arXiv subjects

Steven G. Johnson

Publications and source records attributed to Steven G. Johnson.

At least 19 recordsLinked to original sources

arXiv2026

Axion dark matter search with a photonic bandgap cavity haloscope and dielectric tuning rod over 10.25-10.45 GHz

We report the development of a new widely tunable cavity and demonstrate its use in a search for dark matter axions. We achieve unloaded quality factors above $10^{5}$, roughly $25\times$ larger than a bare copper cavity at the same frequency, using concentric sapphire shells to reduce Ohmic losses on the cavity barrel. A rotating sapphire rod tunes our cavity mode over the $10.1-11.7$ GHz range, approximately $16\%$ of its resonant frequency. Using an amplified receiver chain, we demonstrate sensitivity to new axion parameter space by tuning the cavity over the $200$ MHz range between $10.25-10.45$ GHz (42.4 - 43.2, $\mu$eV) to constrain the axion-to-photon coupling to $|g_{a\gamma\gamma}|$ $\leq$ 1 $\times$ $10^{-12}$ ${GeV}^{-1}$. This cavity can scan its tuning range about $9$ times faster compared to a bare copper cavity when paired with a photon counting device, laying the groundwork for a definitive search for the QCD axion over $10.1-11.7$ GHz.

astro-ph.CO↗

arXiv2026

Three-dimensional confinement of light in photonic crystals without bandgaps

We demonstrate that confinement of light in three dimensions is possible in photonic crystals without a complete photonic bandgap. Our approach exploits symmetry-protected quadratic degeneracies in the bulk band structure, where the photonic density of states vanishes at an isolated frequency. By introducing a point defect, we create a localized mode whose symmetry representation is incompatible with that of the surrounding bulk modes, suppressing coupling to propagating channels. The combination of vanishing density of states and a symmetry mismatch yields bound defect modes despite the absence of a spectral gap, as confirmed by time- and frequency-domain numerical simulations. This approach highlights the role of engineering the photonic environment around the defect to enable confinement, potentially providing a new route for designing optical cavities in three-dimensional photonic crystals.

physics.optics↗

arXiv2026

CLUSTER: Derivative-free optimization of smooth functions with parameter-change costs

We introduce the CLUSTER algorithm (\textbf{c}oordinate-\textbf{l}evel \textbf{u}pdate \textbf{s}trategy for \textbf{t}rust-region step \textbf{e}valuation \textbf{r}efinement) for local derivative-free optimization problems where there is a cost to changing each parameter (or clusters of parameters). For example, this type of cost model is appropriate for optimizing robot-controlled laboratory experiments, in which a robot may incur a separate motion for each parameter cluster to be adjusted. We build off of a class of quadratic-interpolation optimization algorithms by Powell and Conn that are known to perform well for twice-differentiable objectives (e.g. low-noise experiments), and show that the CLUSTER variants improve performance on a variety of test problems (including an optics laboratory experiment) by around 50$\%$, and greatly outperform common competing algorithms for laboratory optimization (Bayesian optimization and Nelder--Mead). We also adapt the convergence proof of the Conn algorithm to obtain a similar convergence guarantee for CLUSTER-Conn.

math.OC↗

arXiv2026

Efficient Multi-Precision Computation of Bessel Functions for Real Orders and Complex Arguments with Fortran Implementation -- Part II: The Modified Bessel Function of the Second Kind, $K_\nu(z)$

This paper, the second in a series, presents an efficient, self-contained algorithm for computing the modified Bessel function of the second kind, $K_{\nu}(z)$ for complex argument and real orders, building on Part~I (for $I_{\nu}$). The method adaptively selects among analytic representations such as power series, large-$|z|$ asymptotics, uniform asymptotics for large $|\nu|$, and numerically stable forward recurrence with region boundaries tuned for accuracy and efficiency. A robust \texttt{Fortran} implementation supports double precision and quadruple precision. The use of quadruple precision extends the reliable computational domain and improves stability in challenging regimes. Accuracy is validated against high-precision \texttt{Maple} results, and benchmarks show runtimes significantly superior to those of established methods, in the literature, while avoiding their numerical failure modes across several decades of the parameter domain. Together with Part~I, this work provides a comprehensive, multiple-precision toolkit for $\{I_{\nu},K_{\nu}\}$ across wide parameter ranges.

math.NA↗

arXiv2026

Efficient Multi-Precision Computation of Bessel Functions for Real Orders and Complex Arguments with a Fortran Implementation -- Part III: Regular Bessel Functions of the First and Second Kinds $J_{\nu}(z)$ and $Y_{\nu}(z)$

This paper is the final part in a series devoted to the development of numerically stable and efficient algorithms, together with multi-precision Fortran implementations, for computing Bessel functions with real orders and complex arguments. Parts~I and~II presented stable and efficient algorithms for the modified Bessel functions I_nu(z) and K_nu(z); here we treat Bessel functions J_nu(z) and Y_nu(z). The proposed algorithms support complex arguments for both positive and negative real orders and are implemented in native double and quadruple precision. Quadruple precision substantially increases dynamic range and accuracy (by roughly an order of magnitude in reliably computable |nu| and |z|), thereby extending applicability to problems requiring 20-30 digits. Comprehensive accuracy and performance comparisons are carried out against both the widely used Algorithm~644, restricted to double-precision arithmetic, and the more recent Algorithm~912, which supports both double- and quad-precision arithmetic as well as complex orders. In double precision, the present implementation consistently outperforms Algorithm~644, achieving execution times of approximately 35-67% for J_nu(z) and 44-72% for Y_nu(z), while also producing reliable results where Algorithm~644 fails. In comparison with Algorithm~912, the present algorithm achieves comparable accuracy in double-precision computations and significantly higher accuracy in quad-precision calculations. At the same time, it requires only a small fraction of the computational cost (from a few thousandths to a few hundredths) of the time taken by Algorithm~912, depending on the precision and parameter regime. Furthermore, unlike Algorithm~912, whose applicability is restricted to a limited region of the (Re(nu),z) plane, the present algorithm remains stable and accurate over the full tested domain for which reliable reference values are available.

math.NA↗

arXiv2026

Fundamental Bounds and Efficient Estimation for Dead-Time-Constrained Event Detection, with Application to Single-Photon Lidar

We develop an asymptotic statistical theory for parameter estimation from a class of non-i.i.d. periodic binary event-detection processes subject to nonparalyzable dead time and gating, which we call "dead-time event detection" (DED) processes. Such processes arise in single-photon lidar, fluorescence lifetime imaging, X-ray astronomy, and particle or radiation flux measurements in nuclear physics, where each detection renders the radiation/particle detector inactive for a recovery interval. Our theory quantifies how dead time and gating affect the fundamental lower bounds of estimation and identifies practical estimators that attain these bounds. First, we identify a sufficient statistic, showing in particular that activation counts can carry statistically useful information discarded by conventional histogramming hardware. We then prove local asymptotic normality and derive the corresponding Fisher-information rate, thereby obtaining fundamental lower bounds for estimation from DED processes. We prove that the maximum likelihood estimator (MLE), widely used in DED applications, attains these lower bounds. Since computing the MLE typically requires solving a nonconvex optimization problem, we also propose Le Cam one-step estimators, which attain the same asymptotic bounds with only a single local correction rather than iterative optimization. We illustrate the validity of our asymptotic theory and the practical usefulness of one-step estimators through the example of single-photon lidar in both simulations and real-data experiments.

eess.SP↗

arXiv2026

Implementing FFTs in Practice

This review article was first published in 2008 as chapter 11 in the book "Fast Fourier Transforms," edited by C. S. Burrus, for the Connexions project at Rice University, which is sadly no longer online. It gives a high-level overview of some of the engineering considerations that arise in high-performance implementations of fast Fourier trasnforms (FFTs). It explains why optimized FFTs are very different from textbook "radix-2 Cooley-Tukey" FFT algorithms, in order to compensate for the memory hierarchy and exploit the large register sets and deep pipelines of modern CPUs. Using the FFTW library as a case study, it talks about tradeoffs in the use of recursion, generation of twiddle factors, code generation, and other algorithmic choices.

math.NA↗

arXiv2026

Topology-optimized distributed 3d anisotropic Raman emission

Topology optimization (TO) of 3D surface-enhanced Raman scattering (SERS) substrates faces challenges in managing field singularities and modeling orientation-averaged anisotropic molecules. We present 3D TO for manufacturable SERS substrates that maximize spatially averaged signals from randomly oriented, anisotropic molecules in both elastic and inelastic scattering. A new trace formulation provides a closed-form rotational average of anisotropic Raman tensors, which are not equivalent to isotropic molecules because of tensor nonlinearity. Optimized silver and Si3N4 devices show that lengthscale constraints are sufficient to suppress designs that rely on unphysical mathematical field divergences at sharp corners. Metallic designs deliver broadband enhancement and remain robust to typical Raman shifts, whereas dielectric designs yield narrower, quality-factor-limited gains that are inferior to metallic designs for quality factors below about 500. Our approach readily incorporates additional physics, such as a nonlinear damage model. Together, these results provide a practical route to improved manufacturable SERS substrates and extend naturally to other distributed-emitter design problems.

physics.optics↗

arXiv2026

Differentiating through binarized topology changes: Second-order subpixel-smoothed projection

A key challenge in topology optimization (TopOpt) is that manufacturable structures, being inherently binary, are non-differentiable, creating a fundamental tension with gradient-based optimization. The subpixel-smoothed projection (SSP) method addresses this issue by smoothing sharp interfaces at the subpixel level through a first-order expansion of the filtered field. However, SSP does not guarantee differentiability under topology changes, such as the merging of two interfaces, and therefore violates the convergence guarantees of many popular gradient-based optimization algorithms. We overcome this limitation by regularizing SSP with the Hessian of the filtered field, resulting in a twice-differentiable projected density during such transitions, while still guaranteeing an almost-everywhere binary structure. We demonstrate the effectiveness of our second-order SSP (SSP2) methodology on both thermal and photonic problems, showing that SSP2 has faster convergence than SSP for connectivity-dominant cases -- where frequent topology changes occur -- while exhibiting comparable performance otherwise. Beyond improving convergence guarantees for CCSA optimizers, SSP2 enables the use of a broader class of optimization algorithms with stronger theoretical guarantees, such as interior-point methods. Since SSP2 adds minimal complexity relative to SSP or traditional projection schemes, it can be used as a drop-in replacement in existing TopOpt codes.

eess.SP↗

arXiv2025

Eigenvalue-accelerated LDOS optimization of high-Q optical resonances

We demonstrate a new method that yields orders-of-magnitude acceleration in inverse design (e.g. topology optimization) of high-$Q$ resonant cavities to maximize the local density of states (LDOS), and which is also applicable to other resonant-response metrics. The key idea is that, once conventional LDOS optimization has identified a strong resonance, subsequent optimizations can exploit a fast shift-invert eigensolver to ensure that the LDOS remains centered at the resonance peak. We show that this eliminates ill-conditioning at sharp resonances that otherwise dramatically slows LDOS (and similar) optimization for $Q \gg 100$. Our method is demonstrated by design of $Q > 10^6$ resonant cavities in 1d and 2d dielectric systems.

physics.optics↗

arXiv2025

Sufficient conditions for localized vibrational modes in one- and two-dimensional discrete lattices

This paper presents a rigorous proof that arbitrarily weak perturbations produce localized vibrational (phonon) modes in one- and two-dimensional discrete lattices, inspired by analogous results for the Schr{\"o}dinger and Maxwell equations, and complementing previous explicit solutions for specific perturbations (e.g., decreasing a single mass). In particular, we study monatomic crystals with nearest-neighbor harmonic interactions, corresponding to square lattices of masses and springs, and prove that arbitrary localized perturbations that decrease the net mass lead to localized vibrating modes. The proof employs a straightforward variational method that should be extensible to other discrete lattices, interactions, and perturbations.

cond-mat.other↗

arXiv2025

Hyperparameter-free minimum-lengthscale constraints for topology optimization

The geometric constraints of Zhou et al. (2015) are a widely used technique in topology/freeform optimization to impose minimum lengthscales for manufacturability. However, its efficacy degrades as design binarization is increased, and it requires heuristic tuning of multiple hyperparameters. In this work, we derive analytical hyperparameters from first principles, depending only on the target lengthscale. We present results for both conic and PDE-based filtering schemes, showing that the latter is less robust due to the singularity of its underlying Green's function. To address this, we also introduce a double-filtering approach to obtain a well-behaved PDE-based filter. Combined with our derived hyperparameters, we obtain a straightforward strategy for enforcing lengthscales using geometric constraints, with minimal hyperparameter tuning. A key enabling factor is the recent subpixel-smooth projection (SSP) method (Hammond et al. 2025), which facilitates the rapidly-converging optimization of almost-everywhere binary designs. The effectiveness of our method is demonstrated for several photonics and heat-transfer inverse-design problems.

physics.optics↗

arXiv2025

Efficient first-principles inverse design of nanolasers

We develop and demonstrate a first-principles approach, based on the nonlinear Maxwell-Bloch equations and steady-state ab-initio laser theory (SALT), for inverse design of nanostructured lasers, incorporating spatial hole-burning corrections, threshold effects, out-coupling efficiency, and gain diffusion. The resulting figure of merit exploits the high-$Q$ regime of optimized laser cavities to perturbatively simplify the nonlinear model to a single linear ''reciprocal'' Maxwell solve. The consequences for laser-cavity design, and in particular the strong dependence on the nature of the gain region, are demonstrated using topology optimization of both 2d and full 3d geometries.

physics.optics↗

arXiv2025

Inverse design for robust inference in integrated computational spectrometry

We propose an inverse-design approach for computational spectrometers in which the scattering media are topology-optimized to achieve better performance in inference of unknown spectra. Unlike traditional end-to-end approaches, our inverse design of the scattering media does not need a training set of spectra, a distribution of detector noise, or an inference algorithm. Our approach allows the selection of the inference algorithm to be decoupled from that of the scatterer. For smooth spectra, we additionally devise a regularized reconstruction algorithm based on Chebyshev interpolation, which yields higher accuracy compared with conventional methods in which the spectra are sampled at equally spaced frequencies or wavelengths with equal weights. Our approaches are numerically demonstrated via inverse design of integrated computational spectrometers and reconstruction of example spectra. The inverse-designed spectrometers exhibit significantly better performance in the presence of noise than their counterparts with random scatterers. Our method provides a useful complement to end-to-end co-design methods.

physics.optics↗

arXiv2025

Efficient Multi-Precision Computation of Bessel Functions for Real Orders and Complex Arguments with Fortran Implementation -- Part I: The Modified Bessel Function of the First Kind, $I_\nu(z)$

This paper is the first in a series devoted to the development of efficient and highly accurate algorithms, with multiprecision \texttt{Fortran} implementations, for the computation of Bessel functions. In this first part, we present a \emph{novel, self-contained, efficient,} and \emph{multiprecision} algorithm for evaluating the modified Bessel function of the first kind, $I_{\nu}(z)$. The method integrates several analytic representations of $I_{\nu}(z)$, carefully selected to ensure both high accuracy and suitability for high-precision computation, together with optimally determined transition boundaries between computational regions. This design achieves high efficiency while fully preserving numerical accuracy. Unlike other widely used algorithms and libraries, such as AMOS, Boost, and GSL, which either reject negative orders $\nu$ or rely on special-case symmetries valid only for integer orders, the present algorithm provides a stable approach for evaluating $I_{\nu}(z)$ for arbitrary real orders, including $\nu < 0$, and complex arguments $z$. The developed robust \texttt{Fortran} implementation provides support for both double and native quadruple-precision arithmetic. The availability of quadruple precision further enhances numerical stability, extends the reliable computational domain in $(\nu, |z|)$ by approximately an order of magnitude in each direction, and enables accuracies exceeding 26 significant digits. This advancement substantially broadens the applicability of the method to demanding high-precision problems in science and engineering. Compared to AMOS (Algorithm~644), which is restricted to double precision, the present algorithm exhibits superior accuracy and efficiency, with benchmark tests demonstrating execution times reduced to 38--71\% of those of AMOS in double precision.

math.NA↗

arXiv2025

Inverse design of multiresonance filters via quasi-normal mode theory

We present a practical methodology for inverse design of compact high-order/multiresonance filters in linear passive 2-port wave-scattering systems, targeting any desired transmission spectrum (such as standard pass/stop-band filters). Our formulation allows for both large-scale topology optimization and few-variable parametrized-geometry optimization. It is an extension of a quasi-normal mode theory and analytical filter-design criteria (on the system resonances and background response) derived in our previous work. Our new optimization-oriented formulation relies solely on a scattering solver and imposes these design criteria as equality constraints with easily calculated (via the adjoint method) derivatives, so that our algorithm is numerically tractable, robust, and well-suited for large-scale inverse design. We demonstrate its effectiveness by designing 3rd- and 4th-order elliptic and Chebyshev filters for photonic metasurfaces, multilayer films, and electrical LC-ladder circuits.

physics.app-ph↗

arXiv2025

Unifying and accelerating level-set and density-based topology optimization by subpixel-smoothed projection

We introduce a new "subpixel-smoothed projection" (SSP) formulation for differentiable binarization in topology optimization (TopOpt) as a drop-in replacement for previous projection schemes, which suffer from near-non-differentiability and slow convergence as binarization improves. Our new algorithm overcomes these limitations by depending on both the underlying filtered design field and its spatial gradient, instead of the filtered design field alone. We can now smoothly transition between density-based TopOpt (in which topology can easily change during optimization) and a level-set method (in which shapes evolve in an almost-everywhere binarized structure). We demonstrate the effectiveness of our method on several photonics inverse-design problems and for a variety of computational methods (finite difference, Fourier-modal, and finite-element methods). SSP exhibits both faster convergence and greater simplicity.

physics.optics↗

arXiv2025

Time-reversal-symmetry bounds on electromagnetic fields

For linear electromagnetic systems possessing time-reversal symmetry, we present an approach to bound ratios of internal fields excited from different ports, using only the scattering matrix (S matrix), improving upon previous related bounds by Sounas and Al\`u (2017) [Phys. Rev. Lett. 118, 154302 (2017)]. By reciprocity, emitted-wave amplitudes from internal dipole sources are bounded in a similar way. When applied to coupled-resonant systems, our method constrains ratios of resonant coupling/decay coefficients. We also obtain a relation for the relative phase of fields excited from the two ports and the ratio of field intensities in a two-port system. In addition, although lossy systems do not have time-reversal symmetry, we can still approximately bound loss-induced non-unitarity of the S matrix using only the lossless S matrix. We show numerical validations of the near-tightness of our bounds in various scattering systems.

physics.optics↗