Question

PART A: Metamaterials and Photonic Crystals Exercise 1: Propagation of light in photonic crystals { Derive from Maxwells equations the wave-equation for the magnetic field \(\vec{H}(t,\vec{r})\) inside a ( photonic crystal. Explain, why using the magnetic field is favourable over the electric field. a) What are the scaling properties found in the solutions of the wave equation? Discuss what happens, if you reduce the lattice constant by a factor of 2. (5 Points) b) For frequencies at the center of the band gap, no propagating moues are allowed. venat happens in this region with the wave-vector? (2 Points) c) Which behaviour show incoming waves inside the photonic crystal in the band gap and what happens with the time-averaged Poyntina vector? (3 Points)

          PART A: Metamaterials and Photonic Crystals
Exercise 1: Propagation of light in photonic crystals
{ Derive from Maxwells equations the wave-equation for the magnetic field \(\vec{H}(t,\vec{r})\) inside a
( photonic crystal. Explain, why using the magnetic field is favourable over the electric field.
a) What are the scaling properties found in the solutions of the wave equation? Discuss what
happens, if you reduce the lattice constant by a factor of 2. (5 Points)
b) For frequencies at the center of the band gap, no propagating moues are allowed. venat
happens in this region with the wave-vector? (2 Points)
c) Which behaviour show incoming waves inside the photonic crystal in the band gap and what
happens with the time-averaged Poyntina vector? (3 Points)

PART A: Metamaterials and Photonic Crystals
Exercise 1: Propagation of light in photonic crystals
Derive from Maxwells equations the wave-equation for the magnetic field H⃗(t,r⃗) inside a
( photonic crystal. Explain, why using the magnetic field is favourable over the electric field.
a) What are the scaling properties found in the solutions of the wave equation? Discuss what
happens, if you reduce the lattice constant by a factor of 2. (5 Points)
b) For frequencies at the center of the band gap, no propagating moues are allowed. venat
happens in this region with the wave-vector? (2 Points)
c) Which behaviour show incoming waves inside the photonic crystal in the band gap and what
happens with the time-averaged Poyntina vector? (3 Points)

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