Correction to "Q-Factor Optimization of Modes in Ordered and Disordered Photonic Systems Using Non-Hermitian Perturbation Theory".

[This corrects the article DOI: 10.1021/acsphotonics.3c00510.].

Self-assembled photonic cavities with atomic-scale confinement.

Despite tremendous progress in research on self-assembled nanotechnological building blocks, such as macromolecules1, nanowires2 and two-dimensional materials3, synthetic self-assembly methods that bridge the nanoscopic to macroscopic dimensions remain unscalable and inferior to biological self-assembly. By contrast, planar semiconductor technology has had an immense technological impact, owing to its inherent scalability, yet it seems unable to reach the atomic dimensions enabled by self-assembly. Here, we use surface forces, including Casimir-van der Waals interactions4, to deterministically self-assemble and self-align suspended silicon nanostructures with void features well below the length scales possible with conventional lithography and etching5, despite using only conventional lithography and etching. The method is remarkably robust and the threshold for self-assembly depends monotonically on all the governing parameters across thousands of measured devices. We illustrate the potential of these concepts by fabricating nanostructures that are impossible to make with any other known method: waveguide-coupled high-Q silicon photonic cavities6,7 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 with sub-nanometre 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.

Q-Factor Optimization of Modes in Ordered and Disordered Photonic Systems Using Non-Hermitian Perturbation Theory.

The quality factor, Q, of photonic resonators permeates most figures of merit in applications that rely on cavity-enhanced light-matter interaction such as all-optical information processing, high-resolution sensing, or ultralow-threshold lasing. As a consequence, large-scale efforts have been devoted to understanding and efficiently computing and optimizing the Q of optical resonators in the design stage. This has generated large know-how on the relation between physical quantities of the cavity, e.g., Q, and controllable parameters, e.g., hole positions, for engineered cavities in gaped photonic crystals. However, such a correspondence is much less intuitive in the case of modes in disordered photonic media, e.g., Anderson-localized modes. Here, we demonstrate that the theoretical framework of quasinormal modes (QNMs), a non-Hermitian perturbation theory for shifting material boundaries, and a finite-element complex eigensolver provide an ideal toolbox for the automated shape optimization of Q of a single photonic mode in both ordered and disordered environments. We benchmark the non-Hermitian perturbation formula and employ it to optimize the Q-factor of a photonic mode relative to the position of vertically etched holes in a dielectric slab for two different settings: first, for the fundamental mode of L3 cavities with various footprints, demonstrating that the approach simultaneously takes in-plane and out-of-plane losses into account and leads to minor modal structure modifications; and second, for an Anderson-localized mode with an initial Q of 200, which evolves into a completely different mode, displaying a threefold reduction in the mode volume, a different overall spatial location, and, notably, a 3 order of magnitude increase in Q.

Efficient low-reflection fully etched vertical free-space grating couplers for suspended silicon photonics.

We design and fabricate a grating coupler for interfacing suspended silicon photonic membranes with free-space optics while being compatible with single-step lithography and etching in 220 nm silicon device layers. The grating coupler design simultaneously and explicitly targets both high transmission into a silicon waveguide and low reflection back into the waveguide by means of a combination of a two-dimensional shape-optimization step followed by a three-dimensional parameterized extrusion. The designed coupler has a transmission of -6.6 dB (21.8 %), a 3 dB bandwidth of 75 nm, and a reflection of -27 dB (0.2 %). We experimentally validate the design by fabricating and optically characterizing a set of devices that allow the subtraction of all other sources of transmission losses as well as the inference of back-reflections from Fabry-Pérot fringes, and we measure a transmission of 19 % ± 2 %, a bandwidth of 65 nm and a reflection of 1.0 % ± 0.8 %.

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 nonpiezoelectric demonstrations have been inefficient. In this Letter, 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 around 6.8 GHz, operating at room temperature. 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.

Room-Temperature Silicon Platform for GHz-Frequency Nanoelectro-Opto-Mechanical Systems.

Nanoelectro-opto-mechanical systems enable the synergistic coexistence of electrical, mechanical, and optical signals on a chip to realize new functions. Most of the technology platforms proposed for the fabrication of these systems so far are not fully compatible with the mainstream CMOS technology, thus, hindering the mass-scale utilization. We have developed a CMOS technology platform for nanoelectro-opto-mechanical systems that includes piezoelectric interdigitated transducers for electronic driving of mechanical signals and nanocrystalline silicon nanobeams for an enhanced optomechanical interaction. Room-temperature operation of devices at 2 GHz and with peak sensitivity down to 2.6 cavity phonons is demonstrated. Our proof-of-principle technology platform can be integrated and interfaced with silicon photonics, electronics, and MEMS devices and may enable multiple functions for coherent signal processing in the classical and quantum domains.

Observation of slow light in glide-symmetric photonic-crystal waveguides.

We report optical transmission measurements on suspended silicon photonic-crystal waveguides, where one side of the photonic lattice is shifted by half a period along the waveguide axis. The combination of this glide symmetry and slow light leads to a strongly enhanced chiral light-matter interaction but the interplay between slow light and backscattering has not been investigated experimentally in such waveguides. We build photonic-crystal resonators consisting of glide-symmetric waveguides terminated by reflectors and use transmission measurements as well as evanescent coupling to map out the dispersion relation. We find excellent agreement with theory and measure group indices exceeding 90, implying significant potential for applications in slow-light devices and chiral quantum optics. By measuring resonators of different length, we assess the role of backscattering induced by fabrication imperfections and its intimate connection to the group index.

Quantifying the Robustness of Topological Slow Light.

The backscattering mean free path ξ, the average ballistic propagation length along a waveguide, quantifies the resistance of slow light against unwanted imperfections in the critical dimensions of the nanostructure. This figure of merit determines the crossover between acceptable slow-light transmission affected by minimal scattering losses and a strong backscattering-induced destructive interference when the waveguide length L exceeds ξ. Here, we calculate the backscattering mean free path for a topological photonic waveguide for a specific and determined amount of disorder and, equally relevant, for a fixed value of the group index n_{g} which is the slowdown factor of the group velocity with respect to the speed of light in vacuum. These two figures of merit, ξ and n_{g}, should be taken into account when quantifying the robustness of topological and conventional (nontopological) slow-light transport at the nanoscale. Otherwise, any claim on a better performance of topological guided light over a conventional one is not justified.