Gaussian Beams - uni-jena.deoptics+9+Gaussian+beams.pdf · Gaussian beam: width ... Gaussian Beams...
Transcript of Gaussian Beams - uni-jena.deoptics+9+Gaussian+beams.pdf · Gaussian beam: width ... Gaussian Beams...
Single-Molecule Microscopy Group
Gaussian Beams
Physical Optics
31-05-2017
Maria Dienerowitz
www.single-molecule-microscopy.uniklinikum-jena.de
Revision
• Wave equation to Helmholtz equation
• Plane & spherical waves, Gaussian beams
Gaussian Beams
• Analytical expression
• Beam parameters
Transmission through optical components
• Thin lens, focussing, collimating
• ABCD law
Contents
Fundamentals of Photonics – B.Saleh, M.Teich 2
Introducing the Gaussian beam
3
Where to start?
Gaussian beam
simplifications Laser output
electromagnetic theory
concise solution find mathematical model
4
wave equation
-> complex wave function
amplitude of wave = magnitude
Wave equation to Helmholtz equation
Helmholtz equation => time independent!!
optical intensity
5
Solutions of the Helmholtz equation
Helmholtz equation
plane wave spherical wave
6
Solutions of the Helmholtz equation
Helmholtz equation
plane wave spherical wave
7
rapidly varying envelope
within a distance
Helmholtz equation to paraxial Helmholtz equation
slowly varying envelope
8
Helmholtz equation to paraxial Helmholtz equation
wavefront normals
within a distance
slowly varying envelope
9
Helmholtz equation to paraxial Helmholtz equation
paraxial Helmholtz equation
solution: Gaussian beam
10
Revision
• Wave equation to Helmholtz equation
• Plane & spherical waves, Gaussian beams
Gaussian Beams
• Analytical expression
• Beam parameters
Transmission through optical components
• Thin lens, focussing, collimating
• ABCD law
Contents
Fundamentals of Photonics – B.Saleh, M.Teich 11
Gaussian beam: analytical expression
beam intensity?
beam power? beam diameter? focal depth?
12
Gaussian beam: analytical expression
plane wave wavenumber
Gaussian beam
13
beam intensity
Gaussian beam: intensity
14
beam power
Gaussian beam: power
beam area
!!! continuous and pulsed Gaussian beams
15
Gaussian beam: width
intensity drops by factor 1/e2
Full Width Half Maximum -> half intensity
16
The Rayleigh range
Gaussian
Rayleigh range
17
Beam waist
beam diameter
18
Depth of focus
beam area
19
beam divergence
Beam divergence
20
The phase of a wave
21
The phase of a Gaussian beam
z
y
phase
plane wave Gouy phase wavefront bending
22
Summary - part I
Rayleigh range = ½ peak intensity
Rayleigh range = beam area twice as large than at beam waist
beam width = intensity drops by factor 1/e2
23
Summary - part II
spherical wave
Gaussian beam
wavelength
plane wave
24
Revision
• Wave equation to Helmholtz equation
• Plane & spherical waves, Gaussian beams
Gaussian Beams
• Analytical expression
• Beam parameters
Transmission through optical components
• Thin lens, focussing, collimating
• ABCD law
Contents
Fundamentals of Photonics – B.Saleh, M.Teich 25
phase shift
Transmission through a transparent plate
phase
26
Transmission through a thin lens
phase
27
magnification
beam waist
depth of focus (=2zR) beam divergence
waist location
radius of curvature
Transmission through a thin lens
28
waist location
Ray optics
magnification
29
Matrix Optics
paraxial approximation
thin lens refraction planar boundary
Snell 30
Transmission through arbitrary systems: ABCD law
complex beam parameter
free space
31
Beam shaping: focussing
32
Beam shaping: expansion/narrowing
increasing beam width decreasing beam width
double the beam diameter: f1=50mm, f2=100mm, d=150mm f1=150mm, f2=300mm, d=450mm
33
Conjugate planes in a microscope
© Nikon MicroscopyU
illumination light path
image forming light path
34
Beam relaying: conjugate planes
beam steering acousto-optical deflector
35