It is commonly assumed that the modes of optical waveguides and resonators form a complete set of normal modes in the same fashion as in many other physical systems. The equations that govern the propagating or resonant modes in many common optical systems are, however, nonhermitian in character, and as a result the eigenmodes of these systems are not orthogonal to each other and do not comprise a set of ``normal modes'' in the usual sense of that term. Many of our fundamental concepts related to optical systems and laser physics depend upon the assumed orthogonality of the modes of these systems, and are significantly changed if these modes are not orthogonal. This paper describes and gives physical interpretations for the unusual mathematical and physical properties of nonnormal optical systems, using as examples loss-guided or gain-guided optical waveguides and the resonant modes of unstable optical resonators.

The numerical simulation of the propagation of optical wave fields for large propagation distances can require increasingly larger numbers of numerical samples because of the diffraction spreading of the wave. Such spreading can be avoided if a positive lens is used to confine the propagating field to a tube between input and back focal plane. A one-to-one mapping allows the confined light-tube propagation to be substituted for the unconfined free-space propagation, with a resulting reduction in number of samples required. With proper choice of lens focal length, the number of samples needed for propagation from input to far field remains essentially constant at approximately twice the space-bandwidth product of the input.

Modified finite-difference time-domain (FDTD) approach to numerical investigation of propagation of laser pulses and beams in transparent materials is presented. In contrary to traditional FDTD technique, it is based on description of wave propagation by wave equation. To take into account important material properties, presented approach can include integrating of a set of coupled nonlinear equations including equations describing dispersion of linear and nonlinear parts of refractive index, linear and two-photon absorption. Developed technique is illustrated with several examples including scattering of laser radiation by diffraction grating (sine relief) and focusing by a dielectric cylinder. There are discussed problems of calculation stability, control of errors, decreasing of required computation time and memory. Application of developed approach to modeling of micro-optical elements for modern areas of optoelectronics is considered.

Much of optical analysis and design falls into three major categories: geometrical ray tracing, physical optics modeling, and waveguide modeling. Traditionally optical modeling codes have concentrated primarily on only one of these areas. The subject of this paper is building a single code to model all three optical domains under the heading of wave-optical systems engineering.

Images formed by optical systems comprised of many elements are difficult to assess in a quantitative manner. Because the overall size of the system usually is very large compared to the wavelength, a full rigorous treatment based on numerical solutions of Maxwell+s equations is out of the question even with the fast computers of today. Although ray tracing is extremely important in optical design, ray methods alone can not be used for a quantitative assessment of image quality because these methods break down in the region of the image. Here we give a review of recent developments aimed at combining ray tracing and diffraction calculations to obtain an efficient yet accurate assessment of image quality. This hybrid procedure consists of two steps. Ray tracing is used in step 1 to propagate the field from a point source in object space to a reference plane behind the last optical surface in the system, and the first Rayleigh-Sommerfeld diffraction formula is used in step 2 to propagate the field throughout the focal region. Also, we consider cases of imaging by low f- number diffractive lenses where ray tracing must be replaced by more rigorous methods in step 1, and where asymptotic techniques can be used in step 2 to reduce the computation time significantly.

The limits of ray optical methods to provide a valid model for describing the propagation of electromagnetic radiation are explored. We briefly review fundamentals of ray optics as well as various extensions. This review is partially intended to emphasize that existing ray based methods are able to address most, if not all, wave phenomena. In addition, we propose an extension of ray optics which interprets rays as generalized trajectories in an abstract configuration state. This allows us to propose the use of rays and ray optics as fundamental and practical concept to compute any wave phenomenon, including rigorous diffraction problems. Wave optics, in this context, becomes a convenient and efficient method to calculate the ray transfer properties. In addition, our concept facilitates interfacing conventional ray-tracing methods with wave optical methods to predict diffraction.

The proper treatment of optical elements in a wave-optical approach is of fundamental concern in optical analysis and design. Various wave-optical simulation methods rely on transmission functions instead of real optical elements. However, to perform the transition into the real world, a proper treatment for real optical structures has to be found. The local plane-interface approximation (LPIA) can be used for this transition. We discuss the regions of validity of LPIA and two approximation levels, the geometric-optical version LPIA_ray and the thin-element approximation (TEA). Further, algorithms for the design of structures which realize a prescribed transmission function are presented for both approximation levels. This paper acts to give a throughout overview over the local plane-interface approximation.

We present the numerical tests for a Monte Carlo ray-tracing model. The model has been extended to simulate not only geometrical but also physical optics phenomena, including polarization, diffraction, and interference of light. Light beams are represented by a flux of simulated particles (photons) carrying a complex vector characteristic that contains information about amplitude and phase of electromagnetic field oscillations. The model allows simulations of polarization phenomena in global coordinates. It has been verified by predicting the results that perfectly match those derived from the Fresnel formulae for unpolarized light reflection/refraction at the interface of two media. The capability of handling diffraction and interference has been tested on the problems of Fraunhofer diffraction at an infinite slit and circular aperture, and Fresnel diffraction at a semi-infinite knife-edge plane. The results obtained for the former compare fairly well with the analytical solutions from the wave theory, whereas, for the latter, there is only a qualitative agreement with the fringe pattern deduced from the Cornu spiral.

Time-dependent modeling of controlled opto-mechanical systems (e.g. astronomical telescopes) is part of the VLTI system engineering work at ESO. For creation of optical models to be integrated within a dynamic Matlab/ Simulink simulation, a novel optical modeling tool has been developed. It offers a versatile set of geometrical and wave optical propagation algorithms each with its specific strengths. The article describes the algorithms -both from a theoretical and practical point of view. The VLTI as a "real world" application example is presented.

Raytracing methods for gradient-index materials have been available for many years. However, many new applications of gradient-index materials, for example in telecommunications, employ gradient-index elements in situations for which traditional gradient-index raytracing methods are inadequate. A discussion of the limitations fo gradient-index raytracing methods and more exact techniques for modeling propagation through such materials will be discussed.

The process of image formation in optical systems with partially coherent illumination is represented as a superposition of completely coherent modal images. Two modal representations of a partially coherent imaging system are given. The basic concepts are illustrated by an example of calculating the image intensity distribution.

In this paper we present a design method for meso-scale diffractive optical elements (DOEs). We briefly review the purpose and functionality of DOEs in general and describe our technique for designing on-axis as the basis for more elaborate devices, namely beam splitters. We explore two alternative approaches to beam splitter design and their respective issues. We discuss the limitations of our design method, in both fundamental and practical terms, and present solutions for those problems. We employ electromagnetic modeling techniques to simulate the performance of our devices and we present quantitative results as well as qualitative comparisons of our designs. Finally, we discuss an optimization algorithm for improving DOE performance aimed specifically at achieving beam splitters that are robust to misalignment and nonuniform illumination.

In present work the wave aberration is determined for the general case of the concave diffraction grating monochromator using of the direction cosines of the diffracted ray. These direction cosines are found from the ray tracing through the monochromator. The ray tracing includes the holographic grating recording system and the optical system of the monochromator as well. The results of the optimization of the wave aberration and of the light path function are compared for the example of diffraction monochromator.

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.

We have developed a new design of advanced optics for processing high-power laser material. We introduce the concept of DOE (Diffractive Optical Elements) for high power CO₂ lasers ((lambda) =10.6micrometers ). The superior functionality of DOE means that it could become the new standard in optics for next generation devices. Here we describe the design of our DOE technology using scalar theory and micro fabrication using photolithography and RIE (Reactive Ion Etching). We also present results of our ZnSe-DOE technology, mainly focusing on a novel spot-array generator.

Light demultiplexing plays an important role in optical fiber communications. A lot of efforts have been devoted recently to manufacture a device that combines high efficiency, flat spectral response, and low production costs. The contribution discusses the difficulties due to the influence of the polarization effects on diffraction grating properties. The deviations of the ideal profile during the manufacturing process are also responsible to degrade the efficiency. While standard echelettes (triangular-groove gratings) can provide high efficiency in non-polarized light for low-blazed angles, they are not suitable due to the weak angular dispersion leading to large device dimensions. Higher-angle echelettes have the required angular dispersion for device dimensions of, typically, 10 to 15 cm, but electromagnetic effects lead to strong polarization dependence. Photonic crystals, consisting of rods or holes and working in the forbidden region can provide flat spectral response and no polarization dependence.

We study the properties of the self-similarity function for the intensity distribution of field when different types of gratings, fractal, periodic and aleatory, are used. For this we introduce some definitions considering different points of view that allows us the construction of the diffraction gratings with each geometry. Such structures are applied for the calculation of the electromagnetic field propagation in the Fresnel and Fraunhofer regions.

Various rigorous methods have been developed for the efficient analysis of diffractive optical elements (DOEs). We apply a gradient algorithm of synthesis to design two-dimensional DOEs, with the diffraction of the electromagnetic wave of TE polarization using a hybrid finite element - boundary element method. The hybrid method is capable of modeling inhomogeneous DOEs in unbounded free space in a computationally efficient manner. In this paper we discuss the application of the gradient optimization method to the matrix notation of the hybrid method. Such an application makes it possible to analyze DOE profiles with a large number of features. This allows one to overcome the limitations of calculation time dependent on the amount of the DOE modifications. We use the gradient method to design binary-phase lenses with subwavelength features. Although we have considered only binary-phase lenses, the gradient method presented is also suitable for designing continuous-relief DOEs.

High-density optical interconnect using Photonic Crystals (PhCs'), is proposed as a technique for three-dimensional optical signal distribution and routing through multiple planes and in different directions. These optically conducting networks offer the ability to guide light analogously to electrical printed circuit boards (PCB's), which transport electrons through electrical networks. Due to their unique ability to confine and control light on the subwavelength scale, PhCs' have led a challenging prospect of miniaturization and large-scale integration of high density optical interconnects. Thus in this paper we present a novel approach for implementing a high density optical interconnect network in Photonic crystals. To this end, different techniques for both in plane coupling as well as vertical coupling from one layer of PhC to the other layer through an optical via are discussed. Numerical experiments results for optical confinement in both lateral and vertical directions will be presented.

Three epoxy systems were evaluated for physical dn optical properties. The three systems chosen for the study were selected on the basis of their optical clarity, color and chemistry. Three distinctly different chemistries were chosen, aromatic epoxy-amine cured. Aromatic epoxy- anhydride cured and cycloaliphatic epoxy-anhydride cured. All three systems remained optically clear and water-white after full cure. The three selected systems were tested for physical properties, adhesion and light transmission properties. Light transmission was measured after thermal and humidity exposure. Adhesion was measured after humidity exposure only. Both of the epoxy-anhydride systems performed well in optical properties but poorer in adhesion as compared to the epoxy-amine system. The aromatic epoxy- amine system discolored badly during thermal exposure at 100 C. Data generated from this work will be used in selecting clear encapsulating materials for photonics applications. No single system offers optimal performance in all areas. The best compromise material is the aromatic epoxy-anhydride system.

We propose a new optical method for the determination of the rigidity modulus G of solid materials. With this method, the rigidity modulus is determined by measuring of the twisted angle (theta) of the material, depending on an applied force. The measuring of this twisted angle is obtained by using an ultra sensitive polarimetric sensor. The effective measurement of rigidity modulus G for Aluminum and Plexiglas are experimentally achieved, we obtained respectively 1,44464.10¹⁰N/m² and 0,99417.10⁹N/m².

The transverse interference pattern from a fusion-spliced optical fiber is obtained by illuminating the fiber with a laser sheet of light. The buckling on the fiber material in one direction of the spliced point is clear inside the transverse interference pattern. The buckling height ranges from 1 to 10 microns in a waveguide of a 50 micron core adn125 micron clad diameters. The refractive index profile inside the fiber core is calculated using a new method showing the change in the refractive index due to fusion splicing of the fiber. The refractive index profile is calculated by means of the transverse interference patterns obtained at different illumination directions. A CCD camera is used to record the transverse interference pattern from the fusion-spliced optical fiber. In order to calculate the visibility of the obtained fringe patterns and the deflection angle of light through the fiber (displaying the change in the refractive index) it is necessary to measure the fringe maximum and minimum intensities using a special software package.

The comparative theoretical and experimental examination of Talbot effect behind linear, circular gratings with constant period and zone plates is carried out. The features, connected both with the shape and with a period of dashes are detected. It is shown that the quality of the self-image of gratings is determined by boundaries of the range of spatial frequencies, represented in the image. The experimental results of the phase objects visualization with the help of the Talbot interferometer with zone plates are given.

The numerical modeling of influence of aberrations on pictur quality of thin periodic structures with taking into account a high entrance numerical aperture (NA) on the basis of the vector theory of diffraction is presented. The simulation algorithm and brief theoretical considerations are discussed. It is shown the influence of the entrance NA on image quality of microscope objectives is different for various values of NA and the contrast increases with the higher entrance NA.

Random phase is usually assigned to the amplitude of the desired image to synthesis the phase-only computer-generated hologram(CGH). As a matter of fact, the CGH can be obtained directly if proper phase is assigned. But it is rather difficult since there are infinite ways of phase assignment. Based on the symmetry, a new deterministic binary phase coding technique is introduced in this paper. According to this method, the amplitude of the desired image is coded by a binary array derived form the desired image itself. The coarse CGH can be obtained by applying inverse discrete Fourier transform of the previous result. In order to get higher diffraction efficiency the usual iterative method is used to optimize the CGH. Using this method we have obtained several CGHs with high diffraction efficiency. The pattern of the binary CGH is transferred into the glass plate by inductive coupled plasma (ICP) technology. Experimental results are also given in this paper.

A design method for unstable laser resonators is presented offering the possibility of generating a user defined outcoupled beam profile. The described method based upon surface structured resonator mirrors as they are known from mode shaping of stable laser resonators. The design method is demonstrated by an example design of a hard-edged unstable resonator having a Gaussian intensity profile of the outcoupled beam.