# Publications

# van der Pauw correction factor

The van der Pauw Method is a technique commonly used to measure the Resistivity and the Hall Coefficient of a sample. A correction factor goes into calculating the resistivity as described in van der Pauw paper. A iterative method is generally used to calculate the correction factor and this correction factor is plotted in Figure 5 of van der Pauw paper I reproduced the same figure below using fsolve function in octave. This figure was produced by the octave code shown below. The raw data is here. %This octave/matlab code calculates the correction factor,f as a function of Rmnop/Rnopm. This Read More …

# All entries of array except certain indices in octave/matlab

In Octave or Matlab, some times one needs to eliminate certain elements in an array. For example, if a=[10,20,30,40,50,60]; and suppose I want to create a matrix “b” such that it has all the elements of “a” except 20 and 40. This can be achieved by: b=a(1:end~=2&1:end~=4); The result is: b = 10 30 50 60

# Scattering / extinction / absorption cross-sections of silver nanowires (infinite cylinders) using meep

Particles scatter and absorb electromagnetic radiation. One often needs to compare the amount of scattering/absorption/extinction for particles of different shapes, composition, sizes and incident light properties (polarization, frequency and angle). In this regard, the concept of cross-sections comes into picture. There are three types of cross-sections, 1) scattering 2) absorption and 3) extinction. All of them have units of area, $m^2$, and provide a measure to quantify scattering/absorption process. Here using MEEP I calculate the crossections of silver nanowires and compare them with numerical solution (code from Bohren and Hauffman book). To achieve this, I wrote a meep code Read More …

# Gnuplot rgb color schemes in matlab as colormaps

I like the color schemes that are used as palettes in gnuplot’s pm3d plots. I wanted similar color schemes that can be used as colormaps in matlab. After reading this article, I found that one can easily incorporate the traditional rgbpallette schemes in matlab To start, there are several schemes in gnuplot that can be used in pm3d plots and they are: 7,5,15 … traditional pm3d (black-blue-red-yellow) 3,11,6 … green-red-violet 23,28,3 … ocean (green-blue-white); try also all other permutations 21,22,23 … hot (black-red-yellow-white) 30,31,32 … color printable on gray (black-blue-violet-yellow-white) 33,13,10 … rainbow (blue-green-yellow-red) 34,35,36 … AFM hot (black-red-yellow-white) The Read More …

# Arbitrary 2d shapes in MEEP

In MEEP (1.1.1), dielectric structures are often created by constructive geometry (adding and subtracting primitive shapes). The primitive shapes that are allowed are blocks, cylinders, ellipsoids and cones. To create a complex shape, one has to decompose the geometry into these primitive shapes. Over the weekend, I was wondering if it was possible to somehow create any complex shape in 2d without figuring out the exact positions and operations with the available primitive shapes. Here I report how I solve this problem. The first thing I figured out was to create a 2d triangle with known vertices using a certain Read More …

# Electric Field in Metal Nanoparticle Dimers

Metal nanoparticles exhibit localized surface plasmon resonance (LSPR). One can think of LSPR as resonance of electron sea oscillations driven by incident electric field. This is similar to the way a spring-mass system attains resonance under external periodic driving force. The result of this plasmon resonance is enhanced dipole moment or charge separation, which leads to 1) large extinction (extinction is defined as sum of scattering and absorption) and 2) large electric field near the particle. Both of which are shape, size and surrounding dependent. Researchers have taken advantage of this large electric field localization to enhance Raman signals from molecules Read More …

# Charge density in metal nanoparticles at plasmon resonance

It is important to know the magnitude and distribution of electric field near the metallic nanoparticles at plasmon resonance. One can look at the electric field and say whether the plasmon mode is dipolar or higher order mode such as qudrapolar mode. At many times one is also interested to know the surface charge density which makes easier to identify the plasmon mode. One can get the surface charge density by talking the divergence of electric field (near field) either calculated by DDA method or FDTD method [Reference paper]. Below I have calculated the electric field near nanoparticle at plasmon Read More …

# Spoof Plasmons / Designer Surface Plasmons

Aim of this article/post: To 1) introduce the concept of Designer surface plasmons or Spoof plasmons and 2) Dispersion relations and Visualization of the fields using MEEP code. (Some of the text/simulations are taken from my paper in the area of DSPs.) Surface Plasmons are electromagnetic waves that travel at the interface of metals such as Ag/Au (follow Lorentz-Drude dielectric model) and a dielectric. Surface plasmons are not expected in perfect electric conductors (PEC’s) as the electric field inside the metal is zero. However, highly localized surface-bound states appear when the PEC is periodically modulated with arrays of sub-wavelength square Read More …

# DDSCAT and electric field at plasmon resonance

Discrete Dipole Approximation (DDA) is an important tool in plasmonics research. Using DDA, one can calculate scattering properties of nanoparticles at various wavelengths, polarizations and surrounding medium. The specialty of DDA is that one can calculate scattering properties of irregular shape particles (particles other than spheroids). DDA is based on representing a particle into a set of interacting dipoles and solving their dipole moments such that they are all self-conistent with each other and are linked by far-field and near-field interactions. Once these dipole moments are calculated, they can be used to calculate scattering properties such as scattering efficiency, absorption Read More …

# Nmie: Extinction, Scattering and Absorption efficiencies of multilayer nanoparticles

Since 2009, I have been a regular user of Nanohub.org. www.Nanohub.org is a website that provides a platform for online simulation, research and teaching resources. Of interest is the ability to perform simulation online without installing software on your local computer. I envision that this type of cloud computing model will be the future of scientific computing. Developers can use their Rappture toolkit (nice video to learn Rappture toolkit) to write wrappers for codes that are written in Fortran, C or Matlab and enable an easy to use GUI for the executables. There are few tools for Plasmonics on nanohub Read More …