Dispersive Fourier Transform Calculator
Dispersive Fourier Transform is an analog technique to map a signal's spectrum to its time, enabling direct measurement of the Fourier Transform. In the context of optics, this has enabled extremely high-throughput (> 1 MHz), real-time spectroscopy using a wideband pulsed source, the sample itself, a dispersive element, and a fast photodiode.
With this calculator, you will be able to calculate the relationship between time and optical color (wavelength or frequency), as well as practical limitations such as spectral resolution, maximum group delay, and dispersive element loss.
Click on each parameter for further explanation.
Sampling rate of digitizer (GSa/s) - f | |
Photodetector bandwith (GHz) - β | |
Dispersive Element Length (km) - z | Error! |
Bandwidth (nm) - Δλ | Error! |
Phase Ripples | |||||
Loss (dB) - L_{tot} | |||||
(ps/nm) - D_{tot} | |||||
GVD Spectral Resolution | δλ_{GVD} (nm) | δf_{GVD} (GHz) | |||
Detector Spectral Resolution | δλ_{det} (nm) | δf_{det} (GHz) | |||
Digitizer Spectral Resolution | δλ_{dig} (nm) | δf_{dig} (GHz) | |||
Overall Spectral Resolution | δλ_{lim} (nm) | δf_{lim} (GHz) | |||
Limiting Factor |
The Dispersive Fourier Transform achieves the Fourier Transformation in the analog domain by separating the optical colors via dispersion. The colors are physically resolvable once the pulse is stretched to the "far-field", called so because of the mathematical and physical analogy between optical dispersion and one-dimensional diffraction. Without enough dispersion, these features are not mapped into time; this limitation on the spectral resolution is the GVD spectral resolution. In addition, the photodetector and digitizer must have enough bandwidth to capture these transients; these are the digitizer and detector spectral resolutions.
In addition, upon passing through a dispersive element, there will inevitably be loss due to a variety of physical reasons as well as engineering imperfections. Though optical fibers have extremely low loss, incurring sufficient dispersion requires propagation over extremely large distances (> 10 km), and so impose loss; the ultimate loss limits in the fibers here are Rayleigh scattering and infrared absorption. Chirped fiber Bragg gratings (CFBGs) and the multimode fibers used in Chromo Modal Dispersion (CMD) impose much less loss for practical amounts of dispersion, but have their own limitations: CFBGs have a maximum delay given by longest CFBG pattern that one can write into a fiber, while CMD is limited by the mode-coupling length of multimode fibers. Finally, CFBGs suffer from an additional effect, phase ripple, due to inevitable fabrication imperfections, which causes a significant ripple in the group delay, and even nonmontonic time to wavelength mapping, a severe issue for this application.
Click on each parameter for further explanation.
The Dispersive Fourier Transform maps the optical color (wavelength or frequency) into time. The exact mapping depends on the dispersion parameters of the technology involved, as well as the length. Here you can see that mapping explicitly.