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.

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.

Local Spherical Interface Approximation (LSIA) for modelling the propagation of electromagnetic wave fields through analog interfaces is introduced. The method belongs to a class of Local Elementary Interface Approximation (LEIA) in which the propagation is modelled by decomposing the field into local elementary fields. In the method introduced here both the phase-distribution of the field and the boundary of discontinuity are assumed to be locally spherical, which enables the use of Coddington's equations in the determination of the reflected and transmitted fields. The amplitude reflection and transmission is treated with the help of the intensity law of geometrical optics and the energy conservation law. Convergence comparison between LSIA and Local Plane Interface Approximation (LPIA) is performed for a sinusoidal diffraction grating. The accuracy of the method is illustrated with a numerical example.

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.

We discuss the significance of the Wigner Optics (WiO) and the Wigner Distribution Function (WDF), in understanding problems usually dealt with using Wave Optics (WaO). We first present a derivation of the WDF transport equation, equivalent to the Helmhotz equation. We then discuss the corresponding first order WDF differential equation and the 'paraxial’ equation. The Fresnel transform can be derived from the Paraxial Approximation (PA). However another integral transform is required to describe our first order equation. This equation is not a paraxial transform but does take account of the characteristics of the field. We clarify how these transforms are linked to electromagnetic theory. Finally we justify the practical significance we attach to WiO by describe how a new way of understanding motion measurement systems can be achieved using these ideas.

Optical vortices are ubiquitous in coherent optical beams -- they appear naturally in speckle fields and can also be excited artificially with, for instance, diffractive optical elements. An understanding of the propagation of such vortices would be useful for applications of this phenomenon. A method is provided to compute the trajectories of optical vortices in complicated scenarios. The Gaussian beam in which the vortices are embedded is expressed in terms of paraxial modes. The positions of the vortices as a function of the propagation distance can then be computed analytically. The case of a vortex dipole is analyzed and shown to undergo annihilation and revival of the pair under certain conditions. Expressions are provided for the trajectories of a canonically launched vortex dipole. The analytical predictions are compared with numerical simulations.

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.

Wave-optical effects are becoming more pronounced as optical lithography is pushed towards its limit. Photomask topography scattering and wafer polarization effects caused by differences in coupling between transverse electric and transverse magnetic waves degrade image quality. But polarization may provide an extra dimension that allows lithographers to devise simple solutions to otherwise difficult problems such as phase assignment.

Simulation of lithographic processes in semiconductor manufacturing has gone from a crude learning tool 20 years ago to a critical part of yield enhancement strategy today. Although many disparate models, championed by equally disparate communities, exist to describe various photoresist development phenomena, these communities would all agree that the one piece of the simulation picture that can, and must, be computed accurately is the image intensity in the photoresist. The imaging of a photomask onto a thin-film stack is one of the only phenomena in the lithographic process that is described fully by well-known, definitive physical laws. Although many approximations are made in the derivation of the Fourier transform relations between the mask object, the pupil, and the image, these and their impacts are well-understood and need little further investigation. The imaging process in optical lithography is modeled as a partially-coherent, Kohler illumination system. As Hopkins has shown, we can separate the computation into 2 pieces: one that takes information about the illumination source, the projection lens pupil, the resist stack, and the mask size or pitch, and the other that only needs the details of the mask structure. As the latter piece of the calculation can be expressed as a fast Fourier transform, it is the first piece that dominates. This piece involves computation of a potentially large number of numbers called Transmission Cross-Coefficients (TCCs), which are correlations of the pupil function weighted with the illumination intensity distribution. The advantage of performing the image calculations this way is that the computation of these TCCs represents an up-front cost, not to be repeated if one is only interested in changing the mask features, which is the case in Model-Based Optical Proximity Correction (MBOPC). The down side, however, is that the number of these expensive double integrals that must be performed increases as the square of the mask unit cell area; this number can cause even the fastest computers to balk if one needs to study medium- or long-range effects. One can reduce this computational burden by approximating with a smaller area, but accuracy is usually a concern, especially when building a model that will purportedly represent a manufacturing process. This work will review the current methodologies used to simulate the intensity distribution in air above the resist and address the above problems. More to the point, a methodology has been developed to eliminate the expensive numerical integrations in the TCC calculations, as the resulting integrals in many cases of interest can be either evaluated analytically, or replaced by analytical functions accurate to within machine precision. With the burden of computing these numbers lightened, more accurate representations of the image field can be realized, and better overall models are then possible.

This article proposes a new optimization procedure for mask and illumination geometries in optical projection lithography. A general merit function is introduced that evaluates the imaging performance of arbitrary line patterns over a certain focus range. It also takes into account certain technological aspects that are defined by the manufacturability and inspectability of the mask. Automatic optimization of the mask and illumination parameters with a genetic algorithm identifies optimum imaging conditions without any additional a-priori knowledge about lithographic processes. Several examples demonstrate the potential of the proposed concept.

There is a need for a frequency-domain real filter that visualizes pure-phase objects with thickness either considerably smaller or much bigger than 2π rad and gives output image irradiance proportional to the first derivative of object phase function for a wide range of phase gradients. We propose to construct a nonlinearly graded filter as a combination of Foucault and the square-root filters. The square root filter in frequency plane corresponds to the semiderivative in object space. Between the two half-planes with binary values of amplitude transmittance a segment with nonlinearly varying transmittance is located. Within this intermediate sector the amplitude transmittance is given with a biased antisymmetrical function whose positive and negative frequency branches are proportional to the square-root of spatial frequencies contained therein. Our simulations show that the modified square root filter visualizes both thin and thick pure phase objects with phase gradients from 0.6π up to more than 60π rad/mm.

Confocal scanning microscopes are imaging systems that are mainly featured by their unique depth-discrimination capacity when imaging three-dimensional objects. Along the past few years, our research group has done several attempts to improve their axial resolution by means of the so-called point-spread-function (PSF) engineering method. That is, by designing diffractive elements that properly shape the PSF. Our PSF engineering techniques have been designed to work in the nonparaxial regime and are applied both to bright-field and single-photon fluorescence confocal microscopy, and also to more elaborated architectures like 4Pi confocal microscopy.

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.

Intensity transformation by using paraxial-domain polarization-modulating diffractive elements is discussed. It is shown that taking the electromagnetic nature of light into account may lead to a dramatic increase in the diffraction efficiency also in the paraxial domain, in which the vectorial nature of light is usually ignored. Examples are given for signals for which the full 100% conversion efficiency is possible.

This work is devoted to the investigation of specific properties of eigenfunctions of the operator of light propagation in a lenslike medium. We present results obtained by synthesis and investigation of beams consisting of more than one two-dimensional Gaussian-Hermite laser modes with the same value of propagation constant - multimode dispersionless beams.

The Optical Fourier Transform (OFT) is the most fundamental operation in analogue Optical Signal Processing (OSP). The Scaled Optical Fourier Transform (SOFT) is widely used as it provides a great deal of flexibility, which is invaluable in real implantations. In this paper we study some of the practical limits introduced by the use of an illuminating lens of finite aperture. We show, by deriving simple rules of thumb based on examining phase and intensity deviations, that the worst case diffraction errors can be avoided.

Allowing arbitrary profiles for the mirrors of laser resonators offer a wide range of design freedom for the optimization of lasers. This is not only restricted to modifications of the output beam shape but can be widely used to change the mode characteristic inside the cavity and thus, the behavior of the complete laser system. However, the different kinds of lasers require strongly different design methods for the resonators. Whereas well known and straight forward design algorithms exist for stable resonator types other lasers such as unstable ones or waveguide lasers require much more elaborated designs.

Intracavity beam shaping using diffractive elements has already been successfully demonstrated in the field of solid state lasers, gas lasers and external cavity diode laser arrays. In this paper, we discuss the transition from free-space to integrated optics and report on the technological concepts to experimentally realize intracavity beam shaping in polymeric waveguide dye lasers.

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.

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.

A novel approach to optical surface metrology in the nano-scale region was introduced recently. The approach is based on scanning of the interrogated space by specially structured light distributions and the analysis of the scattered light in the far field. For high resolution metrology, various dark beams as the scanning beams were found to be most effective. After a short overview of the measuring procedure, this paper addresses appropriate optical wave front engineering methods. These include the employment of diffractive optical elements designed for wave engineering within a three-dimensional section of space as well as laser beam structuring within the laser cavity.

Recently a new technique has been proposed for laser-assisted generation of phase microrelief to manufacture diamond diffractive lenses for the far IR range. In the present paper the realization of diamond diffractive optical elements (DOEs) is considered, able to focus an incoming CO₂ laser beam into certain pregiven focal domains. Exemplarily, two completely different DOEs for different tasks of laser beam focusing have been designed by different methods, manufactured and finally investigated by means of optical experiment and computer simulation. Measured intensity distributions in the DOEs’focal planes as well as measured diffraction efficiencies have been compared with related results of computer simulation, and have been found to be in good mutual concordance. Obtained first results indicate that technique of laser-assisted ablation can be effectively used for manufacturing of high quality diamond DOEs for laser beam focusing.

We introduce a technique called optical scanning cryptography (OSC). The technique can perform encryption on-the-fly using laser beams and can be implemented using an optical heterodyne scanning. We shall first describe the optical heterodyne scanning system and then provide some computer simulations to clarify and confirm the idea of encryption and decryption.

Planar optical light guides that are suitable for compact, relatively large virtual image projection displays, of either see-through or non-see-through capabilities, are presented. Such light guides are comprised of three diffractive elements that are recorded on a single substrate. The basic principles, design methods, experimental procedures, calculated as well as experimental results are presented. The results reveal that a relatively large field of view and uniform luminance over the entire output image can be obtained, even when the distance from the light guide to the viewer is relatively large.

Most commonly used Fourier-domain optical diffractive structures are focused in infinity. For many applications, however, structures with a focal plane in finite distance are needed (s.c. Fresnel-domain structures). Furthermore, in special cases, structures with simultaneous multiple focuses at different distances are of concern. As it turned out, design and optimization algorithms for Fourier-domain structures can be effectively used in such cases, only after some modifications. In this contribution, design procedures based on iterative approaches such as iterative Fourier transform algorithm (IFTA) and direct binary search (DBS), applied to designing such structures, are presented. Furthermore, the elements with tilted focal plane have been of interest due to their potential applications, and design algorithms for such elements have been developed. A comparison of computer simulated and experimental reconstructions is also discussed. The IFTA and DBS algorithms have been analyzed, improved and efficiently implemented to achieve high performance for a general class of Fresnel-domain multifocal diffractive structures. Convergence of the algorithms has been studied with respect to various important design parameters. In comparison with Fourier-domain structures, also several new quality parameters for Fresnel-domain element quality evaluation have been identified, and their importance has been demonstrated. The designed structures have been fabricated using two different technologies, i.e. realization of designed structures (1) on a nematic liquid crystal spatial light modulator, (2) using e-beam lithography. Several designed testing elements have been fabricated with different design and fabrication parameters chosen in e-beam photoresist, and their performance have been evaluated, achieving a good qualitative agreement with computer simulations.

A novel experimental arrangement to produce high-order Bessel beams is proposed. The system is based on the decomposition of the even and odd spatial components of the Bessel beam. The reconstruction is made with a Mach-Zender interferometer. The original annular squeme of Durnin is used to generate each component of the Bessel beam. The main advantage of our setup is that the annular transmittances have only discrete changes of phase.

A multi-order phase-only binary diffractive optical element was designed and fabricated to generate simultaneously in different diffractive orders 32 (doubled) LP-modes with indices n=0,11, m=1,5. The modes can propagate in a step-index optical fiber with cutoff value V=15. The same DOE can be used to launch LP-modes into a weakly guiding optical fiber and to select (detect) such modes at the fiber output. In the second case, the DOE works as a spatial filter matched to a definite set of modes. Several bounded modes can be excited in a step-index fiber that is single-mode bounded at wavelength 1300 nm using a laser beam at wavelength 632.8 nm (for which the DOE is fabricated). The experimental results of analyzing a multi-mode beam at the fiber output using the designed filter are reported.

In this paper, a new optical method for characterizing nonuniform thin films is employed. For applying this method the special experimental arrangement containing CCD camera as a detector is used. Using this experimental arrangement the spectral dependencies of the local reflectances are obtained. After treating these experimental data of the distributions of the values of the local thicknesses and local refractive index along a large areas of the substrates of the nonuniform films are found. Moreover, it is shown that this method can be used to determine strong nonuniformities in both the optical parameters. The method is illustrated through the optical characterization of a nonuniform ZnSe epitaxial thin film deposited onto gallium arsenide single-crystal substrate and nonuniform film formed by the mixture of CN_x and SiO_y deposited onto silicon single-crystal substrate.