Laser Pulse Simulator
© VisuPhy
About and discussion
Source
Original Author
Hussein-Tofaili
Other Contributors
none

Spectrum & spectral phase

Controls

Spectral phase coefficients

Φ(ω) = c₀ + c₁δω+ ½c₂δω² + ⅙c₃δω³

Here δω = ω − ω₀.

Plot limits

MinimumMaximum ω t

Fits the pulse when frequency limits or ω₀ change; other controls keep this view fixed.

How the pulse is calculated

A(ω) = √S(ω). The complex field is F(t) = ∫ A(ω) exp[iΦ(ω) − iωt] dω / (2π), over nonnegative angular frequencies. E(t) = Re F(t).

The numerical sum includes amplitudes down to 0.01% of the spectral peak. Seven illustrative waves span the intensity FWHM; custom spectra use the outermost half-maximum crossings.

Custom spectra use a smooth cubic curve through the control points. The same curve determines the spectrum, centroid, FWHM, and pulse calculation.

Pulse intensity is proportional to |F(t)|². The optional E(t)² trace shows carrier oscillations; its cycle average is |F(t)|² / 2 for a slowly varying envelope. Units and the overall intensity scale are arbitrary.

ωinst(t) = −Im[F′(t) / F(t)]. Frequency is hidden below 10−6 of the transform-limited peak intensity, where the field phase becomes unreliable.

Individual cosine waves A(ω) cos[Φ(ω) − ωt]

Seven waves across the FWHM. Arrows indicate the rest of the spectrum.

Electric field E(t) Sum of the waves

Pulse intensity I(t) ∝ |F(t)|²

Instantaneous angular frequency ωinst(t)

Frequency is shown where the pulse has appreciable intensity; gaps mark a weak or zero field.