Diffraction and interference Jan. 30, 2018

+ Diffraction: resulting from the wave nature of light.
Tendency for a small beam to spread.
Smaller is the hole, biggest is the difference between [equation] and [equation], i.e. [equation]; [equation] beam diameter.
Similar to Bandwidth ([equation]) relates to pulse width ([equation]) by [equation].

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

+ Observations: Any sharp change in intensity generates ripples after propagation in space.
Consider a [equation] rectangular slit, this slit increases the divergence angle [equation] & [equation].
Consider an aperture with radius [equation], divergence angle defined as [equation].

Ref. 2 Sec. 4.3, 4.5

+ Gaussian beam: [equation] where beam radius (waist) [equation], [equation] initial beam radius at focus, [equation] diffraction length.
From these, divergence angle [equation].

Ref. 2 Sec. 3.1

+ Interference: [equation] and [equation].
Result of interference depends on phase difference [equation].
Destructive when [equation] where p is odd integer.
Constructive when [equation] where q is even integer.
Observation - [equation] is controlled by refractive index and/or distance.
Applications - interferometer (filter) (e.g. Mach-Zehnder, Michelson, Sagnac), antireflective coatings.

Ref. 2 Sec. 2.5

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

+ Holography: interfere of object wave [equation] and reference wave [equation] [equation] [equation].
Notice that [equation] & [equation] [equation] where [equation].
The interference pattern is recorded on film.
Playback output [equation].
Similar technique is used to fabricate grating onto optical fibers.

Ref. 2 Sec. 4.3, 4.5

Last Modified: January 29, 2018
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