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In Patil et. al 2024a, we developed a multitaper power spectrum estimation method, mtNUFFT, for analyzing time-series with quasi-regular spacing, and showed that it not only improves upon the statistical issues of the Lomb-Scargle periodogram, but also provides a factor of three speed up in some applications. In this paper, we combine mtNUFFT with the harmonic F-test to test the hypothesis that a strictly periodic signal or its harmonic (as opposed to e.g. a quasi-periodic signal) is present at a given frequency. This mtNUFFT/F-test combination shows that multitapering allows detection of periodic signals and precise estimation of their frequencies, thereby improving both power spectrum estimation and harmonic analysis. Using asteroseismic time-series data for the Kepler-91 red giant, we show that the F-test automatically picks up the harmonics of its transiting exoplanet as well as certain dipole ($l=1$) mixed modes. We use this example to highlight that we can distinguish between different types of stellar oscillations, e.g., transient (damped, stochastically-excited) and strictly periodic (undamped, heat-driven). We also illustrate the technique of dividing a time-series into chunks to further examine the transient versus periodic nature of stellar oscillations. The harmonic F-test combined with mtNUFFT is implemented in the public Python package tapify (https://github.com/aaryapatil/tapify), which opens opportunities to perform detailed investigations of periodic signals in time-domain astronomy., Comment: 15 pages, 6 figures, Submitted to AJ as a companion paper to arXiv:2209.15027

Electro-optic silicon-based modulators contribute to ease the integration of high-speed and low-power consumption circuits for classical optical communications or quantum computers. However, the inversion symmetry in the silicon crystal structure inhibits the use of Pockels effect. An electric field-induced optical modulation equivalent to a Pockels effect can nevertheless be achieved in silicon by the use of DC Kerr effect. Although some theoretical and experimental studies have shown its existence in silicon, the DC Kerr effect in optical modulation have led to a negligible contribution so far. This paper reports demonstration of high-speed optical modulation based on the electric field-induced linear electro-optic effect in silicon PIN junction waveguides. The relative contributions of both plasma dispersion and Kerr effects are quantified and we show that the Kerr induced modulation is dominant when a high external DC electric field is applied. Finally, the high-speed modulation response is analyzed and eye diagram up to 100 Gbits/s in NRZ format are obtained. This work demonstrates high speed modulation based on Kerr effect in silicon, and its potential for low loss, quasi-pure phase modulation., Comment: 7+6 pages, 5+4 figures

Asteroseismic time-series data have imprints of stellar oscillation modes, whose detection and characterization through time-series analysis allows us to probe stellar interior physics. Such analyses usually occur in the Fourier domain by computing the Lomb-Scargle (LS) periodogram, an estimator of the power spectrum underlying unevenly-sampled time-series data. However, the LS periodogram suffers from the statistical problems of (1) inconsistency (or noise) and (2) bias due to high spectral leakage. Here, we develop a multitaper power spectrum estimator using the Non-Uniform Fast Fourier Transform (mtNUFFT) to tackle the inconsistency and bias problems of the LS periodogram. Using a simulated light curve, we show that the mtNUFFT power spectrum estimate of solar-like oscillations has lower variance and bias than the LS estimate. We also apply our method to the Kepler-91 red giant, and combine it with PBjam peakbagging to obtain mode parameters and a derived age estimate of $3.97 \pm 0.52$ Gyr. PBjam allows the improvement of age precision relative to the $4.27 \pm 0.75$ Gyr APOKASC-2 (uncorrected) estimate, whereas partnering mtNUFFT with PBjam speeds up peakbagging thrice as much as LS. This increase in efficiency has promising implications for Galactic archaeology, in addition to stellar structure and evolution studies. Our new method generally applies to time-domain astronomy and is implemented in the public Python package tapify, available at https://github.com/aaryapatil/tapify., Comment: 27 pages (3 pages in the Appendix), 12 figures, 3 tables, Revision submitted to AJ. This paper focuses solely on multitaper power spectrum estimation, whereas a companion paper showcases harmonic analysis using the multitaper F-test (v1 of this paper has been split). Both these papers have applications in asteroseismology

Adaptable, reconfigurable and programmable are key functionalities for the next generation of silicon-based photonic processors, neural and quantum networks. Phase change technology offers proven non-volatile electronic programmability, however the materials used to date have shown prohibitively high optical losses which are incompatible with integrated photonic platforms. Here, we demonstrate the capability of the previously unexplored material Sb$_2$Se$_3$ for ultralow-loss programmable silicon photonics. The favorable combination of large refractive index contrast and ultralow losses seen in Sb$_2$Se$_3$ facilitates an unprecedented optical phase control exceeding 10$\pi$ radians in a Mach-Zehnder interferometer. To demonstrate full control over the flow of light, we introduce nanophotonic digital patterning as a conceptually new approach at a footprint orders of magnitude smaller than state of the art interferometer meshes. Our approach enables a wealth of possibilities in high-density reconfiguration of optical functionalities on silicon chip., Comment: 22 pages, 11 figures

Recent breakthroughs in photonics-based quantum, neuromorphic and analogue processing have pointed out the need for new schemes for fully programmable nanophotonic devices. Universal optical elements based on interferometer meshes are underpinning many of these new technologies, however this is achieved at the cost of an overall footprint that is very large compared to the limited chip real estate, restricting the scalability of this approach. Here, we consider an ultracompact platform for low-loss programmable elements using the complex transmission matrix of a multi-port multimode waveguide. We propose a deep learning inverse network approach to design arbitrary transmission matrices using patterns of weakly scattering perturbations. The demonstrated technique allows control over both the intensity and phase in a multiport device at a four orders reduced device footprint compared to conventional technologies, thus opening the door for large-scale integrated universal networks., Comment: 13 pages, 6 figures + supporting information pdf

Accurate 3D imaging is essential for machines to map and interact with the physical world. While numerous 3D imaging technologies exist, each addressing niche applications with varying degrees of success, none have achieved the breadth of applicability and impact that digital image sensors have achieved in the 2D imaging world. A large-scale two-dimensional array of coherent detector pixels operating as a light detection and ranging (LiDAR) system could serve as a universal 3D imaging platform. Such a system would offer high depth accuracy and immunity to interference from sunlight, as well as the ability to directly measure the velocity of moving objects. However, due to difficulties in providing electrical and photonic connections to every pixel, previous systems have been restricted to fewer than 20 pixels. Here, we demonstrate the first large-scale coherent detector array consisting of 512 ($32 \times 16$) pixels, and its operation in a 3D imaging system. Leveraging recent advances in the monolithic integration of photonic and electronic circuits, a dense array of optical heterodyne detectors is combined with an integrated electronic readout architecture, enabling straightforward scaling to arbitrarily large arrays. Meanwhile, two-axis solid-state beam steering eliminates any tradeoff between field of view and range. Operating at the quantum noise limit, our system achieves an accuracy of $3.1~\mathrm{mm}$ at a distance of 75 metres using only $4~\mathrm{mW}$ of light, an order of magnitude more accurate than existing solid-state systems at such ranges. Future reductions of pixel size using state-of-the-art components could yield resolutions in excess of 20 megapixels for arrays the size of a consumer camera sensor. This result paves the way for the development and proliferation of low cost, compact, and high performance 3D imaging cameras., Comment: 18 pages, 9 figures

A novel technique is presented for realising programmable silicon photonic circuits. Once the proposed photonic circuit is programmed, its routing is retained without the need for additional power consumption. This technology enables a uniform multi-purpose design of photonic chips for a range of different applications and performance requirements, as it can be programmed for each specific application after chip fabrication. Therefore the cost per chip can be dramatically reduced because of the increase in production volume, and rapid prototyping of new photonic circuits is enabled. Essential building blocks for programmable circuits, erasable directional couplers (DCs) were designed and fabricated, utilising ion implanted waveguides. We demonstrate permanent switching between the drop port and through port of the DCs using a localised post-fabrication laser annealing process. Proof-of-principle demonstrators in the form of generic 1X4 and 2X2 programmable switching circuits were then fabricated and subsequently programmed, to define their function., Comment: 19 pages, 6 figures

The relative root mean squared errors (RMSE) of nonparametric methods for spectral estimation is compared for microwave scattering data of plasma fluctuations. These methods reduce the variance of the periodogram estimate by averaging the spectrum over a frequency bandwidth. As the bandwidth increases, the variance decreases, but the bias error increases. The plasma spectra vary by over four orders of magnitude, and therefore, using a spectral window is necessary. We compare the smoothed tapered periodogram with the adaptive multiple taper methods and hybrid methods. We find that a hybrid method, which uses four orthogonal tapers and then applies a kernel smoother, performs best. For 300 point data segments, even an optimized smoothed tapered periodogram has a 24 \% larger relative RMSE than the hybrid method. We present two new adaptive multi-taper weightings which outperform Thomson's original adaptive weighting., Comment: Missing Figures

Several analysis methods for nonstationary fluctuations are described and applied to the edge localized mode (ELM) instabilities of limiter H-mode plasmas. The microwave scattering diagnostic observes poloidal $k_{\theta}$ values of 3.3 cm$^{-1}$, averaged over a 20 cm region at the plasma edge.A short autoregressive filter enhances the nonstationary component of the plasma fluctuations by removing much of the background level of stationary fluctuations. Between ELMs, the spectrum predominantly consists of broad-banded 300-700 kHz fluctuations propagating in the electron diamagnetic drift direction, indicating the presence of a negative electric field near the plasma edge. The time-frequency spectrogram is computed with the multiple taper technique. By using the singular value decomposition of the spectrogram, it is shown that the spectrum during the ELM is broader and more symmetric than that of the stationary spectrum. The ELM period and the evolution of the spectrum between ELMs varies from discharge to discharge. For the discharge under consideration which has distinct ELMs with a 1 msec period, the spectrum has a maximum in the electron drift direction which relaxes to a near constant value %its characteristic shape in the first half millisecond after the end of the ELM and then grows slowly. In contrast, the level of the fluctuations in the ion drift direction increases exponentially by a factor of eight in the five milliseconds~after the ELM. High frequency precursors are found which occur one millisecond before the ELMs and propagate in the ion drift direction. These precursors are very short ($\sim 10 \mu$secs), coherent bursts, and they predict the occurrence of an ELM with a high success rate., Comment: Figures missing

Advanced photonic probing techniques are of great importance for the development of non-contact wafer-scale testing of photonic chips. Ultrafast photomodulation has been identified as a powerful new tool capable of remotely mapping photonic devices through a scanning perturbation. Here, we develop photomodulation maps into a quantitative technique through a general and rigorous method based on Lorentz reciprocity that allows the prediction of transmittance perturbation maps for arbitrary linear photonic systems with great accuracy and minimal computational cost. Excellent agreement is obtained between predicted and experimental maps of various optical multimode-interference devices, thereby allowing direct comparison of a device under test with a physical model of an ideal design structure. In addition to constituting a promising route for optical testing in photonics manufacturing, ultrafast perturbation mapping may be used for design optimization of photonic structures with reconfigurable functionalities.

A common way to simulate the transport and spread of pollutants in the atmosphere is via stochastic Lagrangian dispersion models. Mathematically, these models describe turbulent transport processes with stochastic differential equations (SDEs). The computational bottleneck is the Monte Carlo algorithm, which simulates the motion of a large number of model particles in a turbulent velocity field; for each particle, a trajectory is calculated with a numerical timestepping method. Choosing an efficient numerical method is particularly important in operational emergency-response applications, such as tracking radioactive clouds from nuclear accidents or predicting the impact of volcanic ash clouds on international aviation, where accurate and timely predictions are essential. In this paper, we investigate the application of the Multilevel Monte Carlo (MLMC) method to simulate the propagation of particles in a representative one-dimensional dispersion scenario in the atmospheric boundary layer. MLMC can be shown to result in asymptotically superior computational complexity and reduced computational cost when compared to the Standard Monte Carlo (StMC) method, which is currently used in atmospheric dispersion modelling. To reduce the absolute cost of the method also in the non-asymptotic regime, it is equally important to choose the best possible numerical timestepping method on each level. To investigate this, we also compare the standard symplectic Euler method, which is used in many operational models, with two improved timestepping algorithms based on SDE splitting methods., Comment: 30 pages, 13 figures, 3 tables, revised version, submitted to Journal of Computational Physics

Reconfigurable photonic devices capable of routing the flow of light enable flexible integrated-optic circuits that are not hard-wired but can be externally controlled. Analogous to free-space spatial light modulators, we demonstrate all-optical wavefront shaping in integrated silicon-on-insulator photonic devices by modifying the spatial refractive index profile of the device employing ultraviolet pulsed laser excitation. Applying appropriate excitation patterns grants us full control over the optical transfer function of telecommunication-wavelength light travelling through the device, thus allowing us to redefine its functionalities. As a proof-of-concept, we experimentally demonstrate routing of light between the ports of a multimode interference power splitter with more than 97% total efficiency and negligible losses. Wavefront shaping in integrated photonic circuits provides a conceptually new approach toward achieving highly adaptable and field-programmable photonic circuits with applications in optical testing and data communication., Comment: 9 pages, 5 figures

Advances in silicon photonics have resulted in rapidly increasing complexity of integrated circuits. New methods are desirable that allow direct characterization of individual optical components in-situ, without the need for additional fabrication steps or test structures. Here, we present a new device-level method for characterization of photonic chips based on a highly localized modulation in the device using pulsed laser excitation. Optical pumping perturbs the refractive index of silicon, providing a spatially and temporally localized modulation in the transmitted light enabling time- and frequency-resolved imaging. We demonstrate the versatility of this all-optical modulation technique in imaging and in quantitative characterization of a variety of properties of silicon photonic devices, ranging from group indices in waveguides, quality factors of a ring resonator to the mode structure of a multimode interference device. Ultrafast photomodulation spectroscopy provides important information on devices of complex design, and is easily applicable for testing on the device-level., Comment: 11 pages, 5 figures

It has been generally assumed, since the work of von Karman and Howarth in 1938, that free decay of fully-developed turbulence is self-similar. We present here a simple phenomenological model of the decay of 3D incompressible turbulence, which predicts breakdown of self-similarity for low-wavenumber spectral exponents $n$ in the range $n_c