Content

• Constant
• Optics
• Magnetics

Constant

# Energy
# To Ry
ConvHa2Ry=2
ConvJ2Ry=4.587424e+17
ConveV2Ry=7.349862e-02
ConvK2Ry=6.333624e-06
ConvGHz2Ry=3.039660e-07

Convforceau2eVAng=25.710907566423526 # Ry/Bohr to eV/Ang
ConvBohr2Angstr=0.52918 # Bohr same to a.u.

Avogadro=6.02214076e23
pi=np.pi
kB=1.380649e-23 #J K^-1
h=6.62607015e-34 #J s
hbar=h/(2*pi)
epsilon0 = 8.854187812813e-12 #C^2 m^-2 N^-1
me = 9.1093837e-31 #kg
charge=1.60218E-19 #C
c=299792458 #m/s

Optics

• Relative permittivity, dielectric function\(\varepsilon(\omega)=1+\chi(\omega)\)
• Refractive index\(n(\omega)=\sqrt{\varepsilon(\omega)}\)
  • Real part refractive index \(n=\sqrt{\frac{\sqrt{\varepsilon_r^2+\varepsilon_i^2}+\varepsilon_r}{2}}\)
  • Imag part extinction coefficient \(\kappa=\sqrt{\frac{\sqrt{\varepsilon_r^2+\varepsilon_i^2}-\varepsilon_r}{2}}\)
  • Dielectric function in \(\varepsilon_r=n_r^2-n_i^2\), \(\varepsilon_i=2n_rn_i\)
• Optical absorption coefficient \(\alpha(\omega)=\frac{2\omega}{c}\kappa=\frac{2\omega}{c}n_i\)
• Reflectivity \(R=\frac{(1-n)^2+\kappa^2}{(1+n)^2+\kappa^2}=\frac{(1-n)^2+n_i^2}{(1+n)^2+n_i^2}\)
• Optical conductivity \(\sigma(\omega)=-i\omega\chi(\omega)\)
  • definition \(\vec J(\omega)=\sigma(\omega)\vec E(\omega)\)
  • \[\vec D(\omega)=\varepsilon(\omega)\vec E(\omega)\]
  • \[\varepsilon(\omega)=\varepsilon_0+\frac{i\sigma(\omega)}{\omega}=\varepsilon_0(1+\chi(\omega))\]

Magnetics

• Macroscopic magnetic moment \(m:\rm A\cdot m^2\)
• \[1 \rm A\cdot m^2=1000 \rm emu (erg/G)\]
• Bohr magneton \(\mu_B=9.274×10^{-24} \rm A\cdot m^2\)
• Magnetization is defined as net magnetic moment in an unit volume \(M=\frac{m}{V}: \rm \frac{A\cdot m^2}{kg} ; \frac{A\cdot m^2}{mol}\)
• \[1 \rm A\cdot m^2/kg=1 \rm emu/g\]
• \[1 \rm emu/mol=\frac{10^{−3} μ_B}{9.274×10^{−24}\times6.023\times10^{23} f.u.}=\frac{1}{5585} μ_B/f.u.\]
• Where \(f.u.\) refers to formula unit