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2.1 Wave propagation

Slides: Video 2.1.5 Diffraction from

periodic structuresText reference: Quantum Mechanics

for Scientists and EngineersSection B.4

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Wave propagation

Diffraction from periodic struc

Quantum mechanics for scientists and engineers Da

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Periodic struc

Suppose we have a equally spaced ide

scatterersand we shine a

monochromaticthem from the r

what does the scattered ligh..

..

..

..

..

..

..

..

..Scatterers

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Periodic struc

One scatterer wilof phase fronts

concentric “circ

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Periodic struc

One scatterer wilof phase fronts

concentric “circTwo will give two

which will inter

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One scatterer wilof phase fronts

concentric “circTwo will give two

which will interMultiple equally sscatterers give msets

Periodic struc

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These scatterers aphase for partic

directions, here“straight ahead

called a “zerdiffraction

Periodic struc

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These scatterers aphase for partic

directions, here“straight ahead

called a “zerdiffraction

an upward dire

Periodic struc

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These scatterers aphase for partic

directions, here“straight ahead

called a “zerdiffraction

an upward dire

a downward di

Periodic struc

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Periodic structure

.

...

....

...

.

.

...

..

Scatterer spacingin wavelengths 1.5

At large distances frscatterer

we get a multiplediffraction patte

which looks likpoints on a sc

Larger scatterer sep

gives beams clos

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Periodic structure

At large distances frscatterer

we get a multiplediffraction patte

which looks likpoints on a sc

Larger scatterer sep

gives beams clos....

....

...

.

...

.

.

.

Scatterer spacingin wavelengths 2.0

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Periodic structure

At large distances frscatterer

we get a multiplediffraction patte

which looks likpoints on a sc

Larger scatterer sep

gives beams clos....

...

.

...

.

...

.

..

Scatterer spacingin wavelengths 2.5

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Periodic structure

At large distances frscatterer

we get a multiplediffraction patte

which looks likpoints on a sc

Larger scatterer sep

gives beams clos...

..

..

...

.

.

...

.

Scatterer spacingin wavelengths 3.0

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Periodic structure

At large distances frscatterer

we get a multiplediffraction patte

which looks likpoints on a sc

Larger scatterer sep

gives beams clos

.

.

..

.

..

..

.

..

.

.

Scatterer spacingin wavelengths 3.5

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Periodic structure

At large distances frscatterer

we get a multiplediffraction patte

which looks likpoints on a sc

Larger scatterer sep

gives beams clos...

..

..

.

..

.

.

Scatterer spacingin wavelengths 4.0

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The angle  of thdiffracted waves

is given by simgeometry

Periodic struc

i di

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The angle  of thdiffracted waves

is given by simgeometry

where

  is the w

s is the se

between

Periodic struc s

 

sins

 

    

2 

3 

4 

5 

P i di

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For larger spacing

multiple diffrac

“orders” are p

is a “first orddiffraction

Periodic struc

1 s

 

1sin

s

     1

 

2 

P i di t

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For larger spacing

multiple diffrac

“orders” are p

is a “seconddiffraction

Periodic struc

2 s

2 

2

2sin

s

    2

 

4 

P i di t

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For larger spacing

multiple diffrac

“orders” are p

is a “(negativorder” diffr

the sign isof taste

“normal”

Periodic struc

1

sins

 

  1 

s

 

2 

  1 

P i di t

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For larger spacing

multiple diffrac

“orders” are p

is a “(negativorder” diffr

the sign isof taste

“normal”

Periodic struc

  2 

s

2 

2

sins

 

  2 

4 

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