Random walks and random numbers from supercontinuum generation

Benjamin Wetzel,Guy Millot,Keith J Blow,Sergei K Turitsyn,John M Dudley,Laurent Larger

doi:10.1364/oe.20.011143

Abstract

We report a numerical study showing how the random intensity and phase fluctuations across the bandwidth of a broadband optical super-continuum can be interpreted in terms of the random processes of random walks and Lévy flights. We also describe how the intensity fluctuations can be applied to physical random number generation. We conclude that the optical supercontinuum provides a highly versatile means of studying and generating a wide class of random processes at optical wavelengths.

Highlights

The study of Supercontinuum (SC) generation in optical fiber has been a field of intense research over the last decade, leading to a number of important advances in both fundamental and applied science [1,2,3]
Since SC generation has been reported over a wide parameter range and using pump sources from the MHz-GHz range, our results suggest that the SC should provide a versatile platform for the study and application of random processes at optical wavelengths
We have shown how these fluctuations can be interpreted in a novel fundamental way in terms of the characteristics of random walks, and we have shown an important applications potential of the supercontinuum as a physical random number generator

Summary

Introduction

The study of Supercontinuum (SC) generation in optical fiber has been a field of intense research over the last decade, leading to a number of important advances in both fundamental and applied science [1,2,3]. The physical mechanisms leading to SC spectral broadening are well understood [4], recent studies have focussed on the instability properties of the SC These results have yielded greatly improved insight into the noise-sensitivity of the nonlinear dynamics of SC generation, with regard to establishing intriguing links with the study of extreme events and rogue waves in other systems [5,6,7,8]. The advantage of optical techniques is that they can exploit a physical random process to generate random numbers at high repetition rate and at optical wavelengths directly compatible with future demands of all-optical integration Examples of such physical optical random number generators include chaotic lasers and optoelectronic systems, photon counting and homodyne detection of vacuum fluctuations, and spontaneous emission and superluminescent diodes [9,10,11,12,13,14,15]. Our aim is to anticipate possible future studies of random walk processes and random number generation using optoelectronic implementations, and to show that the supercontinuum can provide a convenient physical source of random fluctuations that can be applied for this purpose

Supercontinuum intensity and phase fluctuations

Random walks and Levy flights

Random number generation

Conclusion