Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link

Jaime A. Anguita; Mark A. Neifeld; Bane V. Vasic

doi:10.1364/AO.47.002414

Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link

Jaime A. Anguita, Mark A. Neifeld, and Bane V. Vasic

Applied Optics
Vol. 47,
Issue 13,
pp. 2414-2429
(2008)
•https://doi.org/10.1364/AO.47.002414

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Jaime A. Anguita, Mark A. Neifeld, and Bane V. Vasic, "Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link," Appl. Opt. 47, 2414-2429 (2008)

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Related Topics
Table of Contents Category
- Fiber Optics and Optical Communications
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Atmospheric propagation (010.1300)
- Laser beam transmission (010.3310)
- Turbulence (010.7060)
- Volume gratings (050.7330)
- Optical vortices (050.4865)
- Multiplexing (060.4230)
- Free-space optical communication (060.2605)

About this Article
History
- Original Manuscript: November 19, 2007
- Revised Manuscript: February 8, 2008
- Manuscript Accepted: February 12, 2008
- Published: April 28, 2008

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Abstract

A multichannel free-space optical (FSO) communication system based on orbital angular momentum (OAM)-carrying beams is studied. We numerically analyze the effects of atmospheric turbulence on the system and find that turbulence induces attenuation and crosstalk among channels. Based on a model in which the constituent channels are binary symmetric and crosstalk is a Gaussian noise source, we find optimal sets of OAM states at each turbulence condition studied and determine the aggregate capacity of the multichannel system at those conditions. OAM-multiplexed FSO systems that operate in the weak turbulence regime are found to offer good performance. We verify that the aggregate capacity decreases as the turbulence increases. A per-channel bit-error rate evaluation is presented to show the uneven effects of crosstalk on the constituent channels.

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	$- 9$	$- 8$	$- 7$	$- 6$	$- 5$	$- 4$	$- 3$	$- 2$	$- 1$	0
0	2.21e-005	4.77e-005	0.000109	0.000269	0.000707	0.00205	0.00659	0.0244	0.106	0.534
1	6.13e-005	0.000123	0.000256	0.000535	0.00118	0.00273	0.00644	0.0162	0.0423	0.105
2	0.000114	0.000207	0.000383	0.000719	0.00135	0.0026	0.00481	0.00917	0.0164	0.0244
3	0.000167	0.000284	0.000472	0.000777	0.00129	0.00205	0.00326	0.00487	0.00661	0.00668
4	0.000213	0.000329	0.000507	0.000759	0.0011	0.00154	0.00208	0.00262	0.00274	0.0021
5	0.000244	0.000349	0.000488	0.000659	0.00087	0.00109	0.0013	0.00133	0.00116	0.000707
6	0.000254	0.00034	0.000438	0.000554	0.000669	0.00075	0.000783	0.000711	0.000543	0.000267
7	0.00025	0.000311	0.000373	0.00045	0.000484	0.000508	0.000465	0.000385	0.000252	0.000111
8	0.000237	0.000271	0.000315	0.000342	0.000353	0.000329	0.000279	0.000205	0.000125	4.77e-005
9	0.000204	0.000228	0.000252	0.000255	0.000245	0.000211	0.000168	0.000114	6.05e-005	2.15e-005
10	0.000176	0.000188	0.00019	0.000182	0.000164	0.000135	9.72e-005	6.25e-005	3.16e-005	1.06e-005
11	0.000144	0.000151	0.000144	0.000129	0.000112	8.7e-005	5.88e-005	3.46e-005	1.66e-005	5.44e-006
12	0.000119	0.000115	0.000107	9.2e-005	7.29e-005	5.47e-005	3.52e-005	2.01e-005	9.06e-006	2.98e-006
13	9.47e-005	8.79e-005	7.75e-005	6.32e-005	4.87e-005	3.42e-005	2.09e-005	1.13e-005	5.16e-006	1.73e-006
14	7.39e-005	6.5e-005	5.53e-005	4.31e-005	3.15e-005	2.12e-005	1.27e-005	6.71e-006	2.9e-006	1.05e-006
15	5.58e-005	4.74e-005	3.92e-005	2.95e-005	2.08e-005	1.35e-005	7.89e-006	3.96e-006	1.8e-006	6.7e-007
16	4.21e-005	3.48e-005	2.76e-005	2.02e-005	1.37e-005	8.46e-006	4.86e-006	2.47e-006	1.09e-006	4.63e-007
17	3.14e-005	2.54e-005	1.87e-005	1.34e-005	8.86e-006	5.32e-006	3e-006	1.56e-006	7.24e-007	3.16e-007
18	2.31e-005	1.79e-005	1.29e-005	8.82e-006	5.82e-006	3.49e-006	1.89e-006	9.83e-007	4.81e-007	2.29e-007
19	1.63e-005	1.22e-005	8.98e-006	6.01e-006	3.74e-006	2.22e-006	1.24e-006	6.67e-007	3.44e-007	1.7e-007
20	1.19e-005	8.75e-006	6.14e-006	4.04e-006	2.51e-006	1.48e-006	8.44e-007	4.6e-007	2.51e-007	1.34e-007
	1	2	3	4	5	6	7	8	9	10
0	0.106	0.0244	0.00659	0.00205	0.000707	0.000269	0.000109	4.77e-005	2.21e-005	1.07e-005
1	0.376	0.133	0.0416	0.0137	0.00477	0.0018	0.000746	0.000313	0.000139	6.44e-005
2	0.133	0.291	0.139	0.0534	0.02	0.00772	0.00311	0.00132	0.000598	0.000283
3	0.0418	0.138	0.243	0.139	0.0617	0.0258	0.0108	0.00462	0.00209	0.000968
4	0.0138	0.0536	0.138	0.211	0.135	0.0666	0.0303	0.0135	0.00611	0.00281
5	0.00473	0.0199	0.0617	0.136	0.187	0.13	0.0707	0.0341	0.016	0.00763
6	0.0018	0.00774	0.0257	0.0664	0.13	0.168	0.128	0.0726	0.037	0.0187
7	0.000734	0.00309	0.0106	0.0298	0.0705	0.126	0.156	0.121	0.0734	0.0402
8	0.000316	0.00134	0.00463	0.0135	0.0343	0.0732	0.12	0.147	0.115	0.0748
9	0.00014	0.000604	0.00211	0.00608	0.0163	0.0382	0.0729	0.117	0.136	0.113
10	6.69e-005	0.000281	0.000955	0.00289	0.00764	0.0182	0.0397	0.0744	0.113	0.131
11	3.22e-005	0.000136	0.000462	0.00136	0.00372	0.00908	0.0209	0.0423	0.0745	0.109
12	1.65e-005	6.92e-005	0.000232	0.000694	0.00183	0.00457	0.0107	0.0226	0.0446	0.0735
13	8.57e-006	3.52e-005	0.000119	0.000347	0.000946	0.0023	0.00543	0.012	0.0246	0.0459
14	4.78e-006	1.84e-005	6.19e-005	0.000183	0.000486	0.00121	0.00283	0.00629	0.0134	0.0262
15	2.78e-006	1.03e-005	3.34e-005	9.87e-005	0.000263	0.000652	0.00152	0.00338	0.00714	0.0144
16	1.67e-006	5.86e-006	1.89e-005	5.31e-005	0.000143	0.000359	0.000828	0.00184	0.0039	0.00804
17	1.07e-006	3.46e-006	1.07e-005	3.09e-005	8.25e-005	0.000201	0.000461	0.00105	0.0022	0.00452
18	6.85e-007	2.09e-006	6.25e-006	1.75e-005	4.62e-005	0.000112	0.000263	0.000571	0.00123	0.00256
19	4.63e-007	1.32e-006	3.71e-006	1.02e-005	2.59e-005	6.38e-005	0.000148	0.000334	0.000697	0.00144
20	3.38e-007	8.63e-007	2.32e-006	6.14e-006	1.57e-005	3.79e-005	8.69e-005	0.000193	0.000406	0.000843
	11	12	13	14	15	16	17	18	19	20
0	5.43e-006	3.04e-006	1.74e-006	1.06e-006	6.65e-007	4.57e-007	3.19e-007	2.27e-007	1.73e-007	1.36e-007
1	3.17e-005	1.63e-005	8.64e-006	4.78e-006	2.76e-006	1.65e-006	1.03e-006	6.72e-007	4.67e-007	3.27e-007
2	0.000136	6.84e-005	3.56e-005	1.88e-005	1.04e-005	5.86e-006	3.44e-006	2.1e-006	1.31e-006	8.71e-007
3	0.000467	0.00023	0.000119	6.27e-005	3.37e-005	1.87e-005	1.06e-005	6.32e-006	3.81e-006	2.3e-006
4	0.00138	0.000682	0.000345	0.000185	9.94e-005	5.47e-005	3.08e-005	1.74e-005	1.01e-005	6.15e-006
5	0.00366	0.00183	0.000922	0.000488	0.000265	0.000144	7.96e-005	4.49e-005	2.6e-005	1.56e-005
6	0.00926	0.00467	0.00234	0.00123	0.000645	0.000355	0.0002	0.000112	6.42e-005	3.78e-005
7	0.0206	0.0107	0.00551	0.00286	0.00154	0.000835	0.000455	0.000256	0.000149	8.74e-005
8	0.0425	0.0232	0.0121	0.00639	0.00343	0.00189	0.00104	0.00058	0.00033	0.000192
9	0.0744	0.0438	0.0247	0.0134	0.00729	0.00396	0.00221	0.00123	0.000704	0.000408
10	0.108	0.0748	0.0457	0.0261	0.0144	0.00799	0.00448	0.00257	0.00146	0.000818
11	0.124	0.103	0.0741	0.0467	0.0276	0.0158	0.00898	0.0051	0.00293	0.00171
12	0.103	0.119	0.102	0.073	0.0484	0.0288	0.017	0.00976	0.00559	0.00331
13	0.0745	0.1	0.115	0.0975	0.0737	0.0486	0.0304	0.018	0.0105	0.00611
14	0.0465	0.0744	0.0998	0.108	0.0969	0.073	0.049	0.0312	0.019	0.0112
15	0.027	0.0476	0.0735	0.0978	0.103	0.0951	0.0728	0.0489	0.0318	0.0196
16	0.016	0.0296	0.0486	0.0727	0.0929	0.101	0.0916	0.0698	0.0496	0.033
17	0.0089	0.017	0.0299	0.0488	0.0721	0.0909	0.0982	0.089	0.0711	0.0498
18	0.00511	0.00957	0.0176	0.0306	0.0492	0.0708	0.0921	0.0961	0.087	0.0693
19	0.00288	0.00559	0.0105	0.0185	0.0319	0.0497	0.0713	0.0881	0.0922	0.0853
20	0.00169	0.00328	0.00621	0.0114	0.0198	0.0332	0.05	0.0695	0.086	0.0879

Axial	Receive OAM State n
displ. %	3	4	5	6	7
5	$7.86 \times 10^{- 6}$	0.00624	0.985	0.00748	$1.65 \times 10^{- 5}$
10	0.000124	0.0244	0.941	0.0291	0.000259
15	0.000612	0.0529	0.871	0.0627	0.00127
20	0.00187	0.0891	0.781	0.105	0.00382
25	0.00435	0.13	0.675	0.151	0.00876

$C_{n}^{2} [m^{- 2 / 3}]$	Optimal OAM State Numbers
$10^{- 15}$	$- 6$	$- 4$	$- 2$	$- 1$	$+ 1$	$+ 2$	$+ 4$	$+ 6$
$10^{- 14}$	$- 10$	$- 6$	$- 3$	$- 1$	$+ 1$	$+ 3$	$+ 6$	$+ 10$
$3 \times 10^{- 14}$	$- 10$	$- 6$	$- 4$	$- 2$	$+ 2$	$+ 4$	$+ 6$	$+ 10$
$10^{- 13}$	$- 4$	$- 3$	$- 2$	$- 1$	$+ 1$	$+ 2$	$+ 3$	$+ 4$

$C_{n}^{2} [m^{- 2 / 3}]$	Optimal OAM State Numbers
$10^{- 15}$	$- 6$	$- 4$	$- 2$	$- 1$	$+ 1$	$+ 2$	$+ 4$	$+ 6$
$10^{- 14}$	$- 16$	$- 9$	$- 5$	$- 2$	$+ 2$	$+ 5$	$+ 9$	$+ 16$
$3 \times 10^{- 14}$	$- 22$	$- 13$	$- 6$	$- 2$	$+ 2$	$+ 6$	$+ 13$	$+ 22$
$10^{- 13}$	$- 10$	$- 7$	$- 5$	$- 4$	$+ 4$	$+ 5$	$+ 7$	$+ 10$

$C_{n}^{2} [m^{- 2 / 3}]$	Optimal OAM State Numbers
$10^{- 15}$	$- 6$	$- 4$	$- 2$	$- 1$	$+ 1$	$+ 2$	$+ 4$	$+ 6$
$10^{- 14}$	$- 20$	$- 11$	$- 6$	$- 2$	$+ 2$	$+ 6$	$+ 11$	$+ 20$
$3 \times 10^{- 14}$	$- 33$	$- 18$	$- 9$	$- 3$	$+ 3$	$+ 9$	$+ 18$	$+ 33$
$10^{- 13}$	$- 31$	$- 18$	$- 10$	$- 4$	$+ 4$	$+ 10$	$+ 18$	$+ 31$

$C_{n}^{2} [m^{- 2 / 3}]$	$P_{Tx} / N_{0}$	Optimal OAM state numbers
$10^{- 15}$	$12 dB$	$- 5$	$- 3$	$- 2$	$- 1$	0	$+ 1$	$+ 2$	$+ 4$
$10^{- 15}$	$18 dB$	$- 6$	$- 4$	$- 2$	$- 1$	0	$+ 1$	$+ 2$	$+ 4$
$10^{- 14}$	$20 dB$	$- 10$	$- 6$	$- 3$	$- 1$	0	$+ 1$	$+ 3$	$+ 6$
$10^{- 14}$	$30 dB$	$- 11$	$- 6$	$- 3$	$- 1$	$+ 1$	$+ 3$	$+ 6$	$+ 11$
$3 \times 10^{- 14}$	$40 dB$	$- 33$	$- 18$	$- 9$	$- 3$	0	$+ 3$	$+ 9$	$+ 18$
$3 \times 10^{- 14}$	$46 dB$	$- 33$	$- 18$	$- 9$	$- 3$	$+ 3$	$+ 9$	$+ 18$	$+ 33$
$10^{- 13}$	$44 dB$	$- 43$	$- 26$	$- 13$	$- 4$	0	$+ 7$	$+ 18$	$+ 35$
$10^{- 13}$	$48 dB$	$- 49$	$- 31$	$- 15$	$- 5$	0	$+ 7$	$+ 18$	$+ 35$

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