The code that is used to model the LSP resonances of quasistatic concentric-shell Drude-metal nanoparticles.
A short description of each file:
Directory -- modelCode
fitFunc_s.wls:
A Wolfram Language Script file that provides functions that solve Poisson's equation symbolically for a set of concentric spherical shells and use the solutions to calculate various observales. In particular, these functions 1) use the solutions to produce the dielectric-function-dependent polarizability of the particle, 2) plug Drude-model dielectric functions into the polarizability to reveal that the polarizability can be rewritten as the sum of polarizabilities of a set of oscillators, 3) characterize the relevant parameters of these oscillators, and 4) solve for the corresponding absorption cross-sections of each oscillator. The "_s" suffix denotes that this code is designed to be uploaded to and used on a server or other remote computer. The solution of Poisson's equation becomes prohibitively slow after N = 7 (alpha7lm takes tens of hours to compute on a supercomputer) and so the use of fitFuncConst_s.wls is recommended for calculations of >7-shell particles.
fitFuncConst_s.wls:
Similar to fitFunc_s.wls, but solves the Poisson equation numerically. Much faster than fitFunc_s.wls, but requires that Poisson's equation be solved anew each time a change in dielectric material is required. Integration of this code with a cure-fitting script has not been completed succesfully.
Directory -- variables
radInhomSph.py:
A python script that generates a shape file for the Discrete Dipole Approximation (see: BT Draine. The discrete-dipole approximation and its application to interstellar graphite grains. Astrophys. J. 333, 848-872 (1988).) electromagnetism simulation software. The shape is that of a sphere with a radially varying dielectric function. This dielectric function can have any form.
dielGen.py:
A python script that generates a directory with a set of dielectric .tab files organized in numerical order corresponding to the material indices given in radInhomSph.py. The alphanumeric ordering of the .tab files in the directory will determine which index in a given shape file each dielectric file is associated with. The dielectric files and the naming conventions are otherwise unrestricted.
shapePlotter.py:
A sample python script for plotting DDA shape files. Under construction.
d2g.py:
A sample .py file for plotting the data output from DDA onto a plot (d2g == "data to graph"). Should be heavily modified by user as needed.
Directory -- variables
alphaNlm.wl:
A Wolfram Language object that holds a symbolic polarization variable (alpha) to be uploaded by a Wolfram Language script and used to calculate an absorption cross-section. The numbers N, l, and m stand for the number of shells in the model, the l index of the solution, and the m index of the solution, respectively. When l = 1 and m = 0, the variable describes the polarizability of a set of N z-oriented dipole modes.
Directory -- notes
multiShellNotes.tex:
A LaTeX file that contains my notes on how to navigate from first-principles electrostatics to a description of the oscillator parameters of each mode of a multi-shell Drude-model nanosphere.