Spectrograms | previous | next | feedback |
Definition: a type of diagrams which visualize optical or other signals
Spectrograms are common in acoustics, but are also sometimes used in optics, particularly in the context of ultrashort pulses (→ ultrafast optics). The underlying idea is essentially to display a kind of time-dependent spectrum: a Fourier transform is applied to different temporal sections of the signal. Mathematically, this leads to a signal of the form
where E(t) is the signal under investigation (e.g. the electric field of a pulse) and g(t) is a gate function, which may e.g. have a Gaussian shape. The temporally narrower the gain function, the higher is the temporal resolution, but also the lower is the spectral resolution.
It is common to use a horizontal time axis and a vertical frequency (or wavelength) axis, and to encode the intensity for each combination of time and frequency with a gray scale or a color scale. The result is intuitive e.g. for an up-chirped ultrashort pulse (see Figure 1).
Figure 1: Spectrogram of an ultrashort pulse with a pronounced up-chirp, i.e., with a rising instantaneous frequency.
The spectrogram shown in Figure 1 is reminiscent of a graph showing the instantaneous frequency as a function of time. However, a vertical slice of the spectrogram always has some finite width, whereas the instantaneous frequency at any temporal position is a sharply defined value.
Figure 2: Spectrogram of a supercontinuum, simulated with the software RP ProPulse. A logarithmic color scale is used.
Figure 2 shows the spectrogram of an ultrashort pulse after passage through a photonic crystal fiber, in which supercontinuum generation occurred as a result of strong nonlinearities, with a strong influence of chromatic dispersion. In order to span a wider range of spectral intensities, a logarithmic color scale has been chosen. The pulse has split up into several pulses (soliton fission), as the temporal trace (black trace at the bottom) shows. The lower part of the diagram shows various bright spots representing soliton pulses, which carry a significant part of the overall energy. It is also apparent that there is some unconverted light from the wings of the initial pulse (horizontal line in the middle) and a weak background extending to high optical frequencies. This background is to some extent correlated with the above-mentioned solitons, because it is generated in a phase-matched four-wave mixing process. Both the lowest and the highest frequency components exhibit a larger time delay than the medium frequency components; this is due to the chromatic dispersion of the fiber, which has its zero-dispersion wavelength near 1 μm.
See also: instantaneous frequency, pulse characterization, supercontinuum generation
Since October 2008, the Encyclopedia of Laser Physics and Technology is also available in the form of a two-volume book. Maybe you would enjoy reading it also in that form! The print version has a carefully designed layout and can be considered a must-have for any institute library, laser research group, or laser company.
You may order the print version via Wiley-VCH.
