Transcript Document

Announcements 3/30/12



Prayer
HW 23 is due Saturday night.
a. Poll: should we have it due Monday and start exam on
Tuesday? (Exam would still end Friday night)
Exam review problems on Monday.
a. Get your solutions to me in pdf form before 1:45 pm.
b. Approx. 5.5 mins/group
Speed Bump
Reading Quiz

The “Diffraction of a Gaussian field profile”
section involves diffraction through:
a. a circular aperture
b. a square aperture
c. no aperture
Reading Quiz

The smallest radius of a laser beam is known as
the beam _______:
a. ankle
b. knee
c. neck
d. pinky
e. waist
Reading Quiz

The distance over which the beam radius near a
focus stays about constant is the _______
range.
a. Fresnel
b. Gaussian
c. Home_on_the
d. Plank
e. Rayleigh
Gaussian field profile



E0 = Gaussian shape
Fresnel approximation
Diffracting through infinitely large aperture
Gaussian beams: result
(r = cylindrical r)
Rayleigh Range
beam width
relates to curvature: plane
wave to spherical wave
transition
A few different z values
Some plots
Original
Gaussian
profile:
width = 1
height = 1
At z = z42½0 zz00
width = 4.12
1.12
1.41
2.24
height = 0.059
0.8
0.5
0.2
Beam width vs. distance
This is width vs. z, for a
beam with a larger
Rayleigh range—stays
near the waist for longer.
But doesn’t get as
narrow!
What happens at large z
Beam width vs. distance
Figures
from P&W
Unspoken assumption about wavefronts at z=0
Gaussian Wavefronts
Plane
Spherical
(Figures from Saleh and
Teich, Photonics, 2nd
edition, pg 82)
Gaussian
The three phase factors
(r = cylindrical r)
Rayleigh Range
relates to curvature: plane
wave to spherical wave
transition
More complicated modes
Gaussian beams & laser stability
Reading Quiz

The ABCD law for Gaussian beams is used for:
a. finding the ABCD matrices for a Gaussian
laser beam
b. finding the diffraction pattern in the nearfield
c. finding the Gaussian beam parameters after
an optical element
ABCD Law for Gaussian beams