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We present a succinct way to quantize Maxwell's equations. We begin by discussing the random nature of quantum observables. Then we present the quantum Maxwell's equations and give their physical meanings. Due to the mathematical homomorphism between the classical and quantum cases [1], the derivation of quantum Maxwell's equations can be simplified. First, one needs only to verify that the classical equations of motion are derivable from a Hamiltonian by energy-conservation arguments. Then the quantum equations of motion follow due to homomorphism, which applies to sum-separable Hamiltonians. Hence, we first show the derivation of classical Maxwell's equations using Hamiltonian theory. Then the derivation of the quantum Maxwell's equations follows in an analogous fashion. Finally, we apply this quantization procedure to the dispersive medium case. (This article is written for the classical electromagnetic community assuming little knowledge of quantum theory, an introduction of which can be found in [2, Lecs. 38 and 39].)

In this paper, we numerically study a curved frequency selective surface (FSS) radome, which encloses a waveguide slot array antenna operating at 10GHz, using the ray tracing technique and flat model. The transmission loss (TL) and boresight error (BSE) are calculated for various degrees of freedom, such as elevation and azimuth angular scanning or gimbal systems of array antennas to examine the electromagnetic properties of the curved FSS radome. Our calculations of radiation patterns, TL, and BSE for a multi-layered dielectric radome are compared with those of a commercial EM solver for validation. Importantly, we quantify phase distortions, incurred by the curved FSS radome, using the insertion phase delay (IPD) of transmitted fields on the radome surface. Thereby, we demonstrate that the BSEs strongly depend on (1) the spatial distribution of phase distortions on the radome surface and (2) their average level. The present method is highly suited for analyzing radomes with arbitrary surface patterns inserted.

We employ another approach to quantize electromagnetic fields in the coordinate space, instead of the mode (or Fourier) space, such that local features of photons can be efficiently, physically, and more intuitively described. To do this, coordinate-ladder operators are defined from mode-ladder operators via the unitary transformation of systems involved in arbitrary inhomogeneous dielectric media. Then, one can expand electromagnetic field operators through the coordinate-ladder operators weighted by non-orthogonal and spatially-localized bases, which are propagators of initial quantum electromagnetic (complex-valued) field operators. Here, we call them QEM-CV-propagators. However, there are no general closed form solutions available for them. This inspires us to develop a quantum finite-difference time-domain (Q-FDTD) scheme to numerically time evolve QEM-CV-propagators. In order to check the validity of the proposed Q-FDTD scheme, we perform computer simulations to observe the Hong-Ou-Mandel effect resulting from the destructive interference of two photons in a 50/50 quantum beam splitter.

Quantifying symptoms of tar spot of corn has been conducted through visual-based estimations of the proportion of leaf area covered by the pathogenic structures generated by Phyllachora maydis (stromata). However, this traditional approach is costly in terms of time and labor, as well as prone to human subjectivity. An objective and accurate method, which is also time and labor-efficient, is of an urgent need for tar spot surveillance and high-throughput disease phenotyping. Here, we present the use of contour-based detection of fungal stromata to quantify disease intensity using Red-Green-Blue (RGB) images of tar spot-infected corn leaves. Image blocks (n = 1,130) generated by uniform partitioning the RGB images of leaves, were analyzed for their number of stromata by two independent, experienced human raters using ImageJ (visual estimates) and the experimental stromata contour detection algorithm (SCDA; digital measurements). Stromata count for each image block was then categorized into five classes and tested for the agreement of human raters and SCDA using Cohen's weighted kappa coefficient (κ). Adequate agreements of stromata counts were observed for each of the human raters to SCDA (κ = 0.83) and between the two human raters (κ = 0.95). Moreover, the SCDA was able to recognize “true stromata,” but to a lesser extent than human raters (average median recall = 90.5%, precision = 89.7%, and Dice = 88.3%). Furthermore, we tracked tar spot development throughout six time points using SCDA and we obtained high agreement between area under the disease progress curve (AUDPC) shared by visual disease severity and SCDA. Our results indicate the potential utility of SCDA in quantifying stromata using RGB images, complementing the traditional human, visual-based disease severity estimations, and serve as a foundation in building an accurate, high-throughput pipeline for the scoring of tar spot symptoms.

To analyze the outcomes of Bone marrow aspirate concentrate and Matrix-Induced Chondrogenesis (BMIC) in Osteochondral Lesions of the Talus (OLTs).Patients with OLTs treated with BMIC from June 2013 to July 2020 were included. Visual Analogue Scale (VAS), Foot Function Index (FFI), and Foot Ankle Outcome Score (FAOS) before treatment and at last follow-up were subjected to analysis.Forty-five patients were included and mean follow-up was 39.1 months (range, 13-97 months). Mean lesion size and depth were 180.7 ± 110.4 mmThe BMIC procedure is feasible and should be considered a viable treatment option for OLTs associated with large subchondral bone defects.

We review progress in kinetic plasma modeling by electromagnetic particle-in-cell (EM-PIC) algorithms on unstructured grids. These algorithms are implemented in modular CONPIC and BORPIC C++ codes that integrate a matrix-free explicit finite-element (FE) Maxwell solver based on a parallel sparse-approximate inverse (SPAI) algorithm and a first-principles charge-conserving scatter algorithm to transfer the charged particle information into dynamic variables on the grid. The Maxwell solver of the EM-PIC algorithm utilizes a mixed FE basis and discretizes the time-dependent coupled first-order Maxwell’s system explicitly. The explicit solver approximates the inverse FE system matrix (“mass” matrix) using hierarchical sparsity patterns based on the sparsity pattern of the original matrix. The resulting algorithm effectively accounts for multiscale plasma phenomena. We discuss the application of the developed EM-PIC algorithm to the analysis of laboratory plasmas, vacuum electronic devices for generation of high-power microwave signals, and RF electronics multipactor effects and apply the algorithm to the analysis of multipactor effects and its mitigation in coaxial cables.

The proper orthogonal decomposition technique is applied to a finite-element time-domain particle-in-cell (PIC) algorithm for the simulation of kinetic plasmas, resulting in a reduced-order system. The reduced model is tested with representative examples involving an accelerated electron beam and a plasma ball expansion and compared with full-order simulations. The strengths and weakness of this type of model order reduction when applied to PIC algorithms are discussed through the analysis of the results. In particular, the method allows for a major reduction in the field degrees of freedom necessary to capture the relevant physics, but it can also lead to spurious results if proper care is not taken when assembling the reduced-order system.

Purpose: To analyze prognostic factors for the treatment of periprosthetic femoral fractures (PFFs) using the cable-plate construct. Materials and Methods: A retrospective review of a consecutive series of 41 PFFs treated by osteosynthesis using the cable-plate system. The mean age of patients was 67.3±12.1 years (range, 42-86 years) and the mean follow-up period was 31.5±11.6 months (range, 12-58 months). Fresh frozen cortical strut allografts were leveraged in three cases for additional stability. Prognostic factors that may potentially affect clinical outcomes were analyzed. Results: At the time of final follow-up, fracture union was obtained in 29 hips (70.7%; Group I) after an average of 13.5 weeks (range, 12-24 weeks). Healing failure after surgical treatment was observed in 12 cases (29.3%; Group II), including delayed union (n=10) cases and nonunion (n=2). Factors significantly associated with fracture union included fracture pattern (P=0.040), plate overlap percentage to stem length (P

Fourier transform classically has been attributed to Jean-Baptist Joseph Fourier (1768 - 1830) [1] who invented the Fourier series, from which Fourier transform is descended. Fourier worked for Napoleon Bonaparte and accompanied him to serve in Egypt. Rumor has it that Fourier series was inspired by his study of vibrational modes in a cannon.

Study Design: Level III retrospective study.Purpose: We investigated the impact of short-segment lumbar fusion on the restoration of global sagittal alignment and the correlations between spino-pelvic parameters and clinical outcomes.Overview of Literature: Sagittal imbalance leads to energy consumption and pain in maintaining a standing position. For adult spinal deformity, it is critical to create optimal lumbar lordosis (LL) in order to achieve restoration of sagittal imbalance. However, surgeons do not pay attention to correcting LL in short-segment lumbar fusion.Methods: A total of 69 patients with transforaminal lumbar interbody fusion (TLIF) for degenerative spinal disease were evaluated with a minimum 2-year follow-up. All patients underwent TLIF with hyper-lordotic angle cages to achieve higher LL. Radiological spino-pelvic parameters including sagittal vertical axis (SVA) and clinical outcomes using the Oswestry Disability Index (ODI) and Numeric Rating Scale (NRS) were evaluated.Results: The average LL was 35.8°±9.9° before surgery, 42.3°±9.3° 1 year after surgery, and 40.3°±10.2° 2 years after surgery (p p p

We present a new math-physics modeling approach, called canonical quantization with numerical mode-decomposition, for capturing the physics of how incoming photons interact with finite-sized dispersive media, which is not describable by the previous Fano-diagonalization methods. The main procedure is to (1) study a system where electromagnetic (EM) fields are coupled to non-uniformly distributed Lorentz oscillators in Hamiltonian mechanics, (2) derive a generalized Hermitian eigenvalue problem for conjugate pairs in coordinate space, (3) apply computational electromagnetics methods to find a countably/finite set of time-harmonic eigenmodes that diagonalizes the Hamiltonian, and (4) perform the subsequent canonical quantization with mode-decomposition. Moreover, we provide several numerical simulations that capture the physics of full quantum effects, impossible by classical Maxwell's equations, such as non-local dispersion cancellation of an entangled photon pair and Hong-Ou-Mandel (HOM) effect in a dispersive beam splitter., Comment: submitted to Physical Review A (under review)

Background: For total knee arthroplasty (TKA), implant design and proper coverage are important for achieving patient satisfaction. An asymmetrical anatomic implant (Persona® knee system, Zimmer Biomet, Warsaw, Indiana) enables accurate coverage and minimal bone cutting. This study aimed to analyze the clinical and radiological outcomes of TKA using an asymmetrical anatomic implant over a minimum 3-year follow-up.Methods: The medical records of 94 patients who underwent 132 TKAs using the Persona® knee system, between April 2015 and January 2016 were reviewed. Pre- and post-operative clinical outcomes (assessed using the International Knee Documentation Committee (IKDC), Western Ontario and McMaster Universities Arthritis Index (WOMAC), and Knee Injury and Osteoarthritis Outcome Score (KOOS) scores, and range of motion (ROM) were reviewed. The mechanical hip-knee-ankle (HKA) axis, component overhang and underhang and presence of a radiolucent line (RLL) were evaluated. Liner thickness were also reviewed.Results: At 3-year follow-up, the mean ROM improved from 108.4° to 130.3°. The mean IKDC subjective, WOMAC and global KOOS score significantly improved from 29.2 to 70.3, from 64.2 to 11.5, and from 66.6 to 21.7, respectively (p The mean mechanical HKA axis indicated the correction of the malalignment (from 9.2° varus to 0.3° varus, p3-mm bone-to-implant size mismatch were 6.8% and 8.3% for the femoral and tibial components, respectively. RLL was found in seven cases, but they were small (>2 mm) and did not progress. In 36.3% of the knees, the additional liner thickness (11 or 13mm) was used. No case of implant loosening or early failure related to the implant design occurred. Conclusion: TKA using the Persona® knee system improved all the clinical knee scores and ROM without signs of early failure. This knee system also provides more implant size options than the conventional TKA systems and facilitates ligament balancing.

In quantum optics, the conventional method to quantize electromagnetic fields is canonical quantization which is analogue to the classical modal expansion method. Here, on the other hand, we show a quantum finite-difference time-domain scheme that can track the time evolution of quantum electromagnetic operators in the coordinate Hilbert space. This can be done by using coordinate-ladder operators derived from mode-ladder operators via the unitary transformation, and quantum hopping functions. This novel methodology will serve as a guideline for the development of advanced computational algorithms to perform numerical experiments on various quantum optical phenomena, particularly, involved in dispersion and dissipative effects.

We investigate quantum information preserving computational electromagnetics. To do so, we propose two different methods which are (1) numerical canonical quantization and (2) quantum finite-difference time-domain scheme. The proposed algorithms find numerical solutions of quantum Maxwell’s equations involved in arbitrary inhomogeneous dielectric media based on the macroscopic theory on quantum electrodynamics; hence, they are useful to study the quantum nature of electromagnetic fields in arbitrary passive and lossless quantum optical instruments. We provide a numerical example associated with two photon interference occurring in a quantum beam splitter, which is the underlying principle of recent quantum technologies.

We present a computational framework for canonical quantization in arbitrary inhomogeneous dielectric media by incorporating quantum electromagnetic effects into complex solutions of quantum Maxwell's equations. To do so, the proposed algorithm integrates and performs (1) numerical computation of normal modes and (2) evaluation of arbitrary products of ladder operators acting on multimode Fock states. The former is associated with Hermitian-Helmholtz linear systems using finite-element or finite-difference methods; consequently, the complete set of numerical normal modes diagonalizes the Hamiltonian operators up to floating-point precision. Its Hermiticity is retained, allowing its quantization. Then, we perform quantum numerical simulations of two-photon interference occurring in a 50:50 beam splitter to observe the Hong-Ou-Mandel effect. Our prototype model is useful for numerical analyses on various narrow-band quantum-optical multiphoton systems such as quantum metasurfaces, quantum-optical filters, and quantum electrodynamics in open optical cavities.

We present finite-difference time-domain schemes to numerically solve quantum Maxwell's equations for arbitrary inhomogeneous media based on the macroscopic theory on quantum electrodynamics. In the Heisenberg picture, quantum Maxwell dynamical operators are expanded by a set of ladder operators defined in the coordinate space while non-orthogonal basis corresponding to a new long-range propagators different from the classical Green's function. The proposed time-domain quantum Maxwell solver is useful to study the local nature of quantum information propagation such as virtual photons or near single photon sources. We provide numerical examples associated with two photon interference occurring in a quantum beam splitter, called Hong-Ou-Mandel effect. Moreover, we emulate the recent interesting experiment on quantum interference across an astronomical distance [1].

A new computational framework for quantum electromagnetics has recently been proposed (D.-Y. Na, J. Zhu, F. L. Teixeira, and W. C. Chew, arXiv 1911.00947, 2019). In this work, we demonstrate the use of Huygens' Principle for quantum information propagation. Instead of numerical eigenmodes, Fourier modes are used to quantize the field. Wave propagation and second-order correlation function calculated based on this scheme are shown.

We combine a novel finite-element-based electromagnetic particle-in-cell (EM-PIC) algorithm for the solution of Maxwell–Vlasov equations on irregular (unstructured) grids together with the Furman–Pivi probabilistic model governing the secondary electron emission process. The algorithm can be used for the analysis of resonant electron discharging phenomena (multipactor effects) in high-power radio frequency devices. In contrast to previous algorithms, the present EM-PIC algorithm yields a self-consistent time update of fields and particles on irregular grids with energy and charge conservation obtained from first principles. The use of unstructured grids enables local mesh refinement and simulation of complex geometries with minimal geometric defeaturing. We apply the algorithm to model multipactor effects on waveguides with flat or corrugated walls. We contrast the evolution of the electron population in various cases and investigate the respective saturation processes arising from self-field counterbalancing effects.

In this article, we describe a novel implementation of finite-size (super) particles described by polynomial-based spatial shape factors in electromagnetic particle-in-cell (EM-PIC) algorithms for kinetic plasma simulations based on unstructured meshes. The proposed implementation is aimed at mitigating (spurious) numerical Cherenkov radiation effects while preserving exact charge conservation. This is achieved by employing a representation of Maxwell's equations based on the exterior calculus of differential forms and a discretization of twisted differential forms associated with the primal mesh by Whitney forms, while ordinary differential forms are associated with the dual mesh. The set of full-discrete Maxwell's equations is then obtained by using a finite-element Galerkin method and a leap-frog time integration, leading to a mixed D-H finite-element time-domain Maxwell field solver. In the proposed EM-PIC implementation, the gather and scatter steps of the algorithm yield integrals of polynomials over polyhedral domains in 3-D space (or polygonal domains in 2-D space) that can be evaluated analytically. We provide numerical examples confirming charge conservation down to machine precision on an unstructured mesh.