Site Zhang

Tilt operator for electromagnetic fields and its application to propagation through plane interfaces

This article introduces an efficient tilt operator for harmonic fields. In optical modeling and design, a field tilting operation is often needed, e.g., the propagation of a harmonic field between non-parallel planes, since most of the existing propagation operators only deal with the case of propagation between parallel planes. Such operator enables the modeling of various optical components, like the case of prisms and tolerancing with tilted components. The tilt operator is a rigorous method to calculate vectorial harmonic fields on tilted planes. The theory applies a non-equidistant sampling in the k-space of the field before rotation in order to obtain an equidistant sampling of the rotated field. Different interpolation techniques are employed for the non-equidistant sampling in the k-space of the initial field and their performances are evaluated. Besides the tilt operator, the propagation method of harmonic fields through planar interface is proposed as well. The application of both methods makes it possible to model a sequence of tilted optical interfaces, e.g., prisms. At the end of this article, a dispersive prisms example is presented. All simulations are done with the optics software VirtualLabTM.1

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.

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.

Laser resonator modeling by field tracing: a flexible approach for fully vectorial transversal eigenmode calculation

In this work we generalize the scalar Fox and Li algorithm for the dominant transversal resonator eigenmode calculation to a fully vectorial field tracing concept. Therefore we reformulate Fox and Li’s scalar integral equation to a set of coupled operator equations. The introduction of a field tracing round trip operator concept shows that, in principle, any modeling technique which can be formulated to operate for electromagnetic fields can be used to simulate light propagation through the different subdomains of the resonator. This allows a flexible, fast, and accurate simulation of the fully vectorial dominant transversal resonator eigenmode. An example is presented to demonstrate the flexibility and accuracy of the field tracing approach.

Efficient and rigorous propagation of harmonic fields through plane interfaces

The propagation of harmonic fields between non-parallel planes is a challenging task in optical modeling. Many well-known methods are restricted to parallel planes. However, in various situations a tilt of the field is demanded, for instance in case of folded setups with mirrors and tolerancing with tilted components. We propose a rigorous method to calculate vectorial harmonic fields on tilted planes. The theory applies a non-equidistant sampling in the k-space of the field before rotation in order to obtain an equidistant sampling of the rotated field. That drastically simplifies the interpolation challenge of the tilt operation. The method also benefits from an analytical processing of linear phase factors in combination with parabasal field decomposition. That allows a numerically efficient rotation of any type of harmonic fields. We apply this technique to the rigorous propagation of general harmonic fields through plane interfaces. This propagation can be based on a plane wave decomposition of the field. If the field is known on the interface a fast algorithm results from the decomposition. However in general, the field is not known on the interface. Then a rotation operator must be applied first. All simulations were done with the optics software VirtualLab™.

Quasi-Airy beams along tunable propagation trajectories and directions

We present a theoretical and experimental exhibit that accelerates quasi-Airy beams propagating along arbitrarily appointed parabolic trajectories and directions in free space. We also demonstrate that such quasi-Airy beams can be generated by a tunable phase pattern, where two disturbance factors are introduced. The topological structures of quasi-Airy beams are readily manipulated with tunable phase patterns. Quasi-Airy beams still possess the characteristics of non-diffraction, self-healing to some extent, although they are not the solutions for paraxial wave equation. The experiments show the results are consistent with theoretical predictions. It is believed that the property of propagation along arbitrarily desired parabolic trajectories will provide a broad application in trapping atom and living cell manipulation.

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.

Parabasal thin-element approximation approach for the analysis of microstructured interfaces and freeform surfaces

The thin-element approximation (TEA) approach is an efficient algorithm to analyze microstructured interfaces, e.g., diffractive optical elements or scattering surfaces. However, the classical approach is valid only under the condition of paraxial illumination. We hereby develop an extended algorithm to include parabasal illumination, which is characterized by low divergence with arbitrary propagation direction. The extended approach is named as the parabasal TEA approach. In this paper, we present the algorithm of the parabasal TEA approach and compare the results with that of a rigorous calculation in order to demonstrate its validity. We also discuss the role of the parabasal TEA approach in a more general concept for modeling light propagating through freeform surfaces.

Parabasal thin element approximation for the analysis of the diffractive optical elements

The thin element approximation is an efficient algorithm to analyze diffractive optical elements (DOEs), whose feature size is large enough compared with the working wavelength. However, the thin element approximation is only valid under the condition of normal illumination. We hereby extend an algorithm, which is called the parabasal thin element approximation, to include the non-perpendicular illumination. More specifically, the thin element approximation is valid for paraxial incident beam, while the parabasal thin element approximation is valid for parabasal beam. In this article, we present the algorithm of the parabasal thin element approximation and compare the result with that of rigorous method. All the simulations are based on field tracing and done with the optical software VirtualLab™.