Dispersive Pulse Propagation

A pulse built from nearby frequency components travels through a Lorentzian dispersive medium. Different phase accumulation across the spectrum reshapes the packet as it moves from left to right.

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n(f) = n0 + S * 2 Gamma (fr - f) / ((f - fr)^2 + Gamma^2)
beta(f) = 2 pi f n(f)

Pulse inside the medium

The solid waveform is the electric field; the envelope tracks the pulse shape.

field envelope no-dispersion reference
1.050 refractive index at center
1.05 group index at center
0.00 band delay spread
17 frequency components

Spectrum and dispersion

Blue stems are pulse components; the coral curve is the Lorentzian phase index.

spectrum n(f)