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Generation of Divergence-Free Bessel-Gauss Beam from an Axicon Doublet for km-long Collimated Laser
Sirawit Boonsit1,2, Panuwat Srisamran1,2, Pruet Kalasuwan1,2
, Paphavee van Dommelen1,2 and Chalongrat Daengngam*
NanoPhotonics
1Department of Physics, Faculty of Science, Prince of Sonkla University, Songkhla, Thailand
2Thailand Center of Excellence in Physics, Commission on Higher Education, Bangkok, Thailand
October 4th, 2018
LASER
LIDARSENDING SPECRAFTSPACE COMMUNICATIONHIPERSPECTRAL IMAGINGDavid J. Lynch, 2017Lori Keesey, JPL/NASA, 2011R. Mark ElowitzVermont Center for Geographic Information
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Beam divergence
Nibby Williams, ST Laserstrike 2017
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Objective
To perform finite-element simulation to study effect of compound axicon parameters and beam waist radius on the propagation distance of the Bessel-Gauss in comparison to normal Gaussian beam.
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Equation of Gaussian beam
𝐸𝐺 𝑥, 𝑦 = 𝐸𝐺0𝑤0
𝑤(𝑦)𝑒−
𝑥2
𝑤(𝑦)2𝑒−𝑖𝜑
𝑤(𝑦) = 𝑤0 1 +𝑦2
𝑍𝑅2
𝑍𝑅 =𝜋𝑤0
2
𝜆
𝑅(𝑦) = 𝑦 1 +𝜋𝑤0
2
𝜆𝑦
2
where Spot size
Rayleigh
Radius of curvature
φ = ky − 𝑎𝑡𝑎𝑛𝑦
𝑧𝑅+
𝑘𝑥2
2𝑅 𝑦Gouy phase shift
𝜃 =𝜆
𝜋𝑤0
divergence
Gaussian beam
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Amplitude factor
𝑤0 :beam waist
phase
Equation of Bessel beam
“Diffracting-free beam”
𝐸𝐵 𝑥, 𝑦 = 𝐸𝐵0𝐽𝜈 𝑘𝑥𝑥 𝑒−𝑖𝑘𝑦𝑦
where 𝐽𝜐 𝑘𝑥𝑥 is Bessel function of the first kind
For 𝜐 = 0 𝐸𝐵 𝑥, 𝑦 = 𝐽0 𝑘𝑥𝑥 𝑒−𝑖𝑘𝑦𝑦
Eric W. and Weisstein
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Bessel function Bessel beam
𝐸𝐵𝐺 𝑥, 𝑦 = 𝐸0𝐽0 𝑘𝑥𝑥𝑤0
𝑤(𝑦)𝑒−𝑥2
𝑤2𝑒−𝑖∅
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Equation of Bessel-Gauss beam
CROSS SECTION
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Gaussian beam profile Bessel-Gauss beam profile
Thibon, Louis
Axicon
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Axicons How axicon work
CPG Optics
COMSOL MULTIPHYSICS
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Choose the module
Optics
Wave Optics
EMW BEAM ENVELOPES
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Finite element method (FEM)
Variable Expression Description
wl 0.532 µm Wavelength
w0 25 mm Beam waist
Ep 0.150 J Laser Pulse energy
tp 6 ns Laser pulse duration
Define parameters
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parameters of YAG laser
CreateGeometry
Includematerial
Inject thebeam
𝑛𝐵𝐾7 = 1.520
𝑛𝑓𝑢𝑠𝑒𝑑𝑠𝑖𝑙𝑖𝑐𝑎 = 1.461
𝑛𝑔𝑙𝑢𝑒 = 1.573 − 1.580
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𝛾1 = 1.0° 𝛾2 = 0.5°
𝜸𝟏 𝜸𝟏
𝜶𝟏
𝜷𝟏
n1
n3
n2
𝛽1 = π−𝜋
2− 𝛼1 −
𝜋
2+ 𝛾1
k= 𝑘𝑥 + 𝑘𝑦 = 𝑘𝑠𝑖𝑛𝛽1 + 𝑘𝑐𝑜𝑠𝛽1
Propagation constant
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Section I-Sweep the parameter n3 (the interlayer refractive index) from 1.573-1.580 and find the optimum n3.
Effect of 𝑛3 on longitudinal intensity of Bessel-Gauss beam with 𝑤0 = 25 mm
Result I
n3 = 1.577
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Section II-Using the result from sec.I to contribute a Bessel-Gauss beam and compare to normal Gaussian beam with the same beam waist.
Results II
Longitudinal beam intensity for 𝑤0 = 25 mmComparison of intensity profile
n3 = 1.5775
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Section III-Sweep the waist diameter input of the beam from 10-25 mm.
Results III
Effect of input beam waist on longitudinal beam intensity of a produced Bessel-Gauss beam
Conclusions
It is possible to generate a Bessel-Gauss beam by using numerical method from COMSOL® program.
For an input beam waist 25 mm , a compound axicon can generate a beam output that can be delivered over a distance at least 2 km.
Need to compare the results with the experiment.
Future work
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Acknowledgements
Assist. Prof. Dr.Chalongrat Daengngam Ph.D
Department of Physics, Faculty of Science, Prince of Songkhla University
NanoPhotonics Research Group
Development and Promotion of Science and Technology Talents Project (DPST)
COMSOL ® Multiphysics
Gaussian Beam Bessel Gauss Beam
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FOR 𝜸𝟏 = 𝟏. 𝟎°
𝜸𝟐 = 𝟎. 𝟓°
𝒏𝒈 = 𝟏. 𝟒
𝒏𝒈 = 𝟏. 𝟔
𝒏𝒈 = 𝟏. 𝟓
𝒏𝒈 = 𝟏. 𝟕
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𝒏𝒈 = 𝟏. 𝟒
𝒏𝒈 = 𝟏. 𝟔
𝒏𝒈 = 𝟏. 𝟓
𝒏𝒈 = 𝟏. 𝟕
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FOR 𝜸𝟏 = 𝟎. 𝟓°
𝜸𝟐 = 𝟏. 𝟎°