Physics 123 Majors Section Unit 1

Uses of low-symmetry crystalspiezoelectricity (shape change with voltage)electrical control of index of refractionnonlinear optics: frequency sum/difference polarizers

1Light in a low-symmetry crystal With these restoring forces, if we pull on an electron along (1,1,1) direction: which way does it move?

2

Index change with E polarizationResonances that matter, and n may be different depending on E and k directions From the resonance positions shown, the stiffer forces are along the ______ direction

a) x b) y3Light in a low-symmetry crystal P is generally not parallel to E

Can find crystal principal directions for x, y, z so c is diagonal

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The following are always true (definition and basic MaxEqn)Which two common features are not required?S k 2. BE 3. Ek 4. Bk

1,21,32,32,43,4

5can occur in low symmetry crystals

From the equation above we conclude_____: E and P are parallelE and P are perpendicularIf P E then E k If P E then E k

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Calcite

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Unpolarized light entering a calcite crystalB direction?8

What does Snells law mean in low symmetry crystals?It gives the direction of k, not S!9

People on each yard line move identically to pass buckets to the next yard line, but diagonally. Phase change (where they are in a cycle) travels ______, like ___; water travels _______ like _____. bucket brigade analogy10We get k direction from Snell's law but its transcendental!

11

n can depend on the polarization direction ( ) and the phase change direction ( )!

We get k direction from Snell's law but its transcendental!12A polarizable crystal has one more term in Maxwells Eqns than polarizable glass

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14General case: k is not along a crystal principal axis:

To find n for each k direction we must solve:

We get two solutions for n, for two perp. directions of E!Special case: k is along a crystal principal axis. Then the equation above is not valid.

Example: k is along x axis Then we simply use for the two polarizations possible with that k. And Snells law is simple.

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Suppose for a crystal that . In this crystal, light is propagating in a direction halfway between the x and y axes. Write the equation needed to find the two ns.

I got it rightI tried16

If E is in the (1,1,0) direction, then P is in the ____ direction

(0,0,1) (8,3,0) (3,8,0)(3,8,2)(8,3,2)

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The crystal x and y are the dashed axes, and

From the values above and the shape of the wavelets (grow at different speeds in the different directions), we can tell the line labeled optic is the ____ (also called the slow) axis. xy(Huygens view of how elliptical wavelets give k different from S) 18