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Lecture 3 Polarization, Reflection and Transmission at normal incidence

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Uniform plane wave (UPW) power transmission

from

W/m2

Question: Have you ever wondered why aluminum foil is not allowed in

the microwave oven?

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Polarization

- UPW is characterized by its propagation direction and frequency.
- Its attenuation and phase are determined by medium’s parameters.
- Polarization determines the orientation of the electric field in a fixed spatial plane orthogonal to the direction of the propagation.

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Linear polarization

- Consider in free space,

- At plane z = 0, a tip of field traces straight line segment called “linearly polarized wave”

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Linear polarization

- A pair of linearly polarized wave also produces linear polarization

At z = 0 plane

At t = 0, both linearly polarized waves

Have their maximum values

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More generalized linear polarization

- More generalized of two linearly poloraized waves,
- Linear polarization occurs when two linearly polarized waves are

in phase

out of phase

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Elliptically polarized wave

- Super position of two linearly polarized waves that
- If x = 0 and y = 45, we have

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Circularly polarized wave

- occurs when Exoand Eyo are equal and
- Right hand circularly polarized (RHCP) wave
- Left hand circularly polarized (LHCP) wave

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Ex2 The electric field of a uniform plane wave in free space is given by , determine

- f
- The magnetic field intensity

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Incident wave

- Normal incidence – the propagation direction is normal to the boundary

Assume the medium is lossless, let the incident electric field to be

or in a phasor form

since

then we can show that

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Transmitted wave

- Transmitted wave

Assume the medium is lossless, let the transmitted electric field to be

then we can show that

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Reflection and transmission coefficients (1)

- Boundary conditions (reflected wave is included)

from

therefore at z = 0

(1)

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Reflection and transmission coefficients (2)

- Boundary conditions (reflected wave is included)

from

therefore at z = 0

(2)

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Reflection and transmission coefficients (3)

- Solve Eqs. (1) and (2) to get

Reflection coefficient

Transmission coefficient

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Types of boundaries: perfect dielectric and perfect conductor (1)

From

.

Since 2 = 0 then = -1 and Ex10+=Ex10-

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Types of boundaries: perfect dielectric and perfect conductor (2)

This can be shown in an instantaneous form as

Standing wave

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Standing waves (1)

When t = m, Ex1 is 0 at all positions.

and when z = m, Ex1 is 0 at all time.

Null positions occur at

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Standing waves (2)

Since

and ,

the magnetic field is

or .

Hy1 is maximum when Ex1 = 0

Poynting vector

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Power transmission for 2 perfect dielectrics (1)

Then 1and 2are both real positive quantities and 1 = 2= 0

Average incident power densities

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Ex3 Let medium 1 have 1 = 100 and medium 2 have 2 = 300 , given Ex10+ = 100 V/m. Calculate average incident, reflected, and transmitted power densities

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Wave reflection from multiple interfaces (1)

- Wave reflection from materials that are finite in extent such as interfaces between air, glass, and coating
- At steady state, there will be 5 total waves

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