Free space optical communication (2)

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This document discusses orbital angular momentum (OAM) modes in Bessel-Gauss beams and how atmospheric turbulence can cause crosstalk between modes. It describes how Bessel-Gauss beams are generated using axicons and modulated with OAM phases. Experiments were conducted using spatial light modulators to generate multiplexed OAM modes and measure the influence of simulated turbulence on power transmission and spreading between modes. Future work is proposed to further study turbulence effects over longer propagation distances and use mode sorting techniques.

Orbital angular momentum modal crosstalk in Bessel-Gauss beams
Hunter Rew
US Naval Research Laboratory NREIP Intern and College of William and Mary, Williamsburg, VA
Mentored by Dr. Abbie T. Watnik
US Naval Research Laboratory, Washington, D.C.

Communicating with Light
● Orbital angular momentum is the information carrier
○ A property of optical vortices
● Bessel-Gauss beams are the medium
○ Potentially helpful properties
● Turbulence is the enemy
○ Mode hopping and crosstalk
2
A. Dudley, M. Lavery, M. Padgett, and A. Forbes,
"Unraveling Bessel Beams," Opt. Photon. News 24(6), 22-
29 (2013).

Orbital Angular Momentum (OAM) and Optical Vortices
●
○ determines mode order (...-1,0,1,2…)
○ is the azimuthal coordinate
● A helical phase creates angular
momentum
● Propagates as annular rings with a
null in the center (vortex)
3
Vortex Phase (L = 1)
Vortex Beam (L = 10)
Vortex Phase (L = 10)

$Bessel-Gauss (BG) Beams ● A true Bessel beam self-heals and never diffracts ○ requires infinite energy ● BG is a realization of the impossible Bessel beam using axicons Credit: Egmason [https://en.wikipedia.org/wiki/Bessel_beam#/media/File:Bessel_beam_reform.svg] 4$

Beam Creation
●
○ determines the slope of the axicon
○ is the radial coordinate
● BG beams are created with
a spiraled axicon phase
map
5
Vortex Phase Axicon Phase Bessel Vortex Phase

$Atmospheric Turbulence ● Turbulence results from patches of varying heat and velocity in the air ● Refractive index of air varies, inducing phase shifts and aberrations in light Credit: Lawrence Livermore National Laboratory [https://tasc.llnl.gov/galleries/image-gallery] 6$

Turbulence Models
● Essentially random numbers
● Strength determined by Fried’s parameter
7
Vortex Phase Turbulence Phase Map Vortex Phase with Turbulence

Spatial Light Modulators (SLMs)
● High resolution displays that control the phase and/or intensity of incident
light
● Our SLMs are binary and phase only
○ Each pixel can be 0 or pi
○ Forth Dimension Displays, 1280 x 1024 resolution
8
Vortex Phase Tilted Plane Wave
Vortex Interfered with a Plane
Wave
Vortex Interfered with a Plane Wave
(Binary)

Mode Multiplexing
11
Vortex Phase (L = 1) Vortex Phase (L = -1) Null

Mode Multiplexing
12
Vortex Phase (L = 10) Vortex Phase (L = -7) Vortex Phase (L = 3)

Analysis
14
● Fraction of power in on-axis pixel
● Normalized to sum to 1

Influence of Turbulence on Transmission
16
Each point is an average of all modes and
data runs
10 runs were performed for each
turbulence strength, each with a unique,
randomly generated, turbulence map
(D/r0)

Influence of Turbulence on Spread of Power
17
(D/r0)

Future Work
● Further investigation of the effects of turbulence
● Larger propagation distance to test the BG beams
● Log-polar transformation for mode sorting
A. Dudley, T. Mhlanga, M. Lavery, A. McDonald, F. Roux, M. Padgett, and A. Forbes, "Efficient sorting of Bessel beams," Opt. Express 21,
165-171 (2013).
18

Summary of Accomplishments
● Built table top setup for multiplexing/demultiplexing modes
○ Designed SLM mounts for fabrication
● Interfaced SLMs and Camera with MATLAB
● Automated data collection and analysis
19

Acknowledgements
● ASEE
● ONR
● NRL
● Tim Doster
● Ryan Lindle
● Abbie Watnik
20

Orbital angular momentum modal crosstalk in
Bessel-Gauss beams
●
●
●
●

This document summarizes the history and applications of orbital angular momentum (OAM) in optical communication. It discusses key discoveries such as the identification of OAM in photons in 1932, the generation of helical beams using cylindrical lenses in 1992, and the first demonstration of free-space optical communication using OAM-multiplexed beams in 2004. More recent work has achieved terabit data transmission rates using OAM multiplexing combined with polarization multiplexing. OAM enables high-capacity communication by using the unlimited angular momentum states of each photon to encode information.

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Free space optical communication (2)

1. Orbital angular momentum modal crosstalk in Bessel-Gauss beams Hunter Rew US Naval Research Laboratory NREIP Intern and College of William and Mary, Williamsburg, VA Mentored by Dr. Abbie T. Watnik US Naval Research Laboratory, Washington, D.C.

2. Communicating with Light ● Orbital angular momentum is the information carrier ○ A property of optical vortices ● Bessel-Gauss beams are the medium ○ Potentially helpful properties ● Turbulence is the enemy ○ Mode hopping and crosstalk 2 A. Dudley, M. Lavery, M. Padgett, and A. Forbes, "Unraveling Bessel Beams," Opt. Photon. News 24(6), 22- 29 (2013).

3. Orbital Angular Momentum (OAM) and Optical Vortices ● ○ determines mode order (...-1,0,1,2…) ○ is the azimuthal coordinate ● A helical phase creates angular momentum ● Propagates as annular rings with a null in the center (vortex) 3 Vortex Phase (L = 1) Vortex Beam (L = 10) Vortex Phase (L = 10)

4. Bessel-Gauss (BG) Beams ● A true Bessel beam self-heals and never diffracts ○ requires infinite energy ● BG is a realization of the impossible Bessel beam using axicons Credit: Egmason [https://en.wikipedia.org/wiki/Bessel_beam#/media/File:Bessel_beam_reform.svg] 4

5. Beam Creation ● ○ determines the slope of the axicon ○ is the radial coordinate ● BG beams are created with a spiraled axicon phase map 5 Vortex Phase Axicon Phase Bessel Vortex Phase

6. Atmospheric Turbulence ● Turbulence results from patches of varying heat and velocity in the air ● Refractive index of air varies, inducing phase shifts and aberrations in light Credit: Lawrence Livermore National Laboratory [https://tasc.llnl.gov/galleries/image-gallery] 6

7. Turbulence Models ● Essentially random numbers ● Strength determined by Fried’s parameter 7 Vortex Phase Turbulence Phase Map Vortex Phase with Turbulence

8. Spatial Light Modulators (SLMs) ● High resolution displays that control the phase and/or intensity of incident light ● Our SLMs are binary and phase only ○ Each pixel can be 0 or pi ○ Forth Dimension Displays, 1280 x 1024 resolution 8 Vortex Phase Tilted Plane Wave Vortex Interfered with a Plane Wave Vortex Interfered with a Plane Wave (Binary)

9. Experimental Setup 9 M1 M2 M3

10. Alignment 10

11. Mode Multiplexing 11 Vortex Phase (L = 1) Vortex Phase (L = -1) Null

12. Mode Multiplexing 12 Vortex Phase (L = 10) Vortex Phase (L = -7) Vortex Phase (L = 3)

13. Data 13

14. Analysis 14 ● Fraction of power in on-axis pixel ● Normalized to sum to 1

15. Analysis with Turbulence 15

16. Influence of Turbulence on Transmission 16 Each point is an average of all modes and data runs 10 runs were performed for each turbulence strength, each with a unique, randomly generated, turbulence map (D/r0)

17. Influence of Turbulence on Spread of Power 17 (D/r0)

18. Future Work ● Further investigation of the effects of turbulence ● Larger propagation distance to test the BG beams ● Log-polar transformation for mode sorting A. Dudley, T. Mhlanga, M. Lavery, A. McDonald, F. Roux, M. Padgett, and A. Forbes, "Efficient sorting of Bessel beams," Opt. Express 21, 165-171 (2013). 18

19. Summary of Accomplishments ● Built table top setup for multiplexing/demultiplexing modes ○ Designed SLM mounts for fabrication ● Interfaced SLMs and Camera with MATLAB ● Automated data collection and analysis 19

20. Acknowledgements ● ASEE ● ONR ● NRL ● Tim Doster ● Ryan Lindle ● Abbie Watnik 20

21. Orbital angular momentum modal crosstalk in Bessel-Gauss beams ● ● ● ●

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