Statistical fluctuations in laser transients

On the determination of the optimal parameters in the CAM model

In the field of complex systems, it is often possible to arrive at some simple stochastic or chaotic Low Order Models (LOMs) exploiting the time scale separation between leading modes of interest and fast fluctuations. These LOMs, although approximate, might provide interesting qualitative insights regarding some important aspects like the average time between two extreme events. Recently, the simplest example of a LOM with multiplicative noise, namely, a linear system with a linearly state dependent noise [also called correlated additive and multiplicative (CAM) model], has been considered as archetypal for numerous phenomena that present markedly non-Gaussian statistics. We show in this paper that the determination of the parameters of a CAM model from the (few) available data is far from trivial and that the actual most likely parameters might differ substantially from the ones determined directly from a (necessarily limited) short sequence of observations. We illustrate how this problem can be tackled, at least to the extent possible, using an approach that is based on Bayes' theorem. We shall focus on a CAM modeling the El Niño Southern Oscillation but the methodology can be extended to any phenomenon that can be described by a simplified LOM similar to the one examined here and where the available sequence of data is relatively short. We conclude that indeed a Bayesian approach can fix the problem.

Mass production of thin-walled hollow optical fibers enables disposable optofluidic laser immunosensors

Disposable biosensors are of great importance in disease diagnosis due to their inherent merits of no cross-contamination and ease of use. Optofluidic laser (OFL) sensors are a new category of sensitive biosensors; however, it is challenging to cost-effectively mass-produce them to achieve disposability. Here, we report a disposable optofluidic laser immunosensor based on thin-walled hollow optical fibers (HOFs). Using a fiber draw tower, the fabrication parameters, including drawing speed and gas flow rate, are explored, and the HOF geometry is precisely controlled, which allows identical laser microring resonators to be distributed along the fibers. The disposable OFL immunosensor detects the protein concentration in the HOF through a wash-free immunoassay. Enabled by the disposable sensors, the statistical characteristics of 80 tests for each concentration greatly reduces the bioassay uncertainty. A low coefficient of variation (CV) of 3.3% confirms the high reproducibility of the disposable HOF-OFL sensors, and the mean of the normal distribution of the logarithmic OFL intensity serves as the sensing output. A limit of detection of 11 nM within a short assay time of 15 min is achieved. These disposable immunosensors possess the advantages of low cost, high reproducibility, fast assay, and low-volume consumption of sample and reagents. We believe that this work will inspire disposable optofluidics through the mass production of multifunctional microstructured optical fibers.

Role of the interpretation of stochastic calculus in systems with cross-correlated Gaussian white noises

We derive the Fokker-Planck equation for multivariable Langevin equations with cross-correlated Gaussian white noises for an arbitrary interpretation of the stochastic differential equation. We formulate the conditions when the solution of the Fokker-Planck equation does not depend on which stochastic calculus is adopted. Further, we derive an equivalent multivariable Ito stochastic differential equation for each possible interpretation of the multivariable Langevin equation. To demonstrate the usefulness and significance of these general results, we consider the motion of Brownian particles. We study in detail the stability conditions for harmonic oscillators with two white noises, one of which is additive, random forcing, and the other, which accounts for fluctuations of either the damping or the spring coefficient, is multiplicative. We analyze the role of cross correlation in terms of the different noise interpretations and confirm the theoretical predictions via numerical simulations. We stress the interest of our results for numerical simulations of stochastic differential equations with an arbitrary interpretation of the stochastic integrals.

Transient multimodality in the presence of potential fluctuations

When a stochastic system evolves from its unstable state the phenomenon of transient multimodality may appear, namely for a period of time, probability distribution develops a larger number of maxima than it possesses in the initial and in the stationary states. We investigate the influence of potential fluctuations generated by a Gaussian white noise on this effect. Some general conditions which suffice for the occurrence of noise induced transient multimodality are presented. The opposite phenomenon, namely the noise suppression of transient multimodality, is shown as well.

Colored-noise-induced chaotic array synchronization

The effect of a time-correlated Gaussian noise on one-dimensional arrays consisting of diffusively coupled chaotic cells is analyzed. A resonance effect between the time scale of the chaotic attractor and the colored Gaussian noise has been found. As well, depending on the number of cells, coupling, and noise strength, an improvement of the synchronization or a poor synchronization between cells within the array can occur for some values of the time correlation. These nonlinear cooperative effects are studied in terms of a linear stability analysis around the uniform synchronized behavior.

Turn-on transient statistics and dynamics in a multimode, short-cavity laser

The statistics of turn-on delay times for a longitudinal mode and the total intensity from a multimode, standing-wave, short-cavity dye laser are measured and compared with numerical simulations of a multimode theory of laser dynamics. Differences between the measurements and the theory for the average and standard deviation of the turn-on time are due to transitory modes that decay as a result of frequency-dependent losses and gains. Associated with this phenomenon is a kink in the time evolution of the mode intensity that represents a transition in the dynamics from domination by independent growth of all modes to domination by competition between modes with differing net gains. This unequal competition increases the average and standard deviation of the mode turn-on time.