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from ipywidgets import *
from geoscilabs.em.Reflection import PowerReflection

Reflection and Refraction of plane waves

Purpose

Electromagnetic waves are reflected and refracted at a plane interface separating media of different electrical properties. Essential items to understand here are:

  • What are TE and TM modes for reflection, and refraction
  • How reflection and refraction changes due to incidient angle and electrical parameters
  • Total reflection
  • Brewster angle

Set up

A plane wave is reflected and refracted at a plane wave interface. Here $\mathbf{k}$ is wave propagation consant, which is a vector. We consider two different modes:

  • Transverse electric (TE): No vertical electric field
  • Transverse magnetic (TM): No vertical magnetic field

TE mode

Electric field ($\mathbf{E}$) is transverse to the plane of incidence (No vertical electric field).

TM mode

Magnetic field ($\mathbf{H}$) is transverse to the plane of incidence (No vertical electric field).

Reflection and Transmision app

Parameters

  • $\sigma_1$: Conductivity of the first layer (S/m)

  • $\sigma_2$: Conductivity of the first layer (S/m)

  • $f$ (Hz): Frequency (Hz)

  • Type:

    • Reflection: Transmission power as a function of incident angle
    • Transmission: Transmission power as a function of incident angle
    • Angle: relationship between $\theta_i$ and $\theta_t$
In [ ]:
Q = interact(PowerReflection
        , sig1 = FloatText(value=0., description="$\sigma_1$")
        , sig2 = FloatText(value=1e-2, description="$\sigma_2$")
        , f = FloatText(value=6e5, description="$f$ (Hz)")
        , Type = ToggleButtons(options=["Reflection", "Transmission", "Angle"])
        )
In [ ]: