I wrote this comment to Frank about Dave Horne's FTCF article:
I read Hasegawa's paper on solitons. It is very good, far better than Dave's article suggested. What Hasegawa had done is to show that there exists a non-linear Schrodinger equation which models well from a quantum optics perspective the movement of photonic aggregations down a fiber and whose solutions are solitonic. What is especially noteworthy for application, the equation admits solutions which have a complex amplitude that disperses very slowly. This gets around the problem of inverse pulse broadening as a function of frequency, so femto second transmissions are possible over standard fiber. Equivalently, the constant product of distance and bandwidth has been increased by at least 3 orders of magnitude over current single fiber limits.
The soliton spectral tunneling effect was theoretically predicted in [5]. This is characterized in the spectral domain by the passage of a femtosecond soliton through a potential barrier-like spectral inhomogeneity of the group velocity dispersion (GVD), including the forbidden band of a positive GVD. It is interesting to draw an analogy with quantum mechanics where the solitons are considered to exhibit particle-like behavior. The soliton spectral tunneling effect also can be considered as an example of the dynamic dispersion soliton management technique.
It is well known that due to the Raman self-scattering effect [6] (called soliton self-frequency shift [7]) the central femtosecond soliton frequency shifts to the red spectral region and so-called colored solitons are generated. This effect decreases significantly the efficiency of resonant amplification of femtosecond solitons. The mathematical model we consider based on the modified NSE including the effects of molecular vibrations and soliton amplification processes.
The NSE, non-linear Schrodinger equation that is solved is:
idq/dz + f(z)(d/dt)dq/dt + g(z)z^3 = ih(z)q
where q is the complex amplitude, z is the GVD length, and f,g,h are arbitrary control functions. (intensity, pulse duration, amplification management)
The solution provides a picture of particularity in waves, i.e., the waves are bunched in pulses and the amplitudes of each solitonic pulse do not diminish as a function of distance depending on the control functions. The control functions are determined by the properties of fiber and of pulse generation. By extending the solution through Hasegawa's quasi-soliton concept which Hasagawa developed out of Zhakarov's seminal 1972 paper, a chirped soliton solution was made available. By setting the coupled equation of the reduced harmonic oscillator form of the NSE solution to zero frequency, the transformed NSE allows the "infinite ocean" of chirped soliton solutions.
(The solutions provide) the dynamics of the fission of the bound states of two hyperbolically growing solitons produced by self-induced Raman scattering effect are given by the NSE. This remarkable fact also emphasizes the full soliton features of solutions discussed. They not only interact elastically but they can form the bound states and these bound states split under perturbations.
Serkin and Hasegawa are saying here that the introduction of forces into a solitonic stream can cause the beam to refract and the elastic nature of the bound states of solitonic pulses allows them to be coherently integrated.
This is something like what SR does. |
