Abstract

An important example of noise-induced ordering is represented by Stochastic Resonance (SR), introduced to explain the periodicity of the ices in the quaternary era [1]. SR is a specific response of bistable systems to a sinusoidal modulation in presence of noise. An improvement of the quality of the output signal is observed as the amount of noise is increased, up to an optimal (resonant) value. However, while investigations of SR have provided important insights into such systems, the particular nature of the signals analyzed limits somehow their generality. Indeed, the enhancement of the amplification quality for arbitrary input signals is a very promising topic, especially regarding the transmission of informations through noisy, nonlinear channels. We present here an experimental investigation of the response of a nonlinear, optical system to a random binary modulation (telegraph signal) changing the amount of applied external noise. Recently, we have observed and characterized SR in the dynamical behavior of a Vertical Cavity Surface Emitting Laser (VCSEL) [2] verifying for the first time many of the theoretical predictions. The physical system which allows us to observe and characterize the phenomenon described in this letter is formed by a VCSEL followed by a polarizer and a detection system (see [2] for a detailed description of the setup). The signals from a variable intensity, white-noise generator and a pseudo-random binary sequence generator are summed and coupled into the laser input current. The polarized laser intensity, detected by the photodiode for different values of the input noise strength, is shown in Fig. For low noise the laser remains in its initial state. However, a small amplitude modulation is visible. Increasing the noise, some jumps occur. For an input noise around 400 mV_rms, the output follows very well the input signal. For larger noise strengths, the laser dynamics is determined by the noise more than by the input string, with a strong decorrelation between input and output. The evaluation of the cross-correlation between input and output signal shows indeed a peak for a well-defined, resonant value of noise. This is the first experimental evidence of SR for random, binary signals in a real system. To reconstruct the input signal, a suitable indicator can also be extracted from the bit-distribution and utilized to define the output response. The comparison of the input with the output signals is eventually reduced to a comparison of binary strings and can be treated by means of standard methods of information theory.

© 2000 IEEE