Modelling Tools for Plasmonics

Dr. S. S. Verma, Department of Physics, S.L.I.E.T., Longowal, Distt.-Sangrur (Punjab)-148106

Plasmonic fundamentalsPlasmons are an interaction between free electrons in a metallic material and electromagnetic radiation.  Plasmonics is an extremely broad field of study. Its applications vary from integrated optics on silicon microchips to enhancing absorption in state-of-the-art solar cells to sensing individual molecules of biohazardous materials. Surface Plasmons: are waves that propagate along the surface of metallic and certain dielectric materials. The electric field of a plasmon wave reaches its maximum at the surface and decays evanescently away from the surface. The wave properties are highly sensitive to any changes in the refractive index of the material as well as the device’s geometry. Surface plasmon resonance (SPR): is the resonant oscillation of conduction electrons at the interface between a negative and positive permitivity material stimulated by incident light. The resonance condition is established when the frequency of incident photons matches the natural frequency of surface electrons oscillating against the restoring force of positive nuclei. SPR in subwavelength scale nanostructures can be polaritonic or plasmonic in nature. SPR is the basis of many standard tools for measuring adsorption of material onto planar metal (typically gold or silver) surfaces or onto the surface of metal nanoparticles. It is the fundamental principle behind many color-based biosensor applications and different lab-on-a-chip sensors.LSPRs (Localized SPRs): are collective electron charge oscillations in metallic nanoparticles that are excited by light. They exhibit enhanced near-field amplitude at the resonance wavelength. This field is highly localized at the nanoparticle and decays rapidly away from the nanoparticle/dieletric interface into the dielectric background, though far-field scattering by the particle is also enhanced by the resonance. Light intensity enhancement is a very important aspect of LSPRs and localization means the LSPR has very high spatial resolution (subwavelength), limited only by the size of nanoparticles. Because of the enhanced field amplitude, effects that depend on the amplitude such as magneto-optical effect are also enhanced by LSPRs.

Why plasmonic?The study of molecular binding processes is a key aspect to many fields of research. From life science to environmental safety, determining which molecules interact, how they interact, and why they interact can ultimately lead to more effective drugs, higher performance materials, cleaner air/water quality, and much more. Several technologies exist that may be utilized for such molecular binding studies, i.e. ELISA, QCM, and ITC. However, few encompass as many advantages as Surface Plasmon Resonance. SPR enables (1) high sensitivity, (2) label-free detection, (3) real-time monitoring, (4) low volume sample consumption, (5) quantitative evaluation, and (6) determination of kinetic rate constants. Furthermore, SPR is easy to perform

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and can be a cost-effective solution. Surface Plasmon Resonance (SPR) has emerged as a powerful detection technique due to its high sensitivity and label-free capability. This optical-based real-time detection method delivers superior results across diverse categories of research. Applications include life science, drug discovery, electrochemical analysis, food quality and safety, environmental science, and chemical sensor development. The field of plasmonics and metamaterials has attracted a great deal of interest over the past two decades, but despite the many fundamental breakthroughs and exciting science it has produced, it is yet to deliver on the applications that were initially targeted as most promising. This focus examines the primary fundamental hurdles in the physics of plasmons that have been hampering practical applications and highlights some of the promising areas in which the field of plasmonics and metamaterials can realistically deliver.

Plasmonic applicationsPosition and intensity of plasmon absorption and emission peaks are affected by molecular adsorption, which can be used in molecular sensors. For example, a fully operational prototype device detecting casein in milk has been fabricated. The device is based on detecting a change in absorption of a gold layer. Localized surface plasmons of metal nanoparticles can be used for sensing different types molecules, proteins, etc. Plasmons are being considered as a means of transmitting information on computer chips, since plasmons can support much higher frequencies (into the 100 THz range, while conventional wires become very lossy in the tens of GHz). However, for plasmon-based electronics to be useful, a plasmon-based amplifier analogous to the transistor, called a plasmonstor, first needs to be created. Plasmons have also been proposed as a means of high-resolution lithography and microscopy due to their extremely small wavelengths. Both of these applications have seen successful demonstrations in the lab environment. Finally, surface plasmons have the unique capacity to confine light to very small dimensions which could enable many new applications. Surface plasmons are very sensitive to the properties of the materials on which they propagate. This has led to their use to measure the thickness of monolayers on colloid films, such as screening and quantifying protein binding events. Companies such as Biacore have commercialized instruments which operate on these principles. Optical surface plasmons are also being investigated with a view to improve makeup. In 2009, a research team found a way to greatly improve organic light-emitting diode efficiency with the use of plasmons. A group of European researchers led by IMEC has begun work to improve solar cell efficiencies and costs through incorporation of metallic nanostructures (using plasmonic effects) that can enhance absorption of light into different types of solar cells: crystalline silicon (c-Si), high-performance III-V, organic, and dye-sensitized solar cells.  However, in order for plasmonic solar photovoltaic devices to function optimally ultra-thin transparent conducting oxides are necessary. Full color holograms using plasmonics have been demonstrated. The silicon absorbs only a certain fraction of the spectrum, and it's transparent to the rest.

Surface plasmons have been used to enhance the surface sensitivity of several spectroscopic measurements including fluorescence, Raman scattering, and second harmonic generation. However, in their simplest form, SPR reflectivity measurements can be used to detect molecular adsorption, such as polymers, DNA or proteins, etc. Technically, it is common to measure the minimum angle of reflection (maximum angle of absorption). This angle changes in the order of

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0.1° during thin (about nm thickness) film adsorption. (See also the Examples.) In other cases the changes in the absorption wavelength is followed. The mechanism of detection is based on that the adsorbing molecules cause changes in the local index of refraction, changing the resonance conditions of the surface plasmon waves. If the surface is patterned with different biopolymers, using adequate optics and imaging sensors (i.e. a camera), the technique can be extended to surface plasmon resonance imaging (SPRI). This method provides a high contrast of the images based on the adsorbed amount of molecules, somewhat similar to Brewster anglemicroscopy (this latter is most commonly used together with a Langmuir–Blodgett trough). For nanoparticles, localized surface plasmon oscillations can give rise to the intense colors of suspensions or sols containing the nanoparticles. Nanoparticles or nanowires of noble metals exhibit strong absorption bands in the ultraviolet-visible light regime that are not present in the bulk metal. This extraordinary absorption increase has been exploited to increase light absorption in photovoltaic cells by depositing metal nanoparticles on the cell surface. The energy (color) of this absorption differs when the light is polarized along or perpendicular to the nanowire. Shifts in this resonance due to changes in the local index of refraction upon adsorption to the nanoparticles can also be used to detect biopolymers such as DNA or proteins. Related complementary techniques include plasmon waveguide resonance, QCM, extraordinary optical transmission, and dual polarization interferometry

Plasmonic simulationPlasmonics, which is the study of interaction between light and metal, is a very active field of research, owing to the potential offered by the ability to confine light beyond the limits of diffraction. Many properties of plasmonic structures can be derived directly from Maxwell's equations, and methods such as FDTD and finite-element algorithms are widely used for designing and optimising plasmonic nano-structures. FDTD is probably the most widely used method for characterising plasmonics, and it is very effective at providing results quickly with a reasonable accuracy. The downfall of FDTD is when you need to refine the resolution - a 10x refinement in grid spacing will typically result in a 1,000x increase in memory use and a 10,000x increase in calculation time! This can be a big problem when modelling surface plasmons in metallic structures, where very fine resolution is routinely needed to obtain accurate results. This is where our innovative FETD (Finite-Element Time-Domain) simulator steps in, allowing you to obtain highly accurate results in a fraction of the time needed for FDTD. FDTD and FETD are two truly complementary methods, which can be used to model structures of similar size and complexity. With OmniSim, you can choose the most efficient calculation method for your structure, and you can also model your design with two independent engines - ideal to check the accuracy of your simulations. Note that you can also model plasmonic waveguides with FIMMWAVE and FIMMPROP. Having a number of different methods is very useful as it allows you to choose the most efficient method for your specific design, and also to run the calculation with multiple methods to check the accuracy of your calculations. In order to account for dispersive properties of metals and dielectric materials, our time-domain engines FETD and FDTD support a variety of material models include Drude, Drude-Lorentz, Lorentz and Debye; frequency domain tools such as FEFD only solve one wavelength at a time and do not require to fit the material properties.

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Commercial softwares

FDTD: as a full wave modeling method, Finite-Difference Time-Domain (FDTD) is the most effective algorithm to model these types of devices. Surface plasmons are increasing in popularity due to the interaction between light and matter, which is controlled by patterned structures. Surface Plasmon (FDTD) applications: Sub-wavelength optics, Data-storage, Molecular

sensors, Microscopy and Nano imaging, Photonic chip design, Bio-photonics, Surface Plasmon Layout

Benefits: Realistic dynamic near field display. Provides an in-depth understanding of the light wave interaction inside the device, Built-in noble metal materials library and other dispersive models, Ability to analyze field enhancement and surface plasmon resonance, Advanced modeling allows design goals to be achieved quickly and efficiently. This significantly reduces development costs, increased speed with non-uniform mesh and 64-bit multi-core processing,  A common concern for surface plasmon modeling is the material properties. OptiFDTD is the first software to employ the Lorentz-Drude model into the FDTD algorithm. OptiFDTD provides a built-in noble metal library along with other dispersive material models for the user to select. For general devices such as nano-particles, nano-wires, nano-holes and nano-lens, OptiFDTD provides a shape library to define complex geometry and periodic layouts. OptiFDTD also provides Visual Basic scripting and a periodic editor for more detailed designing. The built-in mode solver can solve the surface plasma waveguide. In addition, the observation detector can provide information of the near field distribution and transmission/reflection spectrum.

 COMSOL: organic light emitting diode (OLED) is an emerging technology for next-generation flat panel display and solid-state area lighting thanks to its many advantages such as light weight, low operating voltage, and flexibility, etc. A typical OLED has a multilayer structure that includes a glass or plastic substrate, an anode (ITO), a hole transport layer (HTL), an emitting layer (EML), an electron transport layer (ETL), and a cathode. Due to the mismatch in the refractive index between each layer, as well as absorption by metal cathode, only about 20% of the emitted light can leave the device, limiting the out-coupling efficiency of OLED (Figure 1). Among the many light out-coupling losses, coupling to surface plasmons amounts to about 40% of the total emitted light, and elimination/reduction of plasmon loss represents an ongoing challenge in improving the light extraction efficiency of OLED. Here we can use COMSOL Multiphysics® software and the RF Module to simulate and study the plasmon coupling in OLED and reduction of plasmon loss by using nano grating-structured electrode. Finite element simulation is one of the most powerful numerical methods available. COMSOL Multiphysics, a commercial finite element solver allows for simple connection of different physical differential equations. This is important when simulating devices where many types of physics interact. For instance in solar technology, electromagnetic wave simulation is combined with charge transport to form a very non-linear set of differential equations which are coupled.The phosphor molecular emitter is modeled by a classic point dipole driven by continuous electric current, and Ag is selected as the electrode material in the simulation. Studies using the Electromagnetic Wave, Frequency Domain interface were performed in both 2D and 3D geometries. All boundaries except at the Ag metal surface are surrounded by Perfect Matched Layer (PML) to absorb

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outgoing waves. Special care has been taken for PML set up at the metal/dielectric interface region for appropriate absorption of surface plasmon polariton waves (SPP). Percentage plasmon loss is estimated by the ratio of integrated power into plasmon mode (resistive loss in metal + Poynting vector of SPP) with respect to the total emitted power of the dipole.

Non-commercial (free down load) softwares

DDSCAT: a popular software package for conducting DDA calculations is called DDSCAT. DDSCAT allows for the computation of scattering properties with arbitrary shapes and geometries, and provide graphs of light extinction, absorption, and scattering properties. Using software like DDSCAT, scientists can determine properties of, as mentioned before, everything from space dust to red blood cells (RBCs). The simulation methods can be used to not only understand properties of these systems but design diagnostic platforms as well. A very exciting area of research involves Surface Plasmon Resonance (SPR), which deals with the changing properties of scattering based on the ordering of gold nanoparticles on some surface. This technology can be used to determine the presence and concentrations of certain proteins in solution or find detect very small quantities of other substances. DDSCAT can be used to design the surface and optimize it for maximal sensitivity. In astrochemistry, scientists can use telescope imaging data and use DDSCAT to find geometries of space targets that most closely match the data in order to determine the most probable geometry. Clearly, light scattering has been and will be a primary target of research relevant to a variety of fields. Many methods, tools, and approaches exist to conduct light scattering studies. Here, we present an implementation of a popular tool, DDSCAT, which may be used with another tool, DDACONVERT, to determine the light scattering properties of a variety of irregular particles and targets. Please see the instructions file to learn more about using this tool.

This tool is useful for calculating the plasmonic properties of nanostructures and composites containing dielectric heterostructures. Spectra (absorption and scattering) and electrical (near) fields can be readily calculated using classical electrodynamics. This tool is useful for people building bio-sensors based on refractive index sensing and plasmonic coupling, as well as people who wish to compute fields for SERS or other field enhanced spectroscopies. Through the use of Discrete Dipole Approximation (this tool uses DDSCAT version 7.3) users are able to study absorption, scattering, and electric fields around arrays of nanostructures, including nanobio systems, with varied properties. This tool provides a platform for allowing user-input for the DDSCAT (Discrete Dipole Scattering) software package through an interactive interface. There are a number of geometries supported within this tool including: rectangular prism, anisotropic ellipsoid, ellipsoid, concentric ellipsoids, isotropic cylinder, isotropic cylinder with hemispherical end-caps, cylinder with unixial anisotropic dielectric tensor. The way that an electromagnetic field interacts with small metallic nanoparticles can be very surprising and yield great insights into the particle itself. This phenomenon can be observed on the macro scale – the precise way a halo forms around a solar eclipse, the combination of colors in a rainbow that forms after a rain storm or emerges from a spray hose on a sunny day, or even the changing colors of the sky at sunset. Each of these physical consequences of light scattering can tell us a great deal about the underlying systems. Light scattering has been used to make gains in biological understanding, study entire galaxies and even understand light itself.

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MIE SIMULATOR GUI: this is a Mie Simulator GUI application. Mie Simulator GUI tool is capable of calculating: scattering coefficient, scattering cross section, reduced scattering coefficient, phase function, S1 and S2, average cosine of the phase function for a single or series of wavelengths.

L LAYERED SPHERE: this Fortran program by Dan Bruton calculates scattering quantities for spheres with l outer layers, i.e., a core with l spherical concentric shells.

MIE COATED: C program for a coated sphere by Jianqi Shen. The rar file includes the code, a doc and a paper decribing the algorithm.

MIEPLOT: windows program by Philip Laven based on the classic BHMIE algorithm including calculations using the Debye series. Philip Laven, Simulation of Rainbows, Coronas, and Glories by use of Mie Theory. The Mie algorithm is applicable to scattering of light from a single sphere, but many users of MiePlot need to simulate scattering from many spheres, generally with slightly differing sizes (i.e. disperse). MiePlot program has been designed with an "intuitive" interface - which should be simple to use.  Feedback from actual users will reveal how much "intuition" is needed in practice!  The latest version of MiePlot offers the following additional methods of modeling the scattering of light by a sphere: ray tracing (based on geometrical optics), ray tracing including the effects of interference between rays, airy theory, Rayleigh scattering, diffraction. MiePlot allows the user to select: the type of scattering sphere and surrounding medium (e.g. water in air, glass in a vacuum, air bubbles in water) - and associated variations of refractive index with wavelength of light. Built-in data for refractive index as a function of wavelength of various materials, including water, air, gold, silver and copper, but users can create their own files of refractive index data for any material. The option of using imaginary values of refractive index for water; the spectrum of the incident light, derived from various measurements of daylight or based on black body radiation; the ability to specify the lower and upper limits of wavelength for calculations involving multiple wavelengths; the option of averaging the results over a specified interval. MiePlot also offers polar plots of scattered intensity versus scattering angle.   MIELAB: a Software Tool to Perform Calculations on the Scattering of Electromagnetic Waves by Multilayered Spheres. It is a free computational package for simulating the scattering of electromagnetic radiation by multilayered spheres or an ensemble of particles with normal size distribution. It has been designed as a virtual laboratory, including a friendly graphical user interface (GUI), an optimization algorithm (to fit the simulations to experimental results) and scripting capabilities.

SCATLAB Software: a windows based software developed to perform electromagnetic scattering simulations mainly based on classical Mie theory solution.. ScatLab is a software developed to perform electromagnetic scattering simulations mainly based on classical Mie theory solution. ScatLab program could be successfully used in scientific research projects, industry and education. Fast and reliable program code makes a work with ScatLab smooth and productive. Professionally designed to meet windows type guidelines, ScatLab users can expect a

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familiar and intuitive user interface. ScatLab Features: scattered intensity polar diagrams for coated and uncoated spherical particles; scattered intensity versus theta graphs for coated and uncoated spherical particles; scattered intensity versus radius graphs for homogeneous spherical particles; extinction, scattering and backscattering cross section graphs; angle depolarization graphs; near field imaging for homogeneous spherical particles; Lorentz and Drude dielectric function implementation for refractive index calculation; support for T-matrix method computations and more.

MEEP -- FDTD package: is a free finite-difference time-domain (FDTD) simulation software package developed at MIT to model electromagnetic systems, along with our MPB eigenmode package. MEEP is a very good open source alternative with detailed documentation. Its features include: Free software under the GNU GPL. Simulation in 1d, 2d, 3d, and cylindrical coordinates. Distributed memory parallelism on any system supporting the MPI standard. Portable to any Unix-like system (GNU/Linux is fine). A time-domain electromagnetic simulation simply takes Maxwell's equations and evolves them over time within some finite computational region, essentially performing a kind of numerical experiment. This can be used to calculate a wide variety of useful quantities, but major applications include: Transmission and reflection spectra — by Fourier-transforming the response to a short pulse,

a single simulation can yield the scattering amplitudes over a wide spectrum of frequencies. Resonant modes and frequencies — by analyzing the response of the system to a short pulse,

one can extract the frequencies, decay rates, and field patterns of the harmonic modes of a system (including waveguide and cavity modes, and including losses).

Using these results, one can then compute many other things, such as the local density of states (from the trace of the Green's function). Meep's scriptable interface makes it possible to combine many sorts of computations (along with multi-parameter optimization etcetera) in sequence or in parallel.

Other Electromagnetic Simulation SoftwaresAngora -- Powerful FDTD package with text interface.emGine -- FDTD package with GUI.EM Explorer -- 3D FDTD package with GUI.openEMS -- 3D FDTD package with GUI.OpenFOAM -- Multiphysics FEM package with GUI.MaxFEM -- FEM package with GUI.FEMM -- FEM package with GUI.Elmer -- Multiphysics FEM package with GUI.Fenics Project -- Collection of software for automated, efficient solution of differential equations.freeFEM -- PDE solver with its own scripting language. Multiphysics, nonlinear, 2D, and 3D.NEC-2 -- Method of moments engine with text punchcard interface.MMANA-GAL -- Method of moments solver with GUI.EMCoS Antenna VLab -- Free student version of MoM software with GUI.EM3DS -- Excellent integral equation solver with GUI.GLMoM -- Method of moments EM field simulator with GUI.

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