GLMTSolver

========

This is a simple code that implements a generalized Lorenz-Mie theory (GLMT) solver for electromagnetic scattering from spherically-symmetric bodies.

The geometries that may be handled consist of arbitrarily many spherical layers, of arbitrary inner and outer radii, each with arbitrary frequency-dependent permittivity.

The allowed incident fields are

plane waves
spherical waves

The outputs that may be computed include

scattered and total E and H fields at arbitrary points in space
scattered and absorbed power, force and torque as obtained by integrating the Poynting vector and Maxwell stress tensor over a bounding sphere surrounding the particle

Theory

The theoretical approach and notation used by this code is described in this memo.

Specifying geometries

Geometries are described by simple text files conventionally given file extension .GLMT. Blank lines and comments (lines starting with #) are skipped. Each line specifies a single spherical layer, with the syntax

 RMAX   MATERIAL

where

RMAX is the outer radius of the layer in microns
MATERIAL is a scuff-em material designation.

Here's a .GLMT file describing a sphere of radius 1 μm with dielectric constant 10:

1.0	CONST_EPS_10

And here's a .GLMT file describing the doubly-resonant multilayered spherical particle considered by Hsu et al, "Theoretical criteria for scattering dark states in nanostructured particles,” Nano Letters 14 2783–2788, May 2014 (http://dx.doi.org/10.1021/nl500340n).

0.100 	SiO2
0.051 	Silver
0.031 	SiO2
0.020	Silver

If one of the layered material regions in your geometry is actually a void (no material), give it material property VACUUM. For example, here's a geometry describing the layered particle above, but with the silver removed to yield just two concentric spherical shells of SiO2.

0.100 	SiO2
0.051 	VACUUM
0.031 	SiO2
0.020	VACUUM

Structure of the code

The repository includes a simple Makefile. You will need to have SCUFF-EM installed before you can build this code.

GLMT-scatter.cc builds to yield a standalone executable command-line code called GLMT-scatter that implements a subset of the functionality of [scuff-scatter][scuffScatter] (see examples below).

The main solver is implemented in the code file GLMTSolver.cc. The routine CreateGLMTSolver() parses a .GLMT file and constructs a data structure named GLMTSolver containing all information the scattering geometry. This structure contains tables of spherical-wave coefficients which are initialized for a given frequency and a given incident field by the routine Solve(). Once Solve() has been called, you can call post-processing routines:

GetFields() computes the scattered and total E and H fields at arbitrary points in space
GetDSIPFT() computes the power, force, and torque on the body, using the Displaced Surface Integral computational strategy described in this paper.

Examples

Power scattered by doubly-resonant nanoparticle

This example reproduces the "scattering dark state" example involving a nanoparticle consisting of alternating spherical layers of SiO2 and silver, as described in Hsu et al, "Theoretical criteria for scattering dark states in nanostructured particles,” Nano Letters 14 2783–2788, May 2014 (http://dx.doi.org/10.1021/nl500340n).

#!/bin/bash

for LMAX in 1 2 
do
  ARGS=""
  ARGS="${ARGS} --GLMTFile DoublyResonantParticle.GLMT"
  ARGS="${ARGS} --OmegaFile Lambda100800nm.OmegaFile"
  ARGS="${ARGS} --LMax ${LMAX}"
  ARGS="${ARGS} --PWDirection 0 0 1"
  ARGS="${ARGS} --PWPolarization 1 0 0"
  ARGS="${ARGS} --PFTFile DoublyResonantParticle.L${LMAX}.GLMTPFT"
  ARGS="${ARGS} --DSIRadius 0.2"
  GLMT-scatter ${ARGS}
done

(The --DSIRadius option controls the radius of the bounding sphere over which the Poynting vector and Maxwell stress tensor are integrated to compute powers and forces).

This produces files DoublyResonantParticle.L1.GLMTPFT and DoublyResonantParticle.L2.GLMTPFT. To plot scattered power vs. wavelength in GNUPLOT, go like this:

gnuplot> 
plot 'DoublyResonantParticle.L1.GLMTPFT' u (2*pi/$1):3 t 'LMax=1' w lp pt 7 ps 1, 'DoublyResonantParticle.L2.GLMTPFT'  u (2*pi/$1):3 t 'LMax=2' w lp pt 6 ps 2

E-field vs. radial distance for doubly-resonant nanoparticle

Here's how to obtain a plot of the spatial variation of the E-field magnitude. First, put the x,y,z coordinates of your desired evaluation points into a text file called EvalPoints:

0.00000000 0.00000000 0.00000000
0.00050000 0.00050000 0.00050000
...
0.09950000 0.09950000 0.09950000
0.10000000 0.10000000 0.10000000

Then pass this file as the --EPFile option to GLMT-scatter:

ARGS=""
ARGS="${ARGS} --GLMTFile DoublyResonantParticle.GLMT"
ARGS="${ARGS} --Omega 15"
ARGS="${ARGS} --EPFile EvalPoints"
ARGS="${ARGS} --PWDirection 0 0 1"
ARGS="${ARGS} --PWPolarization 1 0 0"
GLMT-scatter ${ARGS}

This produces an output file called DoublyResonantParticle.EvalPoints.GLMTFields. To plot E-field vs. radius, go like this:

gnuplot> D3(x,y,z)=sqrt($1*$1+$2*$2+$3*$3)
gnuplot> D6(x1,x2,x3,x4,x5,x6)=sqrt(x1*x1+x2*x2+x3*x3+x4*x4+x5*x5+x6*x6)
gnuplot> FILE='DoublyResonantParticle.GLMT'
gnuplot> plot FILE u (D3($1,$2,$3)):(D6($7,$8,$9,$10,$11,$12))

HomerReid/GLMTSolver