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Manuscript Title: Algorithms for calculating coherent anti-Stokes Raman spectra: application to several small molecules.
Authors: J.C. Luthe, E.J. Beiting, F.Y. Yueh
Catalogue identifier: AALG_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 42(1986)73
Programming language: Fortran.
Computer: DEC VAX-11/780.
Operating system: VMS V4.2.
RAM: 215K words
Word size: 32
Peripherals: disc.
Keywords: Molecular physics, Spectroscopy, Cars, Coherent anti-stokes Raman spectroscopy, Lineshape convolutions, With third order Susceptibility, Molecular spectra.
Classification: 16.2.

Nature of problem:
Use of coherent anti-Stokes Raman spectroscopy (CARS) as a diagnostic technique requires the comparison of experimental spectra with calculated spectra to determine temperature and species concentration. In order to extract experimental values by these comparisons, the molecular Raman resonance characteristics and the effect of the laser lineshapes must be accurately modelled.

Solution method:
The Raman resonances of common diatomic molecules (N2, CO, H2) are computed or read from tabulations for more complex species (H2O). The resonant frequencies, line strengths and linewidths are calculated for pressure, temperature and species concentration. The molecular lines then are convoluted with the laser lineshapes. However, the width and shape of the pump and Stokes laser lineshapes give rise to six analytical expressions for the evaluation of the convolution. Both scanning CARS (narrow Stokes profile) and multiplex CARS (broad Stokes profile) routines are provided for combinations of Gaussian and Lorentzian profile pump and Stokes lasers. Accordingly, the package includes the six independent, interchangeable lineshape convolution routines, four interchangeable resonance characteristics routines and an example main program with instrument convolution routine.

The analytical expressions for the CARS intensity convolutions hold only for Lorentzian shape Raman resonances combined with Gaussian and/or Lorentzian laser profiles. Only four molecules (N2, CO, H2, H2O) are included, but the structure of the species dependent routines is adaptable to other molecules, especially diatomics. The molecular rotation vibration states computed are limited to the temperature and pressure regimes typical of combustion.

Running time:
The calculation time for a typical N2 Q-branch 1000 point spectrum at 2000 K, including 3 vibration bands using the multiplex CARS, Gaussian Stokes and pump profiles is 850 s. The longest calculation time for the same N2 spectrum occurs when using scanning CARS, Gaussian Stokes and pump profiles in a Kataoka Teets convolution integral: ^2600 s. All times given are for VAX-11/780 with FPA.