Task 4: Understanding the Noisy Lorentzian in MEEP

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.

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.

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 frequencies  

And 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

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.

#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