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Manuscript Title: Numerical solution of Kramers-Kronig transforms by a Fourier method.
Authors: S.J. Collocott
Program title: KRONIG
Catalogue identifier: ACMN_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 13(1977)203
Programming language: Fortran.
Computer: CDC CYBER 72-26.
Operating system: KRONOS. 2.1.1 LEVEL 393.
RAM: 31K words
Word size: 60
Keywords: Solid state physics, Kramers-kronig, Integral transforms, Optical, Activity, Fourier series, Optics, Experiment.
Classification: 7.4, 18.

Revision history:
Type Tit le Reference
adaptation 0001 TRAPZAL See below

Nature of problem:
The two magneto-optical phenomena, the Faraday rotation and magnetic circular dichroism compose, respectively the real and imaginary parts of the complex optical rotation. The Faraday rotation may then be calculated from the M.C.D. by use of the Kramers-Kronig integral relation.

Restrictions:
The program computes phi(omega) from theta(omega) at equally spaced intervals where each and every M.C.D. data point is used to calculate the Fourier coefficient bm. Currently the program is limited to 200 data points but this may be increased by modifying the program depending on available storage.

Unusual features:
As the program uses a Fourier technique to compute the integral all problems concerning the Cauchy principal part encountered in numerical integration techniques are avoided. The program tests the accuracy of the method by using a gaussian function and comparing the calculated transform with that from theory, the gaussian having an exact analytic solution.

Running time:
Typical running time on a CDC CYBER 72-26 for a transform with 200 data points is 14 sec.

ADAPTATION SUMMARY
Manuscript Title: Adaptation: numerical solution of the Kramers-Kronig transforms by trapezoidal summation as compared to a Fourier method.
Authors: S.J. Collocott, G.J. Troup
Program title: 0001 TRAPZAL
Catalogue identifier: ACMN_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 17(1979)393
Programming language: Fortran.
Classification: 7.4, 18.

Nature of problem:
The program Kronig shows how the Kramers-Kronig (K-K) transforms may be simply calculated using a Fourier method. The adaptation, TRAPZAL is an alternative method which uses a trapezoidal summation to calculate the K-K transform. TRAPZAL has the advantage that it is numerically simpler than Kronig and it requires fewer points to compute the K-K transform. There is very little difference in the accuracy of the two methods.