arXiv subjects

Willem L. Vos

Publications and source records attributed to Willem L. Vos.

At least 19 recordsLinked to original sources

arXiv2026

Defect states in three-dimensional diamond photonic band gap crystals

We perform a theoretical study of defect states within the photonic band gap of three-dimensional diamond crystals composed of point scatterers and doped with substitutional defects. The defects introduce localized states inside the photonic band gap, whose existence conditions and eigenfrequencies are expressed in terms of the on-site Green's function of the ideal defect-free crystal. Off-site Green's functions are also calculated as function of distance and are shown to vanish within approximately two unit cells. Finite-size effects are analyzed by comparing the results obtained in the infinite-crystal limit with numerical simulations based on the coupled-dipole method. The latter not only reproduce the eigenfrequencies of the defect states within the band gap, but also provide their lifetimes originating from the finite crystal size. The lifetimes of the defect states increase exponentially with crystal size, becoming very long for large crystals. In addition to defect states in the three-dimensional photonic band gap, the defects also give rise to strongly detuned states outside the gap, which decouple from the spectrum of the ideal defect-free crystal.

cond-mat.dis-nn↗

arXiv2026

Resolving features and derivatives in noisy data using weighted Whittaker-Henderson smoothing

A frequently occurring challenge in experimental and numerical observations is how to resolve features, such as spectral peaks - with center, width, height - and derivatives from measured data with unavoidable noise. Although many smoothing procedures exist, most are ineffective at reducing noise when the widths of the features varies strongly. Therefore, we modify the Whittaker-Henderson smoothing procedure to locally balance the spectral features and the noise. The central contribution of our procedure is that we introduce adjustable weights that are optimized using cross-validation. Using the measurement errors, a straightforward error analysis of the smoothed results is feasible. To illustrate the effectiveness of our smoothing algorithm, we derive for an optical Bragg reflector nanostructure the chirp of an optical pulse (group delay dispersion) using synthetic phase data with noise. The smoother faithfully reconstructs the group delay dispersion, reducing noise by more than a factor 40, allowing to identify details that otherwise remain buried in noise. Finding the optimal weights using the limited-memory BFGS algorithm for N=1000 complex valued reflectivity data points takes on average less than two seconds on a typical computer. To further illustrate the power of our smoother, we introduce a general framework to solve commonly occurring difficulties in data and data analysis; how to properly smoothen unequally sampled data, how to identify and quantify discontinuities, including discontinuous derivatives or kinks, how to properly smooth data in the vicinity of boundaries to the data domains, and multi-dimensional smoothing.

physics.data-an↗

arXiv2026

The vanishing distance: a practical range boundary for dynamic wavefront shaping

Wavefront shaping (WFS) is a powerful modern method to control light propagation through scattering media, with applications ranging from biomedical imaging via cryptography to free-space optical communication. While WFS has been highly successful in static or slowly evolving media, its practical relevance in dynamic and extended scattering environments remains difficult to assess. In particular, no simple criterion currently identifies the propagation distance beyond which the residual ballistic component is no longer distinguishable from the scattered background. Here, we introduce the vanishing distance, defined as the propagation length where the ballistic power equals that carried by a single diffuse mode. Unlike the transport mean free path, which characterizes angular randomization of the scattered field, the vanishing distance identifies the loss of the ballistic channel on a modal-power basis. Beyond this distance, transmission or imaging can no longer rely on the ballistic component and must instead exploit the scattered field. We present a simple semi-analytical model, validated against Monte Carlo simulations and experiments in both monodisperse and heterogeneous scattering media, allowing the vanishing distance and the associated minimum source power to be estimated. Across representative scattering environments, the transition is found to occur typically after about 30-40 scattering mean free paths. These results provide a simple guideline for assessing the practical relevance of dynamic wavefront shaping.

physics.optics↗

arXiv2026

Optically dense nanowire metamaterials are transparent to polarization

We study the transport of light through dense opaque anisotropic metamaterials consisting of oriented nanowires. The nanowires consist of polymer photoresist that is structured by direct laser writing (DLW) with two-photon induced polymerization, with radii between $a = 0.5$ and $1~μ\text{m}$. Our flat samples have a thickness up to 9 layers, from $L = 3~μ\text{m}$ to $20~μ\text{m}$. Within each layer, the nanowires are parallel and spaced with random nearest-neighbor distances; nanowires in adjacent layers are perpendicular. The diffuse optical transmission at $λ= 633~$nm is as low as $T = 12 \%$, typical of optically dense, multiple scattering metamaterials, with a mean free path down to $\ell = 1.1~μ\text{m}$, much less than the sample thickness. It is striking that the linear polarization of the input light is maintained at the output of the dense nanowire samples, and not scrambled as in dense nanosphere arrays. Moreover, the linear output polarization faithfully tracks the input polarization. We propose that the polarization is maintained in our optically thick samples, since light is predominantly transported perpendicularly to the nanowire layers. The polarization vector then lies in the nanowire plane, consisting of a linear combination of parallel and perpendicular vectors that are both conserved upon subsequent scattering. Hence, the polarization remains independent of nanowire orientation, even after multiple scattering events. We propose that anisotropic scattering samples may find practical uses in white LEDs and its applications in lighting luminaires, optical communication, and encryption systems.

physics.optics↗

arXiv2026

Nanosecond wavefront shaping to focus through agitated turbid media

Multiple scattering rapidly scrambles optical fields in fog, snow and turbid water, causing op- timized wavefront corrections to become obsolete on microsecond timescales. Although wavefront shaping enables focusing through static scattering layers, closed-loop control in dynamically evolving media has remained experimentally challenging because the correction bandwidth must approach the intrinsic decorrelation rate of the speckle. Here, we demonstrate closed-loop wavefront shaping with 32 independent degrees of freedom in an agitated turbid medium exhibiting sub-microsecond decorrelation. The medium thickness exceeds the transport mean free path, meaning the far-field speckle autocorrelation is limited to a diffraction-sized grain. Despite the microsecond decorrelation and this multiple-scattering regime, stable focusing is maintained as the correction cycle approaches the intrinsic dynamics of the medium. These results establish an experimentally accessible regime for coherent wave control in rapidly evolving complex media.

physics.optics↗

arXiv2025

Radiative local density of states in three-dimensional photonic band-gap crystals to interpret time-resolved emission

We investigate the spontaneous emission of light in three-dimensional (3D) photonic crystals through theoretical calculations and simulations. It is well known that spontaneous emission depends on the radiative local density of states (RLDOS). Photonic band-gap crystals radically modulate the RLDOS, thereby controlling spontaneous emission. We compare two different methods to calculate the RLDOS: the plane-wave expansion (PWE) method and the finite-difference time-domain (FDTD) method. The PWE method directly calculates the RLDOS of an infinite photonic crystal, whereas the FDTD method simulates the RLDOS through the power emitted by a dipole in a finite photonic crystal. We demonstrate that the methods yield similar frequency-dependent trends in the RLDOS, with relative differences of less than 12% that originate from the different boundary conditions. We employ the plane-wave expansion method to compute distributions of emission rates that are relevant to many optical experiments where quantum emitters are distributed within a crystal. Such distributions of emission rates enable us to compute and directly interpret the time-resolved decay as observed in experiments. We expect that our results promote the RLDOS to the realm of optical design and products.

physics.optics↗

arXiv2025

Momentum-resolved reflectivity of a 2D photonic crystal in the near-infrared

Two-dimensional (2D) photonic crystals offer strong control over the propagation of light through their bands. Theoretical methods for computing the band structure in 2D are well-established and fast because 2D photonic crystals are homogeneous in the third dimension. Experimental verification is scarce, however, especially in the telecom range, because real photonic crystals and experimental methods inherently cannot be homogeneous in the third dimension. In this work, we report momentum-resolved reflectivity measurements on photonic crystals that are periodic in two dimensions and homogeneous over a thickness of 5 μm. Using Fourier spectroscopy, we carefully select wave vectors in the 2D plane of periodicity of the photonic crystal. Our experiments agree excellently with 2D band structure calculations and with 2D finite-difference time-domain simulations, confirming that our experimental methods truly pertain to nanophotonics in 2D. Our results provide a robust bridge between theory and experiment, and our techniques can be readily extended to other 2D structures, including those with functional defects.

physics.optics↗

arXiv2025

Dispersion of backward-propagating waves in a surface defect on a 3D photonic band gap crystal

We experimentally study the dispersion relation of waves in a two-dimensional (2D) defect layer with periodic nanopores that sits on a three-dimensional (3D) photonic band gap crystal made from silicon by CMOS-compatible methods. The nanostructures are probed by momentum-resolved broadband near-infrared imaging of p-polarized reflected light that is collected inside the light cone as a function of off-axis wave vectors. We identify surface defect modes at frequencies inside the band gap with a narrow relative linewidth ($Δω/ω$ = 0.028), which are absent in defect-free 3D crystals. We calculate the dispersion of modes with relevant mode symmetries using a plane-wave-expansion supercell method with no free parameters. The calculated dispersion matches very well with the measured data. The dispersion is negative in one of the off-axis directions, corresponding to backward-propagating waves where the phase velocity and the group velocity point in opposite directions, as confirmed by finite-difference time-domain simulations. We also present an analytic model of a 2D grating sandwiched between vacuum and a negative real $ε'$ < 0 that mimics the 3D photonic band gap. The model's dispersion agrees with the experiments and with the fuller theory and shows that the backward propagation is caused by the surface grating. We discuss possible applications, including a device that senses the output direction of photons emitted by quantum emitters in response to their frequency.

physics.optics↗

arXiv2024

Mesoscopic Theory of Wavefront Shaping to Focus Waves inside Disordered Media

We describe the {theory of focusing waves} to a predefined spatial point {inside} a disordered {three-dimensional medium} by the external shaping of {$N$} different field sources outside the medium, {also known as wavefront shaping}. We {derive} the energy density of the wave field {both} near the focal point and anywhere else inside the medium, {averaged over realizations\textit{ after} focusing}. {To this end, we conceive of a point source at the focal point that emits waves to a detector array that - by time reversal - emits the desired shaped fields. }%endcolor {It appears that the energy} density is formally equal to intensity speckle described by {the so-called} $C_1$, $C_2$, $C_3$ and even $C_0$ {correlations} in mesoscopic transport theory, {yet the density also obeys a diffusion equation}. The $C_1$ {correlations} describes the focusing in the random medium very well, but do not generate a new source of energy that {is conceived} at the focal point. A source emerges {only} when the $C_2$ speckle is incorporated. The role of $C_0$ speckle, describing fluctuations in the {local density of optical states (LDOS)} is also investigated, {but hardly plays a role in the focusing. } Finally, we use the {concept of an energy source inside the medium} to model the {well-known} optimized transmission by a slab using wavefront shaping.

physics.optics↗

arXiv2024

Probing the position-dependent optical energy fluence rate in three-dimensional scattering samples

The accurate determination of the position-dependent energy fluence rate of scattered light (which is proportional to the energy density) is crucial to the understanding of transport in anisotropically scattering and absorbing samples, such as biological tissue, seawater, atmospheric turbulent layers, and light-emitting diodes. While Monte Carlo simulations are precise, their long computation time is not desirable. Common analytical approximations to the radiative transfer equation (RTE) fail to predict light transport and could even give unphysical results. Therefore, we experimentally probe the position-dependent energy fluence rate of light inside scattering samples where the widely used P1 and P3 approximations to the RTE fail. The samples are three-dimensional (3D) aqueous suspensions of anisotropically scattering and both absorbing and non-absorbing spherical scatterers, namely, microspheres (r = 0.5 um) with and without absorbing dye. To probe the energy fluence rate, we detect the emission of quantum-dot reporter particles that are excited by the incident light and that are contained in a thin capillary. By scanning the capillary through the sample, we access the position dependence. We present a comprehensive discussion of experimental limitations and of both random and systematic errors. Our observations agree well with the Monte Carlo simulations and the P3 approximation of the RTE with a correction for forward scattering. In contrast, the P1 and the P3 approximations deviate increasingly from our observations, ultimately even predicting unphysical negative energies.

physics.optics↗

arXiv2024

Non-utopian optical properties computed of a tomographically reconstructed real photonic nanostructure

State-of-the-art computational methods combined with common idealized structural models provide an incomplete understanding of experiments on real nanostructures, since manufacturing introduces unavoidable deviations from the design. We propose to close this knowledge gap by using the real structure of a manufactured crystal as input in computations to obtain a realistic comparison with observations on the same nanostructure. We demonstrate this approach on the structure of a real silicon inverse woodpile photonic bandgap crystal, obtained by previous synchrotron X-ray imaging. A 2D part of the dataset is selected and processed into a computational mesh suitable for a Discontinuous Galerkin Finite Element Method (DGFEM) to compute optical transmission spectra that are compared to those of a utopian crystal, i.e., a hypothetical model crystal with the same filling fraction where all pores are identical and circular. The nanopore shapes in the real crystal differ in a complex way from utopian pores, leading to a complex transmission spectrum with significant frequency speckle in and beyond the gap. The utopian model provides only a limited understanding of the spectrum: while it accurately predicts low frequency finite-size fringes and the lower band edge, the upper band edge is off, it completely misses the presence of speckle, the domination of speckle above the gap, and possible Anderson localized states in the gap. Moreover, unlike experiments where only external probes are available, numerical methods allow to study all fields everywhere. While the pore shapes hardly affect the fields at low frequency, major differences occur at high frequency such as localized fields deep inside the real crystal. In summary, using only external measurements and utopian models may give an erroneous picture of the fields and the LDOS inside a real crystal, which is remedied by our new approach.

physics.optics↗

arXiv2024

Experimentally mapping the scattering phases and amplitudes of a finite object by optical mutual scattering

Mutual scattering arises when multiple waves intersect within a finite scattering object, resulting in cross-interference between the incident and scattered waves. By measuring mutual scattering, we determine the complex-valued scattering amplitude $f$ - both amplitude and phase - of the finite object, which holds information on its scattering properties by linking incident and outgoing waves from any arbitrary direction. Mutual scattering is present for any coherent wave - acoustic, electromagnetic, particle - and we here demonstrate the effect using optical experiments. We propose an experimental technique for characterization that utilizes mutual scattering and we present our results for four distinct finite objects: a polystyrene sphere (diameter $59\ μ$m), a single black human hair (diameter $92\ μ$m), a strip of pultruded carbon (edge length $140\ μ$m), and a block of ZnO$_2$ (edge length $64\ μ$m). Our measurements exhibit qualitative agreement with Mie scattering calculations where the model is applicable. Deviations from the model indicate the complexity of the objects, both in terms of their geometrical structure and scattering properties. Our results offer new insights into mutual scattering and have significant implications for future applications of sample characterization in fields such as metrology, microscopy, and nanofabrication.

physics.optics↗

arXiv2023

Wavefront shaping through a free-form scattering object

Wavefront shaping is a technique to study and control light transport inside scattering media. Wavefront shaping is considered to be applicable to any complex material, yet in most previous studies, the only sample geometries that are studied are slabs or wave-guides. In this paper, we study how macroscopic changes in the sample shape affect light scattering using the wavefront shaping technique. Using a flexible scattering material, we optimize the intensity of light in a focusing spot using wavefront shaping and record the optimized pattern, comparing the enhancement for different curvatures and beam radii. We validate our hypothesis that wavefront shaping has a similar enhancement regardless of the free-form shape of the sample and thus offers relevant potential for industrial applications. We propose a new figure of merit to evaluate the performance of wavefront shaping for different shapes. Surprisingly, based on this figure of merit, we observe that for this particular sample, wavefront shaping has a slightly better performance for a free-form shape than for a slab shape.

physics.optics↗

arXiv2023

Symmetries and Wavefunctions of Photons Confined in 3D Photonic Band Gap Superlattices

We perform a computational study of confined photonic states that appear in a three-dimensional (3D) superlattice of coupled cavities, resulting from a superstructure of intentional defects. The states are isolated from the vacuum by a 3D photonic band gap, using a diamond-like inverse woodpile crystal structure, and exhibit 'Cartesian' hopping of photons in high-symmetry directions. We investigate the confinement dimensionality to verify which states are fully 3D confined, using a recently developed scaling theory to analyze the influence of the structural parameters of the 3D crystal. We create confinement maps that trace the frequencies of 3D confined bands for select combinations of key structural parameters, namely the pore radii of the underlying regular crystal and of the defect pores. We find that a certain minimum difference between the regular and defect pore radii is necessary for 3D confined bands to appear, and that an increasing difference between the defect pore radii from the regular radii supports more 3D confined bands. In our analysis we find that their symmetries and spatial distributions are more varied than electronic orbitals known from solid state physics. We also discover pairs of degenerate 3D confined bands with p-like orbital shapes and mirror symmetries matching the symmetry of the superlattice. Finally, we investigate the enhancement of the local density of optical states (LDOS) for cavity quantum electrodynamics (cQED) applications. We find that donor-like superlattices, i.e., where the defect pores are smaller than the regular pores, provide greater enhancement in the air region than acceptor-like structures with larger defect pores, and thus offer better prospects for doping with quantum dots and ultimately for 3D networks of single photons steered across strongly-coupled cavities.

physics.optics↗

arXiv2023

Enhanced Secrecy in Optical Communication using Speckle from Multiple Scattering Layers

We study the secrecy of an optical communication system with two scattering layers, to hide both the sender and receiver, by measuring the correlation of the intermediate speckle generated between the two layers. The binary message is modulated as spatially shaped wavefronts, and the high number of transmission modes of the scattering layers allows for many uncorrelated incident wavefronts to send the same message, making it difficult for an attacker to intercept or decode the message and thus increasing secrecy. We collect 50,000 intermediate speckle patterns and analyze their correlation distribution using Kolmogorov-Smirnov (K-S) test. We search for further correlations using the K-Means and Hierarchical unsupervised classification algorithms. We find no correlation between the intermediate speckle and the message, suggesting a person-in-the-middle attack is not possible. This method is compatible with any digital encryption method and is applicable for codifications in optical wireless communication (OWC).

physics.optics↗

arXiv2023

Unsupervised Machine Learning to Classify the Confinement of Waves in Periodic Superstructures

We employ unsupervised machine learning to enhance the accuracy of our recently presented scaling method for wave confinement analysis [1]. We employ the standard k-means++ algorithm as well as our own model-based algorithm. We investigate cluster validity indices as a means to find the correct number of confinement dimensionalities to be used as an input to the clustering algorithms. Subsequently, we analyze the performance of the two clustering algorithms when compared to the direct application of the scaling method without clustering. We find that the clustering approach provides more physically meaningful results, but may struggle with identifying the correct set of confinement dimensionalities. We conclude that the most accurate outcome is obtained by first applying the direct scaling to find the correct set of confinement dimensionalities and subsequently employing clustering to refine the results. Moreover, our model-based algorithm outperforms the standard k-means++ clustering.

physics.optics↗

arXiv2023

Observation of light propagation through a three-dimensional cavity superlattice in a 3D photonic band gap

We experimentally investigate unusual light propagation inside a three-dimensional (3D) superlattice of resonant cavities that are confined within a 3D photonic band gap. Therefore, we fabricated 3D diamond-like photonic crystals from silicon with a broad 3D band gap in the near-infrared and doped them with a periodic array of point defects. In position-resolved reflectivity and scattering microscopy, we observe narrow spectral features that match well with superlattice bands in band structures computed with the plane wave expansion. The cavities are coupled in all three dimensions when they are closely spaced and uncoupled when they are further apart. The superlattice bands correspond to light that hops in high symmetry directions in 3D - so-called Cartesian Light - that opens applications in 3D photonic networks, 3D Anderson localization of light, and future 3D quantum photonic networks.

physics.optics↗

arXiv2022

Sensing the position of a single scatterer in an opaque medium by mutual scattering

We investigate the potential of mutual scattering, i.e., light scattering with multiple properly phased incident beams, as a method to extract structural information from inside an opaque object. In particular, we study how sensitively the displacement of a single scatterer is detected in an optically dense sample of many (up to $N=1000$) similar scatterers. By performing exact calculations on ensembles of many point scatterers, we compare the mutual scattering (from two beams) and the well-known differential cross-section (from one beam) in response to the change of location of a single dipole inside a configuration of randomly distributed similar dipoles. Our numerical examples show that mutual scattering provides speckle patterns with an angular sensitivity at least 10 times higher than the traditional one-beam techniques. By studying the "susceptivity" of mutual scattering, we demonstrate the possibility to determine the original depth relative to the incident surface of the displaced dipole in an opaque sample. Furthermore, we show that mutual scattering offers a new approach to determine the complex scattering amplitude.

physics.optics↗