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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°