  We propose an algorithm for general nonlinear eigenvalue problems to compute
physically relevant eigenvalues within a chosen contour. Eigenvalue information
is explored by contour integration incorporating different weight functions.
The gathered information is processed by solving a nonlinear system of
equations of small dimension prioritizing eigenvalues with high physical
impact. No auxiliary functions have to be introduced since linearization is not
used. The numerical implementation is straightforward as the evaluation of the
integrand can be regarded as a blackbox. We apply the method to a quantum
mechanical problem and to two nanophotonic systems.
