1. Interferogram - spectrometer signal S(λ)
2. Fundamental and XPW reference spectra
3. FTSI - Fourier transform of interferogram (log scale)
4. Extracted sideband f(ω) = E*EXPW: amplitude and phase difference
5. Spectral domain - retrieved vs. true
6. Temporal domain - retrieved vs. true vs. transform limit
7. Spectrogram of retrieved pulse (time-frequency map)
8. Convergence of iterative retrieval
How this simulation works (SRSI pipeline)
1. An unknown pulse E(t) is defined by its spectrum (shape, bandwidth) and spectral phase (GDD, TOD, FOD, sinusoidal ripple).
2. A replica passes through a crystal generating a cross-polarized wave, EXPW(t) ∝ E(t)|E(t)|². Temporal gating broadens its spectrum and flattens its spectral phase, so it serves as the reference pulse.
3. Reference and unknown pulse are recombined with delay τ on a spectrometer: S(ω) = |E(ω) + EXPW(ω)e-iωτ|². The fringes encode the phase difference.
4. Fourier-transform spectral interferometry (FTSI): the inverse FT of S(ω) has peaks at pseudo-times 0 and ±τ. A super-Gaussian filter isolates the +τ sideband; transforming back yields f(ω) = E*(ω)EXPW(ω), giving the phase difference φXPW - φ. The DC peak gives |E|² + |EXPW|², from which both amplitudes are solved.
5. Iterative retrieval: assume φXPW = 0, build a first estimate of E(ω), simulate its XPW, use the simulated XPW phase to refine, and repeat. Convergence typically takes a few iterations when the pulse is reasonably close to the transform limit (the SRSI validity domain).
Note: absolute delay and constant phase are not measurable by interferometry, so the retrieved field is aligned to the true field (piston + linear spectral phase removed) before comparison. All quantities are recomputed in real time when any control changes.