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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
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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
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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
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𝐸𝐵𝐺 𝑥, 𝑦 = 𝐸0𝐽0 𝑘𝑥𝑥𝑤0
𝑤(𝑦)𝑒−𝑥2
𝑤2𝑒−𝑖∅
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Equation of Bessel-Gauss beam
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CROSS SECTION
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Gaussian beam profile Bessel-Gauss beam profile
Thibon, Louis
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Axicon
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Axicons How axicon work
CPG Optics
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COMSOL MULTIPHYSICS
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Choose the module
Optics
Wave Optics
EMW BEAM ENVELOPES
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Finite element method (FEM)
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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
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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°
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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
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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
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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°
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