18.1 Introduction

In this chapter the problem of calculation of complex roots of a function F ( x, p) = 0, where p is a parameter is considered. Function F is not necessarily a polynomial on x, but it can be general form function. Such task often appears in many fundamental and applied problems. In this book it is applied to a finding of the eigenfrequencies in both bare and multilayered microsphere. The real part of a found root x defines the eigenfrequency of oscillation, while with the help of the imaginary part one can calculate the Q (quality) factor in the form Q = Re( x)/2Im( x), as it is written in Part I, Sec. 3.3, Eq. (3.5).

The program is a translation into C++ from Turbo Pascal Numerical Methods Toolbox ( 1986, 87 Borland International, Inc.) and uses the Muller's method. A procedure is rewritten in C++ and is contained in class TMullerComplEq. Since in C++ the complex type is available (see STL [Nicolai, 1999]) it allows us to simplify the program code. Section 18.2 shows the program code (with GUI), which allows one to evaluate the complex roots of function y( p) = 0, where both y and p are complex numbers. The example of the function y =cosh( zp), z = 1 is considered. The reader can construct their own function (see EqToSolve) to...