Field Tracing Accuracy Settings

We use a hybrid sampling concept in VirtualLab Fusion to enable fast physical optics modeling. Electromagnetic fields come with six field components, whereby the three magnetic field components are calculated on demand only. Each field component is represented by a complex amplitude. A part of it is sampled and interpolated on an equidistant grid according to sampling theory and we obtain gridded data. Another part, the wavefront phase which is common to all field components, is sampled on a two-dimensional point cloud and we obtain gridless data. Resampling and changes of the mix between gridded and gridless data are routine key techniques in fast physical optics modeling in VirtualLab Fusion. 

In all situations in which gridless data is generated, we use initial sampling positions on a Cartesian grid or a hexapolar grid dependent on the shape of the domain of the complex amplitude, e.g., a circular domain shape leads to a hexapolar grid. Though the initial positions are on a grid, the positions are changed by subsequent operations without restrictions in gridless data. The number of sampling values used in the gridless data initialization can be adjusted by Oversampling factor Gridless Data. The grey box behind the factor provides the information of the sampling number used.
The sampling factor is multiplied on the initial number per direction in case of a Cartesian initial grid. For a hexapolar grid there is no simple linear rule. Thus, it is best to adjust the number interactively by considering the effect on the sampling value number in the grey box when selecting a specific factor. If you see in the modeling, that the wavefront phase or the complex amplitude show some artifacts, try first to increase the factor for gridless data! We work on an additional automatic sampling feature for gridless data, and it will be released in near future.

Before a complex amplitude is Fourier transformed, its relative diffractive power is determined, which can be understood as the generalization of the Fresnel number. The integral Fourier transform is used if the relative diffractive power is larger than one and the pointwise Fourier transform otherwise. The relative diffractive power is calibrated with respect to the error with which the radius of curvature of a Gaussian beam is calculated when the pointwise Fourier transform is used. The default error is given in the grey box in the line of Fourier Transform Selection Accuracy, that is 0.0025 %. This value can be adjusted by the value of Fourier Transform Selection Accuracy. Smaller values result in a more frequent use of the pointwise Fourier transform and by that higher speed. Physically it means, that more small diffraction effects are neglected.

Consider the example of a truncated plane wave. The wavefront has no curvature which leads to a relative diffractive power much larger than one. Thus, the integral Fourier transform is used and the diffraction at the boundaries of the plane wave are included during further propagation. On the other hand, if the plane wave diameter is a few millimeters or even centimeters the diffraction effect along a short propagation distance is small. That indicates that the inclusion of diffraction is not always needed or even desired, since it can be a minor effect. By Neglect Diffraction-Induced Divergence the use of the pointwise Fourier transform can be enforced for such fields with small diffraction effects. As criterion a threshold for the maximum diffraction induced divergence can be selected in terms of mm per meter propagation from which the divergence angle in the grey box follows. If “1 mm” is selected, diffraction effects which cause a spread of a field smaller than one mm per one meter propagation are neglected.

• Z. Wang, O. Baladron-Zorita, C. Hellmann, and F. Wyrowski, ‘Theory and Algorithm of the Homeomorphic Fourier Transform for Optical Simulations’, Optics Express (2020); https://doi.org/10.1364/OE.388022