Scaled model guidelines for solar coronagraphs' external occulters with an optimized shape.

One of the major challenges faced by externally occulted solar coronagraphs is the suppression of the light diffracted by the occulter edge. It is a contribution to the stray light that overwhelms the coronal signal on the focal plane and must be reduced by modifying the geometrical shape of the occulter. There is a rich literature, mostly experimental, on the appropriate choice of the most suitable shape. The problem arises when huge coronagraphs, such as those in formation flight, shall be tested in a laboratory. A recent contribution [Opt. Lett.41, 757 (2016)OPLEDP0146-959210.1364/OL.41.000757] provides the guidelines for scaling the geometry and replicate in the laboratory the flight diffraction pattern as produced by the whole solar disk and a flight occulter but leaves the conclusion on the occulter scale law somehow unjustified. This paper provides the numerical support for validating that conclusion and presents the first-ever simulation of the diffraction behind an occulter with an optimized shape along the optical axis with the solar disk as a source. This paper, together with Opt. Lett.41, 757 (2016)OPLEDP0146-959210.1364/OL.41.000757, aims at constituting a complete guide for scaling the coronagraphs' geometry.

Propagation of electromagnetic fields between non-parallel planes: a fully vectorial formulation and an efficient implementation.

The propagation of electromagnetic fields between non-parallel planes based on a spectrum-of-plane-wave analysis is discussed and formulations for an efficient numerical implementation are presented in detail. It is shown that with the help of interpolation techniques, the numerical implementation can be done with the standard uniform fast Fourier transform (FFT) of easy access. Different interpolation techniques are numerically examined, and it turns out that the use of cubic interpolation, together with the uniform FFT, brings both significantly increased computational efficiency and high simulation accuracy. Apart from the aspect of computational efficiency, all formulations in this work are generalized in a fully vectorial manner in comparison to previous works.

Fully vectorial laser resonator modeling of continuous-wave solid-state lasers including rate equations, thermal lensing and stress-induced birefringence.

The computer-aided design of high quality mono-mode, continuous-wave solid-state lasers requires fast, flexible and accurate simulation algorithms. Therefore in this work a model for the calculation of the transversal dominant mode structure is introduced. It is based on the generalization of the scalar Fox and Li algorithm to a fully-vectorial light representation. To provide a flexible modeling concept of different resonator geometries containing various optical elements, rigorous and approximative solutions of Maxwell's equations are combined in different subdomains of the resonator. This approach allows the simulation of plenty of different passive intracavity components as well as active media. For the numerically efficient simulation of nonlinear gain, thermal lensing and stress-induced birefringence effects in solid-state active crystals a semi-analytical vectorial beam propagation method is discussed in detail. As a numerical example the beam quality and output power of a flash-lamp-pumped Nd:YAG laser are improved. To that end we compensate the influence of stress-induced birefringence and thermal lensing by an aspherical mirror and a 90° quartz polarization rotator.

Simulation of birefringence effects on the dominant transversal laser resonator mode caused by anisotropic crystals.

Birefringence effects can have a significant influence on the polarization state as well as on the transversal mode structure of laser resonators. This work introduces a flexible, fast and fully vectorial algorithm for the analysis of resonators containing homogeneous, anisotropic optical components. It is based on a generalization of the Fox and Li algorithm by field tracing, enabling the calculation of the dominant transversal resonator eigenmode. For the simulation of light propagation through the anisotropic media, a fast Fourier Transformation (FFT) based angular spectrum of plane waves approach is introduced. Besides birefringence effects, this technique includes intra-crystal diffraction and interface refraction at crystal surfaces. The combination with numerically efficient eigenvalue solvers, namely vector extrapolation methods, ensures the fast convergence of the method. Furthermore a numerical example is presented which is in good agreement to experimental measurements.

Analysis of pulse front tilt in simultaneous spatial and temporal focusing.

Simultaneous spatial and temporal focusing (SSTF) has gained enormous interest for controlling the focal region of ultrashort pulses in the material processing community. In this paper, we provide theoretical insight in the nature of SSTF. We use numerical simulations to propagate the initial pulse through the focusing lens and into the focal region. By that we can investigate the appearance of the pulse front tilt (PFT), which has been experimentally obtained in SSTF. This is further deepened by a mathematical investigation which shows that PFT is a fundamental consequence of SSTF. Next we follow the idea to use an initial PFT in order to influence or even compensate the PFT in the focal region. Again that is done by simulations as well as mathematical investigations. We found that an initial PFT cannot significantly influence the PFT in the focal region.

Efficient semi-analytical propagation techniques for electromagnetic fields.

In this work, four fast and rigorous methods for the simulation of light propagation in a homogenous medium are introduced. It is shown that in free-space propagation, the analytical handling of smooth but strong phase terms is very efficient in reducing the computational effort. Therefore, the angular spectrum of plane waves (SPW) operator is reformulated to handle linear, spherical, and general smooth phase terms without limiting the application of the fast-Fourier-transformation algorithm. Especially for nonparaxial field propagation, the proposed techniques can significantly reduce the required number of sampling points. Numerical results are presented to demonstrate the efficiency and the accuracy of the new methods.

Parabasal field decomposition and its application to non-paraxial propagation.

The fast and accurate propagation of general optical fields in free space is still a challenging task. Most of the standard algorithms are either fast or accurate. In the paper we introduce a new algorithm for the fast propagation of non-paraxial vectorial optical fields without further physical approximations. The method is based on decomposing highly divergent (non-paraxial) fields into subfields with small divergence. These subfields can then be propagated by a new semi-analytical spectrum of plane waves (SPW) operator using fast Fourier transformations. In the target plane, all propagated subfields are added coherently. Compared to the standard SPW operator, the numerical effort is reduced drastically due to the analytical handling of linear phase terms arising after the decomposition of the fields. Numerical results are presented for two examples demonstrating the efficiency and the accuracy of the new method.