How does nonlinearity change the width of the pulse (expand or shrink) in time domain, and how does the dispersion change the width of the pulse (expand or shrink) in time domain? Thank you in advance.
I would like to discuss shortly whether educational questions should be placed at these pages. With Google one can immediately find a reference to Agrawal book. Your opinion,
The index is a function of wavelength, so a short pulse has a finite bandwidth. So the pulse picks up a chirp. In addition the index is also intensity dependent, Dn/dI. There are also higher order terms that become important as the pulse get very short (fs). These effect are pronounced in fiber for short pulses. Its possible to pre-chirp the pulse before going into a fiber, or stretch the pulse to avoid non linear effects and re-compress afterwards. In general the pulse is stretched.
I would like to discuss shortly whether educational questions should be placed at these pages. With Google one can immediately find a reference to Agrawal book. Your opinion,
Usually pulses spread over time, ie pulse duration increases with distance. This is not good in terms of transmission of information. Obviously it is reduced the number of pulses per second (bit / s) and shrinks the distance at which information can be transmitted. To avoid this, the technology of optical fibers with zero dispersion was developed: the fiber waveguide dispersion compensated material dispersion. Special conditions can be created when soliton propagation phenomenon occurs: Due to non-linearity of the material the pulse duration is contracted and may be transmited to any distance with the same shape. But the phenomenon is manifested at higher intensities. So,result is different from case to case.
Re: V. Farber:
Like with any question in science (or for that matter - in life) try to be more precise with the question before you end up getting pages and pages of answers here. People are very helpful at RG - but you should respect their time and be specific as much as possible. Web search can answer a lot; then when it can't anymore - due to very specific inquiry you might have a collective brain on RG can.
What kind of pulse, how long/short? how intense? what fiber?etc, etc...
Re:Alex A: I think that educational question should be here - but provided they are very specific. Therefore the answers could be too.
I agree with Alexander Apolonskiy. Questions concerning basic knowledge , which can be looked up in the textbooks should not be discussed here. It is a. waste of timt.
I mainly was interested in the case of the pico second pulses, when occur a temporal soliton formation which physical phenomenon is responsible for shrinking of the pulse in time and which on the expansion.
The fundamental, temporal soliton is one solution of the nonlinear wave equation (nonlinear Schrödinger equation of Optics). It. has the transverse shape proportional to
the inverse coshx. The pulse broadening is proportional to the second derivation of the refractive index with respect to the frequency w :d2n/dw2. This dispersive effect is compensated by the nonlinear Kerr-effect, which means a nonlinear refractive index proportional to the square of the field ampltude nnonlinear=constant.|E|2. This effect works only for special values of the Intensität. See: Abdullaev,Optical Solitons ,Springer
Have a look at this paper: C. Pask and A. Vatarescu, “Spectral approach to pulse propagation in a dispersive nonlinear medium, ” J. Opt. Soc. Am. B 3, 1018 –1024 (1986).
Vladimir, as usual with you, you generate hundreds (thousands by now?) questions from the kindergarten domain. Look at the word "dispersion" in any reference book... Do your homework, and not bandwidth jamming. If you are really a PhD student, when do you do your research?
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