Phase retrieval algorithm applied to high-energy ultrafast lasers.

A standardized phase retrieval algorithm is presented and applied to an industry-grade high-energy ultrashort pulsed laser to uncover its spatial phase distribution. We describe in detail how to modify the well-known algorithm in order to characterize particularly strong light sources from intensity measurements only. With complete information about the optical field of the unknown light source at hand, virtual back propagation can reveal weak points in the light path such as apertures or damaged components.

Dynamic focus shaping with mixed-aperture coherent beam combining.

A novel concept for dynamic focus shaping based on highly efficient coherent beam combining with micro-lens arrays (MLAs) as the combining element is presented. This concept allows us to control the power weights of diffraction orders by varying the absolute phases of an array of input beams. A proof-of-principle experiment is supported by simulations. For this, an input beam matrix of 5×5 beams is combined proving both the ability for further power scaling and dynamic focus shaping.

Coherent beam combining with micro-lens arrays.

A novel, to the best of our knowledge, concept for coherent beam combining is presented based on a simple setup with micro-lens arrays. These standard components are used in a proof-of-principle experiment for both coherent beam splitting and a combination of 5×5 beams. Here a combination efficiency above 90% is achieved. We call this novel concept "mixed aperture."

Focal field analysis of highly multi-mode fiber beams based on modal decomposition.

In this work, a numerical modal decomposition approach is applied to model the optical field of laser light after propagating through a highly multi-mode fiber. The algorithm for the decomposition is based on the reconstruction of measured intensity profiles along the laser beam caustic with consideration of intermodal degrees of coherence derived from spectral analysis. To enhance the accuracy of the model, different approaches and strategies are applied and discussed. The presented decomposition into a set of linearly polarized modes enables both the wave-optical simulation of radiation transport by highly multi-mode fibers and, additionally, the analysis of free-space propagation with arbitrarily modified complex amplitude distributions.

Facilitated glass separation by asymmetric Bessel-like beams.

The modification of transparent materials is enabled by focused ultrashort laser pulses. Single pass processing up to several millimeters can be achieved by the usage of elongated beam profiles. We studied the mechanical separability in dependence of the material thickness. As simulations show, asymmetric beam profiles can cause modifications with preferential direction reducing the necessary breaking force. Pump-probe microscopy is implemented to examine the laser-matter-interaction. We present a measured 3D-reconstruction of the transient interaction inside the material and elucidate the desired crack formation. We demonstrate beam shaping concepts to create a new, efficient and robust class of Bessel-like beams, which can be used to achieve a preferred crack direction. We verify the concept by modification and separation of silicate glasses.

High-quality tailored-edge cleaving using aberration-corrected Bessel-like beams.

We report on the usage of ultrashort laser pulses in the form of aberration-corrected Bessel-like beams for laser cutting of glass with bevels. Our approach foresees inclining the material's entrance surface with respect to the processing optics. The detailed analysis of phase distortions caused by the beam transition through the tilted glass surface allows precompensating for occurring aberrations using digital holography. We verify theoretical considerations by means of pump-probe microscopy and present high-quality edges in nonstrengthened silicate glass.

Time-resolved tomography of ultrafast laser-matter interaction.

We demonstrate time-resolved tomography with 200 fs resolution for the three-dimensional analysis of the non-linear dynamics of ultrafast laser-matter interaction inside the volume of transparent materials. We reconstruct as an example the three-dimensional spatial distribution of the transient extinction coefficient induced by focusing higher-order Bessel-Gaussian-beams into Gorilla glass. This approach can be employed to gaseous, liquid and transparent solid state matter which interact with laser light.

Mode-resolved gain analysis and lasing in multi-supermode multi-core fiber laser.

Multi-core fibers (MCFs) with coupled-cores are attractive large-mode area (LMA) specialty fiber designs that support the propagation of a few transverse modes often called supermodes (SMs). Compared to other LMA fibers, the uniqueness of MCF arises from the higher degrees of design space offered by a multitude of core-array geometries, resulting in extended flexibility to tailor SM properties. To date, the use of MCF as gain media has focused on lasers that operate in only one selected SM, typically the lowest order in-phase SM, which considerably limited the potential of these multi-core structures. Here, we expand the potential of MCF lasers by investigating multi-SM amplification and lasing schemes. Amplifier and laser systems using a 7 coupled-cores Yb-doped MCF as gain medium were successfully designed and assembled. Individual SM could be decomposed using the correlation filter technique mode analysis and the modal amplification factors (γi) were recorded. With access to amplification characteristics of individual transverse modes, a monolithic MCF laser was demonstrated that operates simultaneously on the two SMs carrying the highest optical gain.

Comparative analysis of numerical methods for the mode analysis of laser beams.

We present a comparative study of four numerical methods to detect the mode content of a laser beam from, at most, two intensity images. The techniques are compared regarding temporal effort, stability, and accuracy, using the example of three multimode optical fibers that differ in the number of supported modes.

Measurement of higher-order mode propagation losses in effectively single mode fibers.

We present a direct and nondestructive measurement of the propagation loss of higher-order modes (HOMs) in effectively single-mode fibers. Lossy HOMs are excited by applying local stress at various points alongside a straight single mode fiber. The change of the HOM power as a function of the propagation distance is recorded at the fiber end by performing a modal decomposition with a correlation filter. The results for the HOM propagation loss are compared to simulations yielding very good agreement.

Modal characterization of fiber-to-fiber coupling processes.

We present a detailed experimental investigation of a fiber-to-fiber coupling process by characterizing the mode content at the output of the system. In our experiment a single-mode fiber is transversally scanned with respect to a multimode fiber, revealing position-dependent higher-order mode excitation. The outlined measurement system can be used for automated optimization of fundamental mode content and beam quality. Additionally, our approach characterizes the modal transmission properties of the multimode waveguide in its present state and is hence of high relevance for the conception of transport fibers and fiber laser systems.

Reconstruction of laser beam wavefronts based on mode analysis.

We present the reconstruction of a laser beam wavefront from its mode spectrum and investigate in detail the impact of distinct aberrations on the mode composition. The measurement principle is presented on a Gaussian beam that is intentionally distorted by displaying defined aberrations on a spatial light modulator. The comparison of reconstructed and programmed wavefront aberrations yields excellent agreement, proving the high measurement fidelity.

Mode resolved bend loss in few-mode optical fibers.

We present a novel approach to directly measure the bend loss of individual modes in few-mode fibers based on the correlation filter technique. This technique benefits from a computer-generated hologram performing a modal decomposition, yielding the optical power of all propagating modes in the bent fiber. Results are compared with rigorous loss simulations and with common loss formulas for step-index fibers revealing high measurement fidelity. To the best of our knowledge, we demonstrate for the first time an experimental loss discrimination between index-degenerated modes.

Beam-quality measurements using a spatial light modulator.

We present a fast and easy technique for measuring the beam propagation ratio, M(2), of laser beams using a spatial light modulator. Our technique is based on digitally simulating the free-space propagation of light, thus eliminating the need for the traditional scan in the propagation direction. We illustrate two approaches to achieving this, neither of which requires any information of the laser beam under investigation nor necessitates any moving optical components. The comparison with theoretical predictions reveals excellent agreement and proves the accuracy of the technique.

Wavefront reconstruction by modal decomposition.

We propose a new method to determine the wavefront of a laser beam based on modal decomposition by computer-generated holograms. The hologram is encoded with a transmission function suitable for measuring the amplitudes and phases of the modes in real-time. This yields the complete information about the optical field, from which the Poynting vector and the wavefront are deduced. Two different wavefront reconstruction options are outlined: reconstruction from the phase for scalar beams, and reconstruction from the Poynting vector for inhomogeneously polarized beams. Results are compared to Shack-Hartmann measurements that serve as a reference and are shown to reproduce the wavefront and phase with very high fidelity.

Mode analysis with a spatial light modulator as a correlation filter.

A procedure for the real-time analysis of laser modes using a phase-only spatial light modulator is outlined. The procedure involves encoding into digital holograms by complex amplitude modulation a set of orthonormal basis functions into which the initial field is decomposed. This approach allows any function to be encoded and refreshed in real time (60 Hz). We implement a decomposition of guided modes propagating in optical fibers and show that we can successfully reconstruct the observed field with very high fidelity.

Fast M2 measurement for fiber beams based on modal analysis.

We report on a fast and experimentally easy technique for measuring the beam propagation ratio M(2) of light guided by optical fibers. A holographic filter enables us to determine amplitudes and phases of the excited fiber eigenmodes. The coherent superposition of modes allows the reconstruction of the optical field. With this information at hand, we are able to simulate the free-space propagation of the beam and to perform a virtual caustic measurement. Associated beam propagation ratios M(2) accurately agree with ISO-standard measurements.

Real-time determination of laser beam quality by modal decomposition.

We present a real-time method to determine the beam propagation ratio M2 of laser beams. The all-optical measurement of modal amplitudes yields M2 parameters conform to the ISO standard method. The experimental technique is simple and fast, which allows to investigate laser beams under conditions inaccessible to other methods.

Measuring the spatial polarization distribution of multimode beams emerging from passive step-index large-mode-area fibers.

We measure the polarization state of each guided transversal mode propagating in step-index large-mode-area fibers (V≈4) using a correlation-filter based measurement technique in combination with a Stokes parameter measurement. The entire emerging beam, expressed in terms of a phase-dependent superposition of linearly polarized modes, demonstrates spatially varying polarization properties. By knowing the information about modal amplitudes and phase differences, full information about the optical field is available.

Complete modal decomposition for optical fibers using CGH-based correlation filters.

The description of optical fields in terms of their eigenmodes is an intuitive approach for beam characterization. However, there is a lack of unambiguous, pure experimental methods in contrast to numerical phase-retrieval routines, mainly because of the difficulty to characterize the phase structure properly, e.g. if it contains singularities. This paper presents novel results for the complete modal decomposition of optical fields by using computer-generated holographic filters. The suitability of this method is proven by reconstructing various fields emerging from a weakly multi-mode fiber (V approximately 5) with arbitrary mode contents. Advantages of this approach are its mathematical uniqueness and its experimental simplicity. The method constitutes a promising technique for real-time beam characterization, even for singular beam profiles.