In wave-optical engineering the propagation of light through optical elements can be simulated using different physical approximations. Independent of the used approximation it is necessary to have full access to the complete wave information (for example the amplitude, phase and polarization) everywhere in the optical system. This means if geometric optics approximation (ray tracing) should be used in wave-optical engineering it must be possible to reconstruct the complex amplitude from the rays after a ray tracing step. Therefore it is also necessary to convert the complex amplitude of a wave into rays before the beginning of the ray tracing. For the reconstruction of the complex amplitude typically interpolation techniques must be used. To make ray tracing in wave-optical engineering practicable efficient interpolation techniques are required. The authors will discuss the conversion of a complex amplitude into rays and vise versa. The use of geometric optics approximation together with other approximations of the wave propagations for the analysis and the design of optical systems will be demonstrated.
Diffractive beam splitting elements are typically designed for replicating beams at positions in the spatial spectrum and with predefined relative weights. There is a growing number of industrial applications for diffractive beam splitters. Many of these applications raise special requirements to the design process, which are considered in this work. Examples are the design of tolerancing optimized beam splitters, the limitation of the maximum intensity of
noise orders, the design technique for allowing arbitrarily positioned signal orders, and the design of non-paraxial beam splitters.
Optical systems can be understood as a sequence of homogeneous and inhomogeneous regions (free spaces and optical elements). In wave-optical engineering these regions are often analyzed separately using different physical approximations. The propagation of a wave within a homogeneous medium is well understood and described by different propagation integrals (for example by the angular spectrum of plane waves propagation, the Rayleigh Sommerfeld propagation and paraxial approximations following from these integrals). To allow a fast numerical evaluation of these integrals, typically Fast Fourier Transforms are used. If the propagation integrals are evaluated using Fast Fourier Transforms it follows automatically that start and end plane of the propagation have to be perpendicular to the optical axis. This can be a disadvantage if the complex amplitude of a propagating wave has to be calculated on a plane non parallel to the start plane of the propagation. Examples are the propagation of a wave to a screen which is tilted to the optical axis, the calculation of reflection of a wave on a tilted mirror and changing of the main propagation direction of a wave after a prism. The authors will demonstrate a modified propagation integral based on the angular spectrum of plane wave propagation that overcomes this limitation and allows a fast numerical evaluation using Fast Fourier Transforms. The advantage of the propagation method will be demonstrated on various examples.
Several approaches exist for the numerical representation of optical fields. These approaches differ with respect to the amount of information from the original field which is represented. Based on these numerical field representations, a number of different propagation methods are known which have different properties concerning physical accuracy and computational effort. Well-known examples are the ray tracing approach and Fourier transform based wave optical propagation methods. A modern optical engineering software should therefore enable the usage of different field representations and propagations methods within the modeling of an optical system. The spread sheet approach for modeling an optical system, which is used for instance in ZEMAX, can be extended for allowing a more flexible assignment of different propagation methods to certain parts of the optical system. This generalized approach, which is implemented in VOL4 VirtualLab, is demonstrated by practical example from laser beam shaping. Furthermore, an overview is given to the wave optical design approach implemented in VOL4 VirtualLab.
Innovation through photonics requires very flexible methods for the design of non-image forming systems in addition to a continuous development of image-forming system engineering. A simple consideration shows, that optical engineering for non-image forming systems needs to be generalized by a systematic inclusion of wave optics. The resulting wave-optical engineering is the base for the design and modeling of systems which generate tailored electromagnetic radiation, that is for photon management.
Although over the past few years state-of-the-art point-to-point optical interconnects have shown the potential to fulfill the ever increasing demand for higher data communication bandwidth, still electronic interconnects are favoured over optical interconnects because electronics is a much more mature and established technology. However, when photonic interconnects could allow more complex and richer sets of interconnect patterns, by e.g. allowing for one-to-many optical interconnects (signal broadcasting) and reconfigurable point-to-point optical interconnects, they might outperform electronics both in terms of bandwidth and ease of reconfiguration. In this paper we do a concept study of several approaches to bring signal broadcast within an existing free-space (FS) plastic micro-optical interconnect intra-chip component. The original component consists of a combination of a refractive microlens array and a classical high-quality microprism. The idea of signal broadcasting can be realized by incorporating a fan-out diffractive optical element (DOE) at certain positions in this component. In a first design we integrate the DOE on the deflection edge of the microprism. For a second design we focus on the replacement of the refractive microlens array by their diffractive counterparts. In this approach the fan-out functionality of the DOE is combined with the lens functionality of the diffractive microlens arrays. In a third approach we target multi-faceted diffractive microlens arrays to implement the fan-out functionality. All presented designs can bring signal broadcast to the intra-chip optical interconnect level, although some of them will turn out to be more attractive for practical implementation in demonstrators. We compare and discuss the advantages and disadvantages of the proposed designs.
Photolithography based on proximity printing offers a high throughput and cost effective patterning technology for production of for instance large area liquid crystal displays. The resolution of this technique is limited due to wave-optical effects in the proximity gap between the binary amplitude mask and the substrate. We can improve the resolution drastically by replacing the conventional photomask with a mask causing both amplitude and phase modulation of the illumination wave. We describe a wave-optical design procedure of such masks. The feasibility of the method is demonstrated by results from computer simulations and practical experiments. We show that for a 50 micron gap a 3 micron line/space pattern is resolved clearly for visible light illumination, whereas under conventional conditions the image is completely degraded. The proximity mask used in our experiments was fabricated by e-beam lithography with four height levels and two amplitude transmission values.
Proximity printing is a high throughput and cost effective lithographic technique for production of e.g. large area flat panel displays. The resolution of this technique, however, is limited due to diffraction effects that occur at mask pattern edges. We can improve the resolution drastically by replacing the conventional photomask with a mask which compensates these diffraction effects. The resulting mask modulates phase and amplitude of the exposure beam in such a way that the required image is formed at a predetermined distance behind the mask. In this work we describe the basic principles behind the resolution enhancement technique and explain the mathematical model to design this new type of proximity mask. The feasibility of th method is demonstrated by theoretical calculations as well as by practical experiments. The diffractive structures that have been examined are designed to form an image at a distance of 50 micron behind the mask. The mask contains 2 amplitude and 4 phase levels and the pixel size is 1 micron. Under these conditions a 3-micron line/space pattern is clearly resolved, whereas under conventional conditions the image is completely distorted.
Photolithography based on proximity printing offers a high throughput and cost effective patterning technology for production of for instance large area liquid crystal displays. The resolution of this technique is limited due to wave-optical effects in the proximity gap between the binary amplitude mask and the substrate. We can improve the resolution drastically by replacing the conventional photomask with a mask causing both amplitude and phase modulation of the illumination wave. We describe a wave- optical design procedure of such masks. The feasibility of the method is demonstrated by results from computer simulations and practical experiments. We show that for a 50 micron gap a 3 micron line/space pattern is resolved clearly for visible light illumination, whereas under conventional conditions the image is completely degraded. The proximity mask used in our experiments was fabricated by e-beam lithography with four height levels and two amplitude transmission values.
A strategy for designing optical systems that are optimized for multiple optical functions on the basis of wave optics is presented. Each optical function is composed of an input field, a set of fixed system parameters, and a merit function. A design algorithm is proposed which is applicable for optical systems consisting of an transmission operator followed by an arbitrary linear operator. The goal is to find the transmission operator which is optimal for all optical functions simultaneously. In later design steps, the found transmission operator can be transformed to real optical elements, for instance by using the thin element approximation. It is shown that the algorithm is efficiently applicable by investigating two sample applications for multifunctional wave optical design: the design of tolerant systems and 3D beam shaping.
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