**Diffraction and interference** Jan. 30, 2018

+
:
resulting from the wave nature of light.` `

Tendency for a small beam to spread.` `

,
i.e. ; beam diameter.` `

Similar to
Bandwidth () relates to pulse width () by
.` `

+ Fourier optics:
field far away from the source
relates to field near the source
by the 2D Fourier transform,
i.e.` `
where and
are spatial freq relating to the
coordinates in far field
and distance from the source.` `

+
Observations:
Any sharp change in intensity generates ripples after propagation in space.` `

Consider a
, this slit
increases the divergence angle
&
.` `

Consider an
with radius ,
divergence angle defined as
.` `

+
:
where beam
radius (waist) ,
initial beam radius at focus,
diffraction length.` `

From these, divergence angle .` `

+
Interference:
and .` `

Result of interference depends on phase difference
.` `

Destructive when where p is odd integer.` `

Constructive when where q is even integer.` `

Observation - is controlled by refractive index and/or
distance.` `

Applications - interferometer (filter) (e.g. ,
Michelson,
),
antireflective coatings.` `

+
Grating: a structure that causes periodic modulation of amplitude or
phase, e.g.` `
that has maximum reflection for wave with a certain
wavelength traveling
at a blaze angle with respect to the normal of the grating
where
is grating period.` `
(read pp. 118-122 2nd Ed. or pp. 124-128 3rd Ed. of the text)

Results from interference.` `

+
.` `

Notice that &
where .` `

The interference pattern is recorded on film.` `

output .` `

Similar technique is used to fabricate grating onto optical fibers.` `

Last Modified: January 29, 2018

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