Microsphere kinematics from the polarization of tightly focused nonseparable light

Stefan Berg-Johansen, Martin Neugebauer, Andrea Aiello, Gerd Leuchs, Peter Banzer, Christoph Marquardt

Recently, it was shown that vector beams can be utilized for fast kinematic sensing via measurements of their global polarization state [Optica 2(10), 864 (2015)]. The method relies on correlations between the spatial and polarization degrees of freedom of the illuminating field which result from its nonseparable mode structure. Here, we extend the method to the nonparaxial regime. We study experimentally and theoretically the far-field polarization state generated by the scattering of a dielectric microsphere in a tightly focused vector beam as a function of the particle position. Using polarization measurements only, we<br>demonstrate position sensing of a Mie particle in three dimensions. Our work extends the concept of back focal plane interferometry and highlights the potential of polarization analysis in optical tweezers employing structured light.<br>

Polarization of Light: In Classical, Quantum, and Nonlinear Optics

Maria V. Chekhova, Peter Banzer

This book starts with the description of polarization in classical optics, including also a chapter on crystal optics, which is necessary to understand the use of nonlinear crystals. In addition, spatially non-uniform polarization states are introduced and described. Further, the role of polarization in nonlinear optics is discussed. The final chapters are devoted to the description and applications of polarization in quantum optics and quantum technologies.

Transverse spinning of unpolarized light

Jörg Eismann, L.H Nicholls, D. J. Roth, M. A. Alonso, Peter Banzer, F. J. Rodríguez-Fortuño, A. V. Zayats, F. Nori, K. Y. Bliokh

It is well known that spin angular momentum of light, and therefore that of<br>photons, is directly related to their circular polarization. Naturally, for<br>totally unpolarized light, polarization is undefined and the spin vanishes.<br>However, for nonparaxial light, the recently discovered transverse spin<br>component, orthogonal to the main propagation direction, is largely independent<br>of the polarization state of the wave. Here we demonstrate, both theoretically<br>and experimentally, that this transverse spin survives even in nonparaxial<br>fields (e.g., tightly focused or evanescent) generated from a totally<br>unpolarized light source. This counterintuitive phenomenon is closely related<br>to the fundamental difference between the degrees of polarization for 2D<br>paraxial and 3D nonparaxial fields. Our results open an avenue for studies of<br>spin-related phenomena and optical manipulation using unpolarized light.<br>

Toward a Corrected Knife-Edge-Based Reconstruction of Tightly Focused Higher Order Beams

Sergejus Orlovas, Christian Huber, Pavel Marchenko, Peter Banzer, Gerd Leuchs

The knife-edge method is an established technique for profiling of even tightly focused light beams. However, the straightforward implementation of this method fails if the materials and geometry of the knife-edges are not chosen carefully or, in particular, if knife-edges are used that are made of pure materials. Artifacts are introduced in these cases in the shape and position of the reconstructed beam profile due to the interaction of the light beam under study with the knife. Hence, corrections to the standard knife-edge evaluation method are required. Here we investigate the knife-edge method for highly focused radially and azimuthally polarized beams and their linearly polarized constituents. We introduce relative shifts for those constituents and report on the consistency with the case of a linearly polarized fundamental Gaussian beam. An adapted knife-edge reconstruction technique is presented and proof-of-concept tests are shown, demonstrating the reconstruction of beam profiles.

Ultrafast spinning twisted ribbons of confined electric fields

Thomas Bauer, Svetlana N. Khonina, Ilya Golub, Gerd Leuchs, Peter Banzer

Topological properties of light attract tremendous attention in the optics communities and beyond. For instance, light beams gain robustness against certain deformations when carrying topological features, enabling intriguing applications. We report on the observation of a topological structure contained in an optical beam, i.e., a twisted ribbon formed by the electric field vector per se, in stark contrast to recently reported studies dealing with topological structures based on the distribution of the time averaged polarization ellipse. Moreover, our ribbons are spinning in time at a frequency given by the optical frequency divided by the total angular momentum of the incoming beam. The number of full twists of the ribbon is equal to the orbital angular momentum of the longitudinal component of the employed light beam upon tight focusing, which is a direct consequence of spin-to-orbit coupling. We study this angular-momentum-transfer-assisted generation of the twisted ribbon structures theoretically and experimentally for tightly focused circularly polarized beams of different vorticity, paving the way to tailored topologically robust excitations of novel coherent light–matter states.

Toward High‐Speed Nanoscopic Particle Tracking via Time‐Resolved Detection of Directional Scattering

Paul Beck, Martin Neugebauer, Peter Banzer

Owing to their immediate relevance for high precision position sensors, a variety of different sub‐wavelength localization techniques has been developed in the past decades. However, many of these techniques suffer from low temporal resolution or require expensive detectors. Here, a method is presented that is based on the ultrafast detection of directionally scattered light with a quadrant photodetector operating at a large bandwidth, which exceeds the speed of most cameras. The directionality emerges due to the position dependent tailored excitation of a high‐refractive index nanoparticle with a tightly focused vector beam. A spatial resolution of 1.1nm and a temporal resolution of 8kHz is reached experimentally, which is not a fundamental but rather a technical limit. The detection scheme enables real‐time particle tracking and sample stabilization in many optical setups sensitive to drifts and vibrations.

Hybrid Orthorhombic Carbon Flakes Intercalated with Bimetallic Au-Ag Nanoclusters: Influence of Synthesis Parameters on Optical Properties

Muhammad Abdullah Butt, Daria Mamonova, Yuri Petrov, Alexandra Proklova, Ilya Kritchenkov, Alina Manshina, Peter Banzer, Gerd Leuchs

Until recently, planar carbonaceous structures such as graphene did not show any birefringence under normal incidence. In contrast, a recently reported novel orthorhombic carbonaceous structure with metal nanoparticle inclusions does show intrinsic birefringence, outperforming other natural orthorhombic crystalline materials. These flake-like structures self-assemble during a laser-induced growth process. In this article, we explore the potential of this novel material and the design freedom during production. We study in particular the dependence of the optical and geometrical properties of these hybrid carbon-metal flakes on the fabrication parameters. The influence of the laser irradiation time, concentration of the supramolecular complex in the solution, and an external electric field applied during the growth process are investigated. In all cases, the self-assembled metamaterial exhibits a strong linear birefringence in the visible spectral range, while the wavelength-dependent attenuation was found to hinge on the concentration of the supramolecular complex in the solution. By varying the fabrication parameters one can steer the shape and size of the flakes. This study provides a route towards fabrication of novel hybrid carbon-metal flakes with tailored optical and geometrical properties.

Towards fully integrated photonic displacement sensors

Ankan Bag, Martin Neugebauer, Uwe Mick, Sillke Christiansen, Sebastian A Schulz, Peter Banzer

The field of optical metrology with its high precision position, rotation and wavefront sensors represents the basis for lithography and high resolution microscopy. However, the on-chip integration - a task highly relevant for future nanotechnological devices - necessitates the reduction of the spatial footprint of sensing schemes by the deployment of novel concepts. A promising route towards this goal is predicated on the controllable directional emission of the fundamentally smallest emitters of light, i.e. dipoles, as an indicator. Here we realize an integrated displacement sensor based on the directional emission of Huygens dipoles excited in an individual dipolar antenna. The position of the antenna relative to the excitation field determines its directional coupling into a six-way crossing of photonic crystal waveguides. In our experimental study supported by theoretical calculations, we demonstrate the first prototype of an integrated displacement sensor with a standard deviation of the position accuracy below λ/300 at room temperature and ambient conditions.

Chiral Surface Lattice Resonances

Eric S. A. Goerlitzer, Reza Mohammadi, Sergey Nechayev, Kirsten Volk, Marcel Rey, Peter Banzer, Matthias Karg, Nicolas Vogel

Towards Polarization-based Excitation Tailoring for Extended Raman Spectroscopy

Simon Grosche, Richard Hünermann, George Sarau, Silke Christiansen, Robert W. Boyd, Gerd Leuchs, Peter Banzer

Undoubtedly, Raman spectroscopy is one of the most elaborated spectroscopy tools in materials science, chemistry, medicine and optics. However, when it comes to the analysis of nanostructured specimens, <br> accessing the Raman spectra resulting from an exciting electric field component oriented perpendicularly to the substrate plane is a difficult task and conventionally can only be achieved by mechanically tilting the sample, or by sophisticated sample preparation.<br>Here, we propose a novel experimental method based on the utilization of polarization tailored light for Raman spectroscopy of individual nanostructures. As a proof of principle, we create three-dimensional electromagnetic field distributions at the nanoscale using tightly focused cylindrical vector beams impinging normally onto the specimen, hence keeping<br>the conventional beam-path of commercial Raman systems. Using this excitation<br>scheme, we experimentally show that the recorded Raman spectra of individual<br>gallium-nitride nanostructures of sub-wavelength diameter used as a test<br>platform depend sensitively on their location relative to the focal vector field. The observed Raman spectra can be attributed to the interaction with transverse or longitudinal electric field components. This novel technique may pave the way towards a characterization of Raman active nanosystems using full information of all Raman modes.

Shaping Field Gradients for Nanolocalization

Sergey Nechayev, Jörg Eismann, Martin Neugebauer, Peter Banzer

Deep sub-wavelength localization and displacement sensing of optical nanoantennas have emerged as extensively pursued objectives in nanometrology, where focused beams serve as high-precision optical rulers while the scattered light provides an optical readout. Here, we show that in these schemes using an optical excitation as a position gauge implies that the sensitivity to displacements of a nanoantenna depends on the spatial gradients of the excitation field. Specifically, we explore one of such novel localization schemes based on appearance of transversely spinning fields in strongly confined optical beams, resulting in far-field segmentation of left- and right-hand circular polarizations of the scattered light, an effect known as the giant spin-Hall effect of light. We construct vector beams with augmented transverse spin density gradient in the focal plane and experimentally confirm enhanced sensitivity of the far-field spin-segmentation to lateral displacements of an electric-dipole nanoantenna. We conclude that sculpturing of electromagnetic field gradients and intelligent design of scatterers pave the way towards future improvements in displacement sensitivity.

Spin-orbit coupling affecting the evolution of transverse spin

Jörg Eismann, Peter Banzer, Martin Neugebauer

We investigate the evolution of transverse spin in tightly focused circularly polarized beams of light, where spin-orbit coupling causes a local rotation of the polarization ellipses upon propagation through the focal volume. The effect can be explained as a relative Gouy-phase shift between the circularly polarized transverse field and the longitudinal field carrying orbital angular momentum. The corresponding rotation of the electric transverse spin density is observed experimentally by utilizing a recently developed reconstruction scheme, which relies on transverse-spin-dependent directional scattering of a nano-probe.

Interaction of light carrying orbital angular momentum with a chiral dipolar scatterer

Pawel Wozniak, Israel De León, Katja Höflich, Gerd Leuchs, Peter Banzer

The capability to distinguish the handedness of circularly polarized light is a well-known intrinsic property of a chiral nanostructure. It is a long-standing controversial debate, however, whether a chiral object can also sense the vorticity, or the orbital angular momentum (OAM), of a light field. Since OAM is a non-local property, it seems rather counter-intuitive that a point-like chiral object could be able to distinguish the sense of the wave-front of light carrying OAM. Here, we show that a dipolar chiral nanostructure is indeed capable of distinguishing the sign of the phase vortex of the incoming light beam. To this end, we take advantage of the conversion of the sign of OAM, carried by a linearly polarized Laguerre-Gaussian beam, into the sign of optical chirality upon tight focusing. Our study provides for a deeper insight into the discussion of chiral light-matter interactions and the respective role of OAM.

Emission of circularly polarized light by a linear dipole

Martin Neugebauer, Peter Banzer, Sergey Nechayev

Controlling the polarization state and the propagation direction of photons is a fundamental prerequisite for many nanophotonic devices and a precursor for future on-chip communication, where the emission properties of individual emitters are particularly relevant. Here, we report on the emission of partially circularly polarized photons by a linear dipole. The underlying effect is linked to the near-field part of the angular spectrum of the dipole, and it occurs in any type of linear dipole emitter, ranging from atoms and quantum dots to molecules and dipole-like antennas. We experimentally observe it by near-field to far-field transformation at a planar dielectric interface and numerically demonstrate the utility of this phenomenon by coupling the circularly polarized light to the individual paths of crossing waveguides.

Vectorial vortex generation and phase singularities upon Brewster reflection

Rene Barczyk, Sergey Nechayev, Muhammad Abdullah Butt, Gerd Leuchs, Peter Banzer

We experimentally demonstrate the emergence of a purely azimuthally polarized vectorial vortex beam with a phase singularity upon Brewster reflection of focused circularly polarized light from a dielectric substrate. The effect originates from the polarizing properties of the Fresnel reflection coefficients described in Brewster’s law. An astonishing consequence of this effect is that the reflected<br>field’s Cartesian components acquire local phase singularities at Brewster’s angle. Our observations are crucial for polarization microscopy and open new avenues for the generation of exotic states of light based on spin-to-orbit coupling, without the need for sophisticated optical elements.

Experimental demonstration of linear and spinning Janus dipoles for polarisation and wavelength selective near-field coupling

M. F. Picardi, Martin Neugebauer, Jörg Eismann, Gerd Leuchs, Peter Banzer, F. J. Rodriguez-Fortuno, A. V. Zayats

The electromagnetic field scattered by nano-objects contains a broad range of wave vectors and can be efficiently coupled to waveguided modes. The dominant ontribution to scattering from subwavelength dielectric and plasmonic nanoparticles is determined by electric and magnetic dipolar<br>responses. Here, we experimentally demonstrate spectral and phase selective excitation of Janus dipoles, sources with electric and magnetic dipoles oscillating out of phase, in order to control near-field interference and directional coupling to waveguides. We show that by controlling the<br>polarisation state of the dipolar excitations and the excitation wavelength to adjust their relative contributions, directionality and coupling strength can be fully tuned. Furthermore, we introduce a novel spinning Janus dipole featuring cylindrical symmetry in the near and far field, which results in either omnidirectional coupling or noncoupling. Controlling the propagation of guided light waves via fast and robust near-field <br> interference between polarisation components of a source is required in many applications in nanophotonics and quantum optics.

Mimicking Chiral Light-Matter Interaction

Sergey Nechayev, Peter Banzer

We demonstrate that electric-dipole scatterers can mimic chiral light-matter interaction by generating far-field circular polarization upon scattering, even though the optical chirality of the incident field as well as that of the scattered light is zero. The presented effect originates from the fact that electric-dipole scatterers respond selectively only to the incident electric field, which eventually results in depolarization of the transmitted beam and in generation of far-field circular polarization. To experimentally demonstrate this effect we utilize a cylindrical vector beam with spiral polarization and a spherical gold nanoparticle positioned on the optical axis -- the axis of rotational symmetry of the system. Our experiment and a simple theoretical model address the fundamentals of duality symmetry in optics and chiral light-matter interactions, accentuating their richness and ubiquity yet in highly symmetric configurations.

Large-Area 3D Plasmonic Crescents with Tunable Chirality

Eric S. A. Goerlitzer, Reza Mohammadi, Sergey Nechayev, Peter Banzer, Nicolas Vogel

Abstract Chiral plasmonic nanostructures hold promise for enhanced chiral sensing and circular dichroism spectroscopy of chiral molecules. It is therefore of interest to fabricate chiral plasmonic nanostructures with tailored chiroptical properties over large areas with reasonable effort. Here, a colloidal lithography approach is used to produce macroscopic arrays of sub-micrometer 3D chiral plasmonic crescent structures over areas >1 cm2. The chirality originates from symmetry breaking by the introduction of a step within the crescent structure. This step is produced by an intermediate layer of silicon dioxide onto which the metal crescent structure is deposited. It is experimentally demonstrated that the chiroptical properties in such structures can be tailored by changing the position of the step within the crescent. These experiments are complemented by finite element simulations and the application of a multipole expansion to elucidate the physical origin of the circular dichroism of the crescent structures.

Multi-twist polarization ribbon topologies in highly-confined optical fields

Thomas Bauer, Peter Banzer, Frédéric Bouchard, Sergej Orlov, Lorenzo Marrucci, Enrico Santamato, Robert W Boyd, Ebrahim Karimi, Gerd Leuchs

Electromagnetic plane waves, solutions to Maxwell's equations, are said to be 'transverse' in vacuum. Namely, the waves' oscillatory electric and magnetic fields are confined within a plane transverse to the waves' propagation direction. Under tight-focusing conditions however, the field can exhibit longitudinal electric or magnetic components, transverse spin angular momentum, or non-trivial topologies such as Möbius strips. Here, we show that when a suitably spatially structured beam is tightly focused, a 3-dimensional polarization topology in the form of a ribbon with two full twists appears in the focal volume. We study experimentally the stability and dynamics of the observed polarization ribbon by exploring its topological structure for various radii upon focusing and for different propagation planes.

Substrate-Induced Chirality in an Individual Nanostructure

Sergey Nechayev, Rene Barczyk, Uwe Mick, Peter Banzer

We experimentally investigate the chiral optical response of an individual nanostructure consisting of three equally sized spherical nanoparticles made of different materials and arranged in \ang{90} bent geometry. Placing the nanostructure on a substrate converts its morphology from achiral to chiral. Chirality leads to pronounced differential extinction, i.e., circular dichroism and optical rotation, or equivalently, circular birefringence, which would be strictly forbidden in the absence of a substrate or heterogeneity. This first experimental observation of the substrate-induced break of symmetry in an individual heterogeneous nanostructure sheds new light on chiral light-matter interactions at substrate-nanostructure interfaces.

Investigating the Optical Properties of a Laser Induced 3D Self‐Assembled Carbon–Metal Hybrid Structure

Muhammad Abdullah Butt, Antonino Calà Lesina, Martin Neugebauer, Thomas Bauer, Lora Ramunno, Alessandro Vaccari, Pierre Berini, Yuriy Petrov, Denis Danilov, et al.

Carbon‐based and carbon–metal hybrid materials hold great potential for applications in optics and electronics. Here, a novel material made of carbon and gold–silver nanoparticles is discussed, fabricated using a laser‐induced self‐assembly process. This self‐assembled metamaterial manifests itself in the form of cuboids with lateral dimensions on the order of several micrometers and a height of tens to hundreds of nanometers. The carbon atoms are arranged following an orthorhombic unit cell, with alloy nanoparticles intercalated in the crystalline carbon matrix. The optical properties of this metamaterial are analyzed experimentally using a microscopic Müller matrix measurement approach and reveal a high linear birefringence across the visible spectral range. Theoretical modeling based on local‐field theory applied to the carbon matrix links the birefringence to the orthorhombic unit cell, while finite‐difference time‐domain simulations of the metamaterial relates the observed optical response to the distribution of the alloy nanoparticles and the optical density of the carbon matrix.

Huygens' Dipole for Polarization-Controlled Nanoscale Light Routing

Sergey Nechayev, Jörg Eismann, Martin Neugebauer, Pawel Wozniak, Ankan Bag, Gerd Leuchs, Peter Banzer

Structured illumination allows for satisfying the first Kerker condition of in-phase perpendicular electric and magnetic dipole moments in any isotropic scatterer that supports electric and magnetic dipolar resonances. The induced Huygens' dipole may be utilized for unidirectional coupling to waveguide modes that propagate transverse to the excitation beam. We study two <br> configurations of a Huygens' dipole -- longitudinal electric and transverse magnetic dipole moments or vice versa. We experimentally show that only the radially polarized emission of the first and azimuthally polarized emission of the second configuration are directional in the far-field. This polarization selectivity implies that directional excitation of either TM or TE waveguide modes is possible. Applying this concept to a single nanoantenna excited with structured light, we are able to experimentally achieve scattering directivities of around 23 dB and 18 dB in TM and TE modes, respectively. This strong directivity paves the way for tunable polarization-controlled nanoscale light routing and applications in optical metrology, <br> ocalization microscopy and on-chip optical devices.

Orbital-to-Spin Angular Momentum Conversion Employing Local Helicity

Sergey Nechayev, Jörg Eismann, Gerd Leuchs, Peter Banzer

Spin-orbit interactions in optics traditionally describe an influence of the polarization degree of freedom of light on its spatial properties. The most prominent example is the generation of a spin-dependent optical vortex upon focusing or scattering of a circularly polarized plane-wave by a nanoparticle, converting spin to orbital angular momentum of light. Here, we present a mechanism of conversion of orbital-to-spin angular momentum of light upon scattering of a linearly polarized vortex beam by a spherical silicon nanoparticle. We show that focused linearly polarized Laguerre-Gaussian beams of first order (ℓ=±1) exhibit an ℓ-dependent spatial distribution of helicity density in the focal volume. By using a dipolar scatterer the helicity density can be manipulated locally, while influencing globally the spin and orbital angular momentum of the beam. Specifically, the scattered light can be purely circularly polarized with the handedness depending on the orbital angular momentum of the incident beam. We corroborate our findings with theoretical calculations and an experimental demonstration. Our work sheds new light on the global and local properties of helicity conservation laws in electromagnetism.

Weak measurement enhanced spin Hall effect of light for particle displacement sensing

Martin Neugebauer, Sergey Nechayev, Martin Vorndran, Gerd Leuchs, Peter Banzer

A spherical nanoparticle can scatter tightly focused optical beams in a spin-segmented manner, meaning that the far field of the scattered light exhibits laterally separated left- and right-handed circularly polarized components. This effect, commonly referred to as giant spin Hall effect of light, strongly depends on the position of the scatterer in the focal volume. Here, a scheme that utilizes an optical weak measurement in a cylindrical polarization basis is put forward to drastically enhance the spin-segmentation and, therefore, the sensitivity to small displacements of a scatterer. In particular, we experimentally achieve a change of the spin-splitting signal of 5% per nanometer displacement.

Weak measurement of elliptical dipole moments by C point splitting

Sergey Nechayev, Martin Neugebauer, Martin Vorndran, Gerd Leuchs, Peter Banzer

We investigate points of circular polarization in the far field of elliptically polarized dipoles and establish a relation between the angular position and helicity of these C points and the dipole moment. In the case of highly eccentric dipoles, the C points of opposite handedness exhibit only a small angular separation and occur in the low intensity region of the emission pattern. In this regard, we introduce an optical weak measurement approach that utilizes the transverse electric (azimuthal) and transverse magnetic (radial) far-eld polarization basis. Projecting the far field<br>onto a spatially varying post-selected polarization state reveals the angular separation and the helicity of the C points. We demonstrate the applicability of this approach and determine the elliptical dipole moment of a particle sitting on an interface by measuring the C points in its far field.

Transverse Kerker Scattering for Ångström Localization of Nanoparticles

Ankan Bag, Martin Neugebauer, Pawel Wozniak, Gerd Leuchs, Peter Banzer

Angstrom precision localization of a single nanoantenna is a crucial step towards advanced nanometrology, medicine and biophysics. Here, we show that single nanoantenna displacements<br>down to few Angstroms can be resolved with sub-Angstrom precision using an all-optical method.<br>We utilize the tranverse Kerker scattering scheme where a carefully structured light beam excites a combination of multipolar modes inside a dielectric nanoantenna, which then upon interference, scatters directionally into the far-field. We spectrally tune our scheme such that it is most sensitive<br>to the change in directional scattering per nanoantenna displacement. Finally, we experimentally show that antenna displacement down to 3 A˚ is resolvable with a localization precision of 0.6 A˚.

Exciting a chiral dipole moment in an achiral nanostructure

Jörg S. Eismann, Martin Neugebauer, Peter Banzer

Controlling the electric and magnetic dipole moments of optical nanostructures is a fundamental prerequisite for light routing and polarization multiplexing at the nanoscale. A versatile approach for inducing tailored dipole moments is structured illumination. Here, we discuss the excitation of a chiral dipole moment in an achiral silicon nanoparticle. In particular, we make use of the electric and magnetic polarizabilities of the silicon nanoparticle to coherently excite a superposition of parallel electric and magnetic dipole moments phase-shifted by +/-pi/2, which resembles the fundamental mode of a three-dimensional chiral nanostructure. We demonstrate the wavelength dependence of the excitation scheme and measure the spin and orbital angular momenta in the emission of the induced chiral dipole moments. Our results highlight the capabilities of such tunable chiral dipole emitters-not limited by structural properties-as flexible sources of spin-polarized light for nanoscopic devices. (c) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Chirality of Symmetric Resonant Heterostructures

Sergey Nechayev, Pawel Wozniak, Martin Neugebauer, Rene Barczyk, Peter Banzer

Chiroptical effects arising in mirror‐symmetric geometrically achiral resonant heterostructures are investigated. It is shown that coalescence of extrinsic chirality, heterogeneous morphology, and substrate‐induced break of symmetry leads to pronounced circular dichroism and circular birefringence. The physics of the involved phenomena is elucidated by studying spin‐splitting in scattering and hybridized dipolar modes of a heterodimer made of gold and silicon nanoparticles of the same shape and size. The work sheds new light on the optical properties of heterogeneous nanostructures and paves the way for designing polarization‐controlled tunable heterogeneous optical elements.

Chiroptical response of a single plasmonic nanohelix

Pawel Wozniak, Israel De Leon, Katja Hoeflich, Caspar Haverkamp, Silke Christiansen, Gerd Leuchs, Peter Banzer

We investigate the chiroptical response of a single plasmonic nanohelix interacting with a weakly focused circularly polarized Gaussian beam. The optical scattering at the fundamental resonance is characterized experimentally and numerically. The angularly resolved scattering of the excited nanohelix is verified experimentally and it validates the numerical results. We employ a multipole decomposition analysis to study the fundamental and first higher-order resonance of the nanohelix, explaining their chiral properties in terms of the formation of chiral dipoles. (C) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Tailoring multipolar Mie scattering with helicity and angular momentum

Xavier Zambrana-Puyalto, Xavier Vidal, Pawel Wozniak, Peter Banzer, Gabriel Molina-Terriza

Linear scattering processes are usually described as a function of the parameters of the incident beam. The wavelength, the intensity distribution, the polarization or the phase are among them. Here, we discuss and experimentally demonstrate how the angular momentum and the helicity of light influence the light scattering of spherical particles. We measure the backscattering of a 4 μm diameter TiO2 single particle deposited on a glass substrate. The particle is probed at different wavelengths by different beams with total angular momenta ranging from −8 to +8 units. It is observed that the spectral behavior of the particle is highly dependent on the angular momentum and helicity of the incoming beam. While some of the properties of the scattered field can be described with a simple resonator model, the scattering of high angular momentum beams requires a deeper understanding of the multipolar modes induced in the sphere. We observe that tailoring these induced multipolar modes can cause a shift and a spectral narrowing of the peaks of the scattering spectrum. Furthermore, specific combinations of helicity and angular momentum for the excitation lead to differences in the conservation of helicity by the system, which has clear consequences on the scattering pattern.

Magnetic and Electric Transverse Spin Density of Spatially Confined Light

Martin Neugebauer, Jörg Eismann, Thomas Bauer, Peter Banzer

When a beam of light is laterally confined, its field distribution can exhibit points where the local magnetic and electric field vectors spin in a plane containing the propagation direction of the electromagnetic wave. The phenomenon indicates the presence of a nonzero transverse spin density. Here, we experimentally investigate this transverse spin density of both magnetic and electric fields, occurring in highly confined structured fields of light. Our scheme relies on the utilization of a high-re fractiv-indcx e-noperticlc as a lecal field probe, exhibiting magnetic and electric dipole resonances in the visible spectral range. Because of the directional emission of dipole moments that spin around an axis parallel to a nearby dielectric interface, such a probe particle is capable of locally sensing the magnetic and electric transverse spin density of a tightly focused beam impinging under normal incidence with respect to said interface. We exploit the achieved experimental results to emphasize the difference between magnetic and electric transverse spin densities.

Towards an integrated AlGaAs waveguide platform for phase and polarisation shaping

G Maltese, Y Halioua, A Lemaitre, C Gomez-Carbonell, E Karimi, Peter Banzer, S Ducci

We propose, design and fabricate an on-chip AlGaAs waveguide capable of generating a controlled phase delay of pi/2 between the guided transverse electric and magnetic modes. These modes possess significantly strong longitudinal field components as a direct consequence of their strong lateral confinement in the waveguide. We demonstrate that the effect of the device on a linearly polarised input beam is the generation of a field, which is circularly polarised in its transverse components and carries a phase vortex in its longitudinal component. We believe that the discussed integrated platform enables the generation of light beams with tailored phase and polarisation distributions.

Free-space propagation of high-dimensional structured optical fields in an urban environment

Martin P. J. Lavery, Christian Peuntinger, Kevin Guenthner, Peter Banzer, Dominique Elser, Robert W. Boyd, Miles J. Padgett, Christoph Marquardt, Gerd Leuchs

Spatially structured optical fields have been used to enhance the functionality of a wide variety of systems that use light for sensing or information transfer. As higher-dimensional modes become a solution of choice in optical systems, it is important to develop channel models that suitably predict the effect of atmospheric turbulence on these modes. We investigate the propagation of a set of orthogonal spatial modes across a free-space channel between two buildings separated by 1.6 km. Given the circular geometry of a common optical lens, the orthogonal mode set we choose to implement is that described by the Laguerre-Gaussian (LG) field equations. Our study focuses on the preservation of phase purity, which is vital for spatial multiplexing and any system requiring full quantum-state tomography. We present experimental data for the modal degradation in a real urban environment and draw a comparison to recognized theoretical predictions of the link. Our findings indicate that adaptations to channel models are required to simulate the effects of atmospheric turbulence placed on high-dimensional structured modes that propagate over a long distance. Our study indicates that with mitigation of vortex splitting, potentially through precorrection techniques, one could overcome the challenges in a real point-to-point free-space channel in an urban environment.

Roadmap on structured light

Halina Rubinsztein-Dunlop, Andrew Forbes, M. V. Berry, M. R. Dennis, David L. Andrews, Masud Mansuripur, Cornelia Denz, Christina Alpmann, Peter Banzer, et al.

Structured light refers to the generation and application of custom light fields. As the tools and technology to create and detect structured light have evolved, steadily the applications have begun to emerge. This roadmap touches on the key fields within structured light from the perspective of experts in those areas, providing insight into the current state and the challenges their respective fields face. Collectively the roadmap outlines the venerable nature of structured light research and the exciting prospects for the future that are yet to be realized.

Free space excitation of coupled Anderson-localized modes in photonic crystal waveguides with polarization tailored beam

Ali Mahdavi, Paul Roth, Jolly Xavier, Taofiq K. Paraiso, Peter Banzer, Frank Vollmer

We experimentally demonstrate free space excitation of coupled Anderson-localized modes in photonic crystal (PhC) line-defect waveguides (W1) with polarization tailored beams. The corresponding light beam is tightly focused on a pristine W1, and out-of-plane scattering is imaged. By integrating the scattering spectra along the guide, at the W1 modal cut-off, Anderson-localized cavities are observed due to residual W1 fabrication-disorder. Their spectral lines exhibit high quality Q factors up to 2 x 10(5). The incident beam polarization and scattering intensities of the localized modes characterize the efficiency of free-space coupling. The coupling is studied for linearly and radially polarized input beams and for different input coupling locations along the W1 guide. The proposed coupling scheme is particularly attractive for excitation of PhC waveguide modes and Anderson-localized cavities by beam steering and scanning microscopy for sensing applications. Published by AIP Publishing.

Linear and angular momenta in tightly focused vortex segmented beams of light

Martin Neugebauer, Andrea Aiello, Peter Banzer

We investigate the linear momentum density of light, which can be decomposed into spin and orbital parts, in the complex three-dimensional field distributions of tightly focused vortex segmented beams. The chosen angular spectrum exhibits two spatially separated vortices of opposite charge and orthogonal circular polarization to generate phase vortices in a meridional plane of observation. In the vicinity of those vortices, regions of negative orbital linear momentum occur. Besides these phase vortices, the occurrence of transverse orbital angular momentum manifests in a vortex charge-dependent relative shift of the energy density and linear momentum density.

Unveiling the optical properties of a metamaterial synthesized by electron-beam-induced deposition

P. Wozniak, K. Hoeflich, G. Broenstrup, P. Banzer, S. Christiansen, G. Leuchs

Direct writing using a focused electron beam allows for fabricating truly three-dimensional structures of sub-wavelength dimensions in the visible spectral regime. The resulting sophisticated geometries are perfectly suited for studying light-matter interaction at the nanoscale. Their overall optical response will strongly depend not only on geometry but also on the optical properties of the deposited material. In the case of the typically used metal-organic precursors, the deposits show a substructure of metallic nanocrystals embedded in a carbonaceous matrix. Since gold-containing precursor media are especially interesting for optical applications, we experimentally determine the effective permittivity of such an effective material. Our experiment is based on spectroscopic measurements of planar deposits. The retrieved permittivity shows a systematic dependence on the gold particle density and cannot be sufficiently described using the common Maxwell-Garnett approach for effective medium.

Experimental generation of amplitude squeezed vector beams

Vanessa Chille, Stefan Berg-Johansen, Marion Semmler, Peter Banzer, Andrea Aiello, Gerd Leuchs, Christoph Marquardt

We present an experimental method for the generation of amplitude squeezed high-order vector beams. The light is modified twice by a spatial light modulator such that the vector beam is created by means of a collinear interferometric technique. A major advantage of this approach is that it avoids systematic losses, which are detrimental as they cause decoherence in continuous-variable quantum systems. The utilisation of a spatial light modulator (SLM) gives the flexibility to switch between arbitrary mode orders. The conversion efficiency with our setup is only limited by the efficiency of the SLM. We show the experimental generation of Laguerre-Gauss (LG) modes with radial indices 0 or 1 and azimuthal indices up to 3 with complex polarization structures and a quantum noise reduction up to -0.9dB +/- 0.1dB. The corresponding polarization structures are studied in detail by measuring the spatial distribution of the Stokes parameters. (C) 2016 Optical Society of America

Influence of the substrate material on the knife-edge based profiling of tightly focused light beams

C. Huber, S. Orlov, P. Banzer, G. Leuchs

The performance of the knife-edge method as a beam profiling technique for tightly focused light beams depends on several parameters, such as the material and height of the knife-pad as well as the polarization and wavelength of the focused light beam under study. Here we demonstrate that the choice of the substrate the knife-pads are fabricated on has a crucial influence on the reconstructed beam projections as well. We employ an analytical model for the interaction of the knife-pad with the beam and report good agreement between our numerical and experimental results. Moreover, we simplify the analytical model and demonstrate, in which way the underlying physical effects lead to the apparent polarization dependent beam shifts and changes of the beamwidth for different substrate materials and heights of the knife-pad. (C) 2016 Optical Society of America

Tighter spots of light with superposed orbital-angular-momentum beams

Pawel Wozniak, Peter Banzer, Frederic Bouchard, Ebrahim Karimi, Gerd Leuchs, Robert W. Boyd

The possibility of focusing light to an ever tighter spot has important implications for many applications and fields of optics research, such as nano-optics and plasmonics, laser-scanning microscopy, optical data storage, and many more. The size of lateral features of the field at the focus depends on several parameters, including the numerical aperture of the focusing system, but also the wavelength and polarization, phase and intensity distribution of the input beam. Here, we study the smallest achievable focal feature sizes of coherent superpositions of two copropagating beams carrying opposite orbital angular momentum. We investigate the feature sizes for this class of beams not only in the scalar limit, but also use a fully vectorial treatment to discuss the case of tight focusing. Both our numerical simulations and our experimental results confirm that lateral feature sizes considerably smaller than those of a tightly focused Gaussian light beam can be observed. These findings may pave the way for improving the resolution of imaging systems or may find applications in nano-optics experiments.

The ubiquitous photonic wheel

Andrea Aiello, Peter Banzer

Single-mode squeezing in arbitrary spatial modes

Marion Semmler, Stefan Berg-Johansen, Vanessa Chille, Christian Gabriel, Peter Banzer, Andrea Aiello, Christoph Marquardt, Gerd Leuchs

As the generation of squeezed states of light has become a standard technique in laboratories, attention is increasingly directed towards adapting the optical parameters of squeezed beams to the specific requirements of individual applications. It is known that imaging, metrology, and quantum information may benefit from using squeezed light with a tailored transverse spatial mode. However, experiments have so far been limited to generating only a few squeezed spatial modes within a given setup. Here, we present the generation of single-mode squeezing in Laguerre-Gauss and Bessel-Gauss modes, as well as an arbitrary intensity pattern, all from a single setup using a spatial light modulator (SLM). The degree of squeezing obtained is limited mainly by the initial squeezing and diffractive losses introduced by the SLM, while no excess noise from the SLM is detectable at the measured sideband. The experiment illustrates the single-mode concept in quantum optics and demonstrates the viability of current SLMs as flexible tools for the spatial reshaping of squeezed light. (C) 2016 Optical Society of America

Chiral optical response of planar and symmetric nanotrimers enabled by heteromaterial selection

Peter Banzer, Pawel Wozniak, Uwe Mick, Israel De Leon, Robert W. Boyd

Polarization-controlled directional scattering for nanoscopic position sensing

Martin Neugebauer, Pawel Wozniak, Ankan Bag, Gerd Leuchs, Peter Banzer

Controlling the propagation and coupling of light to sub-wavelength antennas is a crucial prerequisite for many nanoscale optical devices. Recently, the main focus of attention has been directed towards high-refractive-index materials such as silicon as an integral part of the antenna design. This development is motivated by the rich spectral properties of individual high-refractive-index nanoparticles. Here we take advantage of the interference of their magnetic and electric resonances to achieve strong lateral directionality. For controlled excitation of a spherical silicon nanoantenna, we use tightly focused radially polarized light. The resultant directional emission depends on the antenna's position relative to the focus. This approach finds application as a novel position sensing technique, which might be implemented in modern nanometrology and super-resolution microscopy set-ups. We demonstrate in a proof-of-concept experiment that a lateral resolution in the Angstrom regime can be achieved.

Exotic looped trajectories of photons in three-slit interference

Omar S. Magana-Loaiza, Israel De Leon, Mohammad Mirhosseini, Robert Fickler, Akbar Safari, Uwe Mick, Brian McIntyre, Peter Banzer, Brandon Rodenburg, et al.

Optical Polarization Mobius Strips and Points of Purely Transverse Spin Density

Thomas Bauer, Martin Neugebauer, Gerd Leuchs, Peter Banzer

Tightly focused light beams can exhibit complex and versatile structured electric field distributions. The local field may spin around any axis including a transverse axis perpendicular to the beams' propagation direction. At certain focal positions, the corresponding local polarization ellipse can even degenerate into a perfect circle, representing a point of circular polarization or C point. We consider the most fundamental case of a linearly polarized Gaussian beam, where-upon tight focusing-those C points created by transversely spinning fields can form the center of 3D optical polarization topologies when choosing the plane of observation appropriately. Because of the high symmetry of the focal field, these polarization topologies exhibit nontrivial structures similar to Mobius strips. We use a direct physical measure to find C points with an arbitrarily oriented spinning axis of the electric field and experimentally investigate the fully three-dimensional polarization topologies surrounding these C points by exploiting an amplitude and phase reconstruction technique.

Lateral spin transport in paraxial beams of light

Martin Neugebauer, Simon Grosche, Sergej Rothau, Gerd Leuchs, Peter Banzer

We investigate the lateral transport of (longitudinal) spin angular momentum in a special polarization tailored light beam composed of a superposition of a y-polarized zero-order and an x-polarized first-order Hermite-Gaussian mode. This phenomenon is linked to the relative Gouy phase shift between the individual modes upon propagation, but can also be interpreted as a geometric phase effect. Experimentally, we demonstrate the implementation of such a mode and measure the spin density upon propagation. (C) 2016 Optical Society of America

Strong, spectrally-tunable chirality in diffractive metasurfaces

Israel De Leon, Matthew J. Horton, Sebastian A. Schulz, Jeremy Upham, Peter Banzer, Robert W. Boyd

Metamaterials and metasurfaces provide a paradigm-changing approach for manipulating light. Their potential has been evinced by recent demonstrations of chiral responses much greater than those of natural materials. Here, we demonstrate theoretically and experimentally that the extrinsic chiral response of a metasurface can be dramatically enhanced by near-field diffraction effects. At the core of this phenomenon are lattice plasmon modes that respond selectively to the illumination’s polarization handedness. The metasurface exhibits sharp features in its circular dichroism spectra, which are tunable over a broad bandwidth by changing the illumination angle over a few degrees. Using this property, we demonstrate an ultra-thin circular-polarization sensitive spectral filter with a linewidth of ~10 nm, which can be dynamically tuned over a spectral range of 200 nm. Chiral diffractive metasurfaces, such as the one proposed here, open exciting possibilities for ultra-thin photonic devices with tunable, spin-controlled functionality.

Observation of optical polarization Mobius strips

Thomas Bauer, Peter Banzer, Ebrahim Karimi, Sergej Orlov, Andrea Rubano, Lorenzo Marrucci, Enrico Santamato, Robert W. Boyd, Gerd Leuchs

Mobius strips are three-dimensional geometrical structures, fascinating for their peculiar property of being surfaces with only one "side"-or, more technically, being "nonorientable" surfaces. Despite being easily realized artificially, the spontaneous emergence of these structures in nature is exceedingly rare. Here, we generate Mobius strips of optical polarization by tightly focusing the light beam emerging from a q-plate, a liquid crystal device that modifies the polarization of light in a space-variantmanner. Using a recently developed-method for the three-dimensional nanotomography of optical vector fields, we fully reconstruct the light polarization structure in the focal region, confirming the appearance of Mobius polarization structures. The preparation of such structured light modes may be important for complex light beam engineering and optical micro-and nanofabrication.

Classically entangled optical beams for high-speed kinematic sensing

Stefan Berg-Johansen, Falk Toeppel, Birgit Stiller, Peter Banzer, Marco Ornigotti, Elisabeth Giacobino, Gerd Leuchs, Andrea Aiello, Christoph Marquardt

Tracking the kinematics of fast-moving objects is an important diagnostic tool for science and engineering. Here, we demonstrate an approach to positional and directional sensing based on the concept of classical entanglement in vector beams of light [Found. Phys. 28, 361 -374 (1998)]. The measurement principle relies on the intrinsic correlations existing in such beams between transverse spatial modes and polarization. The latter can be determined from intensity measurements with only a few fast photodiodes, greatly outperforming the bandwidth of current CCD/CMOS devices. In this way, our setup enables two-dimensional real-time sensing with temporal resolution in the GHz range. We expect the concept to open up new directions in metrology and sensing. (C) 2015 Optical Society of America

Selective switching of individual multipole resonances in single dielectric nanoparticles

Pawel Wozniak, Peter Banzer, Gerd Leuchs

Following Mie theory, nanoparticles made of a high-refractive-index dielectric, such as silicon, exhibit a resonator-like behavior and very rich resonance spectra. Which electric or magnetic particle mode is excited depends on the wavelength, the refractive-index contrast relative to the environment, and the geometry of the nanoparticle itself. In addition, the spatial structure of the impinging light field plays a major role in the excitation of the nanoparticle resonances. Here, it is shown that, by tailoring the excitation field, individual multipole resonances can be selectively addressed while suppressing the excitation of other particle modes. This enables a detailed study of selected individual resonances without interference by the other modes.

Quantum uncertainty in the beam width of spatial optical modes

Vanessa Chille, Peter Banzer, Andrea Aiello, Gerd Leuchs, Christoph Marquardt, Nicolas Treps, Claude Fabre

We theoretically investigate the quantum uncertainty in the beam width of transverse optical modes and, for this purpose, define a corresponding quantum operator. Single mode states are studied as well as multimode states with small quantum noise. General relations are derived, and specific examples of different modes and quantum states are examined. For the multimode case, we show that the quantum uncertainty in the beam width can be completely attributed to the amplitude quadrature uncertainty of one specific mode, which is uniquely determined by the field under investigation. This discovery provides us with a strategy for the reduction of the beam width noise by an appropriate choice of the quantum state. (C) 2015 Optical Society of America

Exploiting cellophane birefringence to generate radially and azimuthally polarised vector beams

Johnston Kalwe, Martin Neugebauer, Calvine Ominde, Gerd Leuchs, Geoffrey Rurimo, Peter Banzer

We exploit the birefringence of cellophane to convert a linearly polarised Gaussian beam into either a radially or azimuthally polarised beam. For that, we fabricated a low-cost polarisation mask consisting of four segments of cellophane. The fast axis of each segment is oriented appropriately in order to rotate the polarisation of the incident linearly polarised beam as desired. To ensure the correct operation of the polarisation mask, we tested the polarisation state of the generated beam by measuring the spatial distribution of the Stokes parameters. Such a device is very cost efficient and allows for the generation of cylindrical vector beams of high quality.

Towards an optical far-field measurement of higher-order multipole contributions to the scattering response of nanoparticles

Thomas Bauer, Sergej Orlov, Gerd Leuchs, Peter Banzer

We experimentally show an all-optical multipolar decomposition of the lowest-order eigenmodes of a single gold nanoprism using azimuthally and radially polarized cylindrical vector beams. By scanning the particle through these tailored field distributions, the multipolar character of the eigenmodes gets encoded into 2D-scanning intensity maps even for higher-order contributions to the eigenmode that are too weak to be discerned in the direct far-field scattering response. This method enables a detailed optical mode analysis of individual nanoparticles. (C) 2015 AIP Publishing LLC.

Measuring the Transverse Spin Density of Light

Martin Neugebauer, Thomas Bauer, Andrea Aiello, Peter Banzer

We generate tightly focused optical vector beams whose electric fields spin around an axis transverse to the beams' propagation direction. We experimentally investigate these fields by exploiting the directional near-field interference of a dipolelike plasmonic field probe placed adjacent to a dielectric interface. This directionality depends on the transverse electric spin density of the excitation field. Near-to far-field conversion mediated by the dielectric interface enables us to detect the directionality of the emitted light in the far field and, therefore, to measure the transverse electric spin density with nanoscopic resolution. Finally, we determine the longitudinal electric component of Belinfante's elusive spin momentum density, a solenoidal field quantity often referred to as "virtual."

From transverse angular momentum to photonic wheels

Andrea Aiello, Peter Banzer, Martin Neugebauer, Gerd Leuchs

Scientists have known for more than a century that light possesses both linear and angular momenta along the direction of propagation. However, only recent advances in optics have led to the notion of spinning electromagnetic fields capable of carrying angular momenta transverse to the direction of motion. Such fields enable numerous applications in nano-optics, biosensing and near-field microscopy, including three-dimensional control over atoms, molecules and nanostructures, and allowing for the realization of chiral nanophotonic interfaces and plasmonic devices. Here, we report on recent developments of optics with light carrying transverse spin. We present both the underlying principles and the latest achievements, and also highlight new capabilities and future applications emerging from this young yet already advanced field of research.

Generation and subwavelength focusing of longitudinal magnetic fields in a metallized fiber tip

Daniel Ploss, Arian Kriesch, Hannes Pfeifer, Peter Banzer, Ulf Peschel

We demonstrate experimentally and numerically that in fiber tips as they are used in NSOMs azimuthally polarized electrical fields (broken vertical bar E-azi broken vertical bar(2) / broken vertical bar E-tot broken vertical bar(2) approximate to 55% +/- 5% for lambda(0) = 1550 nm), respectively subwavelength confined (FWHM approximate to 450 nm approximate to lambda(0)/3.5) magnetic fields, are generated for a certain tip aperture diameter (d = 1.4 mu m). We attribute the generation of this field distribution in metal-coated fiber tips to symmetry breaking in the bend and subsequent plasmonic mode filtering in the truncated conical taper. (C) 2014 Optical Society of America

Vectorial complex-source vortex beams

S. Orlov, P. Banzer

The scalar complex source vortex model is an accurate description of highly focused scalar vortices. We use it to construct a variety of vectorial solutions of Maxwell's equations describing highly focused and variously polarized vector vortex beams accurately. Three different families of optical vector vortex beams are presented and studied in detail. In this model, optical vortices derived within Cartesian symmetry correspond to circularly and linearly polarized highly focused vortex beams in the focus of a high numerical aperture focusing system. In addition, we report on vortical complex-source beams derived within cylindrical and spherical symmetries which exhibit very special and intriguing properties.

Polarization Tailored Light Driven Directional Optical Nanobeacon

Martin Neugebauer, Thomas Bauer, Peter Banzer, Gerd Leuchs

We experimentally demonstrate all-optical control of the emission directivity of a dipole-like nanoparticle with spinning dipole moment sitting on the interface to an optical denser medium. The particle itself is excited by a tightly focused polarization tailored light beam under normal incidence. The position dependent local polarization of the focal field allows for tuning the dipole moment via careful positioning of the particle relative to the beam axis. As an application of this scheme, we investigate the polarization dependent coupling to a planar two-dimensional dielectric waveguide.

Geometric spin Hall effect of light in tightly focused polarization-tailored light beams

Martin Neugebauer, Peter Banzer, Thomas Bauer, Sergej Orlov, Norbert Lindlein, Andrea Aiello, Gerd Leuchs

Recently, it was shown that a nonzero transverse angular momentum manifests itself in a polarization-dependent intensity shift of the barycenter of a paraxial light beam [Aiello et al., Phys. Rev. Lett. 103, 100401 (2009)]. The underlying effect is phenomenologically similar to the spin Hall effect of light but does not depend on the specific light-matter interaction and can be interpreted as a purely geometric effect. Thus, it was named the geometric spin Hall effect of light. Here, we experimentally investigate the appearance of this effect in tightly focused vector beams. We use an experimental nanoprobing technique in combination with a reconstruction algorithm to verify the relative shifts of the components of the electric energy density and the shift of the intensity in the focal plane. By that, we experimentally demonstrate the geometric spin Hall effect of light in a highly nonparaxial beam.

Observation of the Geometric Spin Hall Effect of Light

Jan Korger, Andrea Aiello, Vanessa Chille, Peter Banzer, Christoffer Wittmann, Norbert Lindlein, Christoph Marquardt, Gerd Leuchs

The spin Hall effect of light (SHEL) is the photonic analogue of the spin Hall effect occurring for charge carriers in solid-state systems. This intriguing phenomenon manifests itself when a light beam refracts at an air-glass interface (conventional SHEL) or when it is projected onto an oblique plane, the latter effect being known as the geometric SHEL. It amounts to a polarization-dependent displacement perpendicular to the plane of incidence. In this work, we experimentally investigate the geometric SHEL for a light beam transmitted across an oblique polarizer. We find that the spatial intensity distribution of the transmitted beam depends on the incident state of polarization and its centroid undergoes a positional displacement exceeding one wavelength. This novel phenomenon is virtually independent from the material properties of the polarizer and, thus, reveals universal features of spin-orbit coupling.

Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams

Thomas Bauer, Sergej Orlov, Ulf Peschel, Peter Banzer, Gerd Leuchs

Highly confined vectorial electromagnetic field distributions are an excellent tool for detailed studies in nano-optics, such as nonlinear microscopy(1), advanced fluorescence imaging(2,3) or nanoplasmonics(4,5). Such field distributions can be generated, for instance, by tight focusing of polarized light beams(6-9). To guarantee high resolution in the investigation of objects with subwavelength dimensions, precise knowledge of the spatial distribution of the exciting vectorial field is of utmost importance. The full-field reconstruction methods presented to date involve, for example, complex near-field techniques(10-13). Here, we demonstrate a simple and straightforward-to-implement measurement scheme and reconstruction algorithm based on the scattering signal of a single spherical nanoparticle as a field probe. We are able to reconstruct the amplitudes and relative phases of the individual focal field components with subwavelength resolution from a single scan measurement without the need for polarization analysis of the scattered light. This scheme has the potential to improve microscopy and nanoscopy techniques.

The photonic wheel - demonstration of a state of light with purely transverse angular momentum

P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, G. Leuchs

In classical mechanics, a system may possess angular momentum which can be either transverse (e.g. in a spinning wheel) or longitudinal (e.g. for a spiraling seed falling from a tree) with respect to the direction of motion. However, for light, a typical massless wave system, the situation is less versatile. Photons are well-known to exhibit intrinsic angular momentum which is longitudinal only: the spin angular momentum defining the polarization and the orbital angular momentum associated with a spiraling phase front. Here we show that it is possible to generate a novel state of the light field that contains purely transverse angular momentum, the analogue of a spinning mechanical wheel. We realize this state by tight focusing of a polarization tailored light beam and measure it using an optical nano-probing technique. Such a novel state of the light field can find applications in optical tweezers and spanners where it allows for additional rotational degree of freedom not achievable in single-beam configurations so far.

The polarization properties of a tilted polarizer

Jan Korger, Tobias Kolb, Peter Banzer, Andrea Aiello, Christoffer Wittmann, Christoph Marquardt, Gerd Leuchs

Polarizers are key components in optical science and technology. Thus, understanding the action of a polarizer beyond oversimplifying approximations is crucial. In this work, we study the interaction of a polarizing interface with an obliquely incident wave experimentally. To this end, a set of Mueller matrices is acquired employing a novel procedure robust against experimental imperfections. We connect our observation to a geometric model, useful to predict the effect of polarizers on complex light fields. (C) 2013 Optical Society of America

Corrections to the knife-edge based reconstruction scheme of tightly focused light beams

C. Huber, S. Orlov, P. Banzer, G. Leuchs

The knife-edge method is an established technique for profiling light beams. It was shown, that this technique even works for tightly focused beams, if the material and geometry of the probing knife-edges are chosen carefully. Furthermore, it was also reported recently that this method fails, when the knife-edges are made from pure materials. The artifacts introduced in the reconstructed beam shape and position depend strongly on the edge and input beam parameters, because the knife-edge is excited by the incoming beam. Here we show, that the actual beam shape and spot size of tightly focused beams can still be derived from knife-edge measurements for pure edge materials and different edge thicknesses by adapting the analysis method of the experimental data taking into account the interaction of the beam with the edge. (C) 2013 Optical Society of America

Enhanced Raman Scattering of Graphene using Arrays of Split Ring Resonators

George Sarau, Basudev Lahiri, Peter Banzer, Priti Gupta, Arnab Bhattacharya, Frank Vollmer, Silke Christiansen

Combining graphene with plasmonic nanostructures is currently being explored for high sensitivity biochemical detection based on the surface-enhanced Raman scattering (SERS) effect. Here, a novel and tunable platform for understanding SERS based on graphene monolayers transferred on arrays of split ring resonators (SRRs) exhibiting resonances in the visible range is introduced. Raman enhancement factors per area of graphene of up to 75 are measured, demonstrating the strong plasmonic coupling between graphene and the metamaterial resonances. Apart from the incident laser light, both the photoluminescence signal emitted by the SRRs and the Raman scattered light from graphene contribute to the excitation of distinct resonances, resulting in different SERS. This new perspective allows control of SERS in the case of graphene on plasmonic metamaterials or nanostructures and potentially paves the way towards an advanced SERS substrate that could lead to the detection of single molecules attached to graphene in future biochemical sensing devices.

Probing guided modes in a monolayer colloidal crystal on a flat metal film

Sergei G. Romanov, Nicolas Vogel, Karina Bley, Katharina Landfester, Clemens K. Weiss, Sergej Orlov, Alexander V. Korovin, Gennady P. Chuiko, Alois Regensburger, et al.

Two-dimensional slab hybrid metal-dielectric photonic crystals, which are prepared by assembling polymer colloidal spheres into closely packed monolayers of hexagonal symmetry on a gold-coated glass substrate, show an improved confinement of light compared with a colloidal monolayer on a glass substrate. We demonstrated that the optical response of such hybrid crystals consists of diffractively coupled waveguiding modes, Fabry-Perot resonances, and Mie resonances. Correspondingly, two major mechanisms, namely, band transport and hopping of localized excitations, participate in the in-plane light transport in such hybrid crystals.

Analytical expansion of highly focused vector beams into vector spherical harmonics and its application to Mie scattering

S. Orlov, U. Peschel, T. Bauer, P. Banzer

The analytical expansion of linearly, azimuthally, and radially polarized rigorous beam-type solutions of Maxwell's equations into vector spherical harmonics (VSHs) is presented. We report on the dominance of higher order multipoles in highly focused radially and azimuthally polarized beams compared to linearly polarized beams under similar conditions. Furthermore, we theoretically investigate a scenario in which highly focused azimuthally and radially polarized beams interact with a linear polarizer placed in the focal plane and expand the resulting fields into VSHs. The generalized Mie theory is used afterwards to investigate the scattering of the studied beams off a spherical gold nanoparticle.

Resonant metamaterials for contrast enhancement in optical lithography

Sabine Dobmann, Dzmitry Shyroki, Peter Banzer, Andreas Erdmann, Ulf Peschel

The transmission through ultra-thin metal films is noticeable and thus limits their potential for the formation of lithographic masks. By sub-wavelength patterning of a metal film with a post structure, a resonant metamaterial is formed, which can effectively suppress the transmission. Measurements as well as calculations identify the width of the metal islands as a critical geometrical feature. Hence, the extraordinarily low transmission effect can be explained by the resonant response of single scatterers known as Localized Surface Plasmon Resonances (LSPR). A potential application of this suppressed transmission effect to thin metal masks in optical lithography is experimentally investigated. (C) 2012 Optical Society of America

Birefringence and dispersion of cylindrically polarized modes in nanobore photonic crystal fiber

T. G. Euser, M. A. Schmidt, N. Y. Joly, C. Gabriel, C. Marquardt, L. Y. Zang, M. Foertsch, P. Banzer, A. Brenn, et al.

We demonstrate experimentally and theoretically that a nanoscale hollow channel placed centrally in the solid-glass core of a photonic crystal fiber strongly enhances the cylindrical birefringence (the modal index difference between radially and azimuthally polarized modes). Furthermore, it causes a large split in group velocity and group velocity dispersion. We show analytically that all three parameters can be varied over a wide range by tuning the diameters of the nanobore and the core. (C) 2010 Optical Society of America

Interaction of highly focused vector beams with a metal knife-edge

P. Marchenko, S. Orlov, C. Huber, P. Banzer, S. Quabis, U. Peschel, G. Leuchs

We investigate the interaction of highly focused linearly polarized optical beams with a metal knife-edge both theoretically and experimentally. A high numerical aperture objective focusses beams of various wavelengths onto samples of different sub-wavelength thicknesses made of several opaque and pure materials. The standard evaluation of the experimental data shows material and sample dependent spatial shifts of the reconstructed intensity distribution, where the orientation of the electric field with respect to the edge plays an important role. A deeper understanding of the interaction between the knife-edge and the incoming highly focused beam is gained in our theoretical model by considering eigenmodes of the metal-insulator-metal structure. We achieve good qualitative agreement of our numerical simulations with the experimental findings. (C) 2011 Optical Society of America

Experimental cross-polarization detection of coupling far-field light to highly confined plasmonic gap modes via nanoantennas

J. Wen, P. Banzer, A. Kriesch, D. Ploss, B. Schmauss, U. Peschel

We experimentally demonstrate the coupling of far-field light to highly confined plasmonic gap modes via connected nanoantennas. The excitation of plasmonic gap modes is shown to depend on the polarization, position, and wavelength of the incident beam. Far-field measurements performed in crossed polarization allow for the detection of extremely weak signals re-emitted from gap waveguides and can increase the signal-to-noise ratio dramatically. (C) 2011 American Institute of Physics. [doi:10.1063/1.3564904]

Geometric Spin Hall Effect of Light at polarizing interfaces

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, G. Leuchs

The geometric Spin Hall Effect of Light (geometric SHEL) amounts to a polarization-dependent positional shift when a light beam is observed from a reference frame tilted with respect to its direction of propagation. Motivated by this intriguing phenomenon, the energy density of the light beam is decomposed into its Cartesian components in the tilted reference frame. This illustrates the occurrence of the characteristic shift and the significance of the effective response function of the detector. We introduce the concept of a tilted polarizing interface and provide a scheme for its experimental implementation. A light beam passing through such an interface undergoes a shift resembling the original geometric SHEL in a tilted reference frame. This displacement is generated at the polarizer and its occurrence does not depend on the properties of the detection system. We give explicit results for this novel type of geometric SHEL and show that at grazing incidence this effect amounts to a displacement of multiple wavelengths, a shift larger than the one introduced by Goos-Hanchen and Imbert-Fedorov effects.

Entangling Different Degrees of Freedom by Quadrature Squeezing Cylindrically Polarized Modes

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Foertsch, D. Elser, U. L. Andersen, et al.

Quantum systems such as, for example, photons, atoms, or Bose-Einstein condensates, prepared in complex states where entanglement between distinct degrees of freedom is present, may display several intriguing features. In this Letter we introduce the concept of such complex quantum states for intense beams of light by exploiting the properties of cylindrically polarized modes. We show that already in a classical picture the spatial and polarization field variables of these modes cannot be factorized. Theoretically it is proven that by quadrature squeezing cylindrically polarized modes one generates entanglement between these two different degrees of freedom. Experimentally we demonstrate amplitude squeezing of an azimuthally polarized mode by exploiting the nonlinear Kerr effect in a specially tailored photonic crystal fiber. These results display that such novel continuous-variable entangled systems can, in principle, be realized.

Extraordinary transmission through a single coaxial aperture in a thin metal film

P. Banzer, J. Kindler (nee Mueller), S. Quabis, U. Peschel, G. Leuchs

We investigate experimentally the transmission properties of single sub-wavelength coaxial apertures in thin metal films (t = 110 nm). Enhanced transmission through a single sub-wavelength coaxial aperture illuminated with a strongly focused radially polarized light beam is reported. In our experiments we achieved up to four times enhanced transmission through a single coaxial aperture as compared to a (hollow) circular aperture with the same outer diameter. We attribute this enhancement of transmission to the excitation of a TEM-mode for illumination with radially polarized light inside the single coaxial aperture. A strong polarization contrast is observed between the transmission for radially and azimuthally polarized illumination. Furthermore, the observed transmission through a single coaxial aperture can be strongly reduced if surface plasmons are excited. The experimental results are in good agreement with finite difference time domain (FDTD) simulations. (C)2010 Optical Society of America

Complex source beam: A tool to describe highly focused vector beams analytically

S. Orlov, U. Peschel

The scalar-complex-source model is used to develop an accurate description of highly focused radially, azimuthally, linearly, and circularly polarized monochromatic vector beams. We investigate the power and full beam widths at half maximum of vigorous Maxwell equation solutions. The analytical expressions are employed to compare the vector complex source beams with the real beams produced by various high-numerical-aperture (NA) focusing systems. We find a parameter set for which the spatial extents of the analytical beams are the same as those of experimentally realized ones. We ensure the same shape of the considered beams by investigating an overlap of the complex source beams with high-NA beams. We demonstrate that the analytical expressions are good approximations for realistic highly focused beams.

On the experimental investigation of the electric and magnetic response of a single nano-structure

P. Banzer, U. Peschel, S. Quabis, G. Leuchs

We demonstrate an experimental method to separately test the optical response of a single sub-wavelength nano-structure to tailored electric and magnetic field distributions in the optical domain. For this purpose a highly focused y-polarized TEM10-mode is used which exhibits spatially separated longitudinal magnetic and transverse electric field patterns. By displacing a single sub-wavelength nano-structure, namely a single split-ring resonator (SRR), in the focal plane, different coupling scenarios can be achieved. It is shown experimentally that the single split-ring resonator tested here responds dominantly as an electric dipole. A much smaller but yet statistically significant magnetic dipole contribution is also measured by investigating the interaction of a single SRR with a magnetic field component perpendicular to the SRR plane (which is equivalent to the curl of the electric field) as well as by analyzing the intensity and polarization distribution of the scattered light with high spatial resolution. The developed experimental setup as well as the measurement techniques presented in this paper are a versatile tool to investigate the optical properties of single sub-wavelength nano-structures. (C) 2010 Optical Society of America

Fiber-modes and fiber-anisotropy characterization using low-coherence interferometry

Y. Z. Ma, Y. Sych, G. Onishchukov, S. Ramachandran, U. Peschel, B. Schmauss, G. Leuchs

An optical low-coherence interferometry technique has been used to simultaneously resolve the mode profile and to measure the intermodal dispersion of guided modes of a few-mode fiber. Measurements are performed using short samples of fiber (about 50 cm). There is no need for a complex mode-conversion technique to reach a high interference visibility. Four LP mode groups of the few-mode fiber are resolved. Experimental results and numerical simulations show that the ellipticity of the fiber core leads to a distinct splitting of the degenerate high-order modes in group index. For the first time, to the best of our knowledge, it has been demonstrated that degenerate LP11 modes are much more sensitive to core shape variations than the fundamental modes and that intermodal dispersion of high-order degenerate modes can be used for characterizing the anisotropy of an optical waveguide.

Waveguide properties of single subwavelength holes demonstrated with radially and azimuthally polarized light

J. Müller, Peter Banzer, Susanne Quabis, Ulf Peschel, Gerd Leuchs

We investigate the transmission of focused beams through single subwavelength holes in a silver film. We use radially and azimuthally polarized light to excite higher-order waveguide modes as well as to match the radial symmetry of the aperture geometry. Remarkably, the transmission properties can be described by a classical waveguide model even for thicknesses of the silver film as thin as a quarter of a wavelength.

Tailored polarization patterns for performance optimization of optical devices

Gerd Leuchs, Susanne Quabis

In the case of strong focusing the smallest possible focal spot can be reached, provided one uses a specially designed polarization pattern. Other optical set-ups also employing high numerical aperture imaging are likewise expected to improve performance under polarization optimization. We propose a strategy for calculating the polarization pattern required for system optimization. A single element modulating only the polarization and not amplitude and phase may lead to satisfactory performance in some cases.

Using a quantum well heterostructure to study the longitudinal and transverse electric field components of a strongly focused laser beam

G. Kihara Rurimo, M. Schardt, S. Quabis, S. Malzer, Ch. Dotzler, A. Winkler, G. Leuchs, G. H. Dohler, D. Driscoll, et al.

We report a method to measure the electric energy density of longitudinal and transverse electric field components of strongly focused polarized laser beams. We used a quantum well photodetector and exploited the polarization dependent optical transitions of light holes and heavy holes to probe the electric field distribution in the focal region. A comparison of the measured photocurrent spectra for radially and azimuthally polarized beams at the light and heavy hole absorption peaks provides a measure of the amount of the longitudinal electric field component. (c) 2006 American Institute of Physics.

TE- and TM-polarization-resolved spectroscopy on quantum wells under normal incidence

M Schardt, A Winkler, G Rurimo, M Hanson, D Driscoll, S Quabis, S Malzer, G Leuchs, GH Doehler, et al.

We present TE- and TM-polarization-resolved photocurrent measurements on quantum well pin diodes under normal incidence. Usually, optical experiments performed in such a geometry yield information only about transitions involving in-plane (p, and p,) components of the hole wave functions because of the in-plane (TE) polarization of the light. Information on transitions sensitive to the p, components can be obtained by focussing a radially polarized laser beam through a microscope objective with high numerical aperture (NA = 0.9). With our setup, the electrical field vector at the focal tail has a significant component along the optical axis (TM-polarization!) which enables excitation of transitions sensitive to p, components also. Additionally, the existence of a degenerate (azimuthally polarized) optical mode enables switching these p. components on and off easily. Experimental evidence of these features has been achieved by exploiting the selection rules for e-hh and e-lh transitions in a quantum well structure. We present a comparison of our recorded spectra with theoretical predictions obtained from simple geometric optics assumptions. For our quantum wells the polarization effects are small because our measurement averages the intensity distribution of the whole focal plane. We plan to extend our measurements to polarization resolved single quantum dot spectroscopy. By restricting the detection region to the spatial extent of a single dot, one can exploit the almost pure TM-polarization on the optical axis for obtaining high contrast between heavy- and light-hole exciton absorption. (c) 2006 Published by Elsevier B.V.

Generation of a radially polarized doughnut mode of high quality

Susanne Quabis, Ralf Dorn, Gerd Leuchs

We present an experimental set-up to generate laser beams with locally varying polarization distribution. In a linear set-up, a radially polarized beam of high quality regarding intensity distribution, polarization and phase-front distortion is generated. This beam can be used for tight focusing. Further applications are discussed.

Polarization optimized focusing of light and coupling to sub-wavelength antennae

Gerd Leuchs, Susanne Quabis

This chapter describes the polarization optimized focusing of light and coupling to sub-wavelength antennae. In a set-up for focusing of light, the lens system transforms the transverse field distribution at the input into the transverse field distribution at the focal plane. The parameters of the input beam are the transverse intensity and phase distribution as well as its state of polarization. The various optical rays directed by the lens to the focal spot typically carry different polarizations even if the input beam has a homogeneous polarization distribution across the beam. Locally the polarization is linear everywhere but the direction of the electric field vector depends on the transverse coordinates within the cross section of the beam in such a way that the electric field vectors oscillate in the radial direction. In the limit of high numerical aperture, focusing the field distribution at and near the focus is calculated using the Debye approximation. The effects of the vector properties of light on the structure of the focus are best observed if two special input beams are compared with identical intensity distribution but different polarization properties

Sharper focus for a radially polarized light beam

Ralf Dorn, Susanne Quabis, Gerd Leuchs

We experimentally demonstrate for the first time that a radially polarized field can be focused to a spot size significantly smaller [0.16(1)lambda(2)] than for linear polarization (0.26lambda(2)). The effect of the vector properties of light is shown by a comparison of the focal intensity distribution for radially and azimuthally polarized input fields. For strong focusing, a radially polarized field leads to a longitudinal electric field component at the focus which is sharp and centered at the optical axis. The relative contribution of this component is enhanced by using an annular aperture.

The focus of light-linear polarization breaks the rotational symmetry of the focal spot

Ralf Dorn, Susanne Quabis, Gerd Leuchs

We experimentally demonstrate for the first time that a linearly polarized beam is focused to an asymmetric spot when using a high-numerical aperture focusing system. This asymmetry was predicted by Richards and Wolf in 1959 and can only be measured when a polarization-insensitive sensor is placed in the focal region. We used a specially modified photodiode in a knife-edge-type set-up to obtain highly resolved images of the total electric energy density distribution at the focus. The results are in good agreement with the predictions of a vectorial focusing theory.

Diversity detection of speckles for double-wavelength interferometry on rough surfaces

J Trautner, Gerd Leuchs

When the topography of a rough surface is measured with a double-wavelength interferometer, the phase error of the signal corresponding to the synthetic wavelength increases in the vicinity of dark speckles. To overcome this problem we perform an amplitude-dependent averaging of the synthetic phase over independent speckles (diversity detection). We either use spatially neighboring speckles or in the case of depolarizing surfaces, we use speckles of the same spatial mode, but with orthogonal polarizations. For the latter case the lateral resolution stays unaffected. The reduction of the speckle noise is demonstrated experimentally for a laterally scanning double-wavelength interferometer with superheterodyne detection of the synthetic phase. (C) 2002 Optical Society of America.

The focus of light - theoretical calculation and experimental tomographic reconstruction

Susanne Quabis, Ralf Dorn, M. Eberler, O. Glöckl, Gerd Leuchs

We present numerical calculations on the field distribution in the focus of an optical system with high numerical aperture. The diffraction integrals which are based on the Debye approximation are derived and evaluated for a radially polarized input field with a doughnut-shaped intensity distribution. It is shown that this mode focusses down to a spot size significantly smaller as compared to the case of linear polarization. An experimental setup to measure the three-dimensional intensity distribution in the focal region is presented, which is based on the knife-edge method and on tomographic reconstruction.

Focusing light to a tighter spot

Susanne Quabis, Ralf Dorn, M. Eberler, O. Glöckl, Gerd Leuchs

The smallest spot sizes are reached by focusing an annular shaped light beam with a high aperture lens, We show theoretically that the focal area is further reduced when using a novel radially polarized instead of a linearly polarized light annulus. In the vicinity of the focus there is a large longitudinally polarized field component [1] which is still narrower and has no pronounced side lobes. A special photosensitive layer prepared to be sensitive only to this longitudinal field component may be used to reach an even smaller focal area, 0.1 lambda(2), which is determined by the contour of the intensity distribution at half the maximum value. The radially polarized doughnut mode may also be used to build improved near field sensors having a substantially increased brightness. (C) 2000 Elsevier Science B.V. All rights reserved.

Multiple-wavelength interferometry for absolute distance measurement and three-dimensional imaging

J. Trautner, K. Walcher, Gerd Leuchs, B. Bodermann, H. R. Telle

With an absolutely measuring interferometric distance sensor the three-dimensional shape of objects with rough surfaces is recorded from a large distance. The measuring principle of the sensor is multiple-wavelength interferometry. For the measurement of the interferometric phases the heterodyne detection is used. The distance resolution of the sensor is limited only by the roughness of the surface. The operation of the 3D-image sensor is demonstrated for objects with heights of a few millimeters up to several centimeters measured from a distance of about one meter. With an integration time of 60 ms a distance resolution of a few 10 Pm is achieved.

Investigation of phase singularities in the vicinity of small structures using a Linnik Interference microscope

Ralf Dorn, M Eberler, M Piringer, Susanne Quabis, Gerd Leuchs

We present studies of the electric field that is reflected by sub-A structures. The occurrence of singularities in the phase distribution of the field is investigated theoretically and experimentally with regard to the possibility to achieve lateral superresolution. A theoretical model for the calculation of the electric field is discussed that is based on the Green function formalism. Measurements on two-dimensional objects were performed using a Linnik interference microscope.