Experimental conguration for investigating the dynamics and the statistics
of the phase locking level of coupled lasers that have no common frequency
is presented. The results reveal that the probability distribution of the phase
locking level of such coupled lasers ts a Gumbel distribution that describes
the extreme value statistic of Gaussian processes. A simple model, based
on the spectral response of the coupled lasers, is also described, and the
calculated results are in good agreement with the experimental results.
Phase locking of coupled oscillators was studied over the years in many dierent contexts
including chemical oscillators with mutual coherence [1], arrays of Josephson junctions that
are frequency locked [2] and arrays of coupled lasers that are phase locked [3{5]. In these,
complete phase locking occurs when all the oscillators have at least one common frequency.
When there is no common frequency, the oscillators group in several clusters, where each
cluster oscillates at a dierent frequency [6]. So far there is very little, if any, experimental
investigations which deal with the dynamics and statistics of coupled oscillators that do not
have a common frequency.
In this letter, we deal with the phase locking level in an array of lasers that have no common
frequency, and show that the distribution of the phase locking level is in good agreement with
the Gumbel distribution function which describes the extreme value statistics from Gaussian
processes [7, 8]. Specically, we investigate the phase locking level of an array of 25 coupled
ber lasers. Although each ber laser support 100,000 eigenfrequencies, the probability to
nd a common frequency for all the lasers in the array is very small (< 10