From: jd.deschenes@ulaval.ca   
      
   On 04/12/2010 10:49 PM, Salmon Egg wrote:   
   > In article   
   > <72d8ef7f-11b8-4c97-93fd-d40f884dfeaf@s5g2000yqm.googlegroups.com>,   
   >   alex  wrote:   
   >   
   >> I wish to know how I can construct a train of pulses mathematically   
   >>   
   >> Do I consider it, in the time domain, as a convolution of a single   
   >> pulse with an array of deltas?  Like a a grating, but in the time   
   >> domain.  However, this means I must already decide the shape of the   
   >> single pulse to be shifted along time axis.... Presumably I must then   
   >> have this experimental?..   
   >>   
   >> Or do I construct it from the inverse fourer transform of a bandwidth   
   >> limited(by gain bandwidth) comb of longitudinal modes (lorentzian   
   >> function)?  Will this give me some tiny residue pulses (time domain)   
   >> either side of the main pulses similar to the the far field intentsity   
   >> of a grating,...   
   >>   
   >>   
   >> Thanks   
   >> Alex   
   >   
   > It seems to me that you understand your problem as well as anyone.   
   > Whichever way works is good enough.   
   >   
   > Often, when such a richness of technique is available, you pick a   
   > representation that has special properties to help you handle some   
   > pariculae aspect.   
   >   
   > For example, you can use sines and cosines to represent the amplitude   
   > distribution of an optical beam. That might give some computation   
   > advantage because of the ability to calculate fast Fourier transforms,   
   > FFT. On the other hand, If your interest in resonator modes, you might   
   > want to use Hermite  or Laguerre functions.   
   >   
   > It is really up to you.   
   >   
      
   I would not advise to using a lorentzian or any other shape other than   
   dirac deltas for the modes if generating the signal from the frequency   
   domain.  The lorentzian shape comes from frequency noise and the actual   
   lorentzian is just the envelope, the phase has to be random, otherwise   
   the time signal will decay after a certain number of pulses (after   
   approximately 1 over the width of the lorentzian).   
      
   JD   
      
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