1 Reality of Electric Susceptibility and Electric Permittivity

Photonics Devices,

WS 2020

Exercise I+

Abgabe: 11.01.21

1 Reality of Electric Susceptibility and Electric Permittivity

Verify the reality condition for electric susceptibility and electric permittivity given inχ^∗_ij(k, ω) = χ_ij(−k,−ω) and ^∗_ij(k, ω) =_ij(−k,−ω), respectively.

2 Medium with a loss or gain

Express the wavenumberβ and the attenuation coefficientα defined ink=k⁰+ik⁰⁰=β+i^α₂ for propagation of an optical wave in an absorptive medium in terms of the real part,χ⁰, and the imaginary part,χ⁰⁰, of the electric susceptibility of the medium. Show that when χ⁰⁰χ⁰, we haveα≈β_n^χ2.

3 Group Velocity in a Metal

Show that for a medium described by the Drude model(ω) =_o 1−^ω_ω^2p2

, the product of the phase velocity and the group velocity is equal toc²_o.

4 EM Wave Polarizations

Two polarizers placed in tandem along the line of propagation of an optical beam are called cross polarizers if their axes are arranged to be orthogonal to each other. For the purpose of answering the following questions, consider polarizers of transmission type.

a. Show that no light of any polarization can pass through a set of cross polarizers.

b. A third polarizer is inserted in between the two cross polarizers. The transmission of this three-polarizer combination is not zero any more if the axis of the inserted polarizer is not parallel to either of the original two. Find the transmittance of this combination as a function of the angle between the axis of this polarizer and that of the polarizer at the input end.

c. Since each polarizer acts only as a polarization-sensitive filter to transmit the field com- ponent of a particular polarization, the phenomenon described in (b) may not seem possible.

Can you give a physically intuitive explanation for it?

Exercises selected fromFundamentals of Photonics, chapter 5, by B.E.A Saleh and M.C. Teich andPhotonic Devices, chapter 1, by Jia-ming Liu.

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