The design and performance of an astigmatic laser mode converter
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The Design and Performance of an Astigmatic Laser Mode Converter. Alex Ellis, Stuyvesant High School Dr. Harold Metcalf and Dr. John No é, Stony Brook University. A What?.

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The design and performance of an astigmatic laser mode converter

The Design and Performance of an Astigmatic Laser Mode Converter

Alex Ellis, Stuyvesant High School

Dr. Harold Metcalf and Dr. John Noé, Stony Brook University


A what
A What? Converter

An astigmatic mode converter is a pair of cylindrical lenses, accompanied by mode-matching lenses, which introduce an astigmatic phase shift to a laser beam. In particular, it can convert Hermite-Gaussian (HG) rectangularly symmetric transverse modes into Laguerre-Gaussian (LG) circularly symmetric modes.


Hermite gaussian modes
Hermite-Gaussian Modes Converter

  • Rectangularly symmetric

  • Obtainable in spherical-planar resonator by adjusting plane mirror angle

  • Also obtainable by an intra-cavity crosswire, when the laser is operating in a multimode

  • Indices (m,n) refer to the number of intensity minima in the x and y directions

HG0,1

HG1,2


Laguerre gaussian modes optical vortices
Laguerre-Gaussian Modes (Optical Vortices) Converter

  • Circularly Symmetric

  • Obtained by intra-cavity circular absorbers, computer-generated holograms, or an astigmatic mode converter

  • Photons have orbital angular momentum of l*hbar

  • Index l is the number of 2π phase shifts around the diameter

LG3,0

LG1,1


Superpositions
Superpositions Converter

HG0,1+HG1,0 = HG0,1 rotated 45°

HG0,1+i*HG1,0 =LG1,0

i represents a π/2 phase shift


Operating principle of an astigmatic mode converter
Operating Principle of an Astigmatic Mode Converter Converter

Input

The Guoy Phase

45° rotated HG0,1

  • HG: (m+n+1)ψ(z)

  • LG: (l+2p+1)ψ(z)

Ψ(z) = arctan(z/z0)

Cylindrical Lenses

  • First introduces path length difference, altering the superposition due to the Guoy phase (astigmatism in the region)

  • Second one removes the introduced astigmatism


Mode converter rules
Mode Converter Rules Converter

Localized Astigmatism and Proper Guoy Phase Shift

Mode-Matching

A beam waist is required midway between the two cylindrical lenses

w0, z0

w0’, z0’


Apparatus the laser
Apparatus – The Laser Converter

Melles-Griot 05-LHB-570 Helium-Neon tube

R=600mm spherical mirror, 295mm from

plane mirror output coupler

Adjustment of OC gives multimodes, and an

intra-cavity crosswire on a translation stage

selects particular HG modes


Apparatus the mode converter
Apparatus – The Mode Converter Converter

f1 = 300mm fcyl = 150mm

d1 = 513mm d2 = 481mm d3 = 212mm

w0 = 246um z0 = 300mm

w0’ = 227um z0’ = 256mm


Achieved mode conversions
Achieved Mode Conversions Converter

HG0,1

LG1,0

HG0,2

LG2,0

LG3,0

HG0,3

HG1,1

LG1,0

HG1,2

LG1,1


Performance multimodes
Performance – Multimodes Converter

CCD Image

Voltage in Photodetector (V)

2.06

1.59

2.03

2.22

Optical Intensity (mW)

0.44

0.34

0.43

0.47

Achieved HG Modes (m,n)

01,01,02,03,bad01, bad11,bad1202,03, bad12

01,02,03,bad12

02,bad01

02,bad11,bad12



Performance mode compositions1
Performance – Mode Compositions Converter

d1

d1

d2

d2

Analysis of this particular mode gives PHG≈ 73% and PLG ≈ 27%


Applications
Applications Converter

  • Generation of arbitrary order Bessel beams by use of an axicon

  • “Optical spanners” that both trap and spin microscopic particles

  • Further study involving the orbital angular momentum of light


Acknowledgements
Acknowledgements Converter

  • Dr. Harold Metcalf

  • Dr. John Noé

  • Mr. Don Bucher

  • Mrs. Anne Manwell


Further research
Further Research Converter

  • Change of mode converter parameters due to the increased spot size of high-order HG modes

  • Interferometry of LG beams with plane waves to investigate the spiral phase pattern

  • Measurement of the l*hbar per photon orbital angular momentum


Questions
Questions Converter


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