Ruediger Grunwald

Recent research on needle beams and space-time wavepackets (STWPs) is presented. Quasi-nondiffracting STWPs propagate at stable spatial and temporal localization over extended distances. In a simple model, STWPs are interpreted as being composed of differential needle beams. Simulations indicate that pulsed Bessel-like needle beams can reach higher spectral and temporal homogeneity compared to spatio-spectrally shaped focused Gaussian beams. The interference of femtosecond needle beam arrays leads to nondiffracting self-imaging in space and time. High-speed switching of STWPs with combined optical systems, orbital angular momentum generation with self-torque and other emerging fields of research are addressed

The logarithmic derivative has been shown to be a useful tool for data analysis in applied sciences because of either simplifying mathematical procedures or enabling an improved understanding and visualization of structural relationships and dynamic processes. In particular, spatial and temporal variations in signal amplitudes can be described independently of their sign by one and the same compact quantity, the inverse logarithmic derivative. In the special case of a single exponential decay function, this quantity becomes directly identical to the decay time constant. When generalized, the logarithmic derivative enables local gradients of system parameters to be flexibly described by using exponential behavior as a meaningful reference. It can be applied to complex maps of data containing multiple superimposed and alternating ramping or decay functions. Selected examples of experimental and simulated data from time-resolved plasma spectroscopy, multiphoton excitation, and spectroscopy are analyzed in detail, together with reminiscences of early activities in the field. The results demonstrate the capability of the approach to extract specific information on physical processes. Further emerging applications are addressed.

The logarithmic derivative is shown to be a useful tool for data analysis in applied sciences because of either simplifying mathematical procedures or enabling an improved understanding and visualization of structural relationships and dynamic processes. In particular, spatial and temporal variations of signal amplitudes can be described independently on their sign by one and the same compact quantity, the inverse logarithmic derivative. In the special case of a single exponential decay function, this quantity becomes directly identical to the decay time constant. Generalized, the logarithmic derivative enables to flexibly describe local gradients of physical or non-physical system parameters by using exponential behavior as a meaningful reference. It can be applied to complex maps of data containing multiple superimposed and alternating ramping or decay functions as, e.g., in the case of time-resolved plasma spectroscopy, multiphoton excitation or spectroscopy. Examples of experimental and simulated data are analyzed in detail together with reminiscences on early activities in the field. Further emerging applications are addressed.

The application of non-uniform spiral gratings to control the structure, topological parameters and propagation of orbital angular momentum (OAM) beams was studied experimentally with coherent near-infrared light. Adapted digital spiral grating structures were programmed into the phase map of a high-resolution liquid-crystal-on-silicon spatial light modulator (LCoS-SLM). It is shown that characteristic spatio-spectral anomalies related to Gouy phase shift can be used as pointers to quantify rotational beam properties. Depending on the sign and gradient of spatially variable periods of chirped spiral gratings (CSGs), variations in rotation angle and angular velocity were measured as a function of the propagation distance. Propagation-dependent self-torque is introduced in analogy to known local self-torque phenomena of OAM beams as obtained by the superposition of temporally chirped or phase-modulated wavepackets. Applications in metrology, nonlinear optics or particle trapping are conceivable.

The application of non-uniform spiral gratings to control structure, topological parameters and propagation of orbital angular momentum (OAM) beams was studied experimentally with coherent near-infrared light. Adapted digital spiral grating structures were programmed into the phase map of a high-resolution liquid-crystal-on-silicon spatial light modulator (LCoS-SLM). It is shown that characteristic spatio-spectral anomalies related to Gouy phase shift can be used as pointers to quantify rotational beam properties. Depending on sign and gradient of spatially variable periods of chirped spiral gratings (CSG), variations of rotation angle and angular velocity as a function of propagation distance were measured. Propagation-dependent self-torque is introduced in analogy to known local self-torque phenomena of OAM beams as obtained by the superposition of temporally chirped or phase modulated wavepackets.

The recognition, decoding and tracking of vortex patterns is of increasing importance in many fields, ranging from the astronomical observations of distant galaxies to turbulence phenomena in liquids or gases. Currently, coherent light beams with orbital angular momentum (OAM) are of particular interest for optical communication, metrology, micro-machining or particle manipulation. One common task is to identify characteristic spiral patterns in pixelated intensity maps at real-world signal-to-noise ratios. A recently introduced combination of polar mapping and Fast Fourier Transform (FFT) was extended to novel sampling configurations and applied to the quantitative analysis of the spiral interference patterns of OAM beams. It is demonstrated that specific information on topological parameters in non-uniform arrays of OAM beams can be obtained from significantly distorted and noisy intensity maps by extracting one- or two-dimensional angular frequency spectra from single or concatenated circular cuts in either spatially fixed or scanning mode. The method also enables the evaluation of the quality of beam shaping and optical transmission. Results of proof-of-principle experiments are presented, resolution limits are discussed, and the potential for applications is addressed.

Recognition, decoding and tracking of vortex patterns is of increasing importance in many fields reaching from astronomical observation of distant galaxies to turbulence phenomena in liquids or gases. Currently, coherent light beams with orbital angular momentum (OAM) are of particular interest for optical communication, metrology, micro-machining or particle manipulation. One common task is to identify characteristic spiral patterns in pixelated intensity maps at real-world signal-to-noise ratios. Recently, Fast Fourier Transform (FFT) was applied to the quantitative analysis of spiral interference patterns of OAM beams. Our study considers this approach in more detail. It is demonstrated that specific information can be extracted by combining conformal mapping by polar transform with determining one- or two-dimensional angular frequency spectra either in spatially fixed or scanning mode. Results of proof-of-principle experiments are presented.

The working principle of conventional Shack-Hartmann-type wavefront sensors is based on a wavefront division by two-dimensional microlens arrays and a Poynting vector mapping by comparing the focal displacements to reference measurements. At complex phase distortions or steep phase gradients, however, wavefront reconstruction can suffer from ambiguities by crossing or overlapping neighboring sub-beams, or even by a complete loss of beam trajectories. Moreover, the recognition of sub-beams can additionally be affected by parasitic reflections at optical surfaces, or scattering in a medium. A possible solution of the problem is to work with arrays of well distinguishable sub-beams. Recently, high-resolution pixelated liquid crystal spatial light modulators became available which enable to flexibly generate spatially structured light and thus to realize advanced wavefront sensors with individually encoded beams. In our experimental study we investigated the specific advantages of orbital angular momentum beams for a robust beam tracking and wavefront reconstruction. As a key point for a wavefront reconstruction from vortex arrays, the reliable detection of spiral-like image features is addressed and related strategies are proposed.

Simultaneous spatio-temporal focusing of ultrashort pulses is usually performed by single-channel stretcher-compressor geometries where pulse front tilt leads to spatial asymmetry. Here, the basic approach is extended by superimposing two reciprocal sub-beams in a dual-channel stretcher-compressor setup. Spatio-temporal properties of the symmetrized focal zones of few-cycle near-infrared pulses are studied by parametric numerical simulations with physical optics software. Spatial modulations of focal zones depending on focusing conditions appear. Relationships to specific ultrafast interference phenomena are addressed.

Combining the specific advantages of high-resolution liquid-crystal-on-silicon spatial light modulators (LCoS-SLMs) and reflective or refractive micro-electro-mechanical systems (MEMS) presents new prospects for the generation of structured light fields. In particular, adaptive self-apodization schemes can significantly reduce diffraction by low-loss spatial filtering. The concept enables one to realize low-dispersion shaping of nondiffracting femtosecond wavepackets and to temporally switch, modulate or deflect spatially structured beams. Adaptive diffraction management by structured illumination is demonstrated for piezo-based and thermally actuated axicons, spiral phase plates (SPPs) and Fresnel bi-mirrors. Improved non-collinear autocorrelation with angular-tunable Fresnel-bi-mirrors via self-apodized illumination and phase contrast of an SLM is proposed. An extension of the recently introduced nondiffractive Talbot effect to a tunable configuration by combining an SLM and a fluid lens is reported. Experimental results for hexagonal as well as orthogonal array beams are presented.