron is weakened.Further investigation suggests that sodium channel noise and potassium channel noise play opposite roles in modulating the dynamic range.Consequently,the model results suggest a new function of channel noise,that is,a proper value of noise intensity could optimize the dynamic range of neurons.

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.

Structural Intensity Characterization of Composite Laminates Subjected to Impact Load

Structural intensity (SI) characterization of composite laminates subjected to impact load was dis-cussed. The SI pattern of the laminates which have different fiber orientations and boundary conditions was analyzed. The resultant forces and velocities of the laminates were calculated, and the structural intensity was evaluated. The SI streamlines of carbon fiber reinforced epoxy composite laminates and the steel plates were discussed. The results show that the SI streamlines of the graphite/epoxy laminates are different from that of the steel plates, and the SI streamlines are influenced by the boundaries, the stacking sequence of the composite laminates. The change of the historical central displacement of the graphite/epoxy laminates is fasten than that of the steel plates.

Effects of white noise on procedural pain-related cortical response and pain score in neonates:A randomized controlled trial

Objectives To evaluate the effects of white noise on pain-related cortical response,pain score,and behavioral and physiological parameters in neonates with procedural pain.Methods A double-blind,randomized controlled trial was conducted.Sixty-six neonates from the Neonatal Intensive Care Unit in a university-affiliated general hospital were randomly assigned to listen to white noise at 50 dB(experimental group)or 0 dB(control group)2 min before radial artery blood sampling and continued until 5 min after needle withdrawal.Pain-related cortical response was measured by regional cerebral oxygen saturation(rScO_(2))monitored with near-infrared spectroscopy,and facial expressions and physiological parameters were recorded by two video cameras.Two assessors scored the Premature Infant Pain Profile-Revised(PIPP-R)independently when viewing the videos.Primary outcomes were pain score and rScO_(2)during arterial puncture and 5 min after needle withdrawal.Secondary outcomes were pulse oximetric oxygen saturation(SpO_(2))and heart rate(HR)during arterial puncture,and duration of painful expressions.The study was registered at the Chinese Clinical Trial Registry(ChiCTR2200055571).Results Sixty neonates(experimental group,n=29;control group,n=31)were included in the final analysis.The maximum PIPP-R score in the experimental and control groups was 12.00(9.50,13.00),12.50(10.50,13.75),respectively(median difference−0.5,95%CI−2.0 to 0.5),and minimum rScO_(2)was(61.22±3.07)%,(61.32±2.79)%,respectively(mean difference−0.325,95%CI−1.382 to 0.732),without significant differences.During arterial puncture,the mean rScO_(2),HR,and SpO_(2)did not differ between groups.After needle withdrawal,the trends for rScO_(2),PIPP-R score,and facial expression returning to baseline were different between the two groups without statistical significance.Conclusion The white noise intervention did not show beneficial effects on pain-related cortical response as well as pain score,behavioral and physiological parameters in neonates with procedural pain.

Stochastic Resonance in an Over-Damped Bias Linear System with Dichotomous Noise

The stochastic resonance in an over-damped bias linear system subject to multiplicative and additive dichotomous noise （DN） is investigated. By using the linear-response theory and the properties of the DN, the exact expressions are found for the signal-to-noise ratio （SNR）. It is shown that the SNR is a non-monotonic function of the correlation time of the additive DN, and it varies non-monotonically with the bias of the external field, the intensity and asymmetry of the multiplicative DN, as well as the external field frequency. Moreover, the SNR depends on the bias of the system, as well as the strength and asymmetry of the additive DN.

Measurement of Noise Pollution in Northern Industrial Areas of Windhoek, Namibia

The increase in industrial activities and vehicular movement along the northern industrial area of Windhoek has vastly increased the amount of traffic noise and other noise pollution in the area. Noise pollution has an adverse health effect to human population, when exposed for a long period. Residence in proximate communities along the north industrial area and those working in the various industries located in the area may be affected, when the noise pollution level exceed the permissible standard for human exposure. A sound level meter was used to measure the amount of noise pollution at the streets of the northern industrial area. The measurements were done during the daytime, at a time interval of 2 hours, from 08:00 am - 06:00 pm. The amount of noise pollution obtained from the study ranges from (64 - 72) dB (A), with a maximum of 72 dB (A) in Bonsmara Street, (67.4 - 75.3) dB (A), with a maximum of 75.3 dB (A) in New Castle Street, (60.5 - 81.0) dB (A), with a maximum of 72.3 dB (A) in Braham Street. (62.5 - 72.3) dB (A), with a maximum of 82.3 dB (A) in Hosea Kutako Street, (66.0 - 82.3) dB (A), with a maximum of 76.8 dB (A) in Simmentaler Street and (65.1 - 76.8) dB (A), with a maximum of 76.8 dB (A) in Dortmund Street. The variation of noise level index L10, L50, L90 and Leq, Noise Climate (NC) and Traffic Noise index (TNI) were calculated. The maximum noise pollution values obtained from the study were higher than the WHO recommended limit of 70 dB (A).

A Double Shot Noise Process and Its Application in Insurance

The authors consider a compound Cox model of insurance risk with the additional economic assumption of a positive interest rate. As the authors note a duality result relating a compound Cox model of insurance risk with a positive interest rate and a double shot noise process, the authors analyze a double shot noise process systematically for its theoretical distributional properties, based on the piecewise deterministic Markov process theory, and the martingale methodology. The authors also obtain the moments of aggregate accumulated/discounted claims where the claim arrival process follows a Cox process with shot noise intensity. Removing the parameters in a double shot noise process gradually, the authors show that it becomes a compound Cox process with shot noise intensity, a single shot noise process and a compound Poisson process. Numerical comparisons are shown between the moments （i.e. means and variances） of a compound Poisson model and their counterparts of a compound Cox model with/without considering a positive interest rate. For that purpose, the authors assume that claim sizes and primary event sizes follow an exponential distribution, respectively.

The statistical fluctuation of a single-mode laser system driven by coloured pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts

Using the linear approximation method, this paper studies the statistical property of a single-mode laser driven by both coloured pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts, and calculates the steady-state mean normalized intensity fluctuation and intensity correlation time. It analyses the influences of the modulation signal, the net gain coefficient, the noise and its correlation form on the statistical fluctuation of the laser system respectively. It is found that the coloured pump noise modulated by the signal has a great suppressing action on the statistical fluctuation of the laser system; the pump noise self-correlation time and the specific frequency of modulation signal have the result that the statistical fluctuation tends to zero. Furthermore, the ＇colour＇ correlation of pump noise has much influences on the statistical fluctuation of the laser system. Increasing the intensity of pump noise will augment the statistical fluctuation of the laser system, but the intensity of quantum noise and the coefficient of cross-correlation between its real and imaginary parts have less influence on the statistical fluctuation of the laser system. Therefore, from the conclusions of this paper the statistical property can be known and a theoretical basis for steady operation and output of the laser system can be provided.

Effects of Correlated Noises on Statistic Property of Single-Mode Laser

The loss-noise model with saturation effects driven by correlated additive and multiplicative white noise is studied.An analytical expression of the stationary probability distribution is obtained.The mean,variance and skewness of the steady-state laser intensity are calculated numerically.We have also found the correlated noises affect the statistic properties of laser heavily.Moreover,the laser intensity is locked at a fixed value when correlated parameterλis equal to-1.

Effects of a Novel Drift Term Due to Cross Correlation Between Additive and Multiplicative Noises in a Single-Mode Laser

It is found that a novel drift term,purely induced by cross correlation between multiplicative and additive noises,in the one-dimensional Langevin equation for a single-mode laser intensity has a significant effect on the intensity statistical properties near and below threshold,and when colored multiplicative noise is involved.This term makes the laser intensity fluctuations lower but effective eigenvalues larger for positive noise cross correlation.

Influence of Signal and Noise on Statistical Fluctuation of Single-Mode Laser System

On the basis of calculating the steady-state mean normalized intensity fluctuation of a signal-mode laser system driven by both colored pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts, we analyze the influence of modulation signal, noise, and its correlation form on the statistical fluctuation of the laser system. We have found that when the amplitude of modulation signal weakens and its frequency quickens, the statistical fluctuation will reduce rapidly. The by reducing the intensity of pump noise and quantum noise. statistical fluctuation of the laser system can be restrained Moreover, with prolonging of colored cross-correlation time, the statistical fluctuation of laser system experiences a repeated changing process, that is, from decreasing to augmenting, then to decreasing, and finally to augmenting again. With the decreasing of the value of cross-correlation coe~cient, the statistical fluctuation will decrease too. When the cross-correlation form between the real part and imaginary part of quantum noise is zero correlation, the statistical fluctuation of laser system has a minimum. Compared with the influence of intensity of pump noise, the influence of intensity of quantum noise on the statistical fluctuation is smaller.