Shaping of LED white light is of increasing interest for several industrial applications. There are several known design concepts available. However these concepts suffer from high uniformity errors, low efficiencies, chromatic aberrations and/or high tolerance sensitivity. To overcome these limitations we present a novel design concept which is based on the design of aperiodic scattering cell arrays. In a first design step, a unit scattering cell is designed. Afterwards this cell is periodically replicated. Finally the periodicity of the array is broken using parametric optimization. Obtained design results are compared with experimental data.
KEYWORDS: Diffraction, Stray light, Coronagraphy, Space telescopes, Telescopes, Space operations, Diffraction, Stray light, Solar processes, Computer simulations, Photonics, Sun
PROBA-3 is a technological mission of the European Space Agency (ESA), devoted to the in-orbit demon- stration of formation flying (FF) techniques and technologies. ASPIICS is an externally occulted coronagraph approved by ESA as payload in the framework of the PROBA-3 mission and is currently in its C/D phase. FF offers a solution to investigate the solar corona close the solar limb using a two-component space system: the external occulter on one spacecraft and the optical instrument on the other, separated by a large distance and kept in strict alignment. ASPIICS is characterized by an inter-satellite distance of ∼144 m and an external occulter diameter of 1.42 m. The stray light due to the diffraction by the external occulter edge is always the most critical offender to a coronagraph performance: the designer work is focused on reducing the stray light and carefully evaluating the residuals. In order to match this goal, external occulters are usually characterized by an optimized shape along the optical axis. Part of the stray light evaluation process is based on the diffraction calculation with the optimized occulter and with the whole solar disk as a source. We used the field tracing software VirtualLabTM Fusion by Wyrowski Photonics [1] to simulate the diffraction. As a first approach and in order to evaluate the software, we simulated linear occulters, through as portions of the flight occulter, in order to make a direct comparison with the Phase-A measurements [2].
The simulation, design and tolerancing of optical systems for wafer inspection is a challenging task due to
the different feature sizes, which are involved in these systems. On the one hand light is propagated through
macroscopic lens systems and on the other hand light is diffracted at microscopic structures with features in the
range of the wavelength of light. Due to this variety of scale plenty of different physical effects like refraction,
diffraction, interference and polarization have to be taken into account for a realistic analysis of such inspection
systems. We show that all of these effects can be included in a system simulation by field tracing, which
combines physical and geometrical optics. The main idea is the decomposition of the complex optical setup in a
sequence of subdomains. Per subdomain a different approximative or rigorous solution of Maxwell’s equations is
applied to propagate the light. In this work the different modeling techniques for the analysis of an exemplary
wafer inspection system are discussed in detail. These techniques are mainly geometrical optics for the light
propagation through macroscopic lenses, a rigorous Fourier Modal Method (FMM) for the modeling of light
diffraction at the wafer microstructure and different free-space diffraction integrals. In combination with a
numerically efficient algorithm for the coordinate transformation of electromagnetic fields, field tracing enables
position and fabrication tolerancing. As an example different tilt tolerance effects on the polarization state and
image contrast of a simple wafer inspection system are shown.
The energy-efficient use of LED light requires the development of compact illumination systems for the customized homogenization and shaping of partially-coherent LED light. Therefore a design concept which is based on arrays of aperiodic micro structures, namely cells, for primary or secondary optics is introduced. Each cell of the array deflects locally the light into predefined directions and results in a light spot in the target plane. The light spots of all array cells together form the desired light pattern. The performance of three different cell geometries (linear gratings, micro prisms andmicromirrors) on the homogenization and shaping ofmonochromatic as well as white light LEDs is demonstrated. For the realistic evaluation of the illumination system an LED model including power spectrum, polarization, spatial and temporal coherence is chosen. Furthermore wave-optical effects like diffraction at the cell apertures are taken into account. For the grating cells arrays a rigorous analysis of the diffraction efficiencies is included.
The thin element approximation is an efficient algorithm to analyze diffractive optical elements (DOEs), whose feature size is large enough compared with the working wavelength. However, the thin element approximation is only valid under the condition of normal illumination. We hereby extend an algorithm, which is called the parabasal thin element approximation, to include the non-perpendicular illumination. More specifically, the thin element approximation is valid for paraxial incident beam, while the parabasal thin element approximation is valid for parabasal beam∗. In this article, we present the algorithm of the parabasal thin element approximation and compare the result with that of rigorous method. All the simulations are based on field tracing1 and done with the optical software VirtualLabTM.2
Nowadays lasers cover a broad spectrum of applications, like laser material processing, metrology and communications. Therefore a broad variety of different lasers, containing various active media and resonator setups,
are used to provide high design flexibility. The optimization of such multi-parameter laser setups requires powerful simulation techniques. In literature mainly three practical resonator modeling techniques can be found:
Rigorous techniques, e.g. the finite element method (FEM), approximated solutions based on paraxial Gaussian
beam tracing by ABCD matrices and the Fox and Li algorithm are used to analyze transversal resonator modes.
All of these existing approaches have in common, that only a single simulation technique is used for the whole
resonator. In contrast we reformulate the scalar Fox and Li integral equation for resonator eigenmode calculation
into a fully vectorial field tracing operator equation. This allows the flexible combination of different modeling
techniques in different subdomains of the resonator. The work introduces the basic concepts of field tracing in
resonators to calculate vectorial, transversal eigenmodes of stable and unstable resonators.
The thin element approximation is an efficient algorithm to analyze diffractive optical elements (DOEs), whose
feature size is large enough compared with the working wavelength. However, the thin element approximation
is only valid under the condition of normal illumination. We hereby extend an algorithm, which is called the
parabasal thin element approximation, to include the non-perpendicular illumination. More specifically, the thin
element approximation is valid for paraxial incident beam, while the parabasal thin element approximation is
valid for parabasal beam. In this article, we present the algorithm of the parabasal thin element approximation
and compare the result with that of rigorous method. All the simulations are based on field tracing and done
with the optical software VirtualLab™.
The optical function generated by a real optical system differs typically from the simulation result. Differences are
caused for example by light source radiation tolerances, by alignment tolerances or deviations of the fabricated
surfaces from ideal surfaces. In order to simulate the influence of surface deviations of a real system on the
optical function it is required to import surface measurement data into optics software. These measurement
data contain often the profile height at discrete data points. In order to do a simulation it is required to
import these data into optics software and to create a continuous surface profile with the help of a suitable
interpolation method. Surfaces deviations can have high spatial frequencies. This requires often a simulation
of light propagation including diffraction, interference and vectorial effects. In general different models of light
propagation are needed depending on the required physical simulation accuracy.
The authors show the modelling of refractive, diffractive and hybrid surfaces from discrete data sets. It turns
out that for the description of these different surface types different interpolation methods are required to allow
an efficient construction of a continuous surface from measurement data. In addition the authors introduce the
Field Tracing concept that allows using different light propagation models from geometrical optics to rigorous.
It enables the adjustment of the physical modelling accuracy in every part of an optical system. The simulation
of the effect of measured surface deviations will be demonstrated on the examples of a refractive beam shaping
element and of a diffraction grating. It will be shown that it is important to include diffraction and interference
effects in the simulation.
The propagation of harmonic fields through arbitrary optical components is the fundamental task in optical
modeling. Unified optical modeling by field tracing uses different techniques for different components in order
to ensure the best compromise between simulation effort and accuracy. This approach can be extended to
non-harmonic fields. With a set of harmonic fields modeling partial coherence of stationary sources is enabled.
The same approach can be applied to model the propagation of fully coherent ultrashort pulses through optical
systems, which may include for instance lenses, gratings and micro-optical components. For that we can rely
on field tracing with its numerous sophisticated propagation techniques for a single harmonic field. Methods to
reduce frequency domain sampling are presented. They allow a convenient pulse modeling in practice. Several
examples are presented using ultrashort pulse modeling with VirtualLab™.
Systems for the reshaping of laser beams are widely used today. Most applications can be found in the fields
of technical illuminations or material processing. Beam shaping is typically done using one or more diffractive
or refractive surfaces. The fabrication of these surfaces is quite expensive in the most cases, especially if merely
prototypes or a small number of systems are required. The authors will show ideas how to design beam shaping
systems for the reshaping of circular Gaussian beams into circular Top Hats using standard spherical catalog
lenses. These ideas allow the development of low cost beam shaping systems. The required elements can be
ordered for less than $100 in catalogs typically. Concepts for the selection of lenses from catalogs as well as
optimization strategies will be explained. Theoretical design examples will be discussed and simulation results will be compared with measurement data.
With their introduction of diffused illumination Leith and Upatnieks introduced one the most essential inventions in holography and in modern optical engineering in general. They observed for the first time the enormous capability of utilizing the phase of a light field in a random-like manner for manipulating its characteristics when propagating in space. The use of phase freedom beyond lens-like manipulations in optical engineering was born. We like to place their invention into a broader context and discuss its enormous impact on most actual developments in optical engineering.
A general concept based on harmonic decomposition of pulses has been introduced to model ultra short pulse propagation through homogeneous and inhomogeneous dielectrics. This include propagation through free space, apertures and lens systems. This approach permits us to consider pulses of any arbitrary spatial and temporal characteristics. The pulse characteristics are found to be affected by angular and material dispersion. A computationally efficient method for the proper sampling of spectral phase has been introduced which requires only a minimum number of harmonic fields for the simulation. In the case of free space propagation, pulses maintains their shape but experience temporal and spectral shifts whose magnitudes depends on angular dispersion (diffraction angle). The pulse broadens, becomes asymmetric and chirped in dispersive media because of group velocity dispersion and higher order dispersion in the media. The pulse broadens due to radially varying group delay and group delay dispersion on propagation through focusing elements. The pulse energy at the focus is affected by the interplay of spherical and chromatic aberration by distributing the pulse energy over a large region on the axis.
Diffuser technology is known in diffractive optics for several decades and was mainly used together with coherent monochromatic light sources. In the last years diffusers play a more important role for illumination and homogenization task of partial coherent light sources, for example, Excimer lasers and LED's. In difference to illumination systems using lenses and micro lens arrays diffusers can be used to freely redistribute the intensity of the light source with a high homogeneity. Using diffuser technology for partial coherent illuminations needs an understanding of the characteristics of the light sources as coherence, wavelength bandwidth, divergence, radiation characteristic/intensity distribution. Since these characteristics are different for coherent and partial coherent light sources, these must be taken into account during the design of diffuser. This leads to new design concepts and surface structures. The authors will explain concepts of diffuser design for LED's and Excimer lasers and will show practical results.
In modern optical engineering the simulation of imaging and non-imaging optical systems on the basis of wave optics is of increasing importance. A simulation based on wave optics means on one hand to use everywhere in the optical system a wave-optical description of light. This allows the evaluation of more general merit functions for the description of the system quality which requires, for example, access to amplitude, phase, polarization, coherence information of light. On the other hand, including wave optics in optical simulations means to model the light propagation exact enough to describe wave-optical propagation effects. That means in general not to perform all simulations without physical approximations but to use light propagation models that work with sufficient physical precision within the optical system. The authors will discuss which needs follow for modern optical simulation software. This discussion includes a flexible handling of different models for simulation of light propagation, descriptions of different wave-optical light representations and considerations of numerical and physical simulation precision.
Optical systems for photon management, that is the generation of tailored electromagnetic fields, constitute one of the keys for innovation through photonics. An important subfield of photon management deals with the transformation of an incident light field into a field of specified intensity distribution. In this paper we consider some basic aspects of the nature of systems for those light transformations. It turns out, that the transversal redistribution of energy (TRE) is of central concern to achieve systems with high transformation efficiency. Besides established techniques nanostructured optical elements (NOE) are demanded to implement transversal energy redistribution. That builds a bridge between the needs of photon management, optical engineering, and
nanooptics.
KEYWORDS: Light wave propagation, Optical components, Geometrical optics, Electromagnetism, Interfaces, Signal to noise ratio, Radio propagation, Photonics, Target detection, Chemical elements
In wave-optical engineering the propagation of light through an optical system can be simulated by using several physical approximations. Independent of the used method it is necessary to have full access to the complete electromagnetic field information in the desired regions. In this article we firstly go into the question what the required information is to get access to the whole electromagnetic field and as a second step we give some insights into physical modeling accuracy and numerical accuracy which is of high importance to evaluate the quality of the calculated results.
The reshaping of laser beams to intensity distributions with high
homogeneity is of practical interest for a lot of applications.
Often the generation of intensity distributions with high
resolution, very small or large diameters is of practical
interest. These intensities correspond typically with waves with
high divergence angles. For the generation of these intensities
non-paraxial beam shaping systems are needed. The authors will
explain how known paraxial beam shaping techniques can be extended
for the design of systems creating non-paraxial output fields. The
systems, explained in this article, will consist of a paraxial
diffractive element together with a non-paraxial lens. This new
extended design concept will be explained on the example of the
shaping of a circular Top Hat from a Gaussian beam.
An illumination can be generally understood as a light transformation where an input field is transformed into a specified output field. There are several approaches to achieve the desired illumination. These approaches differ with respect to the used concept as well as the realization done by the optical system. For illumination tasks the usage of diffusers is very promising. The concept and the
realization by an optical system are presented and discussed. The
functionality of a diffuser is not restricted to coherent light but it is also applicable to partially coherent light. This seems to be of special interest for illumination tasks. Beyond that, some experimental results of the usage of a non-paraxial diffuser in combination with a light emitting diode are presented.
Photon management stands for the generation of tailored electromagnetic radiation. It demands optical systems which perform general light transformations. Consequently, optical engineering for photon management requires a generalization of established optical engineering which mainly addresses imaging problems. It turns out that
the consequent inclusion of wave optics becomes fundamental in this context. Optics simulation and design software must take this development into account. Of special concern is the thorough use of an electromagnetic field model in all simulation techniques. Moreover, various propagation techniques must be available. Each
of them must allow its assignment to any part of the optical system. Furthermore, a generalization of the ideal lens concept is needed to offer a efficient design technique. The wave-optical engineering software package VirtualLab implements these generalized optical engineering concepts.
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.
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.
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.
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.
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.
Novel method for synthesizing light waves from objects expressed in surface model is presented for fast creation of digitally synthetic holograms. This method has a feature of coordinates rotation in Fourier domain, in which only twice FFTs and an interpolation of spectrum are necessary for calculation of light waves form each object's plane. Therefore, presented method is faster than conventional ray- tracing when large scale full-parallax holograms are synthesized in a surface model. Phases of a surface object are also discussed in relation to controlling the direction and diffusiveness of object waves. Furthermore, fabrication of a hologram based on the method and its reconstruction are presented for a demonstration.
Most optical systems may be understood as wave-transforming systems. One input wave is transformed into a corresponding output wave. The quality of the system is evaluated by merit functions applied to the output wave. In monofunctional or multifunctional design methods free parameters of the optical system are optimized with respect to one or more pairs of input waves and merit functions, respectively. Laser beam shaping may be understood as the transformation of waves originated by laser sources. In this paper we present a strategy for the systematic design of systems to realize monofunctional wave transformations. By this method we obtain not only a suitable phase-only transmission, which must be realized by a suitable element or module, but also their position, the number of transmissions/elements necessary to maximize the conversion efficiency of the system, and the upper limit of the conversion efficiency for a specific number of introduced transmissions/elements. We call this strategy amplitude matching. It is based on an inverse design approach. The input field is propagated forward and a desired output field is propagated backward. The system is designed with the goal to find a plane in which the magnitudes of both fields match perfectly. If required more than one element are introduced in the optical system by synthesis of phase-only transmission functions.
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