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Journal of Yangtze University

The Dynamic Behavior of the Optical Bistability System Driven by Two Colored Noises

Qinghua Cheng

Published Jan 1, 2010• 0 citations
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Abstract

By adopting the linear approximation method,the signal-to-noise ratio of optical bistability system driven by colored pump noise and colored quantum noise was calculated. The influence on the signal-to-noise ratio of the pump noise intensity(P),quantum noise intensity(Q),pump noise self-correlation time (τ1) and quantum noise self-correlation time (τ2) was studied. The stochastic resonance was found in the curve of signal-to-noise ratio R versus the pump noise self-correlation time (τ1) was discussed,while the great influence on the stochastic resonance is posed by quantum noise self-correlation time,when (τ2) increases,the curve of signal-to-noise ratio R versus the pump noise self-correlation time (τ1) upgrates integratedly,and resonance-peak increases.It could prolong the quantum noise self-correlation time (τ2) to increase the signal-to-noise ratio R.There is a maximum in the curve of signal-to-noise ratio R versus the parameter of the optical bistability system c,while pump noise self-correlation time (τ1) greatly influences the curve of signal-to-noise ratio R versus the parameter of the optical bistability system c. With the increase of pump noise self-correlation time (τ1),the maximum declines and the curve becomes flat.It is indicated that the signal-to-noise ratio increases through reducing the pump noise self-correlation time (τ1).Besides,signal-to-noise ratio R monotonously increases with the increase of pump noise intensity P,and motonously decreases with the increase of quantum noise intensity Q.

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Communications in Theoretical Physics•Nov 1, 2005•0 citations
By adopting the linear approximation method,the signal-to-noise ratio of optical bistability system driven by colored pump noise and colored quantum noise was calculated. The influence on the signal-to-noise ratio of the pump noise intensity(P),quantum noise intensity(Q),pump noise self-correlation time (τ1) and quantum noise self-correlation time (τ2) was studied. The stochastic resonance was found in the curve of signal-to-noise ratio R versus the pump noise self-correlation time (τ1) was discussed,while the great influence on the stochastic resonance is posed by quantum noise self-correlation time,when (τ2) increases,the curve of signal-to-noise ratio R versus the pump noise self-correlation time (τ1) upgrates integratedly,and resonance-peak increases.It could prolong the quantum noise self-correlation time (τ2) to increase the signal-to-noise ratio R.There is a maximum in the curve of signal-to-noise ratio R versus the parameter of the optical bistability system c,while pump noise self-correlation time (τ1) greatly influences the curve of signal-to-noise ratio R versus the parameter of the optical bistability system c. With the increase of pump noise self-correlation time (τ1),the maximum declines and the curve becomes flat.It is indicated that the signal-to-noise ratio increases through reducing the pump noise self-correlation time (τ1).Besides,signal-to-noise ratio R monotonously increases with the increase of pump noise intensity P,and motonously decreases with the increase of quantum noise intensity Q.
In the optical bistable system driven by colored pump noise with the bias signal modulating,the signal-to-noise ratio(SNR) is caculated with the linear approximation method,and the influence on SNR imposed by the bias signal,noise,as well as the correlation of the noise is discussed.The stochastic resonance(SR) is observed both in the curves of the SNR versus the pump noise and the quantum noise.Besides,the great influence on the SNR imposed by the correlation coefficient is found between the pump noise and the quantum noise.
The stochastic resonance (SR) of an optical bistable system with cross-correlated additive white and multiplicative colored noises and periodic signal is studied using the unified colored noise approximation and the theory of signal-to-noise ratio (SNR).Results show that cross-correlation intensity λ enforces the SR of the system.The position of the peak on the SNR-τ curves moves to the right direction along with the increase of λ (τ is the self-correlation time of the multiplicative colored noise).We find the SR phenomenon in the SNR-D and SNR-Q curves (D and Q are the intensities of the additive and multiplicative noises, respectively), but not in the SNR-λ curves.
In this paper, the intensity correlation time T is studied for the gain-noise model of a single-mode laser driven by coloured pump noise and coloured quantum noise with coloured cross-correlation with a direct signal modulation. By using the linear approximation method, it is found that when the pump noise is modulated directly by a signal, the effects of the cross-correlation between the pump noise and the quantum noise will disappear. In addition, there exists a maximum (i.e. resonance) in the curve of the intensity correlation time T versus the pump noise self-correlation time τ1. Furthermore, when τ1≤τ2, the intensity correlation time T increases monotonically with the increase of D and decreases monotonically with the increase of Q, but when τ1>τ2, the intensity correlation time T increases monotonically with the increase of Q and decreases monotonically with the increase of D.
Using the linear approximation method,we have studied the time vevolution of intensity correlation function C(t) in a 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.When pump noise self-correlation time τ changes,we have found that,the time evolution of the C(t) will exhibit various change forms:that is,monotonous descending;monotonous rise;the appearance of a maximum;periodically surging with descending envelope.Furthermore,when the τ is a certain value,the value of the C(t) will lessen with the between the real and imaginary parts of quantum noise correlative increases,but when quantum noise intensity Q increases,the value will increase,and when pump noise intensity P increases,the descending of the C(t) with time has been delayed.
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 τ changes, (i) in the case of τ ≪ 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 τ≫ 1, the curve only exhibits periodically surging with descending envelope. When τ ≪ 1 and τ 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 Q , 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 ).