arXiv subjects

Søren Stobbe

Publications and source records attributed to Søren Stobbe.

At least 19 recordsLinked to original sources

arXiv2026

Measurements, simulations, and models of the point-spread function of electron-beam lithography

When a sample is exposed using electron-beam lithography, the electrons scatter deep and far in the substrate, resulting in unwanted deposition of dose at both the nano- and the microscale. This proximity effect can be mitigated by proximity effect correction provided that accurate and validated models of the point-spread function of the electron scattering are available. Most works so far considered a double-Gaussian model of the electron point-spread function, which is very inaccurate for modern electron-beam writers with high acceleration voltages. We present measurements of the process point-spread function for chemically semi-amplified resist on silicon and indium phosphide substrates using a 150 kV electron-beam lithography system. We find that the double-Gaussian model deviates from experiments by up to four orders of magnitude. We propose instead a model comprising the sum of a power-law and a Gaussian, which is in excellent agreement with simulations of the electron scattering obtained by a Monte Carlo method. We apply the power-law plus Gaussian model to quantify the electron scattering and proximity effect correction parameters across material stacks, processing, and voltages from 5 kV to 150 kV. We find that the power-law term remains remarkably constant, whereas the long-range dose contributions and the clearing dose are significantly affected by the substrate and the acceleration voltage. Combined, the results imply that reliance on the double-Gaussian approximation in proximity-effect correction has become a limiting factor for resolution in fabrication at the nanoscale.

physics.app-ph↗

arXiv2026

Broadband silicon photonic phase shifters driven by gradient optical forces

While initially deployed for optical interconnects, silicon photonics is increasingly being explored as a hardware platform for programmable optical systems, including linear optical processors, neuromorphic photonic networks, quantum photonic circuits and multiplexed sensor arrays. Common to most existing implementations is that light is controlled with electronics, and even basic demonstrations wherein light directly controls light remain limited. Here we demonstrate a broadband all-optical silicon photonic phase shifter based on an optomechanically mediated light-light interaction arising from the gradient optical force. Our device concept relies on slot-mode waveguides suspended by subwavelength gratings, which provide mechanical support while preserving optical confinement. We demonstrate all-optical phase shifting using a guided pump beam co-propagating with the signal beam, with only 60 $μ$W required to achieve a $π$ phase shift in a 178.6 $μ$m-long device. In addition, we measure the required pump power across a wide parameter space and find quantitative agreement with a lumped force-equilibrium model. Since the actuation relies on an all-optical geometric deformation rather than on material-index tuning, the approach avoids local electrical connections to the active element, carries no Kramers-Kronig absorption penalty, and is naturally compatible with cryogenic quantum photonic platforms.

physics.optics↗

arXiv2026

Coupled Flexural Optomechanical Cavities with Engineered Nanomechanical Interconnects

Integrated nanomechanical circuits require compact and predictable ways to read out, confine, and connect mechanical motion across multiple nanoscale elements. This challenge is particularly acute for megahertz flexural modes, whose large mechanical response and nonlinear dynamics are attractive for optomechanics, sensing, and signal processing, but whose extended nature makes local confinement and coupling difficult within dense devices. Here we demonstrate an optomechanical nanobeam platform in which optical transduction and mechanical connectivity are both engineered lithographically. Transverse geometric asymmetry in the photonic-crystal cavity breaks the cancellation that suppresses dispersive coupling to in-plane flexural motion, making these modes optically bright without ancillary structures. In parallel, serpentine mechanical links engineered through their complex band structure act as compact mirrors and evanescent couplers for MHz flexural waves. In coupled-cavity devices, the normal-mode splitting decays exponentially with the number of serpentine cells, yielding an experimental attenuation constant in quantitative agreement with full-system simulations. Geometry-dependent measurements further show that the coupling can be tuned by the interconnect design and identify regimes where finite-link modes hybridize with the cavity modes, beyond a simple two-resonator picture. These results establish complex-band-engineered mechanical links as calibrated interconnects for scalable optomechanical nanocircuits based on optically addressable MHz flexural resonators.

physics.optics↗

arXiv2026

Computing with the complex nonlinear dynamics of an optomechanical oscillator

An optomechanical oscillator undergoes a Hopf bifurcation that connects two dynamical regimes with different information-processing capabilities: thermal Brownian motion and coherent self-sustained oscillation. Below threshold, the oscillator occupies a stable fixed point around which thermal fluctuations drive stochastic Brownian motion - a regime dominated by linear response, with only short-lived memory and negligible usable nonlinearity. Above threshold, radiation pressure, free-carrier dynamics, and thermo-optic relaxation act together to sustain a stable limit cycle that simultaneously provides both nonlinear transformation and dynamical memory. Here we show that this coherent regime can be used as a physical reservoir for computation: by perturbing the phonon-lasing attractor, the cavity performs nonlinear input-output transformations and retains short-term memory without any external feedback mechanism. Using only a single chip-integrated device with 20 virtual nodes, we reconstruct nonlinear functions, predict the evolution of chaotic time series, and perform spoken digit classification on a two-digit sub-task. The mechanical resonance frequency sets the intrinsic dynamical timescale of the reservoir and therefore its processing speed; while the present device operates near 0.4 GHz, optomechanical and nanomechanical systems can be engineered to reach multi-GHz and sub-terahertz frequencies, directly translating into a scalable path toward ultrafast integrated physical computing.

physics.optics↗

arXiv2025

Nanoelectromechanical spectral control of silicon bowtie nanocavities for quantum light sources

We present the design, fabrication, and characterization of tunable waveguide-coupled silicon bowtie cavities with strong spatial electromagnetic field confinement. We use nanoelectromechanical in-plane actuation for the tuning, as this combines cryocompatibility with an ultralow power consumption. Our device leverages a mode volume below 0.2 cubic wavelengths in the material to reach theoretical Purcell factors above 6,500 and waveguide-coupling efficiency above 30% across the full experimentally measured spectral-tuning range of 11 nm. Notably, the Purcell factor in our cavity depends only weakly on the applied voltage. Our spectral measurements demonstrate reversible tuning of bowtie cavities, and we directly show the in-plane actuation using in-situ characterization in a scanning electron microscope. Our results constitute the first demonstration of a low-loss dielectric tunable bowtie nanocavity with strong light confinement. This solves a key issue for experiments on strong light-matter interactions for cavity quantum electrodynamics and scalable photonic quantum technologies.

physics.optics↗

arXiv2025

Electronic-photonic circuit crossings

Electrical control of light in integrated photonics is central to a wide range of research and applications. It is conventionally achieved with thermo-optic tuning, but this suffers from high energy consumption and crosstalk. Nanoelectromechanical photonics could resolve these issues, but integrating this technology with conventional multilayer metal architectures is challenging, and conventional approaches do not allow crossings of electrical wires and photonic waveguides. Here, we use topology optimization to devise a single-layer electronic-photonic circuit crossing with up to 99.8 % optical transmission across a 20 nm electrical isolation trench. We focus our experiments on 100 nm trenches and measure an average transmission of 92.9 % over a 100 nm bandwidth, in excellent agreement with theory. We use these concepts to demonstrate a monolithic silicon nanoelectromechanical add-drop switch in which the flow of photons, electrons, and mechanical motions are fully integrated within the same layer. Our work addresses an important challenge in incorporating opto-electro-mechanical topologies into photonic integrated circuits and may lead to new functionalities in nano-opto-electro-mechanical systems, optomechanics, and integrated quantum photonics.

physics.optics↗

arXiv2025

Stealthy-Hyperuniform Wave Dynamics in Two-Dimensional Photonic Crystals

Hyperuniform structures are spatial patterns whose fluctuations disappear on long length scales, making them effectively homogeneous when observed from afar. Mathematically, this means that their spectral density, $\tildeρ({\bf k})$, approaches zero for low wavenumber, $|\textbf{k}|$. Crystalline lattices are hyperuniform, as are certain quasicrystals, maximally random jammed packing of spheres, and electrons in the fractional quantum Hall state. Stealthy-hyperuniformity is an even stronger constraint on the spectral density: it requires that $\tildeρ({\bf k})$ is strictly zero in a finite range of wavevectors around $\mathbf{k}=\mathbf{0}$, called the stealthy regime, or exclusion region. Since the degree of scattering by disorder is, to leading order, proportional to $\tildeρ({\bf k})$, waves propagating through such structures may do so without scattering for sufficiently long wavelengths and short distances. Here, we measure scattering by disorder in photonic crystal slabs with stealthy-hyperuniform disorder by measuring the linewidths of the photonic bands. We observe the transition between the stealthy and non-stealthy regimes, marked by a sharp increase in linewidth. We also observe the effects of multiple scattering in the stealthy regime, which implies diminishing transparency. Moreover, we show that residual single scattering in the stealthy regime arises from an intrinsically non-Hermitian effect: propagating light has a complex effective mass due to radiative loss out of the slab.

physics.optics↗

arXiv2025

Incoherent population trapping in quantum emitters

Deterministic emitters transform electronic excitations to photons with unity efficiency. Their development is crucial for both energy-efficient optical interconnects and photonic quantum technologies, but neither rigorous theoretical frameworks nor systematic experimental methods governing deterministic emitters and their identification were so far available. A central -- and seemingly obvious -- assumption underpinning previous works is that the radiative emission probability is proportional to the internal quantum efficiency. Here, we introduce a stochastic model of the decay dynamics in quantum emitters that disproves this assumption and provides a systematic framework for the development of deterministic quantum light sources. Our model agrees with a wide range of experimental findings, including time-resolved spectroscopy, autocorrelation measurements, and saturation spectroscopy, and it also explains a number of hitherto unexplained experiments. For example, our model shows that above-band continuous-wave excitation selects the exciton transitions with the lowest quantum efficiency, which is of direct importance for photonic quantum technologies relying on aligning nanostructures to emitters. We show that the underlying physics is governed by incoherent trapping of the population in metastable states, which has profound consequences for the physics of quantum emitters. Finally, we provide a straightforward experimental protocol for obtaining deterministic emitters.

quant-ph↗

arXiv2024

Enhancement and speed-up of carrier dynamics in a dielectric nanocavity with deep sub-wavelength confinement

The emergence of dielectric bowtie cavities enable optical confinement with ultrahigh quality factor and ultra-small optical mode volumes with perspectives for enhanced light-matter interaction. Experimental work has so far emphasized the realization of these nanocavities. Here, we experimentally investigate the ultrafast dynamics of a topology-optimized dielectric (silicon) bowtie nanocavity, with device dimensions down to 12 nm, that localizes light to a mode volume deep below the so-called diffraction limit given by the half-wavelength cubed. This strong spatial light concentration is shown to significantly enhance the carrier generation rate through two-photon absorption, as well as reducing the time it takes for the carriers to recover. A diffusion time below 1 ps is achieved for the bowtie cavity, which is more than an order of magnitude smaller than for a conventional microcavity. Additionally, parametric effects due to coherent interactions between pump and probe signals are also enhanced in the bowtie cavity, leading to an improved extinction ratio. These results demonstrate important fundamental advantages of dielectric bowtie cavities compared to conventional point-defect cavities, laying a foundation for novel low-power and ultrafast optical devices, including switches and modulators.

physics.optics↗

arXiv2024

Observation of strong backscattering in valley-Hall photonic topological interface modes

The unique properties of light underpin the visions of photonic quantum technologies, optical interconnects, and a wide range of novel sensors, but a key limiting factor today is losses due to either absorption or backscattering on defects. Recent developments in topological photonics have fostered the vision of backscattering-protected waveguides made from topological interface modes, but, surprisingly, measurements of their propagation losses were so far missing. Here we report on measurements of losses in the slow-light regime of valley-Hall topological waveguides and find no indications of topological protection against backscattering on ubiquitous structural defects. We image the light scattered out from the topological waveguides and find that the propagation losses are due to Anderson localization. The only photonic topological waveguides proposed for materials without intrinsic absorption in the optical domain are quantum spin-Hall and valley-Hall interface states, but the former exhibits strong out-of-plane losses, and our work therefore raises fundamental questions about the real-world value of topological protection in reciprocal photonics.

physics.optics↗

arXiv2024

Waveguide and cavity quantum electrodynamics with topological bowtie modes

We present a theoretical study on photonic topological crystals whose symmetry is governed by quantum valley-Hall topological insulators and whose propagating edge modes are strongly confined due to bowtie geometries. Dielectric bowtie structures exploit the field discontinuities at boundaries between materials with different refractive indices, and here bowties emerge at the topological interface due to the close proximity of two triangular features in the underlying crystal. The topological bowtie mode features a unit-cell mode volume down to $8\times10^{-4}$ cubic wavelengths at the center of the bowtie bridge of width $10~\text{nm}$, and we show that it is possible to use perturbed versions of the unit cells as building blocks for topological heterostructure bowtie cavities with quality factors exceeding $10^7$. Due to the tightly confined bowtie mode, this implies a strongly enhanced light-matter interaction as quantified by a Purcell factor of $3 \times 10^6$.

physics.optics↗

arXiv2023

Multimode optomechanics with a two-dimensional optomechanical crystal

Chip-scale multimode optomechanical systems have unique benefits for sensing, metrology and quantum technologies relative to their single-mode counterparts. Slot-mode optomechanical crystals enable sideband resolution and large optomechanical couplings of a single optical cavity to two microwave-frequency mechanical modes. Still, previous implementations have been limited to nanobeam geometries, whose effective quantum cooperativity at ultralow temperatures is limited by their low thermal conductance. In this work, we design and experimentally demonstrate a two-dimensional mechanical-optical-mechanical (MOM) platform that dispersively couples a slow-light slot-guided photonic-crystal waveguide mode and two slow-sound $\sim 7$ GHz phononic wire modes localized in physically distinct regions. We first demonstrate optomechanical interactions in long waveguide sections, unveiling acoustic group velocities below 800 m/s, and then move on to mode-gap adiabatic heterostructure cavities with a tailored mechanical frequency difference. Through optomechanical spectroscopy, we demonstrate optical quality factors $Q \sim 10^5$, vacuum optomechanical coupling rates, $g_o/2π$, of 1.5 MHz and dynamical backaction effects beyond the single-mode picture. At larger power and adequate laser-cavity detuning, we demonstrate regenerative optomechanical oscillations involving a single mechanical mode, extending to both mechanical modes through modulation of the input laser drive at their frequency difference. This work constitutes an important advance towards engineering MOM systems with nearly degenerate mechanical modes as part of hybrid multipartite quantum systems.

physics.optics↗

arXiv2023

Design, fabrication, and characterization of electrostatic comb-drive actuators for nanoelectromechanical silicon photonics

Nanoelectromechanical systems offer unique functionalities in photonics: The ability to elastically and reversibly deform dielectric beams with subwavelength dimensions enable electrical control of the propagation of light with a power consumption orders of magnitude below that of competing technologies, such as thermo-optic tuning. We present a study of the design, fabrication, and characterization of compact electrostatic comb-drive actuators tailored for integrated nanoelectromechanical silicon photonic circuits. Our design has a footprint of $1.2 \times 10^{3} μ$m$^{2}$ and is found to reach displacements beyond 50 nm at 5 V with a mechanical resonance above 200 kHz, or, using different spring constants and skeletonization, a mechanical resonance above 2.5 MHz with displacements beyond 50 nm at 28 V. This is sufficient to induce very large phase shifts and other optical effects in nanoelectromechanical reconfigurable photonic circuits.

physics.optics↗

arXiv2023

Self-assembly of atomic-scale photonic cavities

Despite tremendous progress in the research on self-assembled nanotechnological building blocks such as macromolecules, nanowires, and two-dimensional materials, synthetic self-assembly methods bridging nanoscopic to macroscopic dimensions remain unscalable and inferior to biological self-assembly. In contrast, planar semiconductor technology has had an immense technological impact owing to its inherent scalability, yet it appears unable to reach the atomic dimensions enabled by self-assembly. Here we use surface forces including Casimir-van der Waals interactions to deterministically self-assemble and self-align suspended silicon nanostructures with void features well below the length scales possible with conventional lithography and etching, despite using nothing more than conventional lithography and etching. The method is remarkably robust and the threshold for self-assembly depends monotonically on all governing parameters across thousands of measured devices. We illustrate the potential of these concepts by fabricating nanostructures, which are impossible to make with any other known method: Waveguide-coupled high-Q silicon photonic cavities that confine telecom photons to 2 nm air gaps with an aspect ratio of 100, corresponding to mode volumes more than 100 times below the diffraction limit. Scanning transmission electron microscopy measurements confirm the ability to build devices even with subnanometer dimensions. Our work constitutes the first steps towards a new generation of fabrication technology that combines the atomic dimensions enabled by self-assembly with the scalability of planar semiconductors.

physics.optics↗

arXiv2023

Intermodulation of optical frequency combs in a multimode optomechanical system

Phonons offer the possibility to connect the microwave and optical domains while being efficiently transduced with electronic and optical signals. Here, we present a multimodal optomechanical platform, consisting of a mechanical-optical-mechanical resonator configuration. The mechanical modes, with frequencies at 265 MHz and 6.8 GHz, can be simultaneously excited into a phonon lasing regime as supported by a stability analysis of the system. Both the MHz and the GHz modes enter a self-sustained oscillation regime, leading to the intermodulation of two frequency combs in the optical field. We characterize this platform experimentally, demonstrating previously unexplored dynamical regimes. These results suggest the possibility to control multiple mechanical degrees of freedom via a single optical mode, with implications in GHz phononic devices, signal processing, and optical comb sensing applications.

physics.optics↗

arXiv2022

Optomechanical generation of coherent GHz vibrations in a phononic waveguide

Nanophononics has the potential for information transfer, in an analogous manner to its photonic and electronic counterparts. The adoption of phononic systems has been limited, due to difficulties associated with the generation, manipulation, and detection of phonons, especially at GHz frequencies. Existing techniques often require piezoelectric materials with an external radiofrequency excitation that are not readily integrated into existing CMOS infrastructures, while non-piezoelectric demonstrations have been inefficient. In this work, we explore the optomechanical generation of coherent phonons in a suspended 2D silicon phononic crystal cavity with a guided mode around 6.8 GHz. By incorporating an air-slot into this cavity, we turn the phononic waveguide into an optomechanical platform that exploits localized photonic modes resulting from inherent fabrication imperfections for the transduction of mechanics. Such a platform exhibits very fine control of phonons using light, and is capable of coherent self-sustained phonon generation via mechanical lasing around 6.8 GHz. The ability to generate high frequency coherent mechanical vibrations within such a simple 2D CMOS-compatible system could be a first step towards the development of sources in phononic circuitry and the coherent manipulation of other solid-state properties.

physics.optics↗

arXiv2022

Cavity optomechanics with Anderson-localized optical modes

Confining photons in cavities enhances the interactions between light and matter. In cavity optomechanics, this enables a wealth of phenomena ranging from optomechanically induced transparency to macroscopic objects cooled to their motional ground state. Previous work in cavity optomechanics employed devices where ubiquitous structural disorder played no role beyond perturbing resonance frequencies and quality factors. More generally, the interplay between disorder, which must be described by statistical physics, and optomechanical effects has thus far been unexplored. Here, we demonstrate how sidewall roughness in air-slot photonic-crystal waveguides can induce sufficiently strong backscattering of slot-guided light to create Anderson-localized modes with quality factors as high as half a million and mode volumes that are below the diffraction limit. We observe how the interaction between these disorder-induced optical modes and in-plane mechanical modes of the slotted membrane is governed by a distribution of coupling rates, which can exceed $g_{\text{o}}/2π\sim 200$ kHz, leading to mechanical amplification up to self sustained oscillations via optomechanical backaction. Our work constitutes the first steps towards understanding optomechanics in the multiple-scattering regime and opens new perspectives for exploring complex systems with multitude mutually-coupled degrees of freedom.

physics.optics↗

arXiv2022

Nanometer-scale photon confinement in topology-optimized dielectric cavities

Nanotechnology enables in principle a precise mapping from design to device but relied so far on human intuition and simple optimizations. In nanophotonics, a central question is how to make devices in which the light-matter interaction strength is limited only by materials and nanofabrication. Here, we integrate measured fabrication constraints into topology optimization, aiming for the strongest possible light-matter interaction in a compact silicon membrane, demonstrating an unprecedented photonic nanocavity with a mode volume of $V\sim3\times10^{-4}\,λ^3$, quality factor $Q\sim1100$, and footprint $4\,λ^2$ for telecom photons with a $λ\sim 1550$ nm wavelength. We fabricate the cavity, which confines photons inside 8 nm silicon bridges and use near-field optical measurements to perform the first experimental demonstration of photon confinement to a single hotspot well below the diffraction limit in dielectrics.

physics.optics↗