Finite-difference Frequency-domain Simulations Research Articles

Accelerating finite-difference frequency-domain simulations of inverse designed structures in nanophotonics using deep learning

The inverse design of nanophotonic devices is becoming increasingly relevant for the development of complex photonic integrated circuits. Electromagnetic first-order simulations contribute to the overwhelming computational cost of the optimization routines in established inverse design algorithms, requiring more efficient methods for enabling improved and more complex design process flows. Here we present such a method to predict the electromagnetic field distribution for pixel-discrete planar inverse designed structures using deep learning. Our model is able to infer accurate predictions used to initialize a conventional finite-difference frequency-domain algorithm and thus lowers the average time required for simulating the electromagnetic response of nanophotonic device layouts by up to 53% in iterative design process flows. We demonstrate the applicability of our deep learning method for the inverse design of photonic integrated powersplitters and mode converters, and we highlight the possibility of exploiting previous learning results in subsequent design tasks of novel functionalities via fine-tuning reduced data sets, thus improving computational speed further.

Computational scaling in inverse photonic design through factorization caching

Inverse design coupled with adjoint optimization is a powerful method to design on-chip nanophotonic devices with multi-wavelength and multi-mode optical functionalities. Although only two simulations are required in each iteration of this optimization process, these simulations still make up the vast majority of the necessary computations and render the design of complex devices with large footprints computationally infeasible. Here, we introduce a multi-faceted factorization caching approach to drastically simplify the underlying computations in finite-difference frequency-domain (FDFD) simulations and significantly reduce the time required for device optimization. Specifically, we cache the numerical and symbolic factorizations for the solution of the corresponding system of linear equations in discretized FDFD simulations and re-use them throughout the device design process. As proof-of-concept demonstrations of the resulting computational advantage, we present simulation speedups reaching as high as 9.2× in the design of broadband wavelength and mode multiplexers compared to conventional FDFD methods. We also show that factorization caching scales well over a broad range of footprints independent of the device geometry, from as small as 16μm2 to over 7000μm2. Our results present significant enhancements in the computational efficiency of inverse photonic design and can greatly accelerate the use of machine-optimized devices in future photonic systems.

Inverse design of plasma metamaterial devices with realistic elements

In an expansion of a previous study (Rodríguez et al 2021 Phys. Rev. Appl. 16 014023), we apply inverse design methods to produce two-dimensional plasma metamaterial devices with realistic plasma elements which incorporate quartz envelopes, collisionality (loss), non-uniform density profiles, and resistance to experimental error/perturbation. Finite difference frequency domain simulations are used along with forward-mode differentiation to design waveguides and demultiplexers operating under the transverse magnetic polarization. Optimal devices with realistic elements are compared to previous devices with idealized elements, and several parameter initialization schemes for the optimization algorithm are explored, yielding a robust procedure for producing such devices. Demultiplexing and waveguiding are demonstrated for microwave-regime devices composed of plasma elements with reasonable space-averaged plasma frequencies GHz and a collision frequency GHz, allowing for future in-situ training and experimental realization of these designs.

SIMULASI PERAMBATAN GELOMBANG ELEKTROMAGNETIK PADA KRISTAL FOTONIK 2D MENGGUNAKAN METODE FINITE DIFFERENCE FREQUENCY DOMAIN

Numerical simulations on two-dimensional photonic crystals with defects were analyzed using the Finite Difference Frequency Domain (FDFD). This approach consists of Maxwell's formulation that uses Central Finite Difference to place fields and materials at discrete points of the Yee grid, so that the matrix wave equation is obtained in the form of column vectors. Absorbent boundary conditions use Perfectly Matched Layer (PML) with fictitious magnetic conductivity to shed incoming waves at the edge of the domain calculation. Photonic crystals can be assumed to be a periodic lattice of dielectric material that produces the phenomenon of photonic band gap (PBG). The results of FDFD simulations are compared with the literature with a difference of 0.056. This small difference value means that this method is good enough to analyze PBG phenomena. For point defects and the accumulation of electromagnetic waves, linear defects are investigated and analyzed with spectral responses. Insertion of defects in photonic crystals will produce a photonic pass band (PPB). The simulation results show that PPB depends on the angle of arrival vector, material permittivity, and width of the defect structure.

Plasmon polaritons in cubic lattices of spherical metallic nanoparticles

We theoretically investigate plasmon polaritons in cubic lattices of spherical metallic nanoparticles. The nanoparticles, each supporting triply-degenerate localized surface plasmons, couple through the Coulomb dipole-dipole interaction, giving rise to collective plasmons that extend over the whole metamaterial. The latter hybridize with photons forming plasmon polaritons, which are the hybrid light-matter eigenmodes of the system. We derive general analytical expressions to evaluate both plasmon and plasmon-polariton dispersions and the corresponding eigenstates. These are obtained within a Hamiltonian formalism, which takes into account retardation effects in the dipolar interaction between the nanoparticles and considers the dielectric properties of the nanoparticles as well as their surrounding. Within this model we predict polaritonic splittings in the near-infrared to the visible range of the electromagnetic spectrum that depend on polarization, lattice symmetry, and wave-vector direction. Finally, we show that the predictions of our model are in excellent quantitative agreement with conventional finite-difference frequency-domain simulations, but with the advantages of analytical insight and significantly reduced computational cost.

Deep-Subwavelength Semiconductor Nanowire Surface Plasmon Polariton Couplers

The increased importance of plasmonic devices has prompted a sizable research activity directed toward the development of ultracompact and high-performance couplers. Here, we present a novel scheme for efficient, highly localized, and directional sourcing of surface plasmon polaritons (SPPs) that relies on the excitation of leaky mode optical resonances supported by high-refractive index, semiconductor nanowires. High coupling efficiencies are demonstrated via finite difference frequency domain simulations and experimentally by leakage radiation microscopy. This efficiency is quantified by means of a coupling cross section, the magnitude of which can exceed twice the geometric cross section of the nanowire by exploiting its leaky resonant modes. We provide intuition into why the SPP coupling via certain wire modes is more effective than others based on their symmetry properties. Furthermore, we provide an example showing that dielectric scatterers may perform as well as metallic scatterers in coupling to SPPs.

Contribution of Au nanoparticles to the longitudinal magneto-optical Kerr effect of Bragg reflector based magneto-plasmonicmultilayers

In this paper, we investigate a significant enhancement of the longitudinal magneto-optical Kerr effect when a magneto-optical thin film is covered by the Bragg reflector mirror and Au nanoparticles on its right and left side respectively. Our results indicate the sufficient longitudinal magneto-optical Kerr effect enhancement in this new structure by the aid of combination of surface plasmon resonance and light localization in magneto-optical garnet layer at one practical communication wavelength in the middle of the visible spectrum. These results confirmed by the aid of Finite difference frequency domain simulation method.

Optical cavity efficacy and lasing of focused ion beam milled GaN/InGaN micropillars

Focused ion beam milled micropillars employing upper and lower distributed Bragg reflectors (DBRs) and incorporating InGaN quantum dots were analysed both microstructurally and optically. Comparison of the surface characteristics and the optical resonance of pillars milled employing two recipes, using comparatively higher and lower beam currents, were carried out through electron back scatter diffraction, atomic force microscopy and low temperature micro-photoluminescence. Low temperature micro-photoluminescence highlighted singly resolved InGaN quantum dot emission as well as modes with typical quality factors (Q) of ∼200–450 for typical 1–4 μm diameter pillars, while one exceptional 4 μm diameter pillar displayed optically-pumped lasing with a Q of ∼1100 at a threshold of ∼620 kWcm−2. The higher current recipe resulted in pillars with thicker surface amorphous layers, while the lower current recipe resulted in pillars with thinner surface amorphous layers but rougher surfaces. Micropillars milled through the recipe utilising higher beam currents were tentatively shown to possess lower Qs on average, correlating with the thickness of the surface amorphous layer. Finite difference frequency domain simulations in combination with analytical approximations of the various optical loss pathways suggested that surface scattering related optical loss was not significant compared to internal-based and surface absorption-based losses. The magnitude of the internal loss was observed to fluctuate significantly, which was thought to relate to the fluctuating micro-structure within the lower DBR and within the InGaN quantum dot layer.

Understanding the dispersion of coaxial plasmonic structures through a connection with the planar metal-insulator-metal geometry

We elucidate the dispersion behavior of deep-subwavelength propagating modes in coaxial plasmonic structures by making an explicit connection with the planar metal-insulator-metal geometry. We provide an intuitive picture that allows for a qualitative understanding and a quantitative prediction of the entire dispersion behavior, which includes the number of modes at every frequency, the modal propagation constants, the propagation losses, and the cutoff frequencies of propagating modes supported by these technologically important structures. We validate our analytical approach by comparing its predictions to first-principles finite-difference frequency-domain simulations.

Electromagnetic fields in the presence of an infinite metamaterial wedge

Electromagnetic fields, excited by an electric line source in the presence of an infinite metamaterial wedge, are determined by application of the Kontorovich–Lebedev transform. Uncoupled singular integral equations for the spectral functions are derived and a numerical scheme is devised and implemented to solve them. Numerical results showing the influence of a metamaterial wedge presence on the directivity of a line source are presented and verified through finite-difference frequency-domain simulations.

Electromagnetic fields in the presence of an infinite dielectric wedge: the phased line source excitation case

Electromagnetic fields, excited by an electric phased line source in the presence of an infinite dielectric wedge, are determined by application of the Kontorovich-Lebedev transform. The Maxwell's equations together with the conditions of continuity of the tangential field components at the material interfaces are formulated as a vector boundary-value problem. By representing the field components as Kontorovich-Lebedev integrals, the problem is reduced to a system of singular integral equations for the unknown spectral functions. We construct numerical solutions to those equations that permit fields evaluation for values of the wedge refractive index, not necessarily close to unity, and for arbitrary positioned source and observer. Numerical results showing the influence of a wedge presence on the directivity of a phased line source are presented and verified through finite-difference frequency-domain simulations.

Correction of picosecond voltage pulses measured with external electro-optic sampling tips

We quantify the distortion that an external electro-optic sampling tip imprints on a measured picosecond voltage pulse propagating on a coplanar stripline. In order to characterize the sampling tip, we take advantage of the electro-optic effect of the GaAs substrate onto which the stripline is fabricated. In these measurements, the electro-optic tip just acts as a disturbance of the transmission line. We derive a correction function that allows us to eliminate the influence of the invasive sampling tip on a measured voltage pulse up to a frequency of 400 GHz. The corrected voltage pulse shows good agreement with the true, undisturbed voltage pulse obtained from a sampling measurement using the electro-optic effect of the GaAs substrate. Moreover, the experimental results are supported by finite-difference frequency-domain simulations. Our work paves the way towards a more accurate characterization of high-speed electronic devices using external electro-optic sampling tips.

Electromagnetic fields in the presence of an infinite dielectric wedge

Electromagnetic fields excited by a line source in the presence of an infinite dielectric wedge with refractive index N are determined by application of the Kontorovich–Lebedev transform. Singular integral equations for spectral functions are solved by perturbation procedure, and the solution is obtained in the form of a Neumann series in powers of . The devised numerical scheme permits evaluation of the higher-order terms and, thus, extends the perturbation solution to values of N not necessarily close to unity. Asymptotic approximations for the near and far fields inside and outside the dielectric wedge are derived. The combination of the Neumann-type expansion of the transform functions with the representation of the field as a Bessel function series extends solutions derived with the Kontorovich–Lebedev method to the case of real-valued wavenumbers and arbitrarily positioned source and observer. Numerical results showing the influence of wedges with various values of dielectric and magnetic constants on the directivity of a line source are presented and verified through finite-difference frequency-domain simulations.

Subsampling of fine features in finite-difference frequency-domain simulations

An improved three-point finite-difference scheme is presented, which deals correctly with all terms up to 2nd order in the expansion of the derivative, regardless of the existence of multiple dielectric interfaces between sample points. The improved differencing scheme is implemented into a 1D slab-mode solver for validation of accuracy and a 2D mode solver. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 44: 95–101, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20558