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Optical Solitons

Under certain circumstances, the effects of self-phase modulation (SPM) and group delay dispersion (GDD) on a pulse in a laser resonator can essentially cancel each other:

• The signs of GDD and SPM must be different.

• The pulse must be unchirped and have a sech² temporal shape:

  

  Note that the FWHM pulse duration is ≈1.76 · τ.

• The pulse energy E_p and the soliton pulse duration t meet the condition
  

  where the GDD has units of s², and γ is the nonlinear phase shift per watt of optical power.

It is assumed that the GDD is constant, that is, there is no higher-order chromatic dispersion. Also, SPM and GDD are assumed to be smoothly distributed in the laser resonator, and the pulse energy stays approximately constant. Under these conditions, SPM and GDD do not lead to any temporal or spectral broadening.

There are also higher-order solitons of order j, where the pulse energy is j² times higher, and the pulse shape undergoes periodic oscillations (with the so-called soliton period). These, however, are relatively unstable and are not used in mode-locked lasers.

Other types of solitons, such as spatial solitons, are not important in the context of mode-locked lasers.