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Is there a way to create a short laser pulse that has, at least in the near field, a very narrow frequency range?

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There's an inherent limit on the spectral linewidth of a laser modulated to produce short pulses. This comes from the modulation property of the Fourier transform:

$$\mathscr{F}\{g(t) h(t)\}=G(f)\ast{}H(f)$$

This means that the linewidth of a pulsed laser beam is no narrower than the spectral width of the pulse waveform. If you produce 1 ns pulses, the linewidth will be at least on the order of 0.5 GHz.

Practically, if you produce pulses by direct modulating a diode laser, you won't approach this limit. If you use an external modulation scheme with a narrow linewidth CW laser, you're likely to achieve very close to the limit.

As for near and far field, that isn't really relevant to the spectral linewidth of the laser. It's more related to the angular spread of the output beam. To the extent that some lasing modes of a multimode laser might be seen only in the near field output, the beam measured in the far field is actually likely to have a narrower linewidth.

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    $\begingroup$ For a four ns pulse, if the polarization was modulated so it changed from horizontal to vertical four times in the pulse, would the linewidth be the same as a vertically polarized one ns pulse? $\endgroup$ – Jim Lewis Jan 30 '15 at 1:21
  • $\begingroup$ Yes, assuming that the spectrometer that you were using to measure the spectrum had no polarizing elements (which they usually do). $\endgroup$ – user113857 Apr 13 '16 at 14:18

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