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.

Schematics (Click on image to expand)

References

  1. K. Goda and B. Jalali, "Dispersive Fourier transformation for fast continuous single-shot measurements," Nature Photonics, Vol. 7, Issue 2, pp. 102-112, Jan. 2013. PDF
  2. E. D. Diebold, N. K. Hon, Z. Tan, J. Chou, T. Sienicki, C. Wang and B. Jalali, "Giant tunable optical dispersion using chromo-modal excitation of a multimode waveguide," Optics Express, Vol. 19, Issue 24, pp. 23809-23817, Nov. 2011. PDF
  3. K. Goda, D. R. Solli, K. K. Tsia and B. Jalali, "Theory of amplified dispersive Fourier transformation," Physical Review A, Vol. 80, Issue 4, pp. 043821, Oct. 2009. PDF
  4. D. R. Solli, J. Chou and B. Jalali, "Amplified wavelength-time transformation for real-time spectroscopy," Nature Photonics, Vol. 2, Issue 1, pp. 48-51, Dec. 2007. PDF
  5. J. Chou, Y. Han and B. Jalali, "Time-Wavelength Spectroscopy for Chemical Sensing," Photonics Technology Letters, IEEE, Vol. 16, Issue 4, pp. 1140-1142, Apr. 2004. PDF

Click on each parameter for further explanation.

Input Parameters (Adjustable)

Dispersion Technology:

Phase Ripples
Centre wavelength (nm) - λ0
Dispersion parameter (ps/nm.km) - D

Error!

Ratio of dispersion to loss (ps/nm.dB) - FOM
Loss at 0 dispersion (dB) - Lfixed
Maximum group delay (ns) - τmax

Error!


Sampling rate of digitizer (GSa/s) - f
Photodetector bandwith (GHz) - β
Dispersive Element Length (km) - z

Error!

Bandwidth (nm) - Δλ

Error!

Output Parameters (Calculated)

Phase Ripples
Loss (dB) - Ltot
(ps/nm) - Dtot
GVD Spectral Resolution δλGVD (nm) δfGVD (GHz)
Detector Spectral Resolution δλdet (nm) δfdet (GHz)
Digitizer Spectral Resolution δλdig (nm) δfdig (GHz)
Overall Spectral Resolution δλlim (nm) δflim (GHz)
Limiting Factor

Dispersion

Total Dispersion (ps/nm.km) - Dtot Dispersive Element Length (km) - z

Explanation

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.

Schematic

Time vs. Frequency

Minimum Frequency (THz)
Maximum Frequency (THz)

Time vs. Wavelength

Minimum Wavelength (nm)
Maximum Wavelength (nm)

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.

Schematic