Announcements 3/30/12 Prayer HW 23 is due Saturday night. a. a.Poll: should we have it due Monday and start exam on Tuesday? (Exam would still end Friday.

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Announcements 3/30/12 Prayer HW 23 is due Saturday night. a. 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. a.Get your solutions to me in pdf form before 1:45 pm. b. b.Approx. 5.5 mins/group Speed Bump

Reading Quiz The “Diffraction of a Gaussian field profile” section involves diffraction through: a. a.a circular aperture b. b.a square aperture c. c.no aperture

Reading Quiz The smallest radius of a laser beam is known as the beam _______: a. a.ankle b. b.knee c. c.neck d. d.pinky e. e.waist

Reading Quiz The distance over which the beam radius near a focus stays about constant is the _______ range. a. a.Fresnel b. b.Gaussian c. c.Home_on_the d. d.Plank e. e.Rayleigh

Gaussian field profile E 0 = Gaussian shape Fresnel approximation Diffracting through infinitely large aperture

Gaussian beams: result  = 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 = ½ z 0 width = 1.12 height = 0.8 At z = z 0 width = 1.41 height = 0.5 At z = 2 z 0 width = 2.24 height = 0.2 At z = 4 z 0 width = 4.12 height = 0.059

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 Gaussian (Figures from Saleh and Teich, Photonics, 2nd edition, pg 82)

The three phase factors  = 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. a.finding the ABCD matrices for a Gaussian laser beam b. b.finding the diffraction pattern in the near- field c. c.finding the Gaussian beam parameters after an optical element

ABCD Law for Gaussian beams