We report polarization tomography experiments on metallic nanohole arrays with square and hexagonal symmetry. As a main result we find that a fully polarized input beam is partly depolarized after transmission through a nanohole array. This loss of polarization coherence is found to be anisotropic; i.e., it depends on the polarization state of the input beam. The depolarization is ascribed to a combination of two factors: (i) the nonlocal response of the array as a result of surface-plasmon propagation and (ii) the non-plane-wave nature of a practical input beam. © 2005 Optical Society of America OCIS codes: 230.3990, 240.6680, 260.3910. Currently there is much interest in the optical properties of thin metal films perforated with arrays of subwavelength holes, or nanohole arrays. The optical transmission of these arrays shows a strongly peaked spectrum with anomalously large transmission peak values; this is usually ascribed to resonant excitation of propagating surface electromagnetic waves or surface plasmons (SPs). -3In this Letter we focus on the polarization properties of the anomalous transmission and show that these are strongly inf luenced by the propagating nature of the SPs.So far, polarization properties of nanohole arrays have been studied in a limited context: a beam with a given uniform state of polarization (SOP in ) is transformed by an anisotropic array or an isotropic array with nonspherical holes into a different uniform state of output polarization (SOP out ). 4 -6 This corresponds to a mapping of the Poincaré sphere onto itself; for instance, a rectangular array or a square array with elliptical holes acts as a birefringent and (or) a dichroic element that may convert a linear SOP into an elliptical SOP, conserving polarization coherence. In the present Letter we focus instead on cases where the degree of polarization (DOP) is reduced, DOP out , DOP in , corresponding to a reduction in radius and, in general, a deformation of the Poincaré sphere. 7,8 To underline this point we have chosen for our experiments square and hexagonal arrays, i.e., arrays that, for symmetry reasons, 9 cannot modify the SOP for plane-wave illumination at normal incidence. As we will show, depolarization occurs when two (quite common) conditions are simultaneously fulfilled: (i) the response of the array is nonlocal because of SP propagation, and (ii) the input beam is not a plane wave [but, e.g., a Gaussian beam, with a finite numerical aperture (NA)].In general, depolarization occurs when an optical system acts nonuniformly on polarization within the (spatial or temporal) bandwidth of the incident wave, thereby coupling polarization to other degrees of freedom. Experimentally, a study of depolarization requires a measurement of the Mueller matrix by a tomographic method. 7,8Here we report such polarization-tomography experiments on nanohole arrays and interpret the results in the context of SP propagation.We start by recapitulating the essence of our theoretical model. 9The input and output optical fields ...

The effective Young's modulus of silicon nitride cantilevers is determined for thicknesses in the range of 20-684 nm by measuring resonance frequencies from thermal noise spectra. A significant deviation from the bulk value is observed for cantilevers thinner than 150 nm. To explain the observations we have compared the thickness dependence of the effective Young's modulus for the first and second flexural resonance mode and measured the static curvature profiles of the cantilevers. We conclude that surface stress cannot explain the observed behavior. A surface elasticity model fits the experimental data consistently. © 2009 American Institute of Physics. ͓DOI: 10.1063/1.3152772͔ Micro-and nanoelectromechanical systems are widely studied for their application in sensing and actuation devices. 1 Down-scaling of such devices improves their sensitivity however at the same time mechanical properties may start to deviate from the bulk behavior. The finite-size effects have been the subject of theoretical studies for the past years. [2][3][4][5][6][7][8] In experimental work on single-crystalline Si cantilevers it has been shown that the Young's modulus strongly depends on the thickness. 9 This behavior has also been observed for suspended crystalline silver nanowires. 10 In describing the properties of nanoscale devices, the bulk Young's modulus ͑E͒ is generally replaced by the effective Young's modulus ͑E eff ͒ to account for size-dependent effects, including surface stress. The total surface stress ͑⌺͒ can be written as a sum of a strain-independent part ͑ ͒ and a strain-dependent part ͑strain ⑀͒, which is related to surface elasticity ͑C s ͒ ⌺ = + C s ⑀. [11][12][13][14][15] In this letter, we study the size-dependency of the Young's modulus in silicon nitride cantilevers when one dimension ͑cantilever thickness͒ is scaled down from 684 to 20 nm. As the SiN x is amorphous, it is difficult to distinguish between the two contributions since parameters ͑e.g., C s ͒ are unknown and difficult to calculate. However, by comparing the experimental data for the first and second mode to theory, we show that the straindependent part of the total surface stress is responsible for the size-dependency.Cantilevers are fabricated from low-pressure chemical vapor deposited ͑LPCVD͒ silicon nitride ͑SiN x ͒ on Si͑100͒ substrates and are patterned with an electron-beam pattern generator. After resist development we use reactive ion etching in a CHF 3 / O 2 ͑20:1͒ plasma to transfer the pattern to the SiN x layer. After this step cantilevers are released using a KOH etch process ͑15 min etching time at 85°C; Si etch rate about 1 m / min͒, yielding facetting along the ͑111͒ planes, as shown in Fig. 1͑a͒. This process introduces a negligible undercut, so that length corrections can be disregarded. 16 Cantilevers are fabricated with the following dimensions: lengths ͑L͒ from 8 to 100 m, widths ͑w͒ 8, 12, or 17 m, and thicknesses ͑h͒ ranging from 20 to 684 nm.The thickness was measured using an ellipsometer ͑Leitz SP͒ with an accuracy of ...

We present a systematic investigation of the dynamic properties of silicon nitride cantilevers in air. The thermal noise spectra of cantilevers have been measured using a home-made optical deflection setup. Torsional and flexural resonances up to the seventh mode are observed. The dependence of resonance frequencies on the dimensions and mode number is studied in detail. It is found that undercut increases the effective length of the cantilever by a value L, which depends on the undercut distance and the resonance mode shape, but not on the cantilever length. Finite element modelling confirms these experimental findings. A simple model is suggested for the shape of the undercut region, which agrees well with experimental findings. Using this model, the undercut cantilever can be approximated by a stepped beam, where the clamp distance depends on the underetch duration and the mode shape.

Terahertz beam focusing based on plasmonic waveguide scattering Appl. Phys. Lett. 101, 151116 (2012) Record-low propagation losses of 154dB/cm for substrate-type W1 photonic crystal waveguides by means of hole shape engineering Appl. Phys. Lett. 101, 131108 (2012) Optical absorption in graphene integrated on silicon waveguides Appl. Phys. Lett. 101, 111110 (2012) Integrating a plasmonic coupler to photo detector of terahertz frequency Appl. Phys. Lett. 101, 091114 (2012) Silicon nanomembrane based photonic crystal waveguide array for wavelength-tunable true-time-delay lines Amorphous silicon a-Si was made by ion irradiation of crystalline silicon with 1ϫ10 15 Xe ions cm Ϫ2 at 77 K in the 1-4 MeV energy range. Thermal relaxation of the amorphous network at 500°C for 1 h leads to an amorphous layer with a refractive index of nϭ3.73, significantly higher than that of crystalline silicon ͑nϭ3.45 at ϭ1.55 m͒. a-Si can thus serve as a waveguide core in Si based optical waveguides. Channel waveguides were made by anisotropic etching of a 1.5 m silicon-on-insulator structure that was partly amorphized. Transmission measurements of these waveguides as function of the amorphous silicon length show that the a-Si part of the waveguides exhibit a modal propagation loss of 70 cm Ϫ1 ͑0.03 dB m Ϫ1 ͒ and a bulk propagation loss of 115 cm Ϫ1 ͑0.05 dB m Ϫ1 ͒. Losses due to sidewall roughness are estimated, and are negligible compared to the modal loss.

The etching mechanisms of silicon carbide in an inductively coupled plasma (ICP) reactor using a SF 6 /O 2 gas mixture, have been investigated using optical emission spectroscopy (OES) and Langmuir probe measurements. The etching is shown to be ion induced with a high degree of anisotropy. An optimum etch rate is achieved with 20% oxygen content within the gas mixture. By studying the independent influence of the ICP power and the substrate bias voltage on the ion current density, as well as the fluorine and oxygen radical densities in the plasma, the etch mechanism is found to be dominated by the number of ions bombarding the SiC surface. The steady state sputter yield observed at P > 0.7 Pa, despite the increase in F radical concentration indicates the dominant role of ion bombardment in this etch regime, while at P < 0.7 Pa, the etch mechanism is limited by the number of F radicals in the plasma. The OES results have shown that the etch rate is dependent upon the concentration of reactive radicals present with the [F]/[0] ratio = 8 at the optimum. Whilst using the optimum gas composition, the parameters which dominate the physical side of the reaction, ICP power and bias voltage, produce an increase of the etch rate as the potential difference between the substrate and the plasma is increased.