Coupled Dipole Approximation in Python

Coupled dipole approximation (CDA) method is a numerical method to calculate the optical properties (scattering and absorption) of interacting dipoles. This method is used in discrete dipole approximation method (like in DDSCAT software), where a big particle (also known as target) is broken into lot of interacting dipoles arranged in cubic lattice. CDA can also be used to calculate the optical properties (scattering and absorption) of random particle distributions (like in L. Zhao et al. J. Phys. Chem. B,  107,  30, 7343,2003 ) and assuming each particle to be small enough that it behaves like a dipole. I have implement Read More …

Fitting Complex Metal Dielectric Functions with Differential Evolution Method

The real and imaginary part of dielectric permittivity of the metals is important to simulate the optical properties of metal films and nanoparticles. Permittivity data is obtained experimentally by ellipsometry and is fitted with analytical models. The most common model for fitting experimental data is with Drude-Lorentz model shown below. $$\epsilon(\omega)=1-\frac{f_1\omega_p^2}{(\omega^2+i\Gamma_1\omega)}+\sum_{j=2}^{n}\frac{f_j\omega_p^2}{(\omega_{o,j}^2-\omega^2-i\Gamma_j\omega)}$$ The first term is the Drude part. It represents the response of electron in the Fermi sea/conduction band when it sees external oscillating electric field (these transitions are called as intraband transitions). The Drude term has the plasma frequency ($\omega_p$, oscillator strengh ($f_1$) and damping term ($\Gamma_1$). The rest Read More …

Plasmonic Materials in MEEP > 1.2

Here is how I was implementing plasmonic materials in meep1.1 scheme code. Unlike Meep 1. 1, Meep >= 1. 2 changed the way materials are defined. Here I will describe how to change the material definition code from meep1.1 to meep 1.2 . Please note that one can still use the material definition written from Meep <1.2 for Meep >=1.2 but not vice versa. Installation of Meep 1.2 on ubuntu You can follow instructions given in my previous post to compile Meep 1.2 from the source code, but the procedure is outdated and one can use the recently pre-compiled meep Read More …

Installing Meep 1.2 on ubuntu

Pre-compiled Meep binaries for meep1.1 exist for Ubuntu distribution. This makes it very easy to install meep on ubuntu using “apt-get install” command or from the ubuntu software center. However recently, Meep developers have release meep1.2 which has more functions compared to meep1.1. I have recently installed meep1.2 from source on ubuntu 12.04 using the instructions shown at http://ab-initio.mit.edu/wiki/index.php/Meep_Installation. I have root access to my computer, so I installed all the libraries/bin files in their default location (i.e, libraries go in /usr/local/lib, programs in /usr/local/bin, etc) These are the steps I followed: 1) To avoid any complications, I uninstalled meep1.1 Read More …

Electric field at localized plasmon resonance using MEEP

This article is about simulating localized plasmon resonances in metal nanospheres using MEEP package. Generally, I am interested in solving three problems in LSPR systems: Calculate the extinction, scattering, absorption spectra of metal nanoparticle The procedure for doing this is very similar to the method I mentioned here. Calculating the electric field enhancement spatially as function of wavelength This involves taking electric field distributions with a particle in time domain and taking FFT of them. Also to be noted is that the electric fields near the particle should be normalized with electric fields with no nanoparticle. This has to be Read More …

Surface plasmon dispersion relation for thin metal films

A thin metal film in dielectric (also known as dielectric-metal-dielectric configuration) can support surface plasmons that are different in nature to the ones observed in thick metal-dielectric interfaces. Unlike, a single mode that is observed in thick metal film, thin metal films exhibit two types of modes for the same wavevector due to excitation and interaction of surface plasmons on both sides of the film. One mode (L+) is at higher energy and other (L-) is at a lower energy. The high energy has anti-symmetric field distribution whereas the low energy one has symmetric field distribution. The dispersion relations of Read More …

Plasmonic materials in MEEP

  The aim of this post is to share my experience in incorporating dielectric function of metals such as gold and silver into MEEP (a free finite difference time domain package) code. The incorporation is not an easy task and can be daunting for the first time user. Metals such as gold and silver have both Drude and Lorentz components for the dielectric function. There are many forms of Lorentz-Drude expressions in literature with slight notation differences. I prefer the Lorentz-Drude expression mentioned in Rakic et al., Optical properties of metallic films for vertical-cavity optoelectronic devices, Applied Optics (1998) and Read More …

WINSPALL software for surface plasmon resonance experiments

One needs to fit the reflectivity curves obtained in surface plasmon resonance experiments with theoretical models. A free software (for non commercial use) called Winspall exactly does that. According to the developers, WINSPALL is a PC based software which computes the reflectivity of optical multilayer systems. It is based on the Fresnel equations and the matrix formalism. It can be used to analyze surface plasmon experiments. WINSPALL was developed in the Knoll group. WINSPALL is available for use without charge. It may not be reused for commercial purposes. It is available for download here. you can download the software from Read More …

Dynamic Exciton-Plasmon Coupling

Our paper titled “Dynamically Tuning Plasmon-Exciton Coupling in Arrays of Nanodisk-J-aggregate Complexes” has been accepted as front cover image of Advanced Materials . In this work, we demonstrated the dynamic tuning of plasmon-exciton resonant coupling in arrays of nanodisk–J-aggregate complexes. The angle-resolved spectra of an array of bare Au nanodisks exhibited continuous shifting of localized surface plasmon resonances and this characteristic enabled the production of real-time, controllable spectral overlaps between molecular resonance and plasmonic resonance. In this work we explored resonant interaction strength as a function of spectral overlap. In experiments where we changed the incident angle of a probe Read More …

Radiation from an oscillating dipole

The electric field from an oscillating dipole is given by:, where is the position vector, is the frequency of dipole oscillation, is the dipole moment. The two terms in the electric field consists of 1) near field (area near to the dipole) and 2) far field (area far from the dipole) contributions. Far field falls of as and the near field falls of by . A beautiful simulation showing the electric field radiation from a dipole is shown below. This simulation is part of Sophocles J. Orfanidis book on electromagnetic waves and antennas.  For more details on 1) how the Read More …