Stefan Fasold's research while affiliated with Vistec Electron Beam GmbH and other places

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Publications (57)


Impact of e-beam lithography and data preparation optimization on optical performance of integrated photonic waveguides
  • Conference Paper

April 2024

Markus Greul

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Kevin Edelmann

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Stefan Fasold

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[...]

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Ulf Weidenmueller
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A complex lattice unit cell: The transition from a single particle cell to a dimer cell gives rise to new scattering states.
Two types of silicon metasurfaces with a complex unit cell composed of dissimilar periodic lattices of resonant nanocylinders and nanotubes: (a) Structure and scanning electron micrograph of a metasurface composed of periodic rows of nanocylinders and nanotubes, termed an anisotropic metasurface. Here, $a = 150\;{\rm nm}$ a = 150 n m and $b = 300\;{\rm nm}$ b = 300 n m . The periodicity of the supercell is 930 nm and 550 nm. (b) The isotropic metasurface is composed of a checkerboard lattice of nanoparticles. Here, $c = 185\;{\rm nm}$ c = 185 n m . For both arrangements, the nanotube outer diameter is ${D_1} = 400\;{\rm nm}$ D 1 = 400 n m , the nanotube inner diameter is $d = 200\;{\rm nm}$ d = 200 n m , and the nanocylinder diameter is ${D_2} = 230\;{\rm nm}$ D 2 = 230 n m . The periodicity of the supercell is $500\sqrt 2 \approx 707\;{\rm nm}$ 500 2 ≈ 707 n m . Each nanoparticle has a height of 300 nm. The scale bars are 1 µm.
Transmittance spectra of all-dielectric metasurfaces with anisotropic arrangements of nanocylinders and nanotubes as shown in Fig. 2(a), for two different polarizations of the external field: (a) ${ x}$ x -polarization, and (b) ${ y}$ y -polarization. For ${ x}$ x -polarization, two distinct magnetic dipole resonances are observed at 1010 nm and 1124 nm (mode A and mode B), as shown in the insets of (a). For ${ y}$ y -polarization, a hybrid response with the AFM order is observed at 1397 nm (mode C), as confirmed by the magnetic field distribution shown in the inset. The onset of the first diffraction order is at $930\;{\rm nm} \times 1.5 = 1395\;{\rm nm}$ 930 n m × 1.5 = 1395 n m .
(a)–(d) Experimental and simulated spectral and angular dependence of transmittance of anisotropic metasurface for TE- and TM-polarized light incident in the ${ YZ}$ Y Z plane. (e)–(h) Same dependence of transmittance for light incident in the ${ XZ}$ X Z plane. (i)–(l) Experimental and simulated spectral and angular dependence of transmittance of isotropic metasurface for TE- and TM-polarized light incident in the ${ XZ}$ X Z plane. The black dashed lines highlight the FM and AFM modes of the proposed metasurfaces.
Experimental transmittance spectra of the anisotropic metasurface measured for (a) ${ x}$ x -polarized and (b) ${ y}$ y -polarized plane waves.
Optically induced antiferromagnetic order in dielectric metasurfaces with complex supercells
  • Article
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April 2023

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61 Reads

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2 Citations

Journal of the Optical Society of America B

Journal of the Optical Society of America B

Metasurfaces are 2D planar lattices of nanoparticles that allow the manipulation of incident light properties. Because of that attribute, metasurfaces are promising candidates to replace bulky optical components. Traditionally, metasurfaces are made from a periodic arrangement of identical unit cells. However, more degrees of freedom are accessible if an increasing number of structured unit cells are combined. The present study explores a type of dielectric metasurface with complex supercells composed of Mie-resonant dielectric nanocylinders and nanoscale rings. We numerically and experimentally demonstrate the signature of an optical response that relies on the structures sustaining staggered optically induced magnetic dipole moments. The optical response is associated with an optical antiferromagnetism. The optical antiferromagnetism exploits the presence of pronounced coupling between dissimilar Mie-resonant dielectric nanoparticles. The coupling is manipulated by engineering the geometry and distance between the nanoparticles, which ultimately enhances their effective magnetic response. Our results suggest possible applications in resonant nanophotonics by broadening the modulation capabilities of metasurfaces.

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Toward Perfect Optical Diffusers: Dielectric Huygens’ Metasurfaces with Critical Positional Disorder

December 2021

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330 Reads

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14 Citations

Conventional optical diffusers, such as thick volume scatterers (Rayleigh scattering) or microstructured surface scatterers (geometric scattering), lack the potential for on-chip integration and are thus incompatible with next-generation photonic devices. Dielectric Huygens' metasurfaces, on the other hand, consist of two-dimensional arrangements of resonant dielectric nanoparticles and therefore constitute a promising material platform for ultra-thin and highly efficient photonic devices. When the nanoparticles are arranged in a random but statistically specific fashion, diffusers with exceptional properties are expected to come within reach. In this contribution, we explore how dielectric Huygens' metasurfaces can be used to implement wavelength-selective diffusers with negligible absorption losses and nearly-Lambertian scattering profiles that are largely independent of the angle and polarization of incident waves. We show that the combination of tailored positional disorder with a carefully-balanced electric and magnetic response of the nanoparticles is an integral requirement for the operation as a diffuser. We experimentally and numerically characterize the directional scattering performance of the proposed metasurfaces and highlight their usability in wavefront-shaping applications. Since our metasurfaces operate on the principles of Mie scattering and are embedded in a glassy environment, they may easily be incorporated in integrated photonic devices, fiber optics, or mechanically robust augmented reality displays. This article is protected by copyright. All rights reserved


Experimental observation of the short-range surface plasmon polariton mode and its longitudinal adiabatic compression in a metallic wedge

October 2021

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39 Reads

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1 Citation

In this study, we explore analytically and experimentally long- and short-range surface plasmon polariton (LR-SPP and SR-SPP, respectively) modes in gold wedges. Especially, we aim to observe the 2-dimensional confinement of the electromagnetic field in gold wedges as it could enhance the light-matter interaction by offering a local density of states which depends on the propagation constant, consequently on the wedge height. The LR-SPP mode can propagate over a long distance, but the real part of the propagation constant remains relatively insensitive to the decreasing wedge height. This mode also experiences cut-off at a wedge height of about 50 nm in our experimental condition. Meanwhile, the SR-SPP mode has a large propagation constant that increases further with decreasing wedge height. As a result, the effective wavelength of the mode shrinks confining the electromagnetic wave longitudinally along the propagation direction in addition to enhancing the transverse confinement of SR-SPP. In the experiment, we use gold wedges with different edge heights to excite each SPP mode individually and image the electromagnetic near field by using a pseudo-heterodyne scattering scanning near-field optical microscope. By imaging the LR-SPP mode field, we demonstrate that the theoretical and measured values of the effective wavelength agree quite well. By using short wedges, we measure the SR-SPP mode field and demonstrate that the effective wavelength decreases to 47% in about half a micrometer of propagation distance. This corresponds to a 3.5 times decrease of the vacuum wavelength or an effective index of 3.5. It is important to note that this value is, by no means, the limit of the electromagnetic field’s longitudinal confinement in a gold wedge. Rather, we were only able to measure the electromagnetic field up to this point due to our measurement limitations. The electromagnetic field will be propagating further, and the longitudinal confinement will increase as well. In conclusion, we measured the SR-SPP in a gold wedge and demonstrate the electromagnetic field confinement in the visible spectrum in gold wedges.


(A) Dual-tip SNOM configuration on top of a silicon nanodisk metasurface. (B) Two aperture tips when they are positioned at the minimum distance from each other. The red dashed arrows show the direction of the scan. The length of the double-sided blue arrow indicates the minimum distance between the apertures. The parabolic white area is the avoidance area (the red dashed curve corresponds to its boundary). The red cross denotes the vertex of the avoidance area. Scanning electron micrograph of the aperture of the (C) excitation tip and (D) detection tip. Scale bars are 0.5 μm.
(A) Measured and simulated transmittance for the nanodisk silicon metasurface depicted in the inset with the 1 µm scale bar. Two minima correspond to the wavelengths of the magnetic dipole (MD) and electric dipole (ED) modes of the metasurface. In-plane (B) electric and (C) magnetic field intensity for the ED mode in one unit cell of the metasurface. The white arrows illustrate the polarization vectors of the fields.
(A)–(D) Measured near-field intensity distributions by the dual-tip SNOM when the metasurface is moved by a displacement of Δx along the x-axis. Δx = 0 is the initial position. ±0.05 µm is the respective error due to uncertainty to find the drifts of the excitation tip during the measurements in (B)–(D). White dots indicate the aperture position of the excitation tip in the measurements. For normalizing the data, the measured near-field intensities in (A)–(D) were divided by the maximum measured value of all panels. (E)–(H) Numerical simulations for the in-plane components of the magnetic field intensity for the metasurface displacements in (A)–(D). The gray parabolic-like regions represent the avoidance area. Purple arrows show the position and direction of the magnetic dipole used in the simulations. The simulated intensities with the avoidance area are also normalized, after setting the intensities inside the avoidance area to zero, to the maximum value of the calculated near-field intensity in (E)–(H). Panels (A)–(D) and (E)–(H) share the common color scale while the numbers on the right bottom corners are the maximum normalized intensities in each panel. (I)–(L) Simulation results for the in-plane magnetic field intensities. All the simulation results are shown for the same intensity value to increase the visibility of the near-field intensity patterns. The black scale bar is 1 µm.
(A)–(E) Measured near-field intensity distributions for the metasurface displacements Δy along y-axis. The initial position is Δy = 0. White dots indicate the position of the excitation aperture in the measurements. ±0.05 µm is the error in the displacements (B)–(E) due to the drifts of the excitation tip during the measurements. The measured near-field intensities were divided by the maximum measured value for the normalization. (F)–(J) Numerical simulations of the in-plane magnetic field intensity components for the metasurface displacements in (A)–(E). The gray parabolic-like region is the avoidance area. The purple arrow denotes the magnetic dipole direction and position in the simulations. The simulated intensities, after setting the intensities inside the avoidance areas to zero, were normalized to the maximum calculated near-field intensity. Panels (A)–(E) and (F)–(J) share the common color scale while the numbers on the right bottom corners are the maximum normalized intensities in each panel. (K)–(O) Simulation results (F)–(J) without covering the avoidance area. The simulation results are shown for the same intensity value to increase the visibility of the near-field patterns. The black scale bar is 1 µm.
(A) Normalized integrated intensities for the measurements in Figure 3A–D and simulations in Figure 3D–H for Δx displacements. The error bar only shows the error in finding displacements due to the drift of the excitation tip during the measurements. (B) Corresponding normalized radiative power and the power loss of the magnetic dipole. (C) Normalized integrated intensities for the measurements in Figure 4A–E and simulations in Figure 4H–J for Δy displacements. (D) Corresponding normalized radiative power and the power loss of the magnetic dipole for the same Δy displacements. The integrated intensities were calculated for the raw data of simulations and measurements. To normalize the integrated intensity of the measurements, they were scaled to the maximum value of the integrated intensity in the simulations.
Investigation of dipole emission near a dielectric metasurface using a dual-tip scanning near-field optical microscope

October 2021

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179 Reads

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4 Citations

A wide variety of near-field optical phenomena are described by the interaction of dipole radiation with a nanophotonic system. The electromagnetic field due to the dipole excitation is associated with the Green’s function. It is of great interest to investigate the dipole interaction with a photonic system and measure the near-field Green’s function and the quantities it describes, e.g., the local and cross density of optical states. However, measuring the near-field Green’s function requires a point-source excitation and simultaneous near-field detection below the diffraction limit. Conventional single-tip near-field optical microscope (SNOM) provides either a point source excitation or amplitude and phase detection with subwavelength spatial resolution. The automated dual-tip SNOM, composed of two tips, has overcome the experimental challenges for simultaneous near-field excitation and detection. Here, we investigate the dipole emission in the near-field of a dielectric metasurface using the automated dual-tip SNOM. We have analyzed the near-field pattern and directional mode propagation depending on the position of the dipole emission relative to the metasurface. This study is one further step toward measuring the dyadic Green’s function and related quantities such as cross density of optical states in complex nanophotonic systems for both visible and near-infrared spectra.


Design and targeted dispersion properties of a plasmonic metasurface stack combining two kinds of gold nano-patches. (a) Cross-section showing the principal components and parameters of the stack model: (1) air above the stack, (2) glass layer of height dC = 500 nm as cladding, (3) upper metasurface, (4) glass spacer layer with height dS ranging from 80 to 960 nm, (5) lower metasurface, and (6) glass wafer underneath the stack, presumed to be infinite with respect to the stack. The two metasurface layers have the same height h = 30 nm, but differing periods ΛU,L = (341, 200 nm) and nano-patch widths wU,L = (160, 70 nm). The black arrow denotes the direction of an incident plane wave kin coming from air. (b) Rendering of the ideal stack with cut out sections revealing the two metasurface layers. (c)–(f) Simulation results showing transmittance: (c) Fourier-Modal-Method (FMM) results of the upper (red line) and lower metasurfaces (blue line) as single layers. (d) SASA result of the full stack with dS = 600 nm. (e) SASA result of the full stack with dS = 960 nm. (f) SASA result scanning the spacer height dS from 80 to 960 nm in 40 nm steps. The red dashed lines reference the results in (d) and (e).
Experimental results and comparison to the adapted SASA model. (a) SEM image of a stack with spacer height (dS = 120 nm) before the cladding layer was added. The smaller patches of the lower metasurface are visible underneath the upper layer nano-patches by virtue of secondary electrons. The blue and yellow grids represent the lattices of the upper and lower metasurfaces, respectively. This visualizes the pseudo incommensurability of the two periods. (b) Surface plot of the measured transmittances of all 23 stack variants with spacer heights dS from 80 to 960 nm in 40 nm steps. The red dashed lines reference the results in (d) and (e) at dS = 600 and 960 nm. (c)–(e) Direct comparison between measurement (red) and SASA (blue) results: (c) Individual single layer results for the lower (dashed line) and upper (solid line) metasurfaces. (d) Stack with dS = 600 nm. (e) Stack with dS = 960 nm.
Breakdown of the FMA and limits to the SASA model. Illustration of the coupling of evanescent diffraction orders with a spacer distance below (a) and above (b) the critical distance of the stack. The black arrow denotes the direction of an incident plane wave kin. Red and green arrows represent reflected (kR) and transmitted (kT) fields. Dashed arrows illustrate evanescent diffraction orders. The black boxes correspond to the unit cells of each metasurface. (c) Plot of the critical distance dcrit of the stack, based on the period of the upper metasurface (ΛU = 341 nm). The green, blue, and red areas denote the different phases of coupling: far-field coupling (FMA), near-field coupling (FMA breakdown), and diffractive coupling (diffraction grating). The black dashed lines mark the point from which on the SASA model is considered valid. (d) and (e) show the comparison of SASA and experimental results for two different cases: (d) stack at dS = 360 nm and (e) stack at dS = 400 nm. Blue and green areas correspond to the areas in (c). (f) Normalized root mean square deviation (NRMSD) between SASA and measurement results calculated for all 23 stack heights. The change between the two coupling phases is indicated by dashed lines and colored areas.
(a) Illustration of all reflection paths included up to first order (Ψ = 1). Again, kin denotes an incident plane wave coming from air. Red and green arrows represent reflected (ER) and transmitted (ET) fields. Each occurrence of a bend in the black dashed line of a path corresponds to a reflection at an interface or the metasurface. Together, the transmitted fields of the reflection paths add up (interfere) to the total transmitted field at first order (Ψ = 1). Correspondingly, red dashed arrows represent distinct reflected fields back into air, emerging from the internal reflection paths. Together, they contribute to the total reflected field. (b)–(d) Plots of the geometric expansion of the SASA model of the stack with dS = 960 nm. (b) Computed amplitude of the full stack compared to the geometric expansion from zeroth order up to second order. (c) Enlarged plot interval of (b) showing the differences between expansions of different orders around the Fabry–Pérot resonance at 718 nm wavelength. (d) Computed amplitude of the coefficients of first and second order compared to the full stack and zeroth order expansion.
Experimental validation of the fundamental mode approximation for stacked metasurfaces and its application to the treatment of arbitrary period ratios

September 2021

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62 Reads

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1 Citation

We experimentally realize a series of incommensurable metasurface stacks that transition from near-field coupling to a far-field regime. Based on a comparison between a semi-analytic model and measurements, we, furthermore, present an experimental study on the validity of the fundamental mode approximation (FMA). As the FMA is a condition for the homogeneity of a metasurface, its validity allows for strong simplification in the design of stacked metasurfaces. Based on this, we demonstrate a method for the semi-analytic design of stacked periodic metasurfaces with arbitrary period ratios. In particular, incommensurable ratios require computational domains of impractically large sizes and are usually very challenging to fabricate. This results in a noticeable gap in parameter space when optimizing metasurface stacks for specific optical features. Here, we aim to close that gap by utilizing the principles of the FMA, allowing for additional parameter combinations in metasurface design.


Citations (27)


... The coupling between plasmonic nanocavities and TMD-based materials has been demonstrated as an effective means to enhance the emission properties of TMDs [10][11][12][13]. This enhancement can be analyzed in two ways. ...

Reference:

Photoluminescence Enhancement and Carrier Dynamics of Charged Biexciton in Monolayer WS2 Coupled with Plasmonic Nanocavity
Photoluminescence Enhancement of Monolayer WS 2 by n-Doping with an Optically Excited Gold Disk
  • Citing Article
  • November 2023

Nano Letters

... In this model, it is supposed that the energy of a system of such particles depends on the orientation of different magnetic dipole moments relative to each other as well as to an externally applied magnetic field [14]. Recently, it has been proposed to study different magnetic orders with metasurfaces [15][16][17][18][19][20][21][22][23]. They are arrays of artificially structured subwavelength resonant particles that facilitate reaching the desirable electromagnetic functionality. ...

Optically induced antiferromagnetic order in dielectric metasurfaces with complex supercells
Journal of the Optical Society of America B

Journal of the Optical Society of America B

... The Purcell factor accounts for the enhancement of spontaneous emission of an emitter due to the optical states compared to a homogeneous background [57][58][59][60][61]. The near-field intensity distribution in the surroundings of the nanoparticles determines the LDOS [62,63]. Specifically, strong electromagnetic energy concentrations in small volumes lead to high Purcell factors [64,65]. ...

Investigation of dipole emission near a dielectric metasurface using a dual-tip scanning near-field optical microscope
Nanophotonics

Nanophotonics

... [37,38] Other variants regard membranes with an array of dielectric nanocylinders made, for example, from amorphous silicon and embedded in amorphous silicon oxide. [32,[39][40][41][42][43][44][45][46][47] Although the precision and accuracy of especially lithographic manufacturing processes have steadily increased with the stage of their development, [32,42,43] fabrication errors and disorder remain still decisive issues. The extent to which perturbations of morphological order affect photonic systems depends on the type of disorder and their relation to various geometrical and material quantities. ...

Toward Perfect Optical Diffusers: Dielectric Huygens’ Metasurfaces with Critical Positional Disorder
Advanced Materials

Advanced Materials

... In particular, as the metasurfaces are conceptually handled as homogeneous layers, SASA enables us to layer metasurfaces of inconsummerable periods without the need to define huge unit cells. An in depth discussion and experimental validation of SASA is published in Ref. [32]. ...

Experimental validation of the fundamental mode approximation for stacked metasurfaces and its application to the treatment of arbitrary period ratios
APL Photonics

APL Photonics

... Because the optical response of metasurface usually relies on the dimensions and dielectric properties, substantial efforts have explored the tuning mechanisms of integrating active materials into nanostructures. By leveraging external stimuli such as mechanical actuation [47][48][49] , chemical reactions 50 , optical 51,52 , electrical 53-58 and thermal [59][60][61][62] schemes, light field distributions of these active metasurfaces exhibit dynamically control-lable functionalities, offering a programmable flexibility in information processing and storage. In particular, chalcogenide phase-change materials (PCMs) are uniquely poised for the photonic modulation and resonance tuning of active metasurfaces, owing to their striking portfolio of properties [63][64][65][66][67][68][69] . ...

Multiresponsive Dielectric Metasurfaces

ACS Photonics

... This has already led to profound findings such as light localization in lattice structures written in photorefractive materials [5], the ability to engineer the plasmon dispersion relation in evanescently coupled metasurfaces [2] and the discovery of exotic optical states exhibiting characteristics of both moiré flat bands and (quasi-)bound states in the continuum [6]. However, a deeper understanding of moiré effects from first principles and their impact on photonic band structures remains a prime challenge for current research in nano-optics [1,7,8] and numerical and computational methods that can explore such systems are investigated more recently [9][10][11][12][13][14]. Moiré flat bands have also been explored in graphene nanoribbons [15], electric circuits with extremely high degrees of freedom [16] and 1D electronic geometries [17]. ...

Equivalence of reflection paths of light and Feynman paths in stacked metasurfaces
  • Citing Article
  • December 2020

... CD spectroscopy has found widespread applications in various scientific disciplines including chemistry [2,3], biochemistry [4,5], and material science [6][7][8]. Recently, chiral optical metasurfaces have emerged as a promising platform to enhance CD spectroscopy in compact integrated photonic setups, based on their capabilities to manipulate circularly polarized light at the nanoscale and control the light polarization state efficiently [9][10][11][12]. Chiral metasurfaces consisting of subwavelength nanostructures with symmetry breaking patterns enable the precise chiroptical control of the amplitude, phase, and polarization of the incident light, which have been widely used in many fields such as chiral imaging [13,14], optical encryption [15,16], and optical communication [17]. ...

Chiral Bilayer All-Dielectric Metasurfaces
  • Citing Article
  • November 2020

ACS Nano

... It is known that light waves carry energy and linear and angular momenta [1]. For the nanoparticles (NPs) placed in the path of light propagation, the linear momenta will lead to optical gradient forces, while the angular momenta creates an optical torque, which causes the particle to rotate [2]. ...

Direct and High-Throughput Fabrication of Mie-Resonant Metasurfaces via Single-Pulse Laser Interference
  • Citing Article
  • April 2020

ACS Nano

... The inclusion of high-index nanopillar arrays adds a phase shift to the cavity and leads to a subsequent shift in the resonant peak [19,39]. Then, by adding anisotropy to the nanostructures, the FP cavity becomes sensitive to polarization [40]. However, reconstruction via the use of algorithms must be applied to recover the polarization spectrum, causing low detection speed and insufficient measurement accuracy. ...

Nanostructure-modulated planar high spectral resolution spectro-polarimeter
Optics Express

Optics Express