Richard Kowarschik

Dipole lifetime in stratified media

The field of an electric dipole inside an arbitrary system of parallel slabs is evaluated with a Green’s function approach. Application of boundary conditions yields a matrix formalism that allows compact formulation of the problem. The method is extended to the general case of parallel stratified medialike cavities containing a dipole. Effects on spontaneous-emission rate of dipole emitters are evaluated and discussed for different types of planar microcavities.

Exact solution of the Bragg-diffraction problem in sillenites

A method for the exact solution of the Bragg-difrraction problem for a photorefractive grating in sillenite crystals based on Pauli matrices is proposed. For the two main optical configurations explicit analytical expressions are found for the diffraction efficiency and the polarization of the scattered wave. The exact solution is applied to a detailed analysis of a number of particular cases. For the known limiting cases there is agreement with the published results.

Optical activity in photorefractive Bi12TiO20

The influence of optical activity on two-wave mixing (TWM) in photorefractive BTO and BSO crystals in the absence of an applied field is studied both theoretically and experimentally. For the conventinal orientations of the grating vector, K [001] and K[001], the piezoelectric and photoelastic effects are either zero or negligible. This makes an analytical treatment of the TWM problem possible. We obtain an analytical solution for the coupled wave equations of TWM valid for arbitrary optical activity. This result is of special importance for BTO crystals. In these crystals under the condition of maximum energy transfer (|K|rD=1, where rD is the Debye radius) neither the approximation of small optical activity nor the one of dominating optical activity is applicable and our analytical solution becomes essential. Our experimental setup uses beams with a trapezoidal overlap that allows us to study the thickness-dependence of the gain in a single measurement. Experimental and theoretical results for a BTO crystal are compared with those for a BSO crystal and are explained in the framework of the model used.

Optimum orientation of volume phase gratings in sillenite crystals: is it always [111]?

We study the simultaneous influence of optical activity, piezoelectric effect, and elasto-optic effect on two-wave mixing (TWM) under diffusion recording in photorefractive Bi12TiO20 and Bi12SiO20 crystals and find numerically the maximum of the TWM gain as a function of the orientation of the grating vector. Contrary to widespread belief, the grating orientation K∥[111] is the optimum orientation only if optical activity is negligibly small. Nonzero optical activity results in a strong dependence of the optimum grating orientation on the crystal thickness. The strongest deviation of the optimum from the [111] direction is achieved for ϱd=180°, where ϱ is the rotatory power and d is the crystal thickness. Our theory explains well prior results for crystals of moderate thickness and predicts new effects for thick (e.g., fiberlike) crystals.

Self-calibrating shape-measuring system based on fringe projection

The goal of optical 3D-measurements is the determination of Cartesian coordinates of surfaces. Using principles basing on fringe projection techniques coordinates are calculated of measured phases in fringes, image-coordinates of cameras and parameters of the system configuration. Mostly, three measured values unambiguous lead to one coordinate-tripel. A more comfortable way offers photogrammetric measurements where more than three values are measured to calculate coordinates and additional to parameters describing the system configuration. Applying these experiences to fringe projection techniques it is possible to combine the advantages of both techniques. That guarantees high number of object points, quick data acquirement and a simultaneous determination of coordinates and system parameters with photogrammetric bundle adjustment. Recent measurements show the capabilities of that principle. The reliability of the coordinates is given by a standard deviation of less than 10 microns while the object diameter was up to 280 mm.

Experimental comparison of phase-shifting fringe projection and statistical pattern projection for active triangulation systems

Active triangulation systems are widely used for precise and fast measurements. Many different coding strategies have been invented to solve the correspondence problem. The quality of the measurement results depends on the accuracy of the pixel assignments. The most established method uses phase shifted-patterns projected on the scene. This is compared to a method using statistical patterns. In both coding strategies, the number and the spatial frequency of the projected patterns is varied. The measurements and calculations for all presented results were done with exactly the same measurement setup in a narrow time window to avoid any changes and to guarantee identical technical preconditions as well as comparability.

Aberration correction in coherence imaging microscopy using an image inverting interferometer.

We present an imaging method with the ability to correct even large optical phase aberrations in a purely numerical way. For this purpose, the complex coherence function in the pupil plane of the microscope objective is measured with the help of an image inverting interferometer. By means of a Fourier transform, it is possible to reconstruct the spatially incoherent object distribution. We demonstrate that aberrations symmetric to the optical axis do not impair the imaging quality of such a coherence imaging system. Furthermore, we show that it is possible to gain an almost complete correction of remaining aberrations with the help of a reference measurement. A mathematical derivation is given and experimentally verified. To demonstrate the ability of our method, randomly generated aberrations with peak-to-valley values of up to 8 λ are corrected.

Implementation of Image Inversion Microscopy by Using Digital Holography

The resolution and the contrast of optical scanning microscopes can be enhanced by image field microscopy [1, 2, 3, 4]. The image of the sample is imaged by an image inverting interferometer onto the detectors positioned at both exits of that interferometer. There, the image is superposed with its spatially inverted copy (rotation by 180°). Image points distant from the inversion axis are superposed by points that are equally distant, but from the opposite site of the image. If the light coming from the probe is spatially incoherent, those image points far from the inversion axis are not correlated to each other. Thus the intensity values are added incoherently. In contrast, images of points close to the inversion axis are superposed (in part or fully) with their own copy, resulting in an interference structure. Integrating the full interference pattern gives a signal, which can be allocated with the point of the object on the inversion axis. The integration can be done numerically, if the detector does have spatial resolution. By using this method, it is possible to transfer small structures up to the cut-off frequency of the used microscope objective with a contrast of one. So far, an increased two point resolution of 26% could be realized experimentally [5].

Impact of modulational instability of partially coherent light in photosensitive optical polymers on the fabrication of optical microstructures

Photo-curable optical polymers have established for a wide range of micro-optical applications due to the great flexibility of their processing. Photolithographic patterning of these materials is often the basis for the fabrication of complex micro-optical elements and 3D microstructures. But, in the past, the optical functionality of “thick” microstructures (>50 μm) fabricated by UV-lithography was often limited due to an inhomogeneous internal refractive index distribution. Experiments showed that a homogeneous exposure of an UV-sensitive polymer will not lead to a homogeneous degree of polymerization, but to waveguide-like filament patterns. For photo-initiated polymerization processes a saturable and integrating non-linear refractive index change during the exposure process is characteristic. We present a general analytic analysis which shows that this non-linear material response leads to a modulational instability (MI) of the exposure light, if a certain degree of spatial coherence is exceeded. Then, perturbations of the incident wave are growing during propagation and the wave decays into filaments with well-defined spatial modulation frequency. It will be shown that these effects are characteristic for photosensitive polymers and different from the conventional MI, e.g. in Kerr-like media. Besides MI, the geometry of the resulting 3D patterns strongly depends on the initial intensity and phase distribution. If the degree of spatial coherence is below the threshold value, initial perturbations are not amplified. Therefore, it will be shown that the choice of suitable coherence properties or the specific modification of the spatial coherence of the effective light source within the lithographic patterning is a capable method to improve the homogeneity of optical microstructures. All theoretical results could be proven successfully within experiments.

Stability properties of photorefractive BGO crystals for phase conjugation

The nonlinear optical phase conjugation (NOPC) is an important field of modern optics with applications in the compensation of aberrations in laser systems, image processing, and optical measuring systems. Interferometers with PC-mirrors (PCM) offer a higher accuracy of measurement and the possibility of phase measurement with no additional reference waves. The successful application of NOPC very strongly depends on the PC-materials. So, for example, photorefractive materials like BCO-crystals have a high sensitivity connected with low response times, but their applications as PCMs in interferometers requirers the exact knowledge and characterization of the quality of the phase conjugation process both with respect to the amplitudes and the phases of the signal Wayes and the correspondend spatial and temporal behavior.