Maxim Shkarayev
PhD Candidate
Applied Mathematics GIDP

Lisbon, Portugal
Coherent Nonlinear Optics of Artificial Media
December 12-14, 2006

ABSTRACT
Often exceedingly rare events have disproportionate impact. Probabilities of market crashes, cancerous mutation during cell division or high power earthquakes are very small; however, due to their devastating consequences, the understanding and modeling of such events is extremely important. The low probability of such events presents a big challenge in studying their statis­tics computationally or experimentally. Usually, the time required to collect an amount of data suf.cient for statistical description is far beyond what is practical. In optical communications, allowable error levels for information transmission systems are of order 10^-12(1 per 10¹²bits), which is an extremely small value. However, taking into account the huge volumes of transmitted information per unit time, such events are quite relevant. Understanding of error statistics and development of methods of error­control are important and challenging problems for the com­munication industry. We consider the problem of data transmission in .ber optical systems with spatial disorder and temporal noise. Spatial disorder occurs as a result of imperfections in the op­tical cable’s manufacturing as well as stresses resulting from how the .ber is laid, making the .ber properties spatially inhomogeneous. Temporal noise is a byproduct of optical ampli.ers, which are necessary to compensate for energy losses in the .ber. This temporal noise is short­correlated – its correlation time is much shorter than the pulse duration. In modern high speed systems, the main factor limiting system performance is the presence of disordered .ber birefringence. This .ber birefringence .uctuates with correlation times much longer than pulse duration. The performance of optical .ber systems is described by the bit error rate, de.ned as the ratio of the number of erroneous bits to the total number of bits in a data stream. We have demonstrated that, in contrast to what is commonly accepted, this parameter .uctuates. Large .uctuations of this parameter can be interpreted as the source of system outages. Therefore the statistics of these .uctuations can be considered as the statistics of the outages. We have studied these statistics and for the .rst time demonstrated that the probability distribution of outages has long extended tails described by a log­normal distribution. This means that their likelihood is much higher than previously thought. For evaluation of these probability distributions we exploit the method of optimal .uctuations. These theoretical results were veri.ed against our experimental data.