Falko Diebel

Airy beam induced optical routing

We present an all-optical routing scheme based simultaneously on optically induced photonic structures and the Airy beam family. The presented work utilizes these accelerating beams for the demonstration of an all-optical router with individually addressable output channels. In addition, we are able to activate multiple channels at the same time providing us with an optically induced splitter with configurable outputs. The experimental results are corroborated by corresponding numerical simulations.

Analysis of transverse Anderson localization in refractive index structures with customized random potential

We present a method to demonstrate Anderson localization in an optically induced randomized potential. By usage of computer controlled spatial light modulators, we are able to implement fully randomized nondiffracting beams of variable structural size in order to control the modulation length (photonic grain size) as well as the depth (disorder strength) of a random potential induced in a photorefractive crystal. In particular, we quantitatively analyze the localization length of light depending on these two parameters and find that they are crucial influencing factors on the propagation behavior leading to variably strong localization. Thus, we corroborate that transverse light localization in a random refractive index landscape strongly depends on the character of the potential, allowing for a flexible regulation of the localization strength by adapting the optical induction configuration.

Soliton formation by decelerating interacting Airy beams

We demonstrate a new type of soliton formation arising from the interaction of multiple two-dimensional Airy beams in a nonlinear medium. While in linear regime, interference effects of two or four spatially displaced Airy beams lead to accelerated intensity structures that can be used for optical induction of novel light guiding refractive index structures, the nonlinear cross-interaction between the Airy beams decelerates their bending and enables the formation of straight propagating solitary states. Our experimental results represent an intriguing combination of two fundamental effects, accelerated optical beams and nonlinearity, together enable novel mechanisms of soliton formation that will find applications in all-optical light localization and switching architectures. Our experimental results are supported by corresponding numerical simulations.

All-optical switching in optically induced nonlinear waveguide couplers

We experimentally demonstrate all-optical vortex switching in nonlinear coupled waveguide arrays optically induced in photorefractive media. Our technique is based on multiplexing of nondiffracting Bessel beams to induce various types of waveguide configurations. Using double- and quadruple-well potentials, we demonstrate precise control over the coupling strength between waveguides, the linear and nonlinear dynamics and symmetry-breaking bifurcations of guided light, and a power-controlled optical vortex switch.

Optical induction scheme for assembling nondiffracting aperiodic Vogel spirals

We introduce an experimental approach to realize aperiodic photonic lattices based on multiplexing of nondiffracting Bessel beams. This holographic optical induction scheme takes advantage of the well localized Bessel beam as a basis to assemble two-dimensional photonic lattices. We present the realization of an optically induced two-dimensional golden-angle Vogel spiral lattice, which belongs to the family of deterministic aperiodic structures. With our technique, a very broad class of photonic refractive index landscapes now becomes accessible to optical induction, which could not be realized with established distributed holographic techniques.

Compact flat band states in optically induced flatland photonic lattices

We realize low-dimensional tight-binding lattices that host flat bands in their dispersion relation and demonstrate the existence of optical compact flat band states. The lattices are resembled by arrays of optical waveguides fabricated by the state-of-the-art spatio-temporal Bessel beam multiplexing optical induction in photorefractive media. We work out the decisive details of the transition from the discrete theory to the real optical system ensuring that the experimental lattices stand up to numerical scrutiny exhibiting well-approximated band structures. Our highly flexible system is a promising candidate for further experimental investigation of theoretically studied disorder effects in flat band lattices.

Controlled soliton formation in tailored Bessel photonic lattices

Azimuthally modulated higher order rotationally symmetric Bessel-like optical patterns were generated by coherent superposition of two co-propagating Bessel beams - either in or out of phase. By changing the distance between the beam centers, a whole variety of transition states can be realized. As one prominent example, a 4-fold symmetry quadrupole-like photonic structure was optically inducted in an SBN crystal and nonlinear beam propagation in such a photonic wave-guiding structure is investigated in both self-focusing and self-defocusing regimes. The proposed device serves as an all-optical 2d 1 × 4 photonic interconnect.

Light localization in optically induced deterministic aperiodic Fibonacci lattices

As light localization becomes increasingly pronounced in photonic systems with less order, we investigate optically induced two-dimensional Fibonacci structures which are supposed to be amongst the most ordered realizations of deterministic aperiodic patterns. For the generation of corresponding refractive index structures, we implement a recently developed incremental induction method using nondiffracting Bessel beams as waveguide formation entities. Even though Fibonacci structures present slightly reduced order, we show that transverse light transport is significantly hampered here in comparison with periodic lattices that account for discrete diffraction. Our experimental findings are supported by numerical simulations that additionally illustrate a development of transverse light localization for increasing propagation distance.

Dynamics of the optical swallowtail catastrophe

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.

Design and fabrication of two-dimensional deterministic aperiodic photonic lattices by optical induction

Light propagation in structured photonic media covers many fascinating wave phenomena resulting from the band structure of the underlying lattice. Recently, the focus turned towards deterministic aperiodic structures exhibiting distinctive band gap properties. To experimentally study these effects, optical induction of photonic refractive index landscapes turned out to be the method of choice to fabricate these structures. In this contribution, we present a paradigm change of photonic lattice design by introducing a holographic optical induction method based on pixel-like spatially multiplexed single-site nondiffracting Bessel beams. This technique allows realizing a huge class of two-dimensional photonic structures, including deterministic aperiodic golden-angle Vogel spirals, as well as Fibonacci lattices.