Induced axial and lateral color surface contributions.

Induced aberrations in general are higher-order aberrations caused by ray perturbations of lower order, picked up in the preceding optical system. Therefore, in the case of color aberrations, induced influences can already be observed at the second order. They are generated by the preexisting first-order axial and lateral color. The analysis of relevant designs surface by surface to identify performance dominating lenses is a key method for understanding and optimizing those systems. Hence, in this paper a formula for the surface contribution of axial and lateral color including second-order terms is derived and discussed differentiating between intrinsic and induced parts. It is also shown how this can be used to deduce a thick-lens contribution of the second order. All of the approaches are based on the Seidel concept, which characterizes any arbitrary optical system only by the paraxial marginal and chief ray of the primary wavelength.

Second-order axial color of thin lenses in air.

In present research, the influence of higher-order aberrations on the correction of secondary axial color is under investigation. Analytical solutions have so far been restricted to special cases and simple optical systems. Common theories require the tracing of rays of different wavelengths. Such numerical approaches do not support the comprehension of the underlying physical effects. In this paper, a formula for second-order axial color contributions is derived which is based on paraxial ray data for the reference wavelength only. Therefore, it allows the determination of second-order axial color in early paraxial design stages without further numerical ray trace. For systems of thin lenses in air, three second-order effects are identified and discussed using simple examples. A quantitative comparison with intrinsic secondary axial color is given.

Whispering gallery modes in nanosized dielectric resonators with hexagonal cross section.

The size dependence of whispering gallery modes in dielectric resonators with hexagonal cross section has been observed within the visible spectral range for cavity diameters comparable to the light wavelength. As a model system single, tapered, high aspect ratio zinc oxide nanoneedles were analyzed. They enable systematic investigations as a function of the resonator diameter down to the nanometer regime. A simple plane wave interference model without free parameter describes the spectral positions and the linewidths of the modes in good agreement with the experiment.