Self-phase modulation

Self phase modulation (SPM) (English: self -phase modulation ) is a nonlinear optical effect that occurs on interaction of electromagnetic radiation with matter. The radiation is spectrally extended symmetrically to new frequency components.

Explanation

Cause of the self-phase modulation is the temporal Kerr effect. This means that the refractive index in the media depends on intensity for high intensities:

Optical media in the non-linear refractive index coefficient is very low, so that self phase modulation is only relevant light intensities from approx.

The nonlinear refractive index change causes mainly an intensity-dependent phase velocity. After traversing a distance in such a nonlinear medium, this results in a nonlinear phase shift of:

Wherein the speed of light in vacuum, and the carrier angular frequency is.

The intensity dependent change of the refractive index. The instantaneous frequency is then

With the time-dependent shift of the instantaneous frequency

Example

When using as an example the frequently used model of a hyperbolic secant pulse

Is the non-linear phase of the pulse

Thus the instantaneous frequency is shifted to

Considering the last term one sees immediately that new frequencies are generated symmetrically to the carrier frequency. Also it can be seen that in case of positive ( for example, in which common optical media case) new long-wave frequencies are generated in the front of the pulse, and in its short wavelength side frequencies.

In the time domain is represented by the self-phase modulation, however, the amount of the pulse envelope, and in particular the time duration of the pulse does not change.

Self- steepening

Of pulses whose duration is the same order of magnitude as the period of the carrier frequency, the above intensity-dependent refractive index leads to an intensity-dependent additional group velocity. This effect is called self- steepening (English: self steepening ). Here, then, the newly generated spectral components are not arranged symmetrically about the original carrier frequency. In addition, the value of the temporal pulse envelope is no longer the same, but the pulse flattens on its front and steepens on his back. According to this phenomenon, this effect is named.

Applications

  • Optical solitons: Propagates a light pulse through a material (eg, fiberglass) he will i broaden a time. Base is the group velocity dispersion, in which different frequency components of the pulse have different speeds. If this dispersion is fully compensated by the self-phase modulation, creates a temporal soliton.
  • Pulse compression: Due to the self-phase modulation, a laser pulse receives additional frequency components, thus gaining bandwidth. To use the newly generated frequency components for a shortening of the temporal pulse duration, the pulse by dispersion compensation must be freed from its chirp.

Postgraduate

  • Robert W. Boyd: Nonlinear Optics. 3rd edition. Academic Press, New York 2008, ISBN 978-0123694706.
  • Nonlinear Optics
  • Optical effect
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