Space-variant polarization conversion with artificial birefringent metallic elements.

We present an artificial birefringent space-variant polarization converter for the near infrared, λ = 1550 nm. Each hollow waveguide has a rectangular shape with lateral dimensions of 1550 nm in the x-direction and 1034 nm as the largest length in the y-direction. The whole device consists of approximately 2000 × 2500 hollow waveguides realized in a 2-µm-thick gold structure. They are separated by sidewalls with a width of less than 500 nm. By proper choice of the lateral widths of the individual holes, a pixel-wise polarization conversion of an incoming wave field is possible. By suitable choice of the fabrication parameters, a birefringent phase shift up to 2π can be achieved. Hence, the structure is able to fully convert the state of polarization, e.g., from linear to circular. For fabrication of the device, femtosecond 3D direct laser writing was combined with electroplating. Here, we describe the operation of our device as a space-variant polarization converter by measuring the angle-dependent transmitted power and by calculating the ellipticity and the phase delay dependent on position as well as the azimuth angle from the experimentally determined powers.

Self-imaging of tailored vortex pulse arrays and spectral Gouy rotation echoes.

Self-imaging of femtosecond pulses with orbital angular momentum is studied in spectral domain by illuminating the orthogonal arrays of spiral gratings. Spectral Gouy rotation, i.e., the characteristic circulation of extremal regions near phase singularities in spatial spectral maps, is found to partially reappear at discrete distances. The self-imaging of co-rotating and counter-rotating vortices is compared in intensity and spectral behavior. High-selectivity pattern recognition from weakly modulated spectral maps is demonstrated by analyzing spectral moments. By our experiments, the classical Talbot effect is extended to polychromatic pulsed vortex arrays with controlled maps of rotation sign.

Refractive-diffractive dispersion compensation for optical vortex beams with ultrashort pulse durations.

Wave fields, which are described mathematically by higher order Bessel functions, carry an orbital angular momentum and thus represent particular types of optical vortex beams with helical wavefronts. For the generation of such vortex beams, one may use, for instance, diffractive spiral axicons. Diffraction, however, leads invariably to strong dispersion, which is detrimental for ultrashort pulses since it leads to severe pulse broadening. This pulse broadening can be minimized or reduced completely (at least, in a specific plane of propagation) if the pulses propagate additionally through a medium with normal refractive dispersion. The refractive-diffractive generation of ultrashort vortex pulses was demonstrated earlier for a pulse duration of approximately 8 fs [Opt. Lett.37, 3804 (2012)10.1364/OL.37.003804OPLEDP0146-9592]. Here, we present an analytical description of the generation and propagation of these vortex beams and of the refractive-diffractive compensation of the dispersion.

Diffraction theory for azimuthally structured Fresnel zone plate.

A conventional Fresnel zone plate (FZP) consists of concentric rings with an alternating binary transmission of zero and one. In an azimuthally structured Fresnel zone plate (aFZP), the light transmission of the transparent zones is modulated in the azimuthal direction, too. The resulting structure is of interest for extreme ultraviolet and x-ray imaging, in particular, because of its improved mechanical stability as compared to the simple ring structure of an FZP. Here, we present an analysis of the optical performance of the aFZP based on scalar diffraction theory and show numerical results for the light distribution in the focal plane. These will be complemented by calculations of the optical transfer function.

Few-cycle high-contrast vortex pulses.

Few-cycle high-contrast vortex beams with pulse durations around 8 fs were generated from a Ti:sapphire laser oscillator with a single diffractive-refractive component. Angular and temporal pulse properties were characterized with an advanced time-wavefront sensor. The temporal transfer indicates a fairly complete self-compensation.

Highly precise micro-retroreflector array fabricated by the LIGA process and its application as tapped delay line filter.

We report on the fabrication of a one-dimensional micro-retroreflector array with a pitch of 100 µm. The array was fabricated by x-ray lithography and the lithographie, galvanik und abformung (LIGA) process in a 1 mm thick poly(methyl methacrylate) (PMMA) layer and subsequently covered with Au. The area of the array is 1 mm×10 mm. The high precision of the LIGA-based fabrication process allows one to use the element in spectrometers. Here, it is suggested to apply it to the implementation of a transversal filter for femtosecond pulses. We present a theoretical description of the performance of the retroreflector array as a filtering device and show experimental results.

Plasmonic multimode waveguides with transversely structured core.

We analyze the propagation of surface plasmons in metallic multimode waveguides that consist of alternating stripes of different metals in the transverse direction and that are homogeneous in the longitudinal direction. The purpose of structuring the waveguide in the transverse direction is to take advantage of the different attenuation and propagation constants for different metals. Here, in particular, alternating stripes of Ag and Au are considered. This allows one to influence the modal spectrum. We consider two different, well-defined waveguide configurations. For these, the propagating plasmonic modes are calculated. Based on the numerical simulations, we discuss the attenuation and propagation behavior and show the resulting eigenmodes for different values of the structural parameters, i.e., widths and thicknesses.

Analysis of the self-imaging effect in plasmonic multimode waveguides.

We present studies on the propagation of plasmon waves in metallic multimode waveguides surrounded by a dielectric medium. The permittivity of the metal was determined by a Drude model. The propagation was simulated by the method of lines. The propagating field exhibited the well-known self-imaging phenomenon known as the Talbot effect. The metallic waveguides are lossy. The influence of various parameters on the losses was examined. By a suitable choice of parameters, propagation distances of several Talbot periods are possible. Our investigation also includes simulations for the propagation of eigenmodes of the waveguides and results for the calculation of the effective index.

Optical wave fields with lateral and longitudinal periodicity.

The propagation of stationary wave fields that exhibit simultaneously lateral and longitudinal periodicity is investigated. As a model, we use a Fabry-Perot resonator with periodically structured mirrors under monochromatic plane wave illumination. The resonator leads to a longitudinal periodicity, the grating mirrors to a lateral periodicity. The angular spectrum of the transmitted wave field is given as the product of two terms, one related to the lateral, the other to the longitudinal properties. Its modal structure can vary significantly depending on the ratio of the lateral and longitudinal periods and the reflectivity of the resonator's mirrors. For example, it is possible to generate bandgap behavior despite the fact that the periods may be significantly larger than the wavelength. The results of this investigation apply to the design of phase-coupled array resonators and multiplexers.

Design and construction of the high-speed optoelectronic memory system demonstrator.

The high-speed optoelectronic memory system project is concerned with the reduction of latency within multiprocessor computer systems (a key problem) by the use of optoelectronics and associated packaging technologies. System demonstrators have been constructed to enable the evaluation of the technologies in terms of manufacturability. The system combines fiber, free space, and planar integrated optical waveguide technologies to augment the electronic memory and the processor components. Modeling and simulation techniques were developed toward the analysis and design of board-integrated waveguide transmission characteristics and optical interfacing. We describe the fabrication, assembly, and simulation of the major components within the system.

Integrated three-dimensional optical multilayer using free-space optics.

An integrated three-dimensional optical multilayer system for optical data communications is presented. It is based on the use of free-space optical light propagation and combines two integration principles, namely, planar and stacked integration. The combination of both integration schemes aims at a maximal design flexibility for complex geometric layouts. On the other hand, packaging issues that stem from assembly and tolerance have to be considered. Here we describe the basic concept and demonstrate the implementation of an optical interface module in a processor-memory bus.

Apodized multilevel diffractive lenses that produce desired diffraction-limited focal spots.

An apodized, multilevel diffractive lens that can produce a desired diffraction-limited focal spot is proposed for many applications, such as focusing, imaging, optical storage, and optical trapping. The three key points for the design are the innovative idea of complex conjugate subzones, the use of Babinet's principle, and the equivalent-pupil (or aperture) function theory of diffractive focusing elements composed of concentric transparent rings. As a concrete example, we numerically design a mixed multilevel diffractive lens (the highest phase level is 8) to produce a diffraction-limited Gaussian focal spot. Some related problems, such as the validity range and the combination with high-numerical-aperture refractive lenses, are also discussed.

Fractional Montgomery effect: a self-imaging phenomenon.

Self-imaging means image formation without the help of a lens or any other device between object and image. There are three versions of self-imaging: the classical Talbot effect (1836), the fractional Talbot effect, and the Montgomery effect (1967). Talbot required the object to be periodic; Montgomery realized that quasiperiodic suffices. Classical means that the distance from object to image is an integer multiple of the Talbot distance Z(T) = 2p2/lambda, where p is the grating period. Fractional implies a distance that is a simple fraction of Z(T): say, Z(T)/2, Z(T)/4, 3Z(T)/2.... We explore the most general case of the fractional Montgomery effect.

Achromatic optical fourier transformer with planar-integrated free-space optics.

We address the problem of achromatization of an optical system for the realization of planar-integrated, free-space optics. In particular we demonstrate an integrated optical Fourier transformation module that was achromatized for the visible spectrum by means of a diffractive lens doublet. The optical system design is studied by using the parabolic approximation of the scalar diffraction theory, including terms related to astigmatism. Based on the method of ABCD ray matrices, the optical specifications of the lens doublet are derived and the chromatic correction effect is quantified. For experimental confirmation the diffraction patterns of various grating structures are evaluated.

Azimuthally polarized surface plasmons as effective terahertz waveguides.

Quite recently, it was found that metal wires can effectively guide terahertz radiation. Based on the fact that the absolute values of the relative permittivities of metals in the spectral region of terahertz radiation are huge, we here analyse the properties of this kind of waveguide and explain the related experimental results. In particular, we show that the observed waveguiding is due to the propagation of an azimuthally polarized surface plasmon along the wire. Some related aspects, such as the choice of metal and the slowly decaying modal field, are also discussed. In particular, we show that, if a copper wire with a radius of 0.45 mm is used, the attenuation coefficient is smaller than 2x10-3 cm-1 in the whole range of 0.1~1 THz.

Temporal filtering by double diffraction.

We present a theoretical analysis of the temporal behavior of double-diffraction setups. It applies, in particular, to Talbot and Montgomery interferometers, whose operation is based on the self-imaging effect. The use of both types of interferometer as temporal filters for optical and terahertz applications was recently suggested. We show that double-diffraction setups can be modeled as communications channels with dispersive behavior caused by diffraction. We develop mathematical expressions for the phase delay, the group velocity, and the group-velocity dispersion for both quasi-monochromatic and polychromatic case. Based on these results, the temporal impulse response of a double-diffraction setup is derived. Finally, a general description of its practical implementation are presented.

Generalized confocal imaging systems for free-space optical interconnections.

A generalized confocal imaging system, which is composed of two confocal lenses and one field lens, is proposed for free-space optical interconnections. Unlike in a conventional 4-f system, both the object distance and the image distance can be almost arbitrarily chosen. This advantage is especially important for practical setups in which the object distance and the image distance cannot be designed to be the same. As a concrete example, we have designed and experimentally tested a planar-integrated micro-optical imaging system. The result is in good agreement with the theoretical prediction. Similarly to the conventional 4-f imaging system and the light-pipe imaging system, the system proposed here can also be used as one important part of a hybrid imaging setup.

Comprehensive focusing analysis of various Fresnel zone plates.

A series-form expression for the individual diffracted field of a general annular ring is derived from the Rayleigh-Sommerfeld diffraction integral. It can be used for the accurate and fast simulation of any diffractive focusing element composed of concentric transparent rings. We present a comprehensive analysis, based on the leading term and the linear superposition principle, of the focusing performances of various Fresnel zone plates. Many problems, such as the equivalent aperture function, the diffraction efficiency, the focal spot pattern, the suppression of higher orders and the appearance of "fractional orders," and the explanation for the appearance of Fraunhofer diffraction patterns, are analytically investigated in detail. Because of the great similarity between Fresnel zone plates and multilevel diffractive lenses, most of the obtained results are also applicable to multilevel diffractive lenses.

Modified Fresnel zone plates that produce sharp Gaussian focal spots.

A modified Fresnel zone plate that can produce an approximate Gaussian focal spot is proposed for the focusing and imaging of soft x rays and extreme ultraviolet radiation. The selection conditions for the positions and the widths of the concentric open rings are analytically presented. The focal spot size can be much smaller than the width of the narrowest open ring, and the sidelobes and the higher orders can be effectively suppressed. Through numerical experiments, we confirm that a Gaussian focal spot with a beam width of 7.7 nm can be produced by a modified Fresnel zone plate with a minimum structure size of 30 nm.

Nonparaxial model for the focusing of high-numerical-aperture photon sieves.

Recently, a paraxially individual far-field model was presented for the focusing and imaging analysis of pinhole photon sieves. By use of a local Taylor expansion of the integrated function of the Rayleigh-Sommerfeld diffraction formula, the small-size property of the individual pinholes, and the linear superposition principle, we extend this model to the nonparaxial case of high-numerical-aperture photon sieves. Some related problems, such as the validity range of this nonparaxial model and the selection conditions for the individual pinholes, are also discussed in detail.