Gautschi has developed an algorithm that calculates the value of the Faddeeva function w ( z ) for a given complex number z in the first quadrant, up to 10 significant digits. We show that by modifying the tuning of the algorithm and testing the relative rather than the absolute error we can improve the accuracy of this algorithm to 14 significant digits throughout almost the whole of the complex plane, as well as increase its speed significantly in most of the complex plane. The efficiency of the calculation is further enhanced by using a different approximation in the neighborhood of the origin, where the Gautschi algorithm becomes ineffective. Finally, we develop a criterion to test the reliability of the algorithm's results near the zeros of the function, which occur in the third and fourth quadrants.

Given a complex number z, in the first quadrant of the complex plane, WOFZ (z) computes the value of the Faddeeva-function w(z) = exp(-z2). erfc(-iz) with an accuracy of 14 significant digits. While the body of the algorithm is the same as that of Algorithm 363 ([l, 2]), the initialization part is largely changed so as to improve both the accuracy and the speed of the algorithm. The major distinction between Algorithm 363 and Algorithm 680 lies initially in the choice of the variable QRHO and in the fact that NU isn't a constant if (QRHO.GE.l.O), but decreases with increasing ] z ]. Secondly, in the neighborhood of the origin, a different approximation for the Faddeeva function is used. A full description of the differences between this algorithm and Algorithm 363 is given in [3].

In this paper a comparative theoretical study was made of the magneto-optical response of square lattices of nanoobjects ͑dots and rings͒. Expressions for both the polarizability of the individual objects as their mutual electromagnetic interactions ͑for a lattice in vacuum͒ was derived. The quantum-mechanical part of the derivation is based upon the commonly used envelope function approximation. The description is suited to investigate the optical response of these layers in a narrow region near the interband transitions onset, particularly when the contribution of individual level pairs can be separately observed. A remarkable distinction between clearly quantum-mechanical and classical electromagnetic behavior was found in the shape and volume dependence of the polarizability of the dots and rings. This optical response of a single plane of quantum dots and nanorings was explored as a function of frequency, magnetic field, and angle of incidence. Although the reflectance of these layer systems is not very strong, the ellipsometric angles are large. For these isolated dot-ring systems they are of the order of magnitude of degrees. For the ring systems a full oscillation of the optical Bohm-Ahronov effect could be isolated. Layers of dots do not display any remarkable magnetic field dependence. Both type of systems, dots and rings, exhibit an outspoken angular-dependent dichroism of quantum-mechanical origin.

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