Gaussian Beams - uni-jena.deoptics+9+Gaussian+beams.pdf · Gaussian beam: width ... Gaussian Beams...

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Single-Molecule Microscopy Group Gaussian Beams Physical Optics 31-05-2017 Maria Dienerowitz [email protected] www.single-molecule-microscopy.uniklinikum-jena.de

Transcript of Gaussian Beams - uni-jena.deoptics+9+Gaussian+beams.pdf · Gaussian beam: width ... Gaussian Beams...

Page 1: Gaussian Beams - uni-jena.deoptics+9+Gaussian+beams.pdf · Gaussian beam: width ... Gaussian Beams ... Beam relaying: conjugate planes beam steering acousto-optical deflector 35 .

Single-Molecule Microscopy Group

Gaussian Beams

Physical Optics

31-05-2017

Maria Dienerowitz

[email protected]

www.single-molecule-microscopy.uniklinikum-jena.de

Page 2: Gaussian Beams - uni-jena.deoptics+9+Gaussian+beams.pdf · Gaussian beam: width ... Gaussian Beams ... Beam relaying: conjugate planes beam steering acousto-optical deflector 35 .

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

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Introducing the Gaussian beam

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Where to start?

Gaussian beam

simplifications Laser output

electromagnetic theory

concise solution find mathematical model

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Page 5: Gaussian Beams - uni-jena.deoptics+9+Gaussian+beams.pdf · Gaussian beam: width ... Gaussian Beams ... Beam relaying: conjugate planes beam steering acousto-optical deflector 35 .

wave equation

-> complex wave function

amplitude of wave = magnitude

Wave equation to Helmholtz equation

Helmholtz equation => time independent!!

optical intensity

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Solutions of the Helmholtz equation

Helmholtz equation

plane wave spherical wave

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Solutions of the Helmholtz equation

Helmholtz equation

plane wave spherical wave

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rapidly varying envelope

within a distance

Helmholtz equation to paraxial Helmholtz equation

slowly varying envelope

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Helmholtz equation to paraxial Helmholtz equation

wavefront normals

within a distance

slowly varying envelope

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Helmholtz equation to paraxial Helmholtz equation

paraxial Helmholtz equation

solution: Gaussian beam

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Page 11: Gaussian Beams - uni-jena.deoptics+9+Gaussian+beams.pdf · Gaussian beam: width ... Gaussian Beams ... Beam relaying: conjugate planes beam steering acousto-optical deflector 35 .

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

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Gaussian beam: analytical expression

beam intensity?

beam power? beam diameter? focal depth?

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Gaussian beam: analytical expression

plane wave wavenumber

Gaussian beam

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beam intensity

Gaussian beam: intensity

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beam power

Gaussian beam: power

beam area

!!! continuous and pulsed Gaussian beams

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Gaussian beam: width

intensity drops by factor 1/e2

Full Width Half Maximum -> half intensity

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The Rayleigh range

Gaussian

Rayleigh range

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Beam waist

beam diameter

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Depth of focus

beam area

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beam divergence

Beam divergence

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The phase of a wave

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The phase of a Gaussian beam

z

y

phase

plane wave Gouy phase wavefront bending

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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

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Summary - part II

spherical wave

Gaussian beam

wavelength

plane wave

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Page 25: Gaussian Beams - uni-jena.deoptics+9+Gaussian+beams.pdf · Gaussian beam: width ... Gaussian Beams ... Beam relaying: conjugate planes beam steering acousto-optical deflector 35 .

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

Page 26: Gaussian Beams - uni-jena.deoptics+9+Gaussian+beams.pdf · Gaussian beam: width ... Gaussian Beams ... Beam relaying: conjugate planes beam steering acousto-optical deflector 35 .

phase shift

Transmission through a transparent plate

phase

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Transmission through a thin lens

phase

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magnification

beam waist

depth of focus (=2zR) beam divergence

waist location

radius of curvature

Transmission through a thin lens

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waist location

Ray optics

magnification

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Matrix Optics

paraxial approximation

thin lens refraction planar boundary

Snell 30

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Transmission through arbitrary systems: ABCD law

complex beam parameter

free space

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Beam shaping: focussing

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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

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Conjugate planes in a microscope

© Nikon MicroscopyU

illumination light path

image forming light path

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Beam relaying: conjugate planes

beam steering acousto-optical deflector

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