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Keywords = nonuniformly correlated beams

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11 pages, 3420 KiB  
Communication
Performance of Orbital Angular Momentum Communication for a Non-Uniformly Correlated High-Order Bessel–Gaussian Beam in a Turbulent Atmosphere
by Zihan Cong, Hui Zhang, Yaru Gao, Yangjian Cai and Yangsheng Yuan
Photonics 2024, 11(2), 131; https://doi.org/10.3390/photonics11020131 - 30 Jan 2024
Cited by 1 | Viewed by 1324
Abstract
We derived the formula for the detection probability, signal-to-noise ratio (SNR), and average bit error rate (BER) for the signal orbital angular momentum (OAM) state carried via non-uniformly correlated high-order Bessel–Gaussian beam propagation in a turbulent atmosphere. The wavelength, receiver aperture, beam width, [...] Read more.
We derived the formula for the detection probability, signal-to-noise ratio (SNR), and average bit error rate (BER) for the signal orbital angular momentum (OAM) state carried via non-uniformly correlated high-order Bessel–Gaussian beam propagation in a turbulent atmosphere. The wavelength, receiver aperture, beam width, strength of the turbulent atmosphere, and topological charge effect on detection probability, SNR, and average BER of the signal OAM state were demonstrated numerically. The results show that the signal OAM state with low topological charge, a small receiver aperture, a narrow beam width, and a long wavelength can improve the performance of optical communications systems under conditions of weak atmospheric turbulence. Our results will be useful in long-distance free space optical (FSO) communications. Full article
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Figure 1

Figure 1
<p>Detection probability of the OAM mode for non-uniformly correlated high-order Bessel–Gaussian beams in a turbulent atmosphere with different (<b>a</b>) topological charge differences |Δ<span class="html-italic">l</span>| and (<b>b</b>) propagation distances <span class="html-italic">z</span>.</p> Full article ">Figure 2
<p>Detection probability of the signal OAM state for the non-uniformly correlated high-order Bessel–Gaussian beams at the different receiving aperture diameters (D).</p> Full article ">Figure 3
<p>Detection probability of the different signal OAM states carried by the non-uniformly correlated high-order Bessel–Gaussian beams in a turbulent atmosphere.</p> Full article ">Figure 4
<p>Detection probability of the signal OAM state carried by the non-uniformly correlated high-order Bessel–Gaussian beams in a turbulent atmosphere for the different wavelengths studied.</p> Full article ">Figure 5
<p>Detection probability of the signal OAM state carried by the non-uniformly correlated high-order Bessel–Gaussian beams in the turbulent atmosphere for the different beam widths analyzed.</p> Full article ">Figure 6
<p>SNR of the different signal OAM states carried by the non-uniformly correlated high-order Bessel–Gaussian beams in a turbulent atmosphere against the beam width.</p> Full article ">Figure 7
<p>Average BER of the different signal OAM states carried by the non-uniformly correlated high-order Bessel–Gaussian beams in the turbulent atmosphere against the beam width.</p> Full article ">Figure 8
<p>(<b>a</b>) SNR and (<b>b</b>) average BER of the signal OAM state carried by the non-uniformly correlated high-order Bessel–Gaussian beams with different beam widths against the strength of the turbulent atmosphere.</p> Full article ">
10 pages, 2854 KiB  
Communication
Second-Order Statistics of Partially Coherent Beams with Laguerre Non-Uniform Coherence Properties under Turbulence
by Yang Zhao, Zhiwen Yan, Yibo Wang, Liming Liu, Xinlei Zhu, Bohan Guo and Jiayi Yu
Photonics 2023, 10(7), 837; https://doi.org/10.3390/photonics10070837 - 20 Jul 2023
Cited by 1 | Viewed by 1319
Abstract
We use the extended Huygens–Fresnel integral to analyze the propagation properties of a class of partially coherent beams with Laguerre non-uniform coherence properties (called Laguerre non-uniformly correlated beams) in free space and in a turbulent atmosphere. We focus on how different initial beam [...] Read more.
We use the extended Huygens–Fresnel integral to analyze the propagation properties of a class of partially coherent beams with Laguerre non-uniform coherence properties (called Laguerre non-uniformly correlated beams) in free space and in a turbulent atmosphere. We focus on how different initial beam orders and coherence lengths affect the propagation behavior of the beams, such as the evolution of intensity, degree of coherence, propagation factor, and beam wander. Our results show that non-uniform coherence properties play a role in resisting the degrading effects of turbulence. Furthermore, adjusting the initial beam parameter of the non-uniform coherence structure, i.e., increasing the beam order and decreasing the coherence, can further improve the turbulence resistance of the beams. Our results have potential applications in free-space optical communications. Full article
(This article belongs to the Special Issue Free-Space Optical Communication: Physics and Applications)
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Figure 1

Figure 1
<p>Distribution of the DOC of LNUC sources (<b>a</b>) in the <span class="html-italic">x</span><sub>1</sub>–<span class="html-italic">x</span><sub>2</sub> plane with <span class="html-italic">y</span><sub>1</sub> = <span class="html-italic">y</span><sub>2</sub> = 0; (<b>b</b>) in the <span class="html-italic">x</span><sub>1</sub>–<span class="html-italic">y</span><sub>1</sub> plane with <span class="html-italic">x</span><sub>2</sub> = <span class="html-italic">y</span><sub>2</sub> = 0.</p> Full article ">Figure 2
<p>Normalized (<b>a</b>) intensity distribution and (<b>b</b>,<b>c</b>) intensity on-axis of the LNUC beams propagating in free space for (<b>b</b>) different beam orders and (<b>c</b>) coherence lengths.</p> Full article ">Figure 3
<p>(<b>a</b>) Distribution of the DOC upon propagation in free space and the corresponding cross-line (<span class="html-italic">ρ</span><sub>2x</sub> = 0) with z = 1000 m for (<b>b</b>) different beam orders and (<b>c</b>) coherence lengths.</p> Full article ">Figure 4
<p>Normalized (<b>a</b>) intensity distribution and (<b>b</b>,<b>c</b>) intensity on-axis of the LNUC beams propagating in turbulence for (<b>b</b>) different beam orders and (<b>c</b>) coherence lengths.</p> Full article ">Figure 5
<p>(<b>a</b>) Distribution of the DOC upon propagation in turbulence and the corresponding cross-line (<span class="html-italic">ρ<sub>2</sub><sub>x</sub></span> = 0) with <span class="html-italic">z</span> = 1000 m for (<b>b</b>) different beam orders and (<b>c</b>) coherence lengths.</p> Full article ">Figure 6
<p>Normalized propagation factor in turbulence for (<b>a</b>) different beam orders and (<b>b</b>) coherence lengths.</p> Full article ">Figure 7
<p>Beam wander in turbulence for (<b>a</b>) different beam orders and (<b>b</b>) coherence lengths.</p> Full article ">
11 pages, 7082 KiB  
Article
Propagation of a Lorentz Non-Uniformly Correlated Beam in a Turbulent Ocean
by Dongmei Wei, Ke Wang, Ying Xu, Qian Du, Fangning Liu, Juan Liu, Yiming Dong, Liying Zhang, Jiayi Yu, Yangjian Cai and Xinlei Zhu
Photonics 2023, 10(1), 49; https://doi.org/10.3390/photonics10010049 - 3 Jan 2023
Cited by 6 | Viewed by 1938
Abstract
We study the propagation characteristics (spectral intensity and degree of coherence) of a new type of Lorentz non-uniformly correlated (LNUC) beam based on the extended Huygens–Fresnel principle and the spatial power spectrum of oceanic turbulence. The effects of the oceanic turbulence parameters and [...] Read more.
We study the propagation characteristics (spectral intensity and degree of coherence) of a new type of Lorentz non-uniformly correlated (LNUC) beam based on the extended Huygens–Fresnel principle and the spatial power spectrum of oceanic turbulence. The effects of the oceanic turbulence parameters and initial beam parameters on the evolution propagation characteristics of LNUC beams are studied in detail by numerical simulation. The results indicate that such beams exhibit self-focusing propagation features in both free space and oceanic turbulence. Decreasing the dissipation rate of kinetic energy per unit mass of fluid and the Kolmogorov inner scale, or increasing the relative strength of temperature to salinity undulations and the dissipation rate of mean-square temperature of the turbulent ocean tends to increase the negative effects on the beams. Furthermore, we propose a strategy of increasing the beam width and decreasing the coherence length, to reduce the negative effects of the turbulence. Full article
(This article belongs to the Special Issue Coherent and Polarization Optics)
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Figure 1

Figure 1
<p>Density plot of the absolute value of the spectral DOC of a LNUC beam (<b>a</b>) in the <span class="html-italic">x</span><sub>1</sub> − <span class="html-italic">x</span><sub>2</sub> plane with <span class="html-italic">y</span><sub>1</sub> = <span class="html-italic">y</span><sub>2</sub> = 0, (<b>b</b>) in the <span class="html-italic">x</span><sub>1</sub> − <span class="html-italic">y</span><sub>1</sub> plane with <span class="html-italic">x</span><sub>2</sub> = <span class="html-italic">y</span><sub>2</sub> = 0.</p> Full article ">Figure 2
<p>Evolution of the normalized spectral intensity on propagation in free space, (<b>a</b>) in <b>ρ</b><span class="html-italic"><sub>x</sub></span> − <b>ρ</b><span class="html-italic"><sub>y</sub></span> cross-section; (<b>b</b>) at <b>ρ</b><span class="html-italic"><sub>x</sub></span> − <span class="html-italic">z</span> cross-section; (<b>c</b>) on-axis.</p> Full article ">Figure 3
<p>Evolution of the normalized spectral DOC on propagation in free space.</p> Full article ">Figure 4
<p>Evolution of the (<b>a</b>) normalized spectral intensity and (<b>b</b>) spectral DOC on propagation in oceanic turbulence.</p> Full article ">Figure 5
<p>Density plot of (<b>a</b>) the normalized spectral intensity and (<b>b</b>) the absolute value of the spectral DOC of a LNUC beam in oceanic turbulence with different values of the dissipation rate of kinetic energy per unit mass of fluid at propagation distance <span class="html-italic">z</span> = 150 m.</p> Full article ">Figure 6
<p>(<b>a</b>) Normalized on-axis intensity of LNUC beams propagating in oceanic turbulence and (<b>b</b>) the cross-line (<b>ρ</b><sub>2<span class="html-italic">x</span></sub> = 0) of the absolute value of the spectral DOC at <span class="html-italic">z</span> = 150 m for different rates of dissipation of kinetic energy per unit mass of fluid.</p> Full article ">Figure 7
<p>Normalized on-axis intensity of the LNUC beam propagating in oceanic turbulence and the cross-line (<b>ρ</b><sub>2<span class="html-italic">x</span></sub> = 0) of the absolute value of the spectral DOC at <span class="html-italic">z</span> = 150 m for different oceanic turbulence parameters: (<b>a</b>) the Kolmogorov inner scale; (<b>b</b>) the relative strength of temperature to salinity undulations; (<b>c</b>) the dissipation rate of mean-square temperature.</p> Full article ">Figure 8
<p>Normalized on-axis intensity of LNUC beams propagating in oceanic turbulence for different (<b>a</b>) beam widths and (<b>b</b>) coherence lengths.</p> Full article ">Figure 9
<p>The cross-line (<b>ρ</b><sub>2<span class="html-italic">x</span></sub> = 0) of the absolute value of the spectral DOC of LNUC beams at <span class="html-italic">z</span> = 150 m for different (<b>a</b>) beam widths and (<b>b</b>) coherence lengths.</p> Full article ">
14 pages, 3561 KiB  
Article
Effects of Anisotropic Turbulence on Propagation Characteristics of Partially Coherent Beams with Spatially Varying Coherence
by Wentao Dao, Chunhao Liang, Fei Wang, Yangjian Cai and Bernhard J. Hoenders
Appl. Sci. 2018, 8(11), 2025; https://doi.org/10.3390/app8112025 - 23 Oct 2018
Cited by 7 | Viewed by 3069
Abstract
Based on the extended Huygens-Fresnel (eHF) principle, approximate analytical expressions for the spectral density of nonuniformly correlated (NUC) beams are derived with the help of discrete model decompositions. The beams are propagating along horizontal paths through an anisotropic turbulent medium. Based on the [...] Read more.
Based on the extended Huygens-Fresnel (eHF) principle, approximate analytical expressions for the spectral density of nonuniformly correlated (NUC) beams are derived with the help of discrete model decompositions. The beams are propagating along horizontal paths through an anisotropic turbulent medium. Based on the derived formula, the influence of the anisotropic turbulence (anisotropy factors, structure parameters) on the evolution of the average intensity, the shift of the intensity maxima and the power-in-the-bucket (PIB) are investigated in detail through numerical examples. It is found that the lateral shifting of the intensity maxima is closely related to the anisotropy factors and the strength of turbulence. Our results also reveal that, in the case of weak turbulence, the beam profile can retain the feature of local intensity sharpness, but this feature degenerates quickly if the strength of the turbulence increases. The value of PIB of the NUC beams can be even higher than that of Gaussian beams by appropriately controlling the coherence parameter in the weak turbulence regime. This feature makes the NUC beams useful for free-space communication. Full article
(This article belongs to the Special Issue Recent Advances in Statistical Optics and Plasmonics)
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Figure 1

Figure 1
<p>Variation of spectral density <math display="inline"><semantics> <mrow> <msub> <mi>S</mi> <mi>x</mi> </msub> <mo stretchy="false">(</mo> <mi>ξ</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> with <math display="inline"><semantics> <mi>ξ</mi> </semantics></math> at three different propagation distances in free space (<b>a</b>–<b>c</b>) and in the presence of turbulence (<b>d</b>–<b>f</b>). The solid lines are calculated from the approximate analytical formula shown in Equation (17). The circular dots are the numerical integration directly from Equation (15). It shows that irrespective of propagation in free space or in turbulence, the spectral density obtained from the approximate analytical formula Equation (17) is consistent with that obtained from direct numerical integration.</p> Full article ">Figure 2
<p>Density plots of the spectral density of the NUC beam with <span class="html-italic">x</span><sub>0</sub> = <span class="html-italic">y</span><sub>0</sub> = 0 propagation through free space and in the presence of anisotropic turbulence at several different propagation distances.</p> Full article ">Figure 3
<p>Density plots of spectral density of the NUC beam with <span class="html-italic">x</span><sub>0</sub> = <span class="html-italic">y</span><sub>0</sub> = 0.7<span class="html-italic">ω</span><sub>0</sub> in free space and in anisotropic turbulence at different propagation distances.</p> Full article ">Figure 4
<p>Evolution of intensity maxima of the NUC beams (<span class="html-italic">x</span><sub>0</sub> = <span class="html-italic">y</span><sub>0</sub> = 0) as a function of propagation distance in the presence of anisotropic turbulence with different strengths of the turbulences, (<b>a</b>)<math display="inline"><semantics> <mrow> <mtext> </mtext> <msubsup> <mi>C</mi> <mi>n</mi> <mn>2</mn> </msubsup> </mrow> </semantics></math> = 0, (<b>b</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>C</mi> <mi>n</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>17</mn> </mrow> </msup> <msup> <mi>m</mi> <mrow> <mo>−</mo> <mn>2</mn> <mo>/</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>C</mi> <mi>n</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>16</mn> </mrow> </msup> <msup> <mi>m</mi> <mrow> <mo>−</mo> <mn>2</mn> <mo>/</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>d</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>C</mi> <mi>n</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>15</mn> </mrow> </msup> <msup> <mi>m</mi> <mrow> <mo>−</mo> <mn>2</mn> <mo>/</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math>. The anisotropic factors in (b–d) are <span class="html-italic">μ<sub>x</sub></span> = 2, <span class="html-italic">μ<sub>y</sub></span> = 1.</p> Full article ">Figure 5
<p>Variation of the intensity maxima of the NUC beams (<span class="html-italic">x</span><sub>0</sub> = <span class="html-italic">y</span><sub>0</sub> = 0) with the propagation distance in free space in (<b>a</b>) and in anisotropic turbulence with different anisotropic factors in (<b>b</b>–<b>d</b>).</p> Full article ">Figure 6
<p>3D-plots (black lines) of the evolution of the position of the intensity maxima during propagation in free space and in the presence of atmospheric turbulence. Red, green, and blue lines are the projections in the <span class="html-italic">ξ</span>-<span class="html-italic">η, ξ</span>-<span class="html-italic">z</span> and <span class="html-italic">η</span>-<span class="html-italic">z</span> planes, respectively. (<b>a</b>) free space; (<b>b</b>) <span class="html-italic">μ<sub>x</sub></span> = 1, <span class="html-italic">μ<sub>y</sub></span> = 1; (<b>c</b>) <span class="html-italic">μ<sub>x</sub></span> = 2, <span class="html-italic">μ<sub>y</sub></span> = 1; (<b>d</b>) <span class="html-italic">μ<sub>x</sub></span> = 3, <span class="html-italic">μ<sub>y</sub></span> = 1. The parameters <span class="html-italic">x</span><sub>0</sub> and <span class="html-italic">y</span><sub>0</sub>, used in the calculation, are <span class="html-italic">x</span><sub>0</sub> = <span class="html-italic">y</span><sub>0</sub> = 0.7<span class="html-italic">ω</span><sub>0</sub>.</p> Full article ">Figure 7
<p>(<b>a</b>–<b>c</b>) Variation of the <span class="html-italic">PIB</span> of the NUC beam as a function of the propagation distance, (<b>a</b>) in free space; (<b>b</b>) in the presence of isotropic turbulence; (<b>c</b>) in the presence of anisotropic turbulence; (<b>d</b>) Variation of the parameter <span class="html-italic">P</span> against the propagation distance.</p> Full article ">Figure 8
<p>Dependence of the parameter P on (<b>a</b>) the width of a receiver aperture, (<b>b</b>) the anisotropic factor <span class="html-italic">μ<sub>x</sub></span> with <span class="html-italic">μ<sub>y</sub></span> = 1, <span class="html-italic">D</span> = 0.02 m, (<b>c</b>) the strength of turbulence with <span class="html-italic">D</span> = 0.02 m.</p> Full article ">
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