# LDOS at the hotspot of a bowtie antenna

For our next trick, we'll investigate the local density of states (LDOS) and incident-field enhancement at the hotspot of bowtie antenna.

The input files for this example are in the PolarizationSensitiveAntenna subdirectory of the SCUFFTutorial archive. To avoid typing folder prefixes at the command line, it's convenient to set up scuff-em search paths as follows:

% export SCUFF_MESH_PATH=${HOME}/SCUFFTutorial/PolarizationSensitiveAntenna/mshFiles % export SCUFF_GEO_PATH=${HOME}/SCUFFTutorial/PolarizationSensitiveAntenna/scuffgeoFiles

## GMSH geometries and mesh files

The GMSH geometry file Triangle.geo in the .geoFiles folder is similar to the one we used in the previous exercise, but with different default dimensions:

Triangle_Fine.msh

## SCUFF-EM geometry files

The scuffgeoFiles directory contains a series files named Bowtie35_Medium.scuffgeo ... Bowtie95_Medium.scuffgeo describing 4-point bowtie antennas with various tip-tip separation distances:

Bowtie35_Fine.scuffgeo

OBJECT NorthTriangle
MESHFILE Triangle_Medium.msh
DISPLACED 0.00 0.035 0.000
ENDOBJECT

OBJECT SouthTriangle
MESHFILE Triangle_Medium.msh
ROTATED 180 ABOUT 0 0 1
DISPLACED 0.00 -0.035 0.000
ENDOBJECT

OBJECT WestTriangle
MESHFILE Triangle_Medium.msh
ROTATED 90 ABOUT 0 0 1
DISPLACED -0.035 0.000 0.000
ENDOBJECT

OBJECT EastTriangle
MESHFILE Triangle_Medium.msh
ROTATED 270 ABOUT 0 0 1
DISPLACED 0.035 0.000 0.000
ENDOBJECT

Bowtie95_Fine.scuffgeo

OBJECT NorthTriangle
MESHFILE Triangle_Medium.msh
DISPLACED 0.00 0.095 0.000
ENDOBJECT

OBJECT SouthTriangle
MESHFILE Triangle_Medium.msh
ROTATED 180 ABOUT 0 0 1
DISPLACED 0.00 -0.095 0.000
ENDOBJECT

OBJECT WestTriangle
MESHFILE Triangle_Medium.msh
ROTATED 90 ABOUT 0 0 1
DISPLACED -0.095 0.000 0.000
ENDOBJECT

OBJECT EastTriangle
MESHFILE Triangle_Medium.msh
ROTATED 270 ABOUT 0 0 1
DISPLACED 0.095 0.000 0.000
ENDOBJECT

To visualize these files, we go like this:

 % scuff-analyze --WriteGMSHFiles Bowtie35_Fine.scuffgeo
% scuff-analyze --WriteGMSHFiles Bowtie65_Fine.scuffgeo
% scuff-analyze --WriteGMSHFiles Bowtie95_Fine.scuffgeo
% gmsh Bowtie35_Fine.scuffgeo Bowtie65_Fine.scuffgeo Bowtie95_Fine.scuffgeo

Bowtie35_Fine.scuffgeo

Bowtie65_Fine.scuffgeo

Bowtie95_Fine.scuffgeo

## Calculating LDOS at the hotspot

As explained in this memo, the scattering dyadic Green's functions (DGFs) and local density of states (LDOS) at a given frequency $\omega$ and point x can be computed by performing 6 separate scattering calculations, each involving incident fields radiated by a point source at x. Thus, one way to do LDOS calculations in scuff-em would be to do 6 separate scuff-scatter calculations at each frequency, using the --psDirection and --psStrength options to define point-source incident fields.

However, as explained in the memo above, this calculation can be considerably streamlined by exploiting certain computational redundancies, and this accelerated algorithm for LDOS calculations is implemented by the scuff-ldos application module in the scuff-em suite.

Here's a simple script that uses scuff-ldos to compute LDOS vs. frequency and tip-tip separation at the hotspot (center point) of the bowtie antennas shown above.

RunScript.LDOS

#!/bin/bash

BASEDIR=${HOME}/SCUFFTutorial/PolarizationSensitiveAntenna export SCUFF_MESH_PATH=${BASEDIR}/mshFiles
export SCUFF_GEO_PATH=${BASEDIR}/scuffgeoFiles for RES in Medium Fine do for N in 35 65 95 do ARGS="" ARGS="${ARGS} --geometry Bowtie${N}_${RES}.scuffgeo"
ARGS="${ARGS} --LambdaFile${BASEDIR}/LambdaFile"
ARGS="${ARGS} --EPFile${BASEDIR}/EPFile.HotSpot"
scuff-ldos \${ARGS}
done
done

Here LambdaFile is a list of wavelengths at which to run the calculation and EPFile.HotSpot specifies the coordinates of just a single evaluation point, the hotspot:

EPFile.HotSpot

0.0 0.0 0.0

This yields output files Bowtie35_Fine.LDOS, Bowtie65_Fine.LDOS, and Bowtie95_Fine.LDOS. As noted in the header portion of those files, the frequency is reported on column 4 and the electric LDOS on column 6, so we can plot LDOS vs. frequency in gnuplot like this:

Here's the gnuplot script I used to produce this plot: LDOSPlotter.gp