The combination of both tools enables a fast and reliable design of optical systems, design understanding, multiobjective optimization and robustness analysis in a fully automated manner.
Light is essential for our life on earth. We see our world through light; plants and currently also humans generate energy by light and more and more technical developments need and use light to perform certain tasks. The discipline which deals with the physics and the development of devices to harness light in order to perform useful tasks is referred to as optics and photonics, although both terms are used in a somewhat redundant way.
In general, optics and photonics is understood as a technical enabler; this means it is typically an indispensable supporting part within a larger system. A laser and the optics to deliver the light to a workpiece in a fabrication robot is an example of such a combination. Virtual and mixed reality glasses and displays rely on optics but also on a lot of mechanics, electronics and computer technology. The production of modern electronic chips by lithography and wafer steppers is unthinkable without high-end optical technology as an enabling part of the fabrication process. In the car industry, smart and ambient lighting is another trend which benefi ts from the amazing developments in optics and photonics in recent decades. Think about the backlight illumination and the camera in a cell phone. In medicine, not just optical microscopes, but also modern optics enters more and more the operating theatre as a tool for surgery. We would further like to mention the tremendous progress in fl exible contact and intraocular lenses in the huge ophthalmic optics market. We could add numerous other examples which demonstrate the impact of optics and photonics on modern technology and our daily life. Optics is understood to be an enabling technology in the basic fi elds of, for example, information technology and telecommunication, healthcare and life sciences, optical sensing, lighting and energy, national defense, industrial manufacturing, and fundamental R&D.
Fig. 1: The intensity of the refl ected light which was obtained by multiple interference in a thin fi lm with varying thickness. A white RGB source was applied.
A typical optical system consists of a technical light source or a light-emitting object, optical components which shape and control the spatial and temporal characteristics of the emitted light and components which transport the light from A to B where it is then used to perform some required effect or where it is detected to obtain information about the light-emitting object or some other sample on the way through the system. We mainly distinguish between imaging and non-imaging optical systems. An imaging system deals with providing the detector, e.g. the human eye or the sensor in a camera, with the best possible image of a selfemitting or illuminated object. In non-imaging optics, the light source is to be tailored in order to perform a specifi c task, e.g. the headlight of a car or the generation of a femtosecond pulse for eye surgery. Optics and photonics have benefi ted from various essential advances in technology in recent decades. These include the development of numerous new light sources like lasers, laser diodes and LEDs. Although optics is often understood as dealing with the visible region of the electromagnetic spectrum (only 390–700 nm), nowadays optics and photonics deal with much shorter (1 nm and below) and longer (1–10 µm) wavelengths as well. In the early time of optics, components were mainly restricted to planar and spherical surfaces, but nowadays we talk about freeform surfaces with aspherical, and even more general, height profi les. Optics profi t from the development of lithography for electronics, which has brought about the fi elds of micro- and nano-optics where surfaces are structured on a nanometer scale in order to achieve specifi c optical functions through the surface, or even in the volume of a bulk medium. The combination of optics with modern computer technology makes adaptive-optics concepts and detector technologies which were completely unthinkable one decade ago possible.
The new chances for innovative developments through optics and photonics have unleashed a creative demand for manipulating and controlling light in every imaginable way. The development of such innovative products requires expert tools to model and to design the optical devices in order to be able to combine the light sources, components and detectors in a way which enables the demanded function. The development of modern photonics systems cannot be done in an experimental way, but must be based on simulation technology and digital twins. For more than 2000 years, optical modeling has mainly relied on ray optics, which is often also referred to as geometrical optics. This is possible because it can be shown that the modeling and design of lens systems for imaging can, in most cases, be fully based on ray optics. However, with the development of new sources and components and the ever increasing demand for non-imaging optical functions, optical modeling and design must be based on physical optics, sometimes also referred to as wave optics, in order to provide simulation technologies which are accurate enough and which give access to all those parameters of light which are of concern for the application.
Fig. 2: Example of a complex optical setup (high-NA wafer inspection system) which often requires the application of effi cient optimization tools to identify the optimum of merit functions defi ned by numerous different system parameters.
Physical optics is based on Maxwell’s equations, a system of differential equations. Though mathematicians have provided powerful solvers for those equations, in optics such universal Maxwell solvers, e.g. the Finite Element Method (FEM),
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