FresnelReflection

graphenemodeling.graphene.monolayer.FresnelReflection(q, omega, gamma, FermiLevel, T, eps1, eps2, polarization)

The Fresnel Reflection coefficients of light incident from above (medium 1, eps1).

Equation 5.4 of Ref 1

Parameters:
  • q (array-like, rad/m) – Wavenumber at which to evaluate FresnelReflection. In-plane momentum of incident light.
  • omega (array-like, rad/s) – Angular frequency of incident light.
  • eps1 (scalar, unitless) – Permittivity in upper half-space
  • eps2 (scalar, unitless) – Permittivity in lower half-space
  • polarization (string) – ‘s’/’TE’ or ‘p’/’TM’ for s- or p-polarization.

Examples

Plot the TM polarized Fresnel Reflection coefficient. This will highlight the plasmon. Replicates Fig. 5.2 in Ref [1].

>>> import matplotlib.pyplot as plt
>>> import matplotlib.cm as cm
>>> from graphenemodeling.graphene import monolayer as mlg
>>> from scipy.constants import elementary_charge, hbar
>>> eV = elementary_charge
>>> FermiLevel = 0.4 * eV
>>> gamma = 0.012 * eV / hbar
>>> kF = mlg.FermiWavenumber(FermiLevel,model='LowEnergy')
>>> q = np.linspace(1e-2,3,num=200) * kF
>>> w = np.linspace(1e-2,3,num=200) * FermiLevel / hbar
>>> fresnelTM = mlg.FresnelReflection(q,w[:,np.newaxis],gamma,FermiLevel,T=0,
...                                     eps1=1,eps2=1,
...                                     polarization='TM')
>>> fig, ax = plt.subplots(figsize=(6,6))
>>> ax.imshow(-np.imag(fresnelTM),
...             extent=(q[0]/kF,q[-1]/kF,hbar*w[0]/FermiLevel,hbar*w[-1]/FermiLevel),
...             origin='lower',aspect='auto',cmap=cm.hot,vmin=-16,vmax=0)
>>> ax.set_xlabel('$q/k_F$')
>>> ax.set_ylabel('$\hbar\omega/E_F$')
>>> ax.set_ylim(0,3)
>>> ax.set_xlim(0,3)
>>> fig.suptitle('Fresnel Reflection Coefficient (TM)')
>>> plt.show()

(Source code, png, hires.png, pdf)

_images/graphene-monolayer-FresnelReflection-1.png

References

[1] Christensen, T. (2017). From Classical to Quantum Plasmonics in Three and Two Dimensions (Cham: Springer International Publishing). http://link.springer.com/10.1007/978-3-319-48562-1.