High-efficiency scattering field modeling in metallic components: a machine-learning-inspired approach.

We present a highly efficient method for characterizing the scattering field distribution of surface plasmon polaritons in metallic components by combining the eXtended Pseudospectral Frequency-Domain (X-PSFD) method with an iterative, machine-learning-inspired procedure. Shifting away from traditional matrix operations, we utilize the "Adam" optimizer-an effective and swift machine learning algorithm-to solve the scattering field distribution. Our method encompasses the derivation of the associated cost function and gradient differentiation of the field, leveraging spectral accuracy at Legendre collocation points in the Helmholtz equation. We refine the total-field/scattered-field (TF/SF) formulation within the X-PSFD framework for optimized incident field management and employ Chebyshev-Lagrange interpolation polynomials for rapid, accurate computation of broad-band results. To ensure global accuracy, we introduce unique physical boundary conditions at subdomain interfaces. Demonstrating our method's robustness and computational efficiency, we model perfect electric conductors (PECs) and silver nanocylinders, and we apply our approach to analyze the excited electric field on subtly distorted metallic surfaces, particularly plasmonic structures, thereby validating its wide-ranging effectiveness.

Excitation of surface plasmon mode in bulk semiconductor lasers.

We propose a realistic process for the excitation of surface plasmon polariton (SPP) modes in a silicon photonic waveguide (WG). The process involves the placement of buried oxide (BOX) composed of silica between a WG and silicon substrate. When the BOX thickness is manipulated, different amounts of modal power leak toward the BOX into the substrate and simultaneously acquire compensation from a semiconductor located on the WG. The compensation related to the leakage can be used to infer transparency gain. Similar to the case for a semiconductor laser cavity, the lowest transparency gain among WG modes can be favored; thus, only one mode can survive in the WG, and it is in the region with the specified BOX thickness. Finally, we propose a credible mechanism suitable for demonstrating the region requirements of the existence of SPP modes.

Adaptive penalty method with adam optimizer for enhanced convergence in optical waveguide mode solvers.

We propose a cutting-edge penalty method for optical waveguide mode solvers, integrating the Adam optimizer into pseudospectral frequency-domain (PSFD) frameworks. This strategy enables adaptable boundary fluctuations at material interfaces, significantly enhancing numerical convergence and stability. The Adam optimizer, an adaptive algorithm, is deployed to determine the penalty coefficient, greatly improving convergence rates and robustness while effectively incorporating boundary conditions into the interfaces of subdomains. Our solver evaluates the numerical performance of optical waveguides by calculating effective indices of standard benchmark waveguides with high accuracy. This method diminishes numerical boundary errors and provides a marked increase in convergence speed and superior accuracy when compared to conventional methods and even metaheuristic optimization methods, all while maintaining the inherent global spectral accuracy of the PSFD.

Light extraction efficiency enhancement of flip-chip blue light-emitting diodes by anodic aluminum oxide.

We produced an anodic aluminum oxide (AAO) structure with periodic nanopores on the surface of flip-chip blue light-emitting diodes (FC-BLEDs). The nanopores had diameters ranging from 73 to 85 nm and were separated by distances ranging from approximately 10 to 15 nm. The light extraction efficiency enhancement of the FC-BLEDs subjected to different durations of the second pore-widening process was approximately 1.6-2.9%. The efficiency enhancement may be attributed to the following mechanism: periodic nanopores on the surface of FC-BLEDs reduce the critical angle of total reflection and effective energy transfer from a light emitter into a surface plasmon mode produced by AAO.

Design of metal-dielectric grating lasers only supporting surface-wave-like modes.

We present a prototype of semiconductor lasers with plasmonic periodic structures that only support transverse-magnetic modes at telecommunication wavelengths. The structure does not sustain transverse-electric guided modes which are irrelevant to surface-wave-enhanced applications, and lasing modes must be surface-wave-like. With thin low-index dielectric buffers near the metal surface, the threshold gain is kept at a decent level around the photonic band edge. Thin windows are then opened on the metal surface to let out significant surface fields. This facilitates usages of surface waves for the spectroscopy and sensing.

Frequency-domain formulation of photonic crystals using sources and gain.

We present a formulation to analyze photonic periodic structures from viewpoints of sources and gain. The approach is based on a generalized eigenvalue problem and mode expansions of sources which sustain optical fields with phase boundary conditions. Using this scheme, we calculate power spectra, dispersion relations, and quality factors of Bloch modes in one-dimensional periodic structures consisting of dielectrics or metals. We also compare the results calculated from this scheme with those from the complex-frequency method. The outcomes of these two approaches generally agree well and only deviate slightly in the regime of low quality factors.

Analysis of optical waveguides with ultra-thin metal film based on the multidomain pseudospectral frequency-domain method.

Analysis of optical waveguides with thin metal films is studied by the multidomain pseudospectral frequency-domain (PSFD) method. Calculated results for both guiding and leaky modes are precise by means of the PSFD based on Chebyshev-Lagrange interpolating polynomials with modified perfectly matched layer (MPML). By introducing a suitable boundary condition for the dielectric-metallic interface, the stability and the spectrum convergence characteristic of the PSFD-MPML method can be sustained. The comparison of exact solutions of highly sensitive surface plasmon modes in 1D dielectric-metal waveguides and those calculated by our PSFD-MPML demonstrates the validity and usefulness of the proposed method. We also apply the method to calculate the effective refractive indices of an integrated optical waveguide with deposition of the finite gold metal layer which induces the hybrid surface plasmon modes. Furthermore, the 2-D optical structures with gold films are investigated to exhibit hybrid surface plasmon modes of wide variations. We then apply hybrid surface plasmon modes to design novel optical components-mode selective devices and the polarizing beam splitter.

A high-accuracy pseudospectral full-vectorial leaky optical waveguide mode solver with carefully implemented UPML absorbing boundary conditions.

The previously developed full-vectorial optical waveguide eigenmode solvers using pseudospectral frequency-domain (PSFD) formulations for optical waveguides with arbitrary step-index profile is further implemented with the uniaxial perfectly matched layer (UPML) absorption boundary conditions for treating leaky waveguides and calculating their complex modal effective indices. The role of the UPML reflection coefficient in achieving high-accuracy mode solution results is particularly investigated. A six-air-hole microstructured fiber is analyzed as an example to compare with published high-accuracy multipole method results for both the real and imaginary parts of the effective indices. It is shown that by setting the UPML reflection coefficient values as small as on the order of 10(-40) ∼ 10(-70), relative errors in the calculated complex effective indices can be as small as on the order of 10(-12).

Analysis of two-dimensional photonic crystals using a multidomain pseudospectral method.

An analysis method based on a multidomain pseudospectral method is proposed for calculating the band diagrams of two-dimensional photonic crystals and is shown to possess excellent numerical convergence behavior and accuracy. The proposed scheme utilizes the multidomain Chebyshev collocation method. By applying Chebyshev-Lagrange interpolating polynomials to the approximation of spatial derivatives at collocation points, the Helmholtz equation is converted into a matrix eigenvalue equation which is then solved for the eigenfrequencies by the shift inverse power method. Suitable multidomain division of the computational domain is performed to deal with general curved interfaces of the permittivity profile, and field continuity conditions are carefully imposed across the dielectric interfaces. The proposed method shows uniformly excellent convergence characteristics for both the transverse-electric and transverse-magnetic waves in the analysis of different structures. The analysis of a mini band gap is also shown to demonstrate the extremely high accuracy of the proposed method.