Structured light has revolutionized optical particle manipulation, nano-scaled material processing, and high-resolution imaging. In particular, propagation-invariant light fields such as Bessel, Airy, or Mathieu beams show high robustness and have a self-healing nature. To generalize such beneficial features, these light fields can be understood in terms of caustics. However, only simple caustics have found applications in material processing, optical trapping, or cell microscopy. Thus, these technologies would greatly benefit from methods to engineer arbitrary intensity shapes well beyond the standard families of caustics. We introduce a general approach to arbitrarily shape propagation-invariant beams by smart beam design based on caustics. We develop two complementary methods, and demonstrate various propagation-invariant beams experimentally, ranging from simple geometric shapes to complex image configurations such as words. Our approach generalizes caustic light from the currently known small subset to a complete set of tailored propagation-invariant caustics with intensities concentrated around any desired curve.
We experimentally realize higher-order catastrophic structures in light fields presenting solutions of the paraxial diffraction catastrophe integral. They are determined by potential functions whose singular mapping manifests as caustic hypersurfaces in control parameter space. By addressing different cross-sections in the higher-dimensional control parameter space, we embed swallowtail and butterfly catastrophes with varying caustic structures in the lower-dimensional transverse field distribution. We systematically analyze these caustics analytically and observe their field distributions experimentally in real and Fourier space. Their spectra can be described by polynomials or expressions with rational exponents capable to form a cusp.
Perturbing the external control parameters of nonlinear systems leads to dramatic changes of its bifurcations. A branch of singular theory, the catastrophe theory, analyses the generating function that depends on state and control parameters. It predicts the formation of bifurcations as geometrically stable structures and categorizes them hierarchically. We evaluate the catastrophe diffraction integral with respect to two-dimensional cross-sections through the control parameter space and thus transfer these bifurcations to optics, where they manifest as caustics in transverse light fields. For all optical catastrophes that depend on a single state parameter, we analytically derive a universal expression for the propagation of all corresponding caustic beams. We reveal that the dynamics of the resulting caustics can be expressed by higher-order optical catastrophes. We show analytically and experimentally that particular swallowtail beams dynamically transform to higher-order butterfly caustics, whereas other swallowtail beams decay to lower-order cusp catastrophes.
A broad class of photonic refractive index structures, ranging from high regularity [34] to complete randomness, [35] has been demonstrated using optical induction. In order to access the field of deterministic aperiodic structures, recently an approach based on Bessel beams as single site optical induction entities for 2D nondiffracting lattices has been suggested. [36] Here, we present novel extensions to this established technique that enable the fabrication of helical photonic structures realized as twisted 3D refractive index modulations.In order to cross-link chiral light fields with helical photonic structures and to investigate their mutual interplay, we propose the approach illustrated in Figure 1: Twisted waveguide arrays are inscribed in a photosensitive material and subsequently probed by two discrete vortices carrying optical OAM of opposed topological charge, leading to distinctive output states. By choosing four waveguides and perfectly matching discrete vortices, this system represents a fundamental realization of chiral light fields in helical photonic lattices.In this paper, we report on the creation of 3D modulated intensity distributions and their application for the optical induction of helical structures. Due to the nonlinear formation of the induced photonic structure, we present a novel extension of the numerical simulations that is of prime importance toThe propagation of chiral light in optically induced helical photonic waveguide arrays is investigated. Manifested in their chiral interaction, the system's selectivity to optical orbital angular momentum is demonstrated. In order to realize twisted refractive index waveguide arrays, 3D modulated light fields are tailored to nonlinearly inscribe these helical waveguides in photosensitive material. Additionally, it is shown that this functional system provides controllable output states by optically changing the waveguides' potential depths or the nonlinearity's sign.
Controlling artificial Pearcey and swallowtail beams allows realizing caustic lattices in nonlinear photosensitive media at very low light intensities. We examine their functionality as 2D and 3D waveguiding structures, and show the potential of exploiting these lattices as a linear beam splitter, which we name a Pearcey-Y-splitter. For symmetrized Pearcey beams as auto-focusing beams, the formation of solitons in focusing nonlinearity is observed. Our original approach represents the first realization of caustic photonic lattices and can directly be applied in signal processing, microscopy and material lithography.
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