Nonlinear Pulse Distortion

Author: the photonics expert Dr. Rüdiger Paschotta

Optical pulses, in particular ultrashort pulses with pulse durations of picoseconds or femtoseconds, can have very high peak powers and peak intensities even when the pulse energy is moderate, e.g. in the microjoule regime. As a consequence, such pulses can be strongly influenced by nonlinearities during propagation in transparent media, such as in laser crystals or particularly in optical fibers. Nonlinear effects can result in distortions of various kinds:

• For propagation in homogeneous media (e.g. bulk crystals), the spatial properties can be affected. An example is self-focusing, which can in extreme cases lead into laser-induced breakdown. In less extreme cases, one still has the effect of an aberrative and time-dependent lens.
• Strong spectral distortions can result from, e.g., self-phase modulation: the optical spectrum can acquire strong modulations and broadening.
• The temporal shape of a pulse can also be distorted: the pulse may be broadened, may become asymmetric, and or acquire temporal pedestals. In extreme cases, a pulse can break up into multiple pulses. An example is higher-order soliton fission in the process of supercontinuum generation. A related phenomenon is wave breaking. In many cases, the temporal distortion is not the direct impact of a nonlinearity, but rather the consequence of chromatic dispersion acting on a pulse with nonlinearly broadened optical spectrum. For example, self-phase modulation (in an approximation not containing the effect of self-steepening) or Raman scattering do not directly affect the temporal shape, but modify the optical spectrum so as to make a pulse significantly more susceptible to the effects of chromatic dispersion.

Simulations on Pulse Propagation

Pulses propagating in a fiber amplifier, for example, can undergo a complicated evolution. A suitable simulator is essential for getting complete insight – not only on the resulting output pulses, but also on the pulses at any location in your system. The RP Fiber Power software is an ideal tool for such work.

In amplifiers, the effect of gain saturation can also lead to substantial distortions of the temporal pulse shape: while the leading wing of the pulse experiences strong amplification, later parts are less strongly amplified as the gain is saturated already.

The nature of nonlinear pulse distortions depends strongly on the circumstances, i.e., the type and strength of nonlinearity and on the occurrence of other effects such as chromatic dispersion or waveguiding. It can be investigated with pulse propagation modeling.

Case Studies

Case Study: Raman Scattering in a Fiber Amplifier

We investigate the effects of stimulated Raman scattering in an ytterbium-doped fiber amplifier for ultrashort pulses, considering three very different input pulse duration regimes. Surprisingly, the effect of Raman scattering always gets substantial only on the last meter, although the input peak powers vary by two orders of magnitude.

There are various methods to mitigate nonlinear pulse distortions, e.g. in amplifiers for ultrashort pulses. Examples are the use of thin (and highly doped) amplifier crystals, chirped-pulse amplification and divided-pulse amplification.

More to Learn

Case studies:

• Case Study: Raman Scattering in a Fiber Amplifier

Encyclopedia articles:

• nonlinearities
• Kerr effect
• pulse propagation modeling
• chirped-pulse amplification

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