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.

We investigate the propagation of general electromagnetic fields through optical layer structures made of either isotropic or anisotropic media, by using the spectrum-of-plane-waves analysis together with the S-matrix method. We also develop an algorithm based on the fast Fourier transform technique, with a numerically efficient sampling rule. By using this algorithm in combination with other system modeling techniques, we present a few simulation examples, such as field propagation through an isotropic Fabry-Perot etalon, as well as uniaxial crystal slabs with arbitrary orientation and optic axis direction.

From a physical-optics point of view, the far-field light-shaping problem mainly requires a Fourier pair synthesis. The Iterative Fourier Transform Algorithm (IFTA) is one of the algorithms capable of realizing this synthesis, however, it may lead to stagnation problems when the fields of the Fourier pair exhibit a homeomorphic behavior. To overcome this problem, we use a mapping-type relation for the Fourier pair synthesis. This approach results in a smooth phase response function in a single step, without requiring an iterative procedure. The algorithm is demonstrated with examples and the results are investigated via physical-optics modeling techniques.

Ray optics has constituted the fundament of optical modeling and design for more than 2000 years. In recent decades, the introduction of ray tracing software has brought a powerful optical design technology to everybody dealing with optics and photonics. However, with the development and availability of advanced light sources, the capability to produce micro and nano structures, and a boost in the variety of applications and related demands on optical functions, the limitations of ray optics become obvious more often. Optical modeling based on physical optics is required and is the logical next step in the development of optical design. This requires a generalization of ray tracing and its connection with diffractive modeling techniques.

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