Communications with Chaos : (Back to Research Page)

We (Matt Kennel, Cliff Lewis, Lucas Illing, Michael Buhl, and Lupje Kocarev ) are working on several topics in this area. One of them is an investigation of Erbium doped fiber ring lasers. This is a class of lasers composed of an ordinary, single mode optical fiber which is doped with Erbium to provide amplification of light at 1.5 microns wavelength. The Erbium doped fiber is pumped with a diode laser working at 980 nm, and this amplifier is made part of a ring with passive single mode optical fiber connecting the output to the input of the amplifier. This system is now an efficient laser. This laser produces chaotic oscillations, and these have been used experimentally by Roy and VanWiggeren as a `carrier' of information. The information bearing message m(t) is modulated onto the chaotic waveforms of the laser signal either through injecting m(t) into the optical ring or by multiplying the optical waveform by m(t) through an electro-optical modulator. The following paper describes the theory of operation of such an Erbium doped fiber laser and shows that the origin of the chaos in this system is the nonlinear Kerr effect which is a cubic term in the relation between the polarization of the optical fiber medium and the circulating electric field. The Kerr effect is very weak, but the light circulates about 100,000 times before the nonlinear operation of the laser due to the interaction of the Erbium population inversion and the electric field is important, so this weak effect makes itself felt on such time scales. These results are in the paper (Erbium Ring Laser Dynamics; PDF Format, Postscript File), which will soon appear in Physical Review A. [Each of these looks quite ugly in your browser, but seems to print out well. I guess someone should let Adobe know that their ps-->pdf filter gives ugly output.]

Using this model of the Erbium doped fiber laser, we have investigated the synchronization of two such lasers and explored several communications strategies. These are reported in the following paper which was submitted to Physical Review E in August, 1999: Erbium Ring Laser Dynamics: Synchronization of Chaotic Oscillations; PDF Format

There have been a lot of "announcements" in the literature on chaotic communications of security of communications or privacy of communications using chaotic waveforms as the information carrier. None of these announcements, to our knowledge, have been backed up by a rigorous cryptanalysis of the methods used. In the next to last section of the paper just indicated, we give the cryptographic setting of the methods used in our work, and indicate that in some sense they hark back hundreds of years. As we use the chaotic waveforms and utilize the synchronization of the transmitter and receiver, the cryptographic community calls our methods self-synchronous stream ciphers. There has been a lot of cryptanalysis of such systems, and it should not be a surprise that some are secure and some are not. Complexity of waveform is no guarantee of security at all. One must treat each example on its own merits to find out if it is secure or just complicated. In the paper we do NOT provide a cryptanalysis, and correspondingly we do not make any claims for security of the communication.

An earlier paper gives the basic idea of ring laser synchronization and communication as well as proving that our basic closed-loop transmitter, open-loop receiver configuration guarantees stability of the synchronized state in the particular case of synchronized ring lasers. This stability needs to be investigated in every particular case; here it is a global stability of the synchronized state. Ring Laser Dynamics; Physical Review Letters; PDF Format.

The investigations of ring lasers has reached a stage where the very slow fluorescence time of the "upper" Erbium level, about 10 ms, means that the time scales in such ring lasers is too slow to be of interest in practical communications devices. So we have refocused our attention on ring lasers in which the active medium, here an Erbium doped fiber, is replaced with a semiconductor laser where the time scales are about 1 ns. Keep tuned; more will be available on this.