1 Maxwell's equations continuity

Photonics Devices,

WS 2020

Exercise I

Abgabe: 15.12.20

1 Maxwell's equations continuity

Verify that Maxwell's equations and the continuity equation are invariant under (a) space inversion, (b) time reversal, and (c) space inversion and time reversal simultaneously.

2 Traveling Standing Wave

The EF complex-amplitude vector for a monochromatic wave of wavelengthλtraveling in free space isE(x, y, z) =~ E0sin(βy) exp(−iβz)ˆx.

ˆ Determine a relation between β and λ.

ˆ Derive an expression for the MF complex-amplitude vector H(x, y, z)~ .

ˆ Determine the direction of the ow of the optical power.

ˆ This wave may be regarded as the sum of the two plane waves. Determine the directions of propagation.

3 Dielectric Media

Identify the media described by the following equations, regarding linearity, dispersiveness, spatial dispersiveness and homogeneity. Assume that all media are isotropic.

ˆ P~ =₀χ ~E−a∇ ·E~

ˆ P~ +a ~P²=0E~

ˆ a₁∂ ~P²

∂t² +a₂∂ ~P

∂t +P~ =₀χ ~E

ˆ P~ =₀{a₁+a₂exp[−(x²+y²)]}E~

whereP~ is the polarization, E~ is the EF vector andχ,a,a₁, anda₂ are constants.

4 EM Wave Polarizations

A crystal has the following electric permittivity tensor in the (x, y, z) coordinate system:

=₀





2.25 0 0 0 2.13 0 0 0 2.02





A linearly polarized optical wave that has a free-space wavelengthλ= 600nmis sent into the crystal. Find the wavelength of the wave in the crystal in each of the following arrangements.

a. The wave is polarized alongxˆ and propagates alongzˆ. b. The wave is polarized along yˆand propagates alongzˆ. c. The wave is polarized alongxˆ and propagates alongyˆ. d. The wave is polarized along zˆand propagates along yˆ.

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

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