The efficiency of multi-photon emission is an important characteristic of quantum light sources. Bright multi-photon emission is desirable for high-power lighting and lasers, while its complete suppression is required for high-purity single-photon generation. In colloidal quantum emitters, multi-photon emission can vary significantly between individual particles. Resolving this heterogeneity remains challenging with conventional particle-by-particle approaches. Here, we introduce a crosstalk-suppressed SPAD-array photon-correlation approach for high-throughput quantification of multi-photon emission from more than 1000 colloidal quantum shells. By projecting two images of the same sample onto distant regions of the detector array, we avoid short-range crosstalk between detector pixels. Time gating suppresses dark-count coincidences and distinguishes individual emitters from clusters. Applying this method to quantum shells reveals a near-Gaussian distribution of biexciton emission efficiencies, with a mean of 0.55 and an estimated intrinsic standard deviation of 0.12. Intra-batch correlations between the biexciton efficiency and the particle brightness are consistent with the volume scaling of Auger quenching. These results establish SPAD-array photon correlation as a scalable route to resolve multi-photon heterogeneities in nanoparticle ensembles.

The realization of on-chip photonic circuits requires scalable and deterministic single-photon emitters (SPEs) at room temperature, which remain a challenge in van der Waals materials. In this work, we report a novel three-step fabrication process for the generation of spatially controlled SPE arrays in hexagonal boron nitride (hBN). The process comprises site-selective gallium (Ga) focused ion beam milling, nanoscale conformal carbon deposition over the patterned regions, and subsequent thermal annealing. The synergistic combination of these steps resulted in a site-correlated emitter yield of ($\sim 89\%$) across 100 fabrication sites. Second-order autocorrelation measurements revealed pronounced three-level emitter dynamics where the best emitters exhibited high purity ($g^{(2)}(0)=0.15 \pm 0.09$).To the best of our knowledge, this is the first lithography-free, direct-write approach combining Ga-ion milling, selective carbon engineering, and thermal annealing to deterministically generate \hBN{} \SPE{}s. The reproducibility of the method is validated across multiple independently fabricated samples. These results establish a scalable, lithography-free pathway toward on-demand SPE arrays relevant to integrated quantum photonics.

The Stokes parameters are three real parameters that completely characterize partially coherent optical fields spanned by two modes -- whether a pair of polarization or spatial modes -- and their use is thus ubiquitous in optics. Because the Stokes parameters are defined through an expansion of the $2\times2$ coherence matrix in terms of the Pauli matrices, they cannot be applied to optical fields comprising three modes, which are described by a $3\times3$ coherence matrix. Examples of such fields include the polarization of non-paraxial fields (spanned by three orthogonal polarization modes), and fields comprising three spatial or temporal modes. It has long been theorized that the $3\times3$ Gell-Mann matrices -- developed in high-energy particle physics -- can serve as a basis for $3\times3$ optical coherence matrices, with 8~expansion coefficients known as the Stokes-Gell-Mann (SGM) parameters, but the measurement procedure is daunting, and the SGM parameters have not been measured directly to date in optics. Here we present the first measurements of the SGM parameters for partially coherent three-mode light in a photonic integrated platform comprising a hexagonal mesh of Mach-Zehnder interferometers. Measuring the SGM parameters on chip, from which we reconstruct the $3\times3$ coherence matrix facilitates exploring the full space of iso-entropy fields that can be inter-converted into each other unitarily, and those that share the same value of entropy and yet cannot be inter-converted unitarily. These results pave the way to utilizing multimode partially coherent light in applications involving optical communications, sensing, and information processing.

Randomness amplification, the task of extracting uniform private bits from biased seeds that may be partly known by a malicious third party, is of central importance in cryptography. The highest security in this task is provided by a class of quantum protocols known as device-independent, which however are challenging to integrate into scalable devices. Semi-device-independent (SDI) protocols are a promising alternative that guarantees security under few natural assumptions, such as bounds on the amount of energy used by the devices. Here, we provide the first demonstration of SDI randomness amplification on an integrated silicon photonic chip, achieving a throughput rate of 20 Mbps suitable for practical applications. This rate is achieved through a novel technique for SDI entropy certification, which delivers strictly tighter von Neumann entropy bounds compared to existing methods and remains valid even if the preparation and measurement devices share quantum correlations. Overall, the methods developed in this work enable the integration of SDI technology into portable telecom devices, opening up a new generation of quantum cryptographic hardware.

Fiber optical cavities offer small mode volumes and correspondingly strong light-matter interactions in an open Fabry-Perot geometry. However, existing fabrication techniques do not reliably produce substrates with surface profiles amenable to high mode matching between the cavity mode and fiber core, thereby limiting the achievable collection efficiency. Here we present a technique to fabricate fiber mirror substrates while using $\textit{in situ}$ reflectometry to constrain the achievable mode matching prior to coating. By measuring the back-reflection from freshly cleaved fiber tips, we pre-select 138 fibers compatible with 96.5-99.5% mode matching, and after a single CO$_2$ laser ablation pulse, these fibers remained compatible with 95.3-99.2\%. This simple technique provides rapid feedback during each stage of substrate fabrication, greatly enhancing the yield of viable fiber mirror substrates prior to (expensive) coating runs.

Non-Hermitian systems can evade Anderson localization and exhibit delocalized states even in one dimension. Here, we show that such non-Hermitian delocalized states under periodic boundary conditions (PBC) are intrinsically critical, realizing the universality class of one-dimensional random Dirac fermions. By linking spectral winding to topological Anderson transitions via Hermitization, we demonstrate that the delocalized PBC states exhibit a Dirac-type criticality with universal algebraic correlations. In contrast to Hermitian systems, where this criticality occurs only at fine-tuned transition points, it emerges generically in non-Hermitian systems as a consequence of spectral topology. These results identify a universal mechanism by which non-Hermiticity promotes criticality, providing a unified description of non-Hermitian delocalization in one dimension.

The combinatorial design space of multilayer perovskite solar cells is vast, yet exhaustive experimental or computational screening of all possible material combinations remains impractical. Here, we integrate SCAPS-1D device simulations with machine learning to systematically explore 125 device architectures constructed from five electron transport layers (ETL), five absorbers (including lead-free double perovskites), and five hole transport layers (HTL). A representative subset of configurations is used to train a machine learning (ML) model, which predicts the power conversion efficiency (PCE) of the remaining unexplored structures. Leave-One-Group-Out cross-validation yields a Spearman rank correlation, demonstrating reliable ranking capability. SHAP (SHapley Additive exPlanations) analysis reveals that the HTL band gap, absorber band gap, and ETL electron affinity are the most influential descriptors, providing physical insights into interfacial recombination and charge extraction. The machine learning model identifies several high-performance configurations that are subsequently verified by full SCAPS-1D simulations. Among them, the device FTO/TiO$_2$/Cs$_2$AgBiBr$_6$/NiO/Ag achieves a PCE of 28.85%, and the ML-suggested structure FTO/SnO$_2$/Cs$_2$AgInBr$_6$/NiO/Ag exhibits 28.62%, outperforming a closely related literature architecture by approximately 4% absolute. Notably, eight of the top-11 structures employ the lead-free double perovskite Cs$_2$AgInBr$_6$. This work demonstrates that a physics-based, data-driven workflow combining SCAPS-1D, ML, and SHAP can accelerate the discovery of high-efficiency, environmentally friendly perovskite solar cells while providing transparent design rules. The approach is generalizable to other multilayer optoelectronic systems.

Mirrors that preserve the handedness of optical radiation upon reflection are an essential building block for the design of numerous resonant nanophotonic structures with capabilities for enantiomeric discrimination. Ordinary metallic and Bragg dielectric mirrors are not suitable in these context since they flip handedness of electromagnetic field upon reflection around normal incidence. While there has been considerable progress in the development of such reflecting structures, this research area remains largely unexplored. Here, we present a detailed numerical and theoretical analysis of the potential of low-symmetry periodic lattices composed of high-symmetry non-chiral meta-atoms for resonant reflection with handedness preservation (HP). Using full-wave numerical simulations, we analyze a family of rhombic and monoclinic (oblique) lattices of circular dielectric disks and/or holes, and in each identify the regime of near-perfect HP reflection. We study the robustness of these structures to geometric deviations, material losses, and incidence angle. Finally, we describe the resonant HP response of these structures using the coupled-mode theory formalism.

This Letter presents a novel analytical framework showing that the dark count probability (PDC) of perimeter-gated single-photon avalanche diodes (pg-SPADs) follows a complementary Gompertz function. Specifically, we show that PDC follows a complementary Gompertz form from which we derive a pixel-specific descriptor, the midpoint perimeter gate voltage, which characterizes a pixel's equiprobable operating point. We further show that a perimeter gate voltage compensation rate may be obtained from this descriptor to offset temperature-induced changes in the pixel's activation function. The proposed framework is experimentally validated using 4,096 pg-SPADs arranged in a 64 x 64 array and manufactured in a 0.35 $\mu$m CMOS process. The devices were characterized at temperatures ranging from -5 $^o$C to 55 $^o$C and perimeter gate voltage magnitudes of 0 to 5 V. The measured results demonstrate deterministic bias control of dark count probability across process and temperature variations.

The orbital angular momentum of light is an intriguing property for developing light driven applications. It emerged as an independent degree of freedom by which to manipulate light and, consequently, the interaction of light with matter. Several methods exist for the generation of light carrying orbital angular momentum, mostly employing transmitting or reflecting optical components, which radially modulate the phase profile of the light. As one of such components, transmissive q-plates established themselves as standard elements due to their usability over a broad wavelength range. Here, we present our approach to build a highly reflective q-plate based on a plasmonic metasurface capable of converting orbital angular momentum from the nanostructure to ultrashort laser pulses without temporal broadening. We highlight its working principle over a wide range of wavelengths for reflection under normal and gracing incidence.

Molecular rare-earth-ion complexes offer unique opportunities for quantum technologies by combining the intrinsic coherence properties of rare-earth ions with chemically tunable molecular environments. A crucial capability is the realization of multi-qubit architectures with defined qubit couplings to enable two-qubit quantum gates. Here, we investigate the optical coherence properties and excitation-induced interactions of two Eu$^{3+}$-based molecular complexes, comparing a mononuclear reference system with a dinuclear analogue in which two Eu$^{3+}$ ions are positioned at a well-defined intramolecular distance of about 7 Angstrom. Using cryogenic ensemble spectroscopy, including spectral hole burning, free-induction decay, and photon echo measurements at temperatures down to 100 mK, we demonstrate long optical coherence times $T_{2,\text{o}}$ of up to 9 $\mu$s. As a key step toward scalable multi-qubit architectures, a control-target sequence was implemented to probe conditional ion-ion interactions, revealing a stronger interaction-induced dephasing in the dinuclear complex. Finally, we show the integration of the dinuclear complex into a fiber-based optical microcavity, and observe an 380-fold emission enhancement of the $\mathrm{}^5\mathrm{D}_0\rightarrow\mathrm{}^7\mathrm{F}_0$ transition. Together, these results position molecular rare-earth complexes as versatile and chemically tunable building blocks for scalable quantum technologies.

The native processing of time-dependent signals from optical sensors by integrated photonic circuits can potentially bring significant advantages in terms of energy consumption, latency and processing power, as it allows skipping or reducing the use of fast digital electronics and directly exploiting optical degrees of freedom and parallelism. However, due to a short memory, optical operations usually struggle to directly process optical signals with relatively slow (<MHz) dynamics from optical sensors. In this work, we experimentally show that these limitations can be overcome by exploiting the self-pulsing dynamics in a microring resonator (MRR) network. In particular, we demonstrate that such dynamics can expand and retain information about perturbations sensed by a fiber sensor. This reduces the minimum sampling rate for the digitization of the sensor signal by at least one order of magnitude. The reduction is achieved by combining fiber sensing measurements at two different perturbation locations and frequencies with MRR network measurements at multiple output ports, input power levels and laser wavelengths. This work represents a first step in bridging time-dependent optical processing and optical sensing at sub-{\mu}s time scales.

Frequency conversion of ultrafast lasers is fundamentally constrained by the trade-off between pulse energy and repetition rate, limiting access to regimes critical for fundamental science and industry. Here, we demonstrate a frequency-conversion mechanism in which molecular coherence accumulates across ultrafast pulse trains in gas-filled hollow-core fibers. Unlike conventional nonlinear interactions initiated by individual high-energy pulses, this mechanism relies on the collective buildup of coherent molecular oscillations driven by successive pulses. Using this mechanism, we achieve Raman frequency conversion at repetition rates up to 3 GHz with nanojoule pulse energies. The results establish a regime of nonlinear optical interaction governed by coherence accumulation of gas molecular oscillations with broad implications for ultrafast laser science and frequency conversion technologies.

We investigate polarization-selective absorption in a visible-wavelength heterostructure consisting of a ReS$_2$ stripe grating, an $\alpha$-MoO$_3$ spacer, and an Au back-reflector using finite-difference time-domain simulations. For an optimized geometry with a grating period of 500 nm, stripe width of 250 nm, and ReS$_2$ thickness of 80 nm, the structure exhibits near-unity absorption of 99.99\% at 650.5 nm under TE-polarized illumination. The resonant field is concentrated near the outer edges of the ReS$_2$ stripe, while absorption power density is localized in the same region, consistent with a localized edge mode. The absorption response depends strongly on polarization, producing a TE--TM resonance separation of 16.2 nm. Replacing either the biaxial ReS$_2$ layer or the anisotropic $\alpha$-MoO$_3$ spacer with isotropic equivalents substantially modifies the spectral response and reduces the polarization-dependent wavelength separation. In addition, rotating the crystal orientation of the ReS$_2$/$\alpha$-MoO$_3$ stack shifts both the resonance wavelength and peak absorption without changing the device geometry. The results show that the combination of anisotropic resonator and spacer layers provides an effective means of controlling resonant absorption and polarization selectivity in van der Waals photonic structures.

How should one design efficient chemically open optical cavities for molecular strong coupling? Addressing this question is important for the development of soft-cavity platforms for dynamically tunable light--matter interactions, where direct access to confined electromagnetic modes is essential. Conventional cavity figures of merit such as $Q/\sqrt{V}$ and cooperativity successfully describe spectral confinement and dissipation but do not fully capture the role of linewidth asymmetry between cavity and molecular degrees of freedom. Here, we systematically investigate strong coupling between TDBC dye molecules and whispering gallery modes of polystyrene microspheres by varying the microsphere radius over a broad range. To quantify the robustness of strong coupling, we define the parameter $\chi = \frac{g}{\max(\kappa,\gamma)}$, where $g$ is the coupling strength, while $\kappa$ and $\gamma$ denote the cavity and molecular linewidths, respectively. Although the coupling strength decreases monotonically with increasing cavity size due to mode-volume scaling, we find that $\chi$ exhibits a pronounced maximum near the condition $\kappa \approx \gamma$. This observation suggests that linewidth matching is not merely a criterion for improved spectral visibility, but reflects a dissipation-matching condition that optimizes the robustness of coherent light--matter exchange in soft-cavities. Our results provide an alternative framework for designing morphology-dependent cavities for molecular strong coupling.

On a charged interface, broken inversion symmetry permits a large field-linear Pockels response through $\chi^{(2)}(\omega;\omega,0)$; at the water/ITO interface $|r_{13}|$ has been reported to reach the $10^{2}\,\mathrm{pm/V}$ order. The coexisting third-order DC Kerr term $\chi^{(3)}(\omega;\omega,0,0)$ -- small in bulk water ($|\chi^{(3)}_{\mathrm{bulk}}|\sim5.5\times10^{-21}\,\mathrm{m^2/V^2}$) -- had not been jointly parameterized with the Pockels term along the fundamental-frequency ($\omega$) electro-optic path. Superimposing an AC modulation and a DC bias in 0.1\,M NaCl mixes the $\chi^{(3)}$ contribution with the 1f response through the cross-term $2 s_{1133}\,E_{\mathrm{DC}}$, so that the water refractive-index modulation $\Delta n_{\mathrm{water}}$ varies linearly with $V_{\mathrm{WE}}$; a model-assisted linear fit then determines both terms from a single AC$+$DC sweep. At $V_{\mathrm{WE}}=0\,\mathrm{V}$ vs Ag/AgCl, $|r_{13}|=(1.18 \pm 0.06_{\mathrm{PZC}})\times10^{2}\,\mathrm{pm/V}$ and, under $\eta_{\mathrm{DC}}=1$, the thickness-normalized DC Kerr coefficient $|s_{1133}/d_{\mathrm{EDL}}|=33.0 \pm 5.6\,\mathrm{pm/V^{2}}$. Across physically reasonable $d_{\mathrm{EDL}}$ ($0.6$--$1.6\,\mathrm{nm}$), the interfacial DC Kerr susceptibility reaches $|\chi^{(3),\mathrm{int}}_{1133}| \approx (2\text{--}5.5)\times10^{-20}\,\mathrm{m^2/V^2}$, several-fold above the visible-range bulk-water value. This response is a property of the specific interface, tunable through the choice of electrode, electrolyte, and solvent rather than intrinsic to bulk water. Amid renewed interest in the Kerr response of water (including recent THz-band optical Kerr studies), the method directly probes this DC Kerr term along the $\omega$ path and complements SHG/SFG (the $2\omega$ path).

The coupling theory of quasinormal modes (QNMs) for a coupled system of generally lossy and dispersive optical nanoresonators has been established in a rigorous manner based on the first principle of Maxwell's equations [Phys. Rev. B 102, 045430 (2020)], and can achieve superior computational efficiency and physical intuitiveness compared with full-wave numerical methods if a small set of modes can achieve a high accuracy. The QNMs suffer from an exponential divergence of far field and can form a complete basis inside but not outside the resonator. In the QNM coupling theory (QCT), it is required that the QNMs of each resonator form a complete basis in expanding the scattered field both inside and outside the resonator, which can be achieved by using regularized QNMs (RQNMs). However, a strict numerical demonstration of the impact of the mode completeness of RQNMs on the accuracy of QCT by using a virtually complete basis of RQNMs is still absent. In this paper, we will provide such a numerical demonstration along with an improvement of the QCT and some theoretical demonstrations on a rigorous incorporation of RQNMs into the QCT. The RQNMs are obtained by introducing an equivalent surface current (ESC) encircling the resonator (called ESC-RQNMs) or the perfectly matched layer (PML) surrounding the computational domain (called PML-RQNMs). The numerical example is selected as two one-dimensional resonators of slabs in the extreme coupling case of direct contact, for which a virtually complete basis of RQNMs can be solved either analytically (for ESC-RQNMs) or numerically (for PML-RQNMs). The results show that by using a virtually complete basis of RQNMs, the QCT can achieve a high accuracy in predicting both the source-free eigenmodes and the source-excited scattered field of the coupled system, which is not true if using the incomplete basis of not-regularized QNMs (i.e., physical QNMs).

We present the exact analytical paraxial propagation of structured light beams that transition from Ring annular profiles to top-hat intensity distributions. The initial field is defined as a superposition of a Gaussian-weighted power-law core and a singular inverse-quadratic modulation term, both carrying an azimuthal phase factor. By solving the Fresnel diffraction integral in cylindrical coordinates, we obtain exact closed-form expressions for the propagated field at arbitrary planes. The paraxial evolution is shown to be governed by a Cauchy-Riemann beam term and an infinite series of modified Bessel functions of the second kind weighted by an azimuthal phase factor. This analytical framework demonstrates how tuning the source parameters enables a continuous transition from ring-dominated annular profiles to uniform top-hat beams. For the fundamental mode ($l=0$), the singular component fills the central intensity null, producing a flat transverse plateau.

A time-reversal characteristic-mode decomposition is developed for reciprocal lossy electromagnetic structures. The formulation is built on a transmit--receive interpretation of reciprocity: the far-field pattern radiated by a mode determines the time-reversed incident field that is optimally matched to couple energy back into that same mode. This physical picture leads to an antilinear characteristic-mode equation whose solutions remain radiation-power orthogonal even in the presence of material loss, lossy loading, or matched absorption. As a result, the modal expansion coefficients directly represent the radiated-power contributions of the corresponding modes and avoid the singular biorthogonal normalization that may arise in nonnormal classical characteristic-mode expansions. Equivalent formulations are derived in the scattering-operator, T-matrix, and method-of-moments (MoM) frameworks, thereby connecting external wave-channel descriptions with current-space and port-excitation descriptions. The proposed modes reduce to classical characteristic modes in the lossless limit. Numerical examples involving a lossy two-sphere system and a loaded folded antenna demonstrate the radiation-power orthogonality, modal-expansion stability, and power interpretability of the proposed decomposition near exceptional points, where classical characteristic-mode expansions become singular or lose their radiated-power meaning.

Recent breakthrough studies of nonlinearities at extreme pump intensities ($\sim$1 $\text{TW/cm}^2$) in transparent conducting oxides (TCOs) have rewritten our understanding of the dynamics in these materials. However, exploring TCO dynamics beyond these intensities is prohibited by the damage threshold of the material. In this work, we overcome this problem by using a few-cycle pump laser pulse (sub-8\,fs) to maximize the intensity while keeping the optical fluence below the damage threshold. We observe a reversal in the optical response trend starting at optical pump laser intensities of $\sim$5 $\text{TW/cm}^2$ similar to Segal et al. At the highest pump pulse intensities, we obtain a complete change in the sign of the modulation for both transmission and reflection, producing a full-cycle oscillation of the refractive index modulation within 300\,fs. The amplitude of the sign reversal scales quadratically with the intensity. We therefore propose a simple two-photon absorption (TPA) model to explain the observed behaviour. The TPA, which is normally forbidden by the Pauli blocking, is enabled here by intraband excitations from the lower to the upper non-equilibrium states of the conduction band (CB). Such excitations vacate the states at the bottom of the CB, lifting up the blocking and thus making interband TPA possible. The model is in good agreement with experimental results, capturing the essential trends in the observed data and revealing the dynamics of competing channels caused by the interplay between interband and intraband transitions. This intensity-controlled mechanism could be the key to unlocking new applications of TCOs for time-varying photonics such as photonic time crystals.

By forming hybrid light-matter states, optical cavities offer a route for engineering material properties, however, unambiguously probing the effects of light-matter coupling remains difficult. Here, we show that the polarization-resolved statistics of photons transmitted through a cavity, measurable via $g^{(2)}$, provide one such diagnostic. By relating $g^{(2)}$ to matter correlation functions such as the Raman structure factor, we link photon bunching and antibunching to material properties. By applying this method to the stripy-to-antiferromagnetic transition in the Kitaev-Heisenberg spin model, we find that polarization-dependent patterns of bunching and antibunching encode the magnetic point-group symmetries of each phase and characterize the behavior at the phase boundary. Finally, we predict measuring $g^{(2)}$ for output photon pairs polarized orthogonal to the input field will isolate higher-order light-matter scattering processes that probe higher-order material correlations.

High damage threshold gratings are in demand worldwide as critical components for next generation ultrahigh intensity lasers. Here we investigate the pulse-duration dependence of ultrafast laser-induced damage thresholds (LIDT) in hybrid multilayer dielectric gratings, touted to combine superior performance properties of both metallic and multilayer dielectric (MLD) gratings, using a dynamic finite-difference time-domain model incorporated with linear and non-linear absorption models. Simulations agree with reported experimental LIDT values for three representative designs and predict scaling exponents which vary with pulse durations ranging from 10 to 500 fs. The results reveal strong dependence on both material bandgap and grating field distribution, providing guidance for designing high LIDT gratings.

Quantifying the coherence properties of complex optical fields is essential for applications ranging from high power laser arrays to quantum coherent systems. Here, we present a new paradigm for coherence retrieval inspired by the Gerchberg Saxton framework, enabling reconstruction of the first order spatial coherence function (mutual intensity) of partially coherent light from intensity measurements in the near and far fields. We introduce two complementary approaches: a four dimensional Tensor GS algorithm that directly reconstructs the mutual intensity with high accuracy, and a Monte Carlo GS variant that significantly reduces computational cost at the expense of controlled approximation. We validated both methods by reconstructing partially coherent fields in simulated linear and ring arrays of up to 600 beams with prescribed Gaussian decaying coherence. Experimentally, we applied the Tensor GS method to a triangular array of 130 coupled lasers with inhomogeneous spatial coherence, achieving good agreement with theory and a root mean square phase error as low as 2pi over 250.

Anisotropic surface phonon polaritons (SPhPs) offer extremely strong light confinement and unique light propagation characteristics, particularly on anisotropic polar crystals. Despite the classical importance of \alpha -quartz as a prototypical uniaxial bulk crystal, real-space observation of anisotropic SPhP propagation on \alpha-quartz has remained elusive. In this study, we report the first direct observation of SPhP propagating on an \alpha-quartz surface using scattering-type near-field optical microscopy (s-SNOM). We demonstrate that the dispersion relation and propagation length of SPhPs exhibit remarkable anisotropy depending on the propagation direction relative to the optic axis of \alpha-quartz. Furthermore, we verify that these experimental behaviors agree with theoretical calculations based on the dielectric permittivity tensors. Our results establish \alpha-quartz as a robust, highly promising platform for light-controlling nanodevices and mid-infrared on-chip sensing.

Second Harmonic Generation (SHG) in nonlinear crystals has been extensively investigated, but most existing models still rely on simplifying assumptions. In realistic settings, thermal effects introduce complications that are difficult to capture analytically because the governing equations are highly coupled and nonlinear. Direct experimental characterization is also limited, since studying thermal effects would require spatiotemporal temperature data at every point in the crystal, which is not experimentally accessible. To address these limitations, we have developed a SHG Computational Toolkit Suite, a coordinated collection of independent modeling toolkits that cover different SHG scenarios under various physical conditions. Each toolkit focuses on a particular configuration or coupling mechanism, while the suite as a whole provides well-documented numerical implementations, reproducible workflows, and illustrative examples. Together, this article and the Toolkit Suite provide a coherent infrastructure for computational studies of SHG. It enables researchers to replicate, adapt, and extend our methods without duplicating foundational development efforts, thereby accelerating SHG research and promoting reproducibility.

We study a class of Sturm--Liouville problems of the form $$ -(p\,y')' + q\,y = \lambda\, p\, y, $$ on a finite interval with complex-valued coefficients, where $p$ is piecewise smooth and $q$ is bounded. We prove that all eigenvalues in the open left half-plane are contained in a bounded set, which implies that only finitely many eigenvalues lie in this region. A canonical instance of this class arises in transverse-magnetic (TM) diffraction by metallic lamellar gratings, a benchmark problem in computational photonics that has been central to the development of Fourier modal methods. These methods exhibit long-standing convergence difficulties in this setting, associated with the loss of definiteness of the underlying operator and the emergence of spurious modes. Our result yields a rigorous criterion for identifying such non-physical modes in low-loss metallic gratings. Numerical examples illustrate the practical utility of the criterion.

We report that the biaxial birefringence of $\alpha$-MoO$_3$ can activate two spectrally distinct quasi-bound states in the continuum (quasi-BICs) within a single symmetric TiO$_2$ nanobar-pair metasurface, with each resonance governed by a different crystallographic axis pair of the van der Waals crystal. With a full 60\,nm $\alpha$-MoO$_3$ gap fill, a TE resonance at 883.9\,nm ($Q=92$, Fano $q=0.090$) and a TM resonance at 923.2\,nm ($Q=31$, Fano $q=0.393$) are obtained. The Q ratio follows the inverse-square permittivity contrast, $Q\propto(\Delta\varepsilon)^{-2}$, calibrated across both polarization channels. Oblique-incidence sweeps show that the TE channel acts as a dual-null spatial highpass filter with a broadband stopband ($|H|<0.13$ for $|k_x|\leq0.63\,\mu$m$^{-1}$, $T_\mathrm{bg}=0.962$), while the TM channel transfers as $|H|\propto|k_x|$ ($R^2=0.94$), consistent with first-order spatial differentiation. Both operations are verified on a USAF~1951 resolution chart processed in a simulated 4$f$ framework. Channel selection is purely by input polarization angle with no structural modification.

The function of the zebra's striped coat has been debated since Darwin and Wallace. A growing body of comparative and experimental evidence supports the hypothesis that the stripes act primarily as a defence against visually orienting biting Diptera - in particular tabanids (horse flies), glossinids (tsetse flies) and culicids (mosquitoes). The mechanisms proposed for this protection range from polarotactic disruption and silhouette break-up to motion-based illusions arising in the Reichardt-type motion detectors of the insect visual system. In this work we focus on a complementary, purely optical mechanism: the Moiré interference that arises when a periodic striped stimulus is sampled by the periodic ommatidial lattice of an insect compound eye. We develop a linear, shift-invariant Fourier model of the diptera compound eye, parameterised from published optical data on diurnal Culicidae, and apply it to images of zebra coats observed at biologically relevant viewing. The model predicts that, in a band of approach distances of approximately 1-5 m, the interaction of the stripe pattern with ommatidial sampling generates parasitic spatial frequencies that are absent from the physical stimulus and that fall within the spatial-frequency window most relevant to host fixation and landing control. A post-retinal motion-detector stage demonstrates that these parasitic frequencies translate into spurious local motion vectors, consistent with the empirical observation that tabanid and glossinid flies fail to land cleanly on striped surfaces. Our results are therefore consistent with the biting-fly hypothesis of zebra striping.

Semiconductor quantum dots (QDs) offer outstanding quantum-optical properties, making them highly attractive for quantum information technologies. However, combining wide-range electrical tunability, efficient photon extraction, elevated-temperature operation, monolithic silicon integration, and telecom-wavelength compatibility remains a major challenge. Here, we demonstrate electrically contacted circular Bragg grating (eCBG) resonators incorporating InGaAs QDs directly grown on silicon, enabling bright single-photon emission in the telecom O-band. Deterministic electron-beam lithography and a ridge-based vertical p--i--n diode architecture enable precise device integration and electrical control of individual emitters. The QD--eCBGs exhibit a quantum-confined Stark shift of approximately 16 nm (11 meV) at 4 K, representing a record for QDs embedded in nanophotonic structures at telecom wavelengths. This is achieved alongside a photon extraction efficiency of $(21.7 \pm 3.0)\%$ into the first lens, while maintaining excellent radiative properties and high single-photon purity, with $g^{(2)}(0)=0.0078 \pm 0.0012$ below saturation and $g^{(2)}(0)=0.0183 \pm 0.0021$ at saturation under pulsed excitation. Robust antibunching persists up to 77 K, with $g^{(2)}(0)=0.0663 \pm 0.0056$, enabling operation with liquid-nitrogen or compact Stirling cryocoolers. Furthermore, spatially separated QD--eCBGs can be electrically tuned into spectral resonance without degrading photon statistics. These results establish a silicon-compatible, electrically addressable telecom O-band quantum light platform combining wide spectral tunability, high single-photon purity, and elevated-temperature operation, providing a scalable route toward practical photonic quantum networks.

CsSn$_x$Ge$_{1-x}$I$_3$ as lead-free perovskites are promising for next generation NIR emitting perovskite LEDs due to their tunable bandgaps and stability. However, they suffer from poor light extraction efficiency, and accurate composition-specific optical data for these materials remain scarce. This study presents a DFT-FDTD framework to optimize light extraction via compositional tuning and plasmonic enhancement. First, DFT calculations were performed to obtain composition-specific complex refractive index and extinction coefficient values for $x = 0, 0.25, 0.5, 0.75$, and $1$. Results show bandgap increased from 1.331 eV for CsSnI$_3$ to 1.927 eV for CsGeI$_3$ with increasing Ge content, while refractive index ranges from 2.2 to 2.6 across compositions. These optical constants were then used as inputs for FDTD simulations of a PeLED structure with optimized Au/SiO$_2$ core-shell nanorods for plasmonic enhancement. A 12.1-fold Purcell enhancement was achieved for CsSn$_{0.25}$Ge$_{0.75}$I$_3$, while light extraction efficiency reached 25% for CsSn$_{0.5}$Ge$_{0.5}$I$_3$. LEE enhancement of 36% was obtained for CsSnI$_3$, and spectral overlap between emitter and plasmon resonance reached 96% for Sn-rich compositions. Design guidelines indicate CsSn$_{0.5}$Ge$_{0.5}$I$_3$ offers optimal balance of extraction efficiency (25%), Purcell enhancement (5.3$\times$), spectral overlap (93%), and oxidation stability for wearable and flexible optoelectronic applications, while CsSn$_{0.25}$Ge$_{0.75}$I$_3$ is recommended for applications prioritizing spontaneous emission rate.