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Manuscript Title: DIFCARS: a versatile model of CARS signal generation.
Authors: W. Kaabar, R.E. Teets, R. Devonshire
Program title: DIFCARS
Catalogue identifier: ADAC_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 86(1995)162
Programming language: Fortran.
Computer: SUN SPARC.
Operating system: SUNOS 4.1.2 (version of UNIX).
RAM: 93K words
Word size: 32
Keywords: Laser physics, Molecular physics, Spectra, Diffraction, Non-linear polarisation, Electric field, Laser beams, Cars, Coherent anti-stokes Raman scattering, Phase-matching, Focusing lens, Spatially resolving Laser diagnostics, Lamp.
Classification: 15, 16.2.

Nature of problem:
The DIFCARS code calculates the distribution of coherent anti-Stokes Raman scattering (CARS) signal generation over the region of the overlap of the incident beams, the propagation of the incident beams being calculated at the diffraction-level. The calculation is performed in successive slices along and normal to the CARS signal's propagation axis, the slice contributions being summed in an appropriate manner to give the total CARS power.

Solution method:
DIFCARS creates a three dimensional map of the interaction volume of laser beams from which the CARS field is radiated to an observation point in the far field [1,2]. The CARS signal is a Fourier transform of the product of the laser fields. The Fast Fourier Transform (FFT) method is used to obtain the contributions to the total CARS signal of slices normal to the CARS signal propagation axis. Care must be taken in choosing the integration limits and the number of mesh points, acceptable values leading to a stable solution being determined by trial and error. The electric field distribution arising from each of the input beams in the focal region are calculated at the diffraction level including the effects of possible lens aberrations [3].

Restrictions:
For both the collinear and USED CARS phase-matching configurations the beams arrive at the focusing lens collinearly and symmetrically distributed about the optical axis. For the BOXCARS configuration, however, where two or three parallel and off-axis beams arrive at the same focusing lens, each beam fills a small region of the focusing lens. The loss of the radial symmetry of the lens illumination greatly increases the computational complexity of the diffraction equation. In the present model this complexity is reduced by 'replacing' the single focusing lens with three separate lenses with non-parallel optical axes and whose optical centres coincide with the positions of their respective spots on the single lens. This lens substitution is approximately valid for the case of aberration free lenses. The model is a steady-state model appropriate to CARS experiments based on Q-switched lasers with pulse durations of approx 10 ns, i.e., with pulse lengths in space greater than the length of the CARS signal generation volume by a factor > 100. A diffraction-level model of focused laser beams which explicitly includes temporal effects [4] shows that the electric field behaviour in, for example, picosecond CARS experiments is expected to be complex. The version of DIFCARS published here is intended for use in situations where a scalar treatment of the fields is acceptable (small convergence angles). During CARS signal generation the energy of the incident beams is reduced correspondingly; the present model assumes a negligible degree of incident beam attenuation.

Running time:
The CPU time required to compute total CARS power and CARS spatial distribution for a 32*32*32 grid size is approximately 107 seconds.

References:
[1] R.E. Teets, Appl. Opt. 25(1986)855.
[2] J.D. Jackson, Classical Electrodynamics (Wiley, New York, 1967).
[3] L.R. Evans and C. Grey-Morgan, Phys. Med. Biol. 14(1969)205.
[4] C.J. Evans, Opt. Commun. 16(1976)218.