On the left there is a standard Gaussian pulse, that's the envelope of the field oscillating at a defined frequency.
2.
:: An infinite number of low pass filter sections will give a perfect Gaussian pulse at the output when fed with a pulse of the correct width ( if you can wait for ever ).
3.
For the HeNe laser with a 1.5-GHz spectral width, the shortest Gaussian pulse consistent with this spectral width would be around 300 picoseconds; for the 128-THz bandwidth Ti : sapphire laser, this spectral width would be only 3.4 femtoseconds.
4.
In the same way that an ideal low pass filter will output a Sinc pulse in response to a dirac pulse, but with only the 0 to " half and missing the- " to 0 half, I was assuming that the OP required the 0 to " portion of the Gaussian pulse only.
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