Talk:Self-phase modulation

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"This variation in refractive index will produce a phase shift in the pulse, leading to a symmetric broadening of the pulse's frequency spectrum." This is only true for symmetric pulses where the current chirp has the same sign as n₂. In all other cases SPM only results in a change of the spectrum. I was very suprised the first time I propagated a negatively chirped pulse into a positive n₂ material. The spectrum got narrower. --Erik Zeek 20:06, 1 December 2005 (UTC)

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Re-writing the article because I don't think the derivation below is correct. In particular the frequency shift doesn't seem to have the correct form. --Bob Mellish 00:41, 4 November 2005 (UTC)

[edit] Original derivation

where n is the refractive index, l is the propagation distance in the medium, c is the velocity of light in vacuum and ω₀ is the carrier-frequency of the pulse.

is the second order change of the nonlinear refractive index. The instantaneous frequency is given by

ω(t) = ω₀ + δω(t)

with

being the phase velocity. In case of a common hyperbolic secant pulse shape the intensity is given by

Therefore the nonlinear phase of this pulse becomes

and the instantaneous frequency is shifted by the term