DataFile1 = "SiR.csv"
DataFile2 = "GeR.csv"
DataFile3 = "InGaAsStandardR.csv"
set datafile separator ","
set xlabel "Wavelength (nm)" font ",12"
set ylabel "Responsitivity (A/W)" font ",12"
set ytics
set xrange [400:1800]
set yrange [0:1.7]
set tics font ",12"
plot DataFile1 using 1:2 with lines lw 3 axis x1y1 title "Si",DataFile2 using 1:2 with lines lw 3 axis x1y1 title "Ge",DataFile3 using 1:2 with lines lw 3 axis x1y1 title "InGaAs"

PI = 3.1415926535
y0 = 0 # is the baseline offset.
xc = 1300 # is the center of the peak.
w = 500 # equals the width of the peak at half height.
A = 1000 # is the area under the peak. 
f(x)=y0 + (2*A/PI)*(w/(4*(x-xc)**2 + w**2))
set xrange [400:1800]
plot f(x)

PI = 3.1415926535
y01 = 0 # is the baseline offset.
xc1 = 1000 # is the center of the peak.
w1 = 500 # equals the width of the peak at half height.
A1 = 100  # is the area under the peak. 
xc2 = 1200 # is the center of the peak.
w2 = 500 # equals the width of the peak at half height.
A2 = 100  # is the area under the peak.
xc3 = 1400 # is the center of the peak.
w3 = 500 # equals the width of the peak at half height.
A3 = 800  # is the area under the peak.
xc4 = 1500 # is the center of the peak.
w4 = 500 # equals the width of the peak at half height.
A4 = 800  # is the area under the peak.
xc5 = 1600 # is the center of the peak.
w5 = 500 # equals the width of the peak at half height.
A5 = 100  # is the area under the peak.
f(x)=y01 + (2*A1/PI)*(w1/(4*(x-xc1)**2 + w1**2)) + (2*A2/PI)*(w2/(4*(x-xc2)**2 + w2**2)) + (2*A3/PI)*(w3/(4*(x-xc3)**2 + w3**2))+ (2*A4/PI)*(w4/(4*(x-xc4)**2 + w4**2))+ (2*A5/PI)*(w5/(4*(x-xc5)**2 + w5**2))
set xrange [400:1800]
plot f(x)

DataFile3 = "InGaAsStandardR.cvs"
set datafile separator ","
set xrange [400:1800]
fit f(x) DataFile3 using 1:2 via xc1, w1, A1, xc2, w2, A2, xc3, w3, A3, xc4, w4, A4, xc5, w5, A5

plot f(x), DataFile3 using 1:2 with lines lw 3 axis x1y1 title "InGaAs"

SiR
alpha = 0.5
mu = 700.0
sig = 300.0
n = 4.0
xcs = 500.0
k = 0.007
g(x)= alpha * exp(-((x - mu)**2 / (2 * sig**2))**n)/(1+exp(-k*(x-xcs)))
s(x)=1/(1+exp(-k*(x-xcs)))
DataFile1 = "SiR.csv"
set datafile separator ","
set xrange [400:1200]
fit g(x) DataFile1 using 1:2 via alpha, mu, sig, n, xcs, k
set xtics font ",24"
set ytics font ",24"
set xlabel "Wavelength (nm)" font ",24"
set ylabel "Responsivity (A/W)" font ",24"
set key font ",24"
set term svg
set output "Si_responsivityFit.svg"
plot g(x) lw 3, DataFile1 using 1:2 with lines lw 2 axis x1y1 title "Si",s(x)
Final set of parameters            Asymptotic Standard Error
=======================            ==========================
alpha           = 4.06484          +/- 14.03        (345.2%)
mu              = 671.926          +/- 2.272        (0.3381%)
sig             = 209.564          +/- 3.957        (1.888%)
n               = 1.76504          +/- 0.04197      (2.378%)
xcs             = 1835.83          +/- 2602         (141.7%)
k               = 0.00183068       +/- 0.0007681    (41.96%)

Ge
alpha = 1.0
mu = 1200.0
sig = 300.0
n = 4.0
xcs = 300.0
k = 0.007
g(x)= alpha * exp(-((x - mu)**2 / (2 * sig**2))**n)/(1+exp(-k*(x-xcs)))
s(x)=1/(1+exp(-k*(x-xcs)))
DataFile2 = "GeR.csv"
set datafile separator ","
set xrange [800:1800]
set yrange [0:1.1]
fit g(x) DataFile2 using 1:2 via alpha, mu, sig, n, xcs, k
set xtics font ",24"
set ytics font ",24"
set xlabel "Wavelength (nm)" font ",24"
set ylabel "Responsivity (A/W)" font ",24"
set key font ",24"
set term svg
set output "Ge_responsivityFit.svg"
plot g(x) lw 3, DataFile2 using 1:2 with lines lw 2 axis x1y1 title "Ge"
Final set of parameters            Asymptotic Standard Error
=======================            ==========================
alpha           = 3.45269          +/- 16.64        (481.8%)
mu              = 1168.53          +/- 32.04        (2.742%)
sig             = 376.363          +/- 41.36        (10.99%)
n               = 2.01975          +/- 0.3903       (19.33%)
xcs             = 2106.83          +/- 4654         (220.9%)
k               = 0.00162619       +/- 0.001793     (110.3%)


InGaAsStandardR
alpha = 1.0
mu = 1300.0
sig = 300.0
n = 4.0
xcs = 1200.0
k = 0.007
g(x)= alpha * exp(-((x - mu)**2 / (2 * sig**2))**n)/(1+exp(-k*(x-xcs)))
s(x)=1/(1+exp(-k*(x-xcs)))
DataFile3 = "InGaAsStandardR.cvs"
set datafile separator ","
set xrange [800:1800]
set yrange [0:1.4]
fit g(x) DataFile3 using 1:2 via alpha, mu, sig, n, xcs, k
set xtics font ",24"
set ytics font ",24"
set xlabel "Wavelength (nm)" font ",24"
set ylabel "Responsivity (A/W)" font ",24"
set key font ",24"
set term svg
set output "InGaAs_responsivityFit.svg"
plot g(x) lw 3, DataFile3 using 1:2 with lines lw 2 axis x1y1 title "InGaAs",s(x)
Final set of parameters            Asymptotic Standard Error
=======================            ==========================
alpha           = 1.20747          +/- 0.02844      (2.355%)
mu              = 1261.59          +/- 2.98         (0.2362%)
sig             = 299.896          +/- 2.142        (0.7142%)
n               = 11.6189          +/- 0.518        (4.459%)
xcs             = 1085.17          +/- 11.84        (1.092%)
k               = 0.00535154       +/- 0.0003109    (5.809%)


s(x)=1/(1+exp(-k*(x-xcs)))

mu = 0.0
sig = 1.0
lambda = 0.25
n=2
set xrange [-10:10]
e(x)=lambda/2*exp(lambda/2*(2*mu+lambda*sig**2+2*x**n))*(1-erf((mu+lambda*sig**2+x**n/(sqrt(2)*sig))))

e(x)=lambda/2*exp(lambda/2*(2*mu+lambda*sig**2-2*x))*erfc((mu+lambda*sig**2-x)/(sqrt(2)*sig))
set xrange [400:1800]
plot e(x)
e(x) = erfc((mu+lambda*sig**2-x)/(sqrt(2)*sig))


PI = 3.1415926535
y0 = 0 # is the baseline offset.
xc = 1300 # is the center of the peak.
w = 500 # equals the width of the peak at half height.
A = 1400 # is the area under the peak. 
L = 0.3
T= 1E-9
alpha = 4E6
xcex = 1000
f(x)=(y0 + (2*A/PI)*(w/(4*(x-xc)**2 + w**2)))**3*(L+(1-L)/exp(alpha*T)*(exp(alpha*(x-xcex)*1E-9)-1))

set xrange [400:1800]
DataFile3 = "InGaAsStandardR.cvs"
set datafile separator ","
fit f(x) DataFile3 using 1:2 via xc, w, A, L, T, alpha, xcex
plot f(x), DataFile3 using 1:2 with lines lw 3 axis x1y1 title "InGaAs"


p0=0
p4=-1E-4
xcp=1300
p(x)=p0+p4*(x-xcp)**4
DataFile3 = "InGaAsStandardR.cvs"
set datafile separator ","
plot p(x), DataFile3 using 1:2 with lines lw 3 axis x1y1 title "InGaAs"