Hans Lochbihler

Highly conducting wire gratings in the resonance region.

We present a theoretical approach for calculating the fields diffracted by gratings made of highlyconducting wires that have a rectangular shape. The fields between the wires are represented in terms of modal expansions that satisfy the approximated impedance boundary condition. Our results show thatthis procedure is particularly suited to dealing with gold gratings used in the infrared range, a spectral region where the assumption of a perfect conductor does not hold, and where the rigorous modal method assuming penetrable wires exhibits numerical instabilities linked with the high conductivity of gold. Numerical results are presented, and the theory is used to determine wire parameters by fitting theoretical and experimental data.

Diffraction from Highly Conducting Wire Gratings of Arbitrary Cross-section

Abstract A theory describing the diffraction properties of highly conducting wire gratings with arbitrary cross-sections is presented. The method incorporates the surface impedance boundary condition on the field along metallic interfaces and relies on the solution of a coupled system of ordinary differential equations for finding the field between wires. The theory is exemplified numerically for different wire profiles. The numerical results for gold gratings in the resonance region are compared with those obtained from a theory valid for perfectly conducting wires. Comparisons to measurements validate the effectiveness of the developed algorithm and show that it is particularly suited for dealing with metallic gratings in the infrared region.

Characterization of highly conducting wire gratings using an electromagnetic theory of diffraction

Abstract An electromagnetic method is used to reconstruct the cross section of galvanically manufactured wire gratings from efficiency measurements. The approach, based on a surface impedance approximation, allows us to deal with highly conducting wires of arbitrary cross sections. By varying the wire profile parameters, a total coincidence between theory and transmittance measurements in the resonance region can be found for different gold gratings.

Characterization of x-ray transmission gratings.

Self-supporting transmission gratings with periods of 1 microm or below are used in combination with grazing-incidence telescopes in celestial x-ray astronomy. They can be produced with sizes up to only a few cm(2); therefore, several hundreds or even thousands of individual elements are needed in order to cover the aperture of a telescope. This large number leads to the problem of characterization of the gratings regarding their x-ray performance. We demonstrate that spectrometry in the resonance domain using H polarization is a suitable method for the determination of the grating wire profile and deviations of the grating surface from a plane. Although developed originally for microwave applications it can be shown that the methods of strict solution of the Helmholtz equation are able to explain even small effects related to imperfections of periodic submicrometer structures.

Properties of TM resonances on metallic slit gratings

Electromagnetic resonances on metallic slit gratings induced by TM polarized incident light have been investigated and physically interpreted. We have developed an electromagnetic model imposing surface impedance boundary conditions on the metallic grating surface from which we derive simple formulas explaining all physical properties of these resonances. It is demonstrated that Fabry-Perot (or cavity) resonances are generated by the zeroth slit mode yielding extraordinary transmission. For very narrow slits, the resonant H-field is squeezed to the slit walls and causes enhanced power losses. The excitation of surface plasmon polaritons (SPPs), however, is generated by two mode coupling. SPPs are linked to sharp absorption peaks and dips in transmittance. It is shown that these phenomena are primarily caused by the interaction of the electromagnetic fields with the finite conducting slit walls. These findings have been confirmed by measured transmittance data of gold gratings with periods of 0.5 μm, 1 μm, and 2 μm.

Polarimetry of transmission gratings

We have investigated the polarizing properties of gold wire gratings in the resonance domain. The partial polarizing properties of 1-μm period gratings in the near IR are then used to orient the wire structure of transmission grating facets parallel to each other by means of an alignment polarimeter technique. The absolute alignment accuracy for these gratings is limited by the influence of the support structure on the orientation of the polarization ellipse. If the polarizing properties of this perturbative component are known, the accuracy can be enhanced by treating the polarization by means of the Mueller calculus.

Origin of modulated interference effects in photoelastic modulators

Photoelastic modulators (PEMs) consisting of a plane-parallel dielectric plate exhibit multiple internal reflections like those in a Fabry- Perot interferometer. If a PEM is illuminated by a coherent radiation source at normal incidence, a modulation of the intensity of transmitted light can be observed. In a recent paper by Oakberg, the modulated interference effect was interpreted as periodic thickness variations of the PEM plate. We discuss three different models that describe interference modulation in PEMs. Then, it is experimentally demonstrated for a PEM with a symmetric optical element that the periodic variation of the refractive index in the PEM plate is responsible for this modulated interference effect.

Diffraction from highly conducting lamellar gratings in conical mountings

The modal method based on a surface impedance approximation is extended to conical mountings valid for highly conducting lamellar gratings. The results of this theory are then compared with those obtained by an exact method which are in good coincidence for highly conducting gratings. It is demonstrated that for highly conducting materials this method yields accurate results while the exact modal method has its numerical limitations. Furthermore, polarization conversion in transmittance has been studied experimentally on gold gratings as well as by numerical calculations. It is then shown that wire gratings can act as effective polarization rotators in a transmitted-light configuration. Moreover, polarization conversion can be utilized to study the excitation of surface polaritons on highly conducting gratings. The dispersion of surface polaritons has been evaluated from transmittance measurements in conical mountings.

Field enhancement on metallic wire gratings

Abstract The electromagnetic near field of metallic wire gratings is numerically investigated for wavelengths for which strong resonances occur in the diffracted orders coincident with high radiation losses. Energy flow diagrams confirm that this phenomenon can be explained by excitation of surface polaritons. The distributions of the electromagnetic fields exhibit strong enhancements in the vicinity of the wire surface. The enhancement factor depends on the conductivity and the geometry of the wires.

Recognition of damage in polarizing transmission-grating facets

An optical setup was built for microscopic damage inspection on transmission-grating facets composed of a gold-wire structure. Contrast improvement was achieved by exploiting the polarizing properties of these gratings in the near-infrared region. Spatial filtering yields an additional contrast enhancement and reduces unwanted signals caused by the periodic support structure. An image-processing algorithm is developed that evaluates the number and the size of the faults in a grating facet with high accuracy from only one digital image.