I need to understand the details of the mathematics involved in the noisy lorentzian susceptibility. My top question is how to define a temperature since the inputs to the command is some amplitude, an omega, a gamma, and a sigma.

I haven't understood this yet but I'm going ahead with the next task.

## Tuesday, February 28, 2012

## Tuesday, February 21, 2012

### Task 3: Implement random currents in MEEP

To simulate the effect of temperature on charges, I need to define a random current source in MEEP. I've found the development version of MEEP has this feature. It is given as a noisy lorentzian susceptibility. The math is described in the reference below.

D. Chan, M. Soljačić, and J. Joannopoulos, “Direct calculation of thermal emission for three-dimensionally periodic photonic crystal slabs,”

*Physical Review E*, vol. 74, no. 3, pp. 1-9, Sep. 2006.## Monday, February 20, 2012

### Task 2: Surface Plasmon Dispersion

Dispersion curves are useful to understand transport. I set up a MEEP simulation of two surfaces of Ag separated by a 100e-9m gap. You can see 3 modes: surface plasmons, gap propagation, and bulk plasmons. ~0.7 is omega_p the plasma frequency.

(set! geometry-lattice (make lattice (size 20 no-size no-size))) (set! pml-layers (list (make pml (thickness 1)))) (set-param! resolution 30) (define myAg (make dielectric (epsilon 1) (polarizations (make polarizability (omega 1e-20) (gamma 0.0038715) (sigma 4.4625e+39)) ; (make polarizability ; (omega 0.065815) (gamma 0.31343) (sigma 7.9247)) ; (make polarizability ; (omega 0.36142) (gamma 0.036456) (sigma 0.50133)) ; (make polarizability ; (omega 0.66017) (gamma 0.0052426) (sigma 0.013329)) ; (make polarizability ; (omega 0.73259) (gamma 0.07388) (sigma 0.82655)) ; (make polarizability ; (omega 1.6365) (gamma 0.19511) (sigma 1.1133)) ))) (set! geometry (list (make block (center -3 0 0 0.0) (size 5 infinity infinity) (material myAg )) (make block (center 3 0 0 0.0) (size 5 infinity infinity) (material myAg )) )) (set! sources (list (make source (src (make gaussian-src (frequency 2.5) (fwidth 5))) (component Ex) (center 0 0 0)) (make source (src (make gaussian-src (frequency 2.5) (fwidth 5))) (component Ex) (center -.5 0 0)) (make source (src (make gaussian-src (frequency 2.5) (fwidth 5))) (component Ex) (center .5 0 0)) )) (define-param kmin 0.0) (define-param kmax 4.0) (define-param k-interp 50) (define kpts (interpolate k-interp (list (vector3 0 kmin 0) (vector3 0 kmax 0)))) (define all-freqs (run-k-points 200 kpts)) ; a list of lists of frequenciesAnd here's a python snippet that gives a list of k-vectors their frequencies by giving it the MEEP output as a file object

def getfreqs(meepoutfileobj): fd=[] for aline in meepoutfileobj: if 'freqs:' in aline: ld=aline.split(',') kpt=ld[2:5];freqs=ld[5:] pts=[( [float(an) for an in kpt] ,float(afreq)) for afreq in freqs] fd.extend(pts) if fd==[]:return None return fd

## Tuesday, February 7, 2012

### Task 1: Understanding MEEP's dispersive media

http://juluribk.com/2011/04/27/plasmonic-materials-in-meep/

This page and the linked pdf explain it rather well. I've implemented it in python where the inputs are lorentz-drude model params and the output is MEEPs (lorentz) model.

This page and the linked pdf explain it rather well. I've implemented it in python where the inputs are lorentz-drude model params and the output is MEEPs (lorentz) model.

#Author: Majid al-Dosari #code that takes in lorentz-drude model parameters and converts them to code #usable by meep. just use eVLD2meepcode #example: eVLD2meepcode('mysilver',100e-9,9,[[.845,.048,0],[.065,3.886,.816]]) #output: #(define mysilver (make dielectric (epsilon 1) #(polarizations #(make polarizability #( omega 8.06554724676e-22 ) ( gamma 0.00387146267844 ) ( sigma 6.8445e+41 )) #( omega 0.0658148655336 ) ( gamma 0.313427166009 ) ( sigma 7.9071150519 )) #))) #it's an implementation of #http://juluribk.com/2011/04/27/plasmonic-materials-in-meep/ by Bala Krishna Juluri #normalization length a #w omega #p plasma #G Gamma def sip(stuff):#stuff in parens return '( ' +str(stuff)+ ' )' def wordandvalue(word,value): return sip(word+' '+str(value)) def meepfactor(a): return 2*3.14159265359*299792458/a #2pi*c/a def eV2w(eV):return eV*(2*3.14159265359)/4.135666e-15 def eV2meep(a,eV):return eV2w(eV)/meepfactor(a) def sigmaa(f,wp,w): """f is oscillator strength, wp is plamsa freq""" return (f*wp**2)/w**2 def eVLD2meepL(a,wp,fGw0_list): oGs_list=[] smallno=1e-20; for f,G,w0 in fGw0_list: if w0==0:w0=smallno #hack oGs_list.append([eV2meep(a,w0) ,eV2meep(a,G) ,sigmaa(f,eV2meep(a,wp),eV2meep(a,w0))]) return oGs_list def eVLD2meepcode(name,a,wp,fGw0_list): """ input: name: for code a: meep normalization const wp: plasma freq in eV fGw0_list: nested list of f oscillator strengths Gamma relaxation in eV omega0 in eV,w=0 is handled by converting it to a very small no. """ return writelorentz(name,oGs_list=eVLD2meepL(a,wp,fGw0_list)) def writelorentz(name,oGs_list=None,epsilon=1):#meep is in lorentz txt='' txt+='(define '+str(name)+' (make dielectric (epsilon '+str(epsilon)+') \n' if oGs_list==None or len(oGs_list)==0: txt+='))' return txt txt+='(polarizations \n' for omega,Gamma,sigma in oGs_list: txt+='(make polarizability \n' txt+=wordandvalue('omega',omega)+' ' txt+=wordandvalue('gamma',Gamma)+' ' txt+=wordandvalue('sigma',sigma)+')\n' txt+=')))' return txt #so 1. normalize then 2. cast into meep

### Thermal Properties of Yttrium Aluminum Garnett from Molecular Dynamics Simulations

This is a write up of all the work that I did for my Master's degree. There isn't much of a scientific contribution but I learned alot. The main challenge was in the execution of the work. My previous posts touch on that.

THERMAL PROPERTIES OF YTTRIUM ALUMINUM GARNETT FROM MOLECULAR DYNAMICS SIMULATIONS

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