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DOE OSTI2022

Transparent conducting oxides: from all-dielectric plasmonics to a new paradigm in integrated photonics

During the past few years, the optics and photonics communities have renewed their attention toward transparent conducting oxides (TCOs), which for over two decades have been broadly employed for the fabrication of transparent electrodes in photovoltaic and communication technologies. This reinvigorated research curiosity is twofold: on the one hand, TCOs, with their metal-like properties, low optical absorption, and fabrication flexibility, represent an appealing alternative to noble metals for designing ultra-compact plasmonic devices. On the other hand, this class of hybrid compounds has been proved to possess exceptionally high optical nonlinearities when operating on a frequency window centered around their crossover point, the wavelength point at which the real part of the dielectric permittivity switches sign. Because TCOs are wide-bandgap materials with the Fermi level located in the conduction band, they are hybrid in nature, thus presenting both interband and intraband nonlinearities. This is the cause of a very rich nonlinear physics that is yet to be fully understood and explored. In addition to this, TCOs are epsilon-near-zero (ENZ) materials within a broad near-infrared spectral range, including the entire telecom bandwidth. In this operational window a myriad of novel electromagnetic phenomena have been demonstrated experimentally such as supercoupling, wavefront freezing, and photon doping. Furthermore, TCOs stand out among all other ENZ systems due to one fundamental characteristic, which is hardly attainable even by using structured materials. In fact, around their ENZ wavelength and for a quite generous operational range, these materials can be engineered to have an extremely small real index. This peculiarity leads to a slow-light effect that is ultimately responsible for a significant enhancement of the material nonlinear properties and is the cornerstone of the emerging field of near-zero-index photonics. In this regard, the recent history of nonlinear optics in conductive oxides is growing extremely fast due to a great number of experiments reporting unprecedentedly remarkable effects, including unitary index change, bandwidth-large frequency shift, efficient ultra-low-power frequency conversion, and many others. This review is meant to guide the reader through the exciting journey of TCOs, starting as an industrial material for transparent electrodes, then becoming a new alternative for low-loss plasmonics, and recently opening up new frontiers in integrated nonlinear optics. The present review is mainly focused on experimental observations.

42 ENGINEERING↗

DOE OSTI2020

Room-Temperature Ferroelectric LiNb 6 Ba 5 Ti 4 O 30 Spinel Phase in a Nanocomposite Thin Film Form for Nonlinear Photonics

Tetragonal tungsten bronze (TTB) materials are one of the most promising classes of materials for ferroelectric and nonlinear optical devices, owing to their very unique noncentrosymmetric crystal structure. In this work, a new TTB phase of LiNb 6 Ba 5 Ti 4 O 30 (LNBTO) has been discovered and studied. A small amount of a secondary phase, LiTiO 2 (LTO), has been incorporated as nanopillars that are vertically embedded in the LNBTO matrix. The new multifunctional nanocomposite thin film presents exotic highly anisotropic microstructure and properties, e.g., strong ferroelectricity, high optical transparency, anisotropic dielectric function, and strong optical nonlinearity evidenced by the second harmonic generation results. An optical waveguide structure based on the stacks of α-Si on SiO 2 /LNBTO–LTO has been fabricated, exhibiting low optical dispersion with an optimized evanescent field staying in the LNBTO–LTO active layer. Lastly, this work highlights the combination of new TTB material designs and vertically aligned nanocomposite structures for further enhanced anisotropic and nonlinear properties.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Reverse Polarizability of Rare Earth Ions (La 3+ , Gd 3+ , Lu 3+ , Y 3+ ) in Tellurite Glasses and Glass Ceramics for Optical Limiting

All-optical modulation using inherent third-order optical nonlinearity of a medium has garnered considerable interest in photonics and optoelectronics. Herein, nonlinear optical (NLO) properties of tellurite glasses and glass ceramics (GCs) containing four different rare earths (RE = La, Gd, Lu, and Y) have been deliberated in near-infrared regions under an ultrafast regime. The La-based glass exhibits ~10 times higher nonlinear refraction (n 2 ) and absorption (α 2 ) than reported NLO materials. The NLO susceptibility [χ (3) ] trend in the studied glasses is La > Gd > Lu > Y, matching with RE 3+ polarizability. Furthermore, Ln 2 Te 6 O 15 nanocrystallite-embedded transparent GCs exhibit a larger NLO coefficient due to the enhanced local field from oxygen vacancies in crystallites. Interestingly, the trend of χ (3) in GCs follows the sequence of Y > Lu > Gd > La, precisely opposite to the glasses. This observation challenges the general polarizability approach of RE 3+ ions, emphasizing that quadratic hyperpolarizability of RE 3+ is pivotal for NLO properties of GCs. Among the studied matrices, Y-containing GCs showed the lowest optical limiting (OL) threshold (5.4 mJ/cm 2 at 800 nm), much lower than those of the reported NLO materials, suggesting its potential as a femtosecond NIR-laser safety material. A combination of large α 2 and n 2 from the studied matrices indicates their advantage for harmonic generation, potentially aiding in the design of ultrafast signal processing devices.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Detection of photon statistics and multimode field correlations by Raman processes

Glauber’s g (2) -function provides a common measure of quantum field statistics through two-photon coincidence counting in Hanbury Brown–Twiss measurements. Here, we propose to use nonlinear optical signals as a tool for the characterization of quantum light. In particular, we show that Raman measurements provide an alternative direct probe for a different component of the four-point correlation function underlying the g (2) -function. We illustrate this capacity for a specific quantum state obtained from a frequency conversion process. Our work points out how the analysis of controlled optical nonlinear processes can provide an alternative window toward the analysis of quantum light sources.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Nonclassical light from finite-range interactions in a two-dimensional quantum mirror

Excitons in a semiconductor monolayer form a collective resonance that can reflect resonant light with extraordinarily high efficiency. We investigate the nonlinear optical properties of such atomistically thin mirrors and show that finite-range interactions between excitons can lead to the generation of highly nonclassical light. We describe two scenarios, in which optical nonlinearities arise either from direct photon coupling to excitons in excited Rydberg states or from resonant two-photon excitation of Rydberg excitons with finite-range interactions. The latter case yields conditions of electromagnetically induced transparency and thereby provides an efficient mechanism for single-photon switching between high transmission and reflectance of the monolayer, with a tunable dynamical timescale of the emerging photon-photon interactions. Remarkably, it turns out that the resulting high degree of photon correlations remains virtually unaffected by Rydberg-state decoherence, in excess of nonradiative decoherence observed for ground-state excitons in two-dimensional semiconductors. This robustness to imperfections suggests a promising approach to quantum photonics at the level of individual photons.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Silicon-On-Silicon Carbide Platform for Integrated Photonics

Silicon carbide (SiC)'s nonlinear optical properties and applications to quantum information have recently brought attention to its potential as an integrated photonics platform. However, despite its many excellent material properties, such as large thermal conductivity, wide transparency window, and strong optical nonlinearities, it is generally a difficult material for microfabrication. Here, it is shown that directly bonded silicon-on-silicon carbide can be a high-performing hybrid photonics platform that does not require the need to form SiC membranes or directly pattern in SiC. The optimized bonding method yields defect-free, uniform films with minimal oxide at the silicon–silicon–carbide interface. Ring resonators are patterned into the silicon layer with standard, complimentary metal–oxide–semiconductor (CMOS) compatible (Si) fabrication and measure room-temperature, near-infrared quality factors exceeding 10 5 . The corresponding propagation loss is 5.7 dB cm -1 . The process offers a wafer-scalable pathway to the integration of SiC photonics into CMOS devices.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Improved measurements of nonlinear integrable optics at IOTA

Nonlinear integrable optics (NIO) are a promising novel approach at improving the stability of high intensity beams. Implementations of NIO based on specialized magnetic elements are being tested at the Integrable Optics Test Accelerator (IOTA) at Fermilab. One method of verifying proper implementation of these solutions is by measuring the analytic invariants predicted by theory. The initial measurements of nonlinear invariants were performed during IOTA run in 2019/20, however the covid-19 pandemic prevented the full-scale experimental program from being completed. Several important improvements were implemented in IOTA for the 2022/23 run, including the operation at higher beam energy of 150 MeV, improved optics control, and chromaticity correction. This report presents on the improved calibrations of the NIO for nonlinear invariant measurements.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Lattice Refinements for Nonlinear Integrable Optics in IOTA

Nonlinear integrable optics of the type proposed by Danilov and Nagaitsev place strict constraints on the lattice parameters in the matching section outside of the nonlinear insert. In particular, the effects of energy spread in the beam have significant effects on the stability of the system. Typical chromatic compensation using sextupoles has significant perturbative effects on the dynamics but is operationally necessary to suppress fast losses. Fast decoherence of kicked beam measurements limits the available signal for studies. Refinements to the IOTA lattice parameters based on this experience with electron beam operation are presented.

Wieland, John [Fermilab] (ORCID:0000000289718523)↗

DOE OSTI2025

Lattice refinements for nonlinear integrable optics in IOTA

Wieland, J. [Fermilab; Michigan State U.] (ORCID:0↗

DOE OSTI2023

Improved Measurements of Nonlinear Integrable Optics Invariants at IOTA

Nonlinear integrable optics (NIO) are a promising novel approach at improving the stability of high intensity beams. Implementations of NIO based on specialized magnetic elements are being tested at the Integrable Optics Test Accelerator (IOTA) at Fermilab. One method of verifying proper implementation of these solutions is by measuring the analytic invariants predicted by theory. The initial measurements of nonlinear invariants were performed during IOTA run in 2019/20, however the covid-19 pandemic prevented the full-scale experimental program from being completed. Several important improvements were implemented in IOTA for the 2022/23 run, including the operation at higher beam energy of 150 MeV, improved optics control, and chromaticity correction. This report presents the results of improved measurements of nonlinear invariants.

43 PARTICLE ACCELERATORS↗

DOE OSTI2023

QuDPy: A Python-based tool for computing ultrafast non-linear optical responses

Nonlinear Optical Spectroscopy is a well-developed field with theoretical and experimental advances that have benefited multiple disciplines, including chemistry, biology, and physics. However, for the accurate interpretation of the corresponding multi-dimensional spectra, there is a need for precise quantum dynamical simulations based on model Hamiltonians. In this article, we present the initial release of our code, QuDPy (Quantum Dynamics in Python), which provides a robust numerical platform for performing quantum dynamics simulations based on model systems, including open quantum systems. Furthermore, a distinguishing feature of our approach is the ability to specify various high-order optical response pathways in the form of double-sided Feynman diagrams through a straightforward input syntax. This syntax outlines the time-ordering of ket-sided or bra-sided optical interactions acting on the time-evolving density matrix of the system. We utilize the quantum dynamics capabilities of QuTip to simulate the spectral response of complex systems, allowing us to compute virtually any $n$-th order optical response of the model system. To illustrate the utility of our approach, we provide a series of example calculations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Massively parallel and universal approximation of nonlinear functions using diffractive processors

Nonlinear computation is essential for a wide range of information processing tasks, yet implementing nonlinear functions using optical systems remains a challenge due to the weak and power-intensive nature of optical nonlinearities. Overcoming this limitation without relying on nonlinear optical materials could unlock unprecedented opportunities for ultrafast and parallel optical computing systems. Here, we demonstrate that large-scale nonlinear computation can be performed using linear optics through optimized diffractive processors composed of passive phase-only surfaces. In this framework, the input variables of nonlinear functions are encoded into the phase of an optical wavefront—e.g., via a spatial light modulator (SLM)—and transformed by an optimized diffractive structure with spatially varying point-spread functions to yield output intensities that approximate a large set of unique nonlinear functions–all in parallel. We provide proof establishing that this architecture serves as a universal function approximator for an arbitrary set of bandlimited nonlinear functions, also covering wavelength-multiplexed nonlinear functions as well as multi-variate and complex-valued functions that are all-optically cascadable. Our analysis also indicates the successful approximation of typical nonlinear activation functions commonly used in neural networks, including the sigmoid, tanh, ReLU (rectified linear unit), and softplus. We numerically demonstrate the parallel computation of one million distinct nonlinear functions, accurately executed at wavelength-scale spatial density at the output of a diffractive optical processor. Furthermore, we experimentally validated this framework using in situ optical learning and approximated 35 unique nonlinear functions in a single shot using a compact setup consisting of an SLM and an image sensor. These results establish diffractive optical processors as a scalable platform for massively parallel universal nonlinear function approximation, paving the way for new capabilities in analog optical computing based on linear materials.

Rahman, Md Sadman Sakib [University of California,↗

DOE OSTI2024

Measured dynamic aperture and detuning of nonlinear integrable optics

One of the most promising advantages of nonlinear integrable optics is strong amplitude dependent tune shift without degrading the dynamic aperture. The integrable optics test accelerator (IOTA) at Fermilab is constructed around nonlinear lattice elements of the elliptical type as described by Danilov and Nagaitsev. Detuning and dynamic aperture scans in IOTA were performed using a fast dipole kicker and a low emittance electron beam. The evolution of the dynamic aperture and detuning for different configurations of the integrable optics lattice are presented.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Measured Dynamic Aperture and Detuning of Nonlinear Integrable Optics

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Spontaneously formed phonon frequency combs in van der Waals solid CrGeTe 3 and CrSiTe 3

Optical phonon engineering through nonlinear effects has been utilized in ultrafast control of material properties. However, nonlinear optical phonons typically exhibit rapid decay due to strong mode-mode couplings, limiting their effectiveness in temperature or frequency sensitive applications. Here we report the observation of long-lived nonlinear optical phonons through the spontaneous formation of phonon frequency combs in the van der Waals material CrXTe 3 (X=Ge, Si) using high-resolution Raman scattering. Unlike conventional optical phonons, the highest A g mode in CrGeTe 3 splits into equidistant, sharp peaks forming a frequency comb that persists for hundreds of oscillations and survives up to 200K. These modes correspond to localized oscillations of Ge 2 Te 6 clusters, isolated from Cr hexagons, behaving as independent quantum oscillators. Introducing a cubic nonlinear term to the harmonic oscillator model, we simulate the phonon time evolution and successfully replicate the observed comb structure. Similar frequency comb behavior is observed in CrSiTe 3 , demonstrating the generalizability of this phenomenon. Our findings demonstrate that Raman scattering effectively probes high-frequency nonlinear phonon modes, offering insight into the generation of long-lived, tunable phonon frequency combs with potential applications in ultrafast material control and phonon-based technologies.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Generalized analytical and numerical modeling of optical second harmonic generation in anisotropic crystals and complex heterostructures using #SHAARP package

Optical second harmonic generation (SHG) is a nonlinear optical effect widely used for nonlinear optical microscopy and laser frequency conversion. The closed-form analytical solution of the nonlinear optical responses is essential for evaluating the optical responses of new materials whose optical properties are unknown a priori. Many approximations have therefore been employed in the existing analytical approaches, such as slowly varying approximation, weak reflection of the nonlinear polarization, transparent medium, high crystallographic symmetry, Kleinman symmetry, easy crystal orientation along a high-symmetry direction, phase matching conditions and negligible interference among nonlinear waves, which may lead to large errors in the reported material properties. To avoid these approximations, here we have developed an open-source package named Second Harmonic Analysis of Anisotropic Rotational Polarimetry (#SHAARP) for single interface (si) and in multilayers (ml) for homogeneous crystals. The reliability and accuracy are established by experimentally benchmarking with both the SHG polarimetry and Maker fringes predicted from the package using standard materials. SHAARP.si and SHAARP.ml are available through GitHub https://github.com/Rui-Zu/SHAARP and https://github.com/bzw133/SHAARP.ml, respectively.

complex systems↗

DOE OSTI2023

Plasmonic Nonlinear Energy Transfer Enhanced Second Harmonic Generation Nanoscopy

Nonlinear optical response is a fingerprint of various physicochemical properties of materials related to symmetry, including crystallography, interfacial configuration, and carrier dynamics. However, the intrinsically weak nonlinear optical susceptibility and the diffraction limit of far-field optics restrict probing deep-subwavelength-scale nonlinear optics with measurable signal-to-noise ratio. Here, we propose an alternative approach toward efficient second harmonic generation (SHG) nanoscopy for SHG-active sample (zinc oxide nanowire; ZnO NW) using an SHG-active plasmonic nanotip. Our full-wave simulation suggests that the experimentally observed high near-field SHG contrast is possible when the nonlinear response of ZnO NW is enhanced and/or that of the tip is suppressed. Here, this result suggests possible evidence of quantum mechanical nonlinear energy transfer between the tip and the sample, modifying the nonlinear optical susceptibility. Further, this process probes the nanoscale corrosion of ZnO NW, demonstrating potential use in studying various physicochemical phenomena in nanoscale resolution.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Nanoscale optical nonreciprocity with nonlinear metasurfaces

Optical nonreciprocity is manifested as a difference in the transmission of light for the opposite directions of excitation. Nonreciprocal optics is traditionally realized with relatively bulky components such as optical isolators based on the Faraday rotation, hindering the miniaturization and integration of optical systems. Here we demonstrate free-space nonreciprocal transmission through a metasurface comprised of a two-dimensional array of nanoresonators made of silicon hybridized with vanadium dioxide (VO 2 ). This effect arises from the magneto-electric coupling between Mie modes supported by the resonator. Nonreciprocal response of the nanoresonators occurs without the need for external bias; instead, reciprocity is broken by the incident light triggering the VO 2 phase transition for only one direction of incidence. Nonreciprocal transmission is broadband covering over 100 nm in the telecommunication range in the vicinity of λ = 1.5 µm. Each nanoresonator unit cell occupies only ~0.1 λ 3 in volume, with the metasurface thickness measuring about half-a-micron. Our self-biased nanoresonators exhibit nonreciprocity down to very low levels of intensity on the order of 150 W/cm 2 or a µW per nanoresonator. We estimate picosecond-scale transmission fall times and sub-microsecond scale transmission rise. Our demonstration brings low-power, broadband and bias-free optical nonreciprocity to the nanoscale.

42 ENGINEERING↗