The Debye integral is an essential technique in physical optics, commonly used to efficiently tackle the problem of focusing light in lens design. However, this approximate method is only valid for systems that are well designed and with high enough Fresnel numbers. Beyond this assumption, the integral formula fails to provide accurate results. In this work, we generalize the Debye integral to overcome some of its limitations. The theory explicitly includes aberrations and extends the integral to fields on tilted planes in the focal region. We show, using examples, that the new formulas almost reach the accuracy of a rigorous modeling technique while being significantly faster.

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Component, e.g. Fabry-Perot interferometer, with internal multiple reflections plays an important role in laser technology. Its optical functionality is based on multiple reflections inside the component and the interference effect. In this paper, two electromagnetic concepts that allow the modeling of such components for general incident light are proposed. The first one is based on an iterative field tracing approach. With this approach multiple reflections through and inside the component are handled respectively. One typical example is the simulation of Newton's rings effect or the modeling of an Etalon with thickness variation because of fabrication tolerances. The other one is based on the matrix method for stratified media, which is usually used to handle optical layer systems Fabry-Perot interferometer. We present the details, demonstrate various examples and also discuss sampling issues due to the internal multiple reflections.

The propagation of light in homogeneous media is a crucial technology in optical modeling and design as it constitutes a part of the vast majority of optical systems. Any improvements in accuracy and speed are therefore helpful. The far-field integral is one of the most widely used tools to calculate diffraction patterns. As a general rule, this approximate method requires the observation plane located in the far-field region, i.e., a very considerable propagation distance. Only in the well-designed (namely aberration-free) optical system does the far-field integral not suffer from the limitation of the large distance. Otherwise, the far-field integral cannot provide accurate results. In the present work, we generalize the far-field integral to a more general concept with a much more flexible application scope, which allows for the inclusion of aberrations as well. Finally, as an essential part of this generalization, the propagation to arbitrarily oriented planes is also taken into account.

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