Proposed spectral distribution for a Gaussian pulse beam
C.J.R. SHEPPARD†*, P. MOORE†, M. ROY† and M. D. SHARMA
†University of Sydney, NSW 2006 Australia
*Australian Key Centre for Microscopy and Microanalysis,
University of Sydney, NSW 2006, Australia
mroy@physics.usyd.edu.au
Gaussian pulse beams model the emission from a confocal resonator, such as those commonly
found in lasers. Such beams assume the relatively simple form of a superposition of coherent
waves, each independently the solution of the paraxial wave equation.
Various spectral
distribuition models have been proposed to describe the Gaussian pulse beam [1]. For physically
realisable beams, the spectral distribution includes only positive frequencies Feng and Winful [2]
and Caron and Potvliege [3] have investigated functions similar to the Poisson distribuiion. This
paper discusses the advantages and limitations of those proposals and offers an alternative model
for Gaussian pulse beam. The proposed spectral distribution is based on the function
    2 
    0     0 
0 
, 
  1 .
f    1 
 exp s

 1    1 
   1  
n
where w0, w1 and s are free parameters. The advantages of this proposed spectral distribution are
that it is directly Fourier transformable, and can exhibit positive or negative skewness. Various
properties of the proposed spectral distribuition such as mean and spectral variance are presented.
The amplitude function is also derived using the proposed spectral distribuition for a Gaussian pulse
beam.
References:
[1] C.J.R. Sheppard and X. Gan, 1997, Opt. Comm., 133, 1
[2] S. Feng and H.G. Winful, 2000, Phys. Rev E, 61, 862.
[3] C. F. R. Caron and R. M. Potvliege, 1999, J. Mod. Opt., 45, 1881.