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Structured Light in Turbulence

Mitchell A. Cox, Nokwazi Mphuthi, Isaac Nape, Nikiwe P. Mashaba, Ling Cheng, Andrew Forbes

arXiv:2005.14586v1physics.opticseess.SP

TL;DR

Structured light could add spatial channels to optical communication, but turbulence distorts modes and produces crosstalk. This review surveys concepts, tools, and current findings, including experiments on mode robustness and correction. Its examples report lower scintillation for partially coherent than coherent vector modes and improved scalar-mode fidelity after correction.

  • Problem

    Turbulence distorts spatial modes and causes modal crosstalk, limiting structured-light free-space optical communication.

    Source: E. The memory of turbulence · p. 12, §V · p. 14

  • Method

    The article reviews core concepts and tools, surveys the field, and adds experimental studies and perspectives on structured light in turbulence.

    Source: §I · p. 1, §VI · p. 15

  • Results

    Partially coherent vector modes have been suggested to outperform fully coherent vector modes through lower scintillation, while scalar-mode fidelity improved from 0.74 before correction to 0.98 after correction.

    Source: B. The robustness of structured light · p. 10, C. Correction schemes · p. 11

  • Takeaways & Limitations

    Taking laboratory demonstrations into real-world settings is a necessary step toward increasing link distance and information capacity.

    Source: §VI · p. 15

    The paper identifies transition from laboratory demonstrations to real-world links as an outstanding challenge.

    Source: §VI · p. 15

Abstract

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Optical communication is an integral part of the modern economy, having all but replaced electronic communication systems. Future growth in bandwidth appears to be on the horizon using structured light, encoding information into the spatial modes of light, and transmitting them down fibre and free-space, the latter crucial for addressing last mile and digitally disconnected communities. Unfortunately, patterns of light are easily distorted, and in the case of free-space optical communication, turbulence is a significant barrier. Here we review recent progress in structured light in turbulence, first with a tutorial style summary of the core concepts, before highlighting the present state-of-the-art in the field. We support our review with new experimental studies that reveal which types of structured light are best in turbulence, the behaviour of vector versus scalar light in turbulence, the trade-off of diversity and multiplexing, and how turbulence models can be exploited for enhanced optical signal processing protocols. This comprehensive treatise will be invaluable to the large communities interested in free-space optical communication with spatial modes of light.

I. INTRODUCTION

Structured light uses spatial modes to address fibre-capacity limits and free-space connectivity, but atmospheric turbulence distorts those modes. The article reviews the field’s concepts and toolkit, then surveys current results and open questions.

I. INTRODUCTION

  • Spatial-mode multiplexing offers another degree of freedom for fibre capacity and free-space links, but turbulence-induced modal crosstalk remains an open mitigation challenge.The introduction identifies last-mile connectivity as one reason free-space optical communication is of interest.Source: §I · p. 1
  • The review introduces core concepts and experimental and simulation tools, then surveys current results, open questions, and effects on optical signal processing.It is intended as a tutorial-style resource for new and experienced researchers.Source: §I · p. 1

A. Scalar Modes

  • Scalar modes have spatially homogeneous polarization and include cylindrical-coordinate LG and BG families, Cartesian HG modes, and elliptical-coordinate Ince-Gaussian modes.The cited passage describes LG, HG, and Ince-Gaussian solutions; BG modes are another cylindrical-coordinate Helmholtz solution.Source: A. Scalar Modes · p. 2
  • LG, HG, and BG solutions reduce to the fundamental Gaussian beam at their stated zero-order or zero-parameter conditions.The conditions are ℓ = p = 0 for LG, m = n = 0 for HG, and β = 0 for BG.Source: A. Scalar Modes · p. 2
  • Figure 1 presents intensity patterns with inset phase for LG, HG, BG, and Ince-Gaussian modes, alongside vector-vortex polarization directions.The rows are ordered LG, HG, BG, Ince-Gaussian, then vector vortex.Source: Figure 1 · p. 2

B. Vector Modes

Vector modes combine spatial field components with polarization states, producing spatially varying polarization. Cylindrical vector modes provide a four-dimensional basis and are relevant to high-dimensional communication.

B. Vector Modes

  • A paraxial vector field combines right- and left-circular polarization components with spatial functions that solve the scalar Helmholtz equation.The complex coefficients weight the components; such fields can have spatially inhomogeneous polarization.Source: B. Vector Modes · p. 3
  • Cylindrical vector modes use opposite-OAM spatial components whose relative amplitudes and phases generate states on a higher-order Poincare sphere.The described four-dimensional basis includes radial, azimuthal, and hybrid polarization modes.Source: B. Vector Modes · p. 3
  • Vector modes can be generated with few-mode fibres, controllable resonators, diffractive elements, liquid-crystal spin-orbit devices, metasurfaces, or digital holograms.Deterministic detection methods have also been proposed, alongside detection by reciprocity using the generation methods.Source: B. Vector Modes · p. 3

III. THE ATMOSPHERE AND OPTICAL TURBULENCE

Atmospheric turbulence randomly aberrates propagating beams, affecting intensity, pointing, and spatial modes. The section reviews turbulence models and metrics while noting that structured-mode propagation is not captured by a single generally accurate model.

III. THE ATMOSPHERE AND OPTICAL TURBULENCE

  • Random temperature variations and convection create refractive-index fluctuations that aberrate beam wavefronts; large cells drive beam wander while small-scale effects distort phase and intensity.Beam wander can cause deep fading if the beam misses the receiver aperture or detector.Source: A. Introductory Theory · p. 3
  • Kolmogorov turbulence simplifies modeling by assuming zero inner scale and infinite outer scale, while phase spectra can generate statistically appropriate turbulence screens.More complex spectra include Hill, Tatarskii, and von Karman models.Source: A. Introductory Theory · pp. 3–4
  • The Fried parameter r0 marks an atmospheric coherence radius: beams separated by at least r0 experience independent fading, offering channel diversity.The Greenwood frequency measures the rate at which turbulence affects a beam; Strehl ratio and scintillation index also characterize effects.Source: A. Introductory Theory · p. 4
  • Turbulence causes mode-dependent loss and intermodal crosstalk, and higher-order modes lack a single propagation model because Gaussian-beam models are typically inaccurate for them.The precise interaction and modeling of structured light in turbulence are not yet fully understood.Source: A. Introductory Theory · p. 4
  • Research gaps include mapping Johnson-SB fading parameters to standard turbulence variables and measuring real-atmosphere fading distributions for HG, IG, and nonzero-radial-index LG modes.The cited OAM fading fit is reported in.Source: A. Introductory Theory · p. 4
  • Beam wander is modeled statistically using long-term radial variance and short-term beam size; models also describe angle-of-arrival fluctuations and their relation to modal crosstalk.The short- and long-term beam sizes are related, and beam wander may help understand or predict mode-dependent loss and crosstalk.Source: A. Introductory Theory · p. 5

B. Simulating turbulence in the laboratory

The section presents phase-screen simulation and hologram methods for laboratory turbulence experiments, then describes calibration against theoretical Strehl ratios. It also contrasts device speed and efficiency constraints.

B. Simulating turbulence in the laboratory

  • Naive inverse-spectrum screens miss low-order spectral components and fail theoretical structure-function statistics; sub-harmonic additions address this.The passage illustrates the naive screens in Fig. 3(a) and the added low-order components in Fig. 3(b).Source: B. Simulating turbulence in the… · p. 5, Figure 3 · p. 6
  • The Noll method builds phase screens from Zernike polynomials, which are orthogonal over a unit circle; up to 60 screens may be needed for physical accuracy.The Noll convention maps polynomial indices to mode indices.Source: B. Simulating turbulence in the… · p. 5, Figure 3 · p. 6
  • SLMs modulate at tens of hertz, typically below the Greenwood frequency, while DMDs operate at kilohertz but send less than 10% of input power into the first diffraction order.Some SLMs allow phase modulation up to 8π; DMD holograms use amplitude-only encoding.Source: B. Simulating turbulence in the… · p. 6
  • For DMD turbulence holograms, the phase function maps desired fluctuations into a binary image, with amplitude set to unity when only phase variations are considered.The paper also describes structured blazed gratings for phase-only devices.Source: B. Simulating turbulence in the… · p. 6
  • Measured Strehl ratios from sub-harmonic spectrum inversion and Noll screens closely match theory.Calibration varies D/r0 and compares measured on-axis intensity ratios with theory.Source: Figure 5 · p. 7, B. Simulating turbulence in the… · p. 7
  • Laboratory calibration compares measured and theoretical Strehl ratios across aperture sizes D/r0 to set screens for a specified coherence length r0.The setup records on-axis intensity for each beam image.Source: B. Simulating turbulence in the… · p. 7

C. Real-world turbulence

This section moves from simulated screens to a 150 m free-space link, using sonic-anemometer measurements and modal decomposition to examine atmospheric conditions and structured-light propagation. It reports daily turbulence variation, time-evolving OAM crosstalk, and a comparison of Bessel and helical Gaussian modes.

C. Real-world turbulence

  • Scintillation-based inference of C^2_n is valid only in weak turbulence; wind speed, temperature, and pressure offer an alternative for other regimes.The method uses receiver measurements of the scintillation index.Source: C. Real-world turbulence · p. 7
  • A sonic anemometer measures three-axis wind and sonic temperature, from which the refractive-index structure function is inferred at three-minute intervals over 24 hours.Measurements are transformed using the Gladstone-Dale law.Source: C. Real-world turbulence · p. 7
  • The 24-hour measurements indicate moderate turbulence, with scintillation lowest in the morning, highest around noon, and decreasing after sunset.The inferred refractive-index structure constant is approximately 10^-14–10^-13 m^-2/3.Source: C. Real-world turbulence · p. 7
  • A 150 m horizontal link at 635 nm uses a retro-reflector, telescopes, a high-speed camera, and an SLM for modal decomposition.The link was about 5 m above ground; its beam offset and deviation exceeded the typical coherence length, so reciprocity did not negate beam wander.Source: C. Real-world turbulence · p. 7, Figure 6 · p. 8
  • On the 150 m link, ℓ=1 OAM crosstalk measured at 300 frames per second appears to flow over time with memory.The authors propose correlated angle-of-arrival fluctuations as a way to describe this behavior.Source: C. Real-world turbulence · p. 8, Figure 6 · p. 8
  • The same link demonstrated shape-invariant Bessel modes for free-space communication and compared their crosstalk with helical Gaussian modes of matching OAM values.Longitudinally dependent cone angles preserve the Bessel structure during propagation, unlike traditional Bessel modes outside their specified depth of focus.Source: C. Real-world turbulence · p. 8

IV. PERSPECTIVES

The perspectives section frames open questions about structured light in turbulence, including mode robustness and the amount of information spatial modes can carry. It also asks whether polarization, turbulence itself, and quantum approaches can contribute to free-space links.

IV. PERSPECTIVES

  • The section asks which families of structured light are more robust in turbulence and how much information spatial modes can carry in high-bandwidth FSO links.These are posed as open questions about the field’s state of the art.Source: §IV · p. 8
  • It asks whether polarization as a turbulence-invariant degree of freedom offers a gain, and whether turbulence can be beneficial.Source: §IV · p. 8
  • It asks how far classical approaches to structured light in turbulence can translate to quantum FSO links.The stated aim is to consider fast and secure links.Source: §IV · p. 8

A. Multiplexing versus diversity

Spatial modes can carry either additional information through multiplexing or robustness through diversity. Modal diversity can reduce aperture requirements, while multiplexing’s maximum capacity is not necessarily the most practical FSO objective.

A. Multiplexing versus diversity

  • The fastest reported MDM demonstration sustained 1.036 Pbps, while the farthest MDM FSO demonstration in turbulence reached 80 Gbps over 260 m.The 1.036 Pbps result combined 26 OAM modes with wavelength and polarisation.Source: A. Multiplexing versus diversity · p. 8
  • Modal diversity can provide diversity gain with fewer apertures, including when modes of the same order come from different bases.That same-order, different-basis result was unexpected under conventional turbulence theory and supports basis-dependent turbulence effects.Source: A. Multiplexing versus diversity · pp. 8–9
  • Multiplexing uses modes to increase information content, whereas diversity uses modes that respond differently to turbulence to reduce errors.For structured light, the separation is between orthogonal spatial modes rather than distinct paths.Source: A. Multiplexing versus diversity · p. 9, Figure 7 · p. 9
  • Using same-order orthogonal modes can limit aperture size and system cost, while resilience and range may be more immediately useful in FSO than ultra-high capacity.The review notes that wavelength and polarisation also contribute to FSO communication, so ultra-high MDM capacity may not be necessary in the near future.Source: A. Multiplexing versus diversity · p. 9

B. The robustness of structured light

Turbulence distorts spatial modes and induces crosstalk, but the degree of impact depends on mode family, beam conditions, and measurement. The reviewed evidence identifies resilience advantages for some modes while also showing trade-offs and cases where vector beams do not outperform scalar beams.

B. The robustness of structured light

  • In MDM, turbulence distorts modes and induces crosstalk, making them no longer orthogonal and threatening a core requirement of the scheme.The section frames preservation of orthogonality as the question in seeking a less affected structured-light family.Source: B. The robustness of structured light · p. 9
  • HG modes are more resilient than LG modes under stronger turbulence, with low-order HG symmetry helping resist lateral displacement.The cited comparison excludes the symmetrical HG11 case; the figure reports lower HG crosstalk at strong turbulence.Source: B. The robustness of structured light · p. 9, Figure 8 · p. 10
  • In aligned systems with restricted apertures, HG channel capacity can be lower than LG capacity, while Ince-Gauss superiority remains unverified experimentally.The HG/LG capacity comparison reflects circular optics favoring LG symmetry and does not account for LG modes’ zero on-axis intensity and alignment dependence.Source: B. The robustness of structured light · p. 9
  • Bessel-Gauss modes can outperform LG modes in channel efficiency and bit error rates under high turbulence, but Bessel self-healing offers no advantage when phase is disturbed.The section also reports lower Bessel-beam losses than Gaussian beams over 150 m in weak turbulence.Source: B. The robustness of structured light · p. 9, Figure 8 · p. 10
  • Studies report vector-beam resilience, including preserved spatial-polarisation information and lower scintillation for partially coherent modes.Partial coherence with polarisation modulation is also reported to reduce spreading and beam wander, and C-point singularities are suggested to be more robust than V-point singularities.Source: B. The robustness of structured light · p. 10
  • Vector-mode resilience depends on the measurement: scintillation and mutual-information measures can conflict with modal-overlap and fidelity results.The illustrated vector modes are arranged by increasing turbulence strength; after ignoring tip and tilt, some retain their central polarisation singularity.Source: B. The robustness of structured light · p. 10, Figure 9 · p. 10
  • For inter-modal crosstalk, theoretical and experimental results report identical performance for scalar and vector vortex modes in turbulence.The comparison is shown across turbulence strengths quantified by Strehl ratio.Source: B. The robustness of structured light · p. 10, Figure 8 · p. 10

C. Correction schemes

The section reviews turbulence compensation approaches and demonstrates intensity-based wavefront retrieval for scalar and vector beams. Both beam types improve after correction, while vector beams show higher fidelity before and after correction.

C. Correction schemes

  • Scalar-mode compensation has used adaptive optics, iterative approaches, and deep learning, but atmospheric-turbulence compensation for vector beams remains in its infancy.Some studies favor adaptive optics over iterative methods for distorted OAM beams, while others recommend combining techniques.Source: C. Correction schemes · p. 10
  • The GS algorithm retrieves wavefront errors from camera intensity, using phase vortices for scalar modes and polarisation vortices for vector modes, then subtracts the retrieved phase.A radially polarised cylindrical vector mode was generated from scalar vortex modes with ℓ=1 and ℓ=−1 and tested with astigmatism.Source: C. Correction schemes · pp. 10–11
  • Scalar mode fidelity rose from 0.74 to 0.98 after correction, while aberrated vector fidelity was 0.94 versus 0.74 for scalar beams.The comparison is shown for astigmatism correction; the vector beam’s overall fidelity remained higher, while the scalar improvement was larger.Source: C. Correction schemes · p. 11, Figure 10 · p. 11
  • The scalar fidelity gain was larger because astigmatism’s more distinct lobe pattern was recognizable to the algorithm, while vector modes’ overall fidelity remained higher.The section attributes vector resilience to the independence of the mode’s constituent polarisation states.Source: C. Correction schemes · p. 11

D. Quantum structured light

High-dimensional spatial modes are being explored for quantum communication through turbulence, with reported benefits in encoding capacity and error thresholds. Real-world links have demonstrated spatial-mode quantum communication, but high-dimensional spatial-mode entanglement through real-world turbulence remains an open challenge.

D. Quantum structured light

  • Quantum communication with high-dimensional spatial modes is being investigated for future networks, with proposed advantages including heightened security, higher error thresholds, and robustness against decoherence.Turbulence may inhibit the full potential of spatial-mode encoding.Source: D. Quantum structured light · p. 11
  • High-dimensional spatially encoded photons have shown robustness against turbulence in theoretical and experimental studies, and mitigation approaches include adaptive optics and channel correction.The cited experimental evidence includes dimensionality measures and quantum-state tomography; channel correction work includes compressive-sensing techniques.Source: D. Quantum structured light · pp. 11–12
  • A 3 km entangled spatial-mode link was the longest spatial-mode quantum link reported, while a 300 m hybrid spin-OAM link demonstrated high-dimensional encoding benefits.The 300 m experiment reported increased encoding capacity and higher error thresholds; the 3 km demonstration did not exploit the full potential of high-dimensional encoding.Source: D. Quantum structured light · p. 12
  • No successful attempt had transmitted high-dimensional spatial-mode entanglement through real-world turbulence, leaving this an open challenge.The reviewed real-world demonstrations include weak-, strong-, and moderate-turbulence conditions.Source: D. Quantum structured light · p. 12

E. The memory of turbulence

The section introduces a time-correlated model of beam wander to represent fading and crosstalk dynamics that memoryless statistical models do not capture. An ARMA model fits the measured beam-wander series and reproduces its temporal run-length behavior, supporting simulations and potential predictive signal processing.

E. The memory of turbulence

  • Memoryless turbulence models omit deep-fade durations and crosstalk dynamics, information relevant to frame length, interleaver depth, and error-correction-code length.The section identifies beam wander and angle-of-arrival fluctuations as dominant causes of mode-dependent loss and crosstalk.Source: E. The memory of turbulence · p. 12
  • An ARMA(2,2) process fit approximately 3,000 beam-wander samples using least squares, with model order checked by minimizing AIC and BIC.Measurements used a 150 m link and 300 FPS camera under moderate turbulence; one axis was analyzed, with two independent models proposed when both axes are needed.Source: E. The memory of turbulence · pp. 12–13
  • The simulated beam-wander intensities reproduce the measured fading statistics and existing beam-wander models, while the approach adds channel memory.The model maps beam position to received intensity and can serve as a fading factor in Monte Carlo FSO-link simulations; small-scale scintillation is not included.Source: E. The memory of turbulence · p. 13
  • Run-length distributions track how long beam intensity stays above or below a threshold, and comparisons require data sets with equal sample counts.The section uses a 50% maximum-intensity transition threshold for illustration.Source: E. The memory of turbulence · pp. 13–14
  • The ARMA model's run-length distribution matches measured beam-wander fading, unlike the conventional PDF-based model, which does not match the measured temporal memory.Figure 13 compares the simulated and measured distributions; its 50% intensity threshold is illustrative.Source: Figure 13 · p. 14, E. The memory of turbulence · p. 14
  • A more accurate model may support more computationally efficient MDM signal-processing algorithms, where strong error correction and MIMO are costly at link speeds.The suggested possibility includes shortcuts in maximum-likelihood algorithms.Source: E. The memory of turbulence · p. 14
  • The proposed correlated-wander model can simulate and potentially predict temporal mode-crosstalk evolution for modal diversity or mode-division multiplexing.The example calculates OAM crosstalk from a transmitted Gaussian mode and links its temporal correlation to beam-wander correlation.Source: E. The memory of turbulence · p. 14, Figure 14 · p. 14

V. IMPACT ON OPTICAL SIGNAL PROCESSING

Turbulence can create bursty channels, where received intensity remains below a usable threshold for extended periods, complicating error correction and signal processing. The section reviews diversity, coding, adaptive optics, and other mitigation approaches alongside their practical trade-offs.

V. IMPACT ON OPTICAL SIGNAL PROCESSING

  • Extended deep fades and channel memory can cause very large bit losses, making turbulence errors difficult to mitigate with signal processing and error-correction coding.The section describes low received intensity persisting below the reliable-communication threshold as a bursty channel.Source: §V · p. 14
  • Passive transmit and receive diversity are effective but require multiple apertures, while modal diversity may use one large aperture but remains in its infancy.Combining and coding strategies include EGC, MRC, space-time block codes, repetition codes, MIMO, and FEC; repetition coding may address memory but adds latency.Source: §V · pp. 14–15
  • Active optical techniques address turbulence directly but are generally more expensive than digital techniques; pre-distortion is effective but requires bandwidth-consuming feedback.A tip/tilt mirror can align the received beam, while deformable-mirror adaptive optics can correct wavefront error.Source: §V · p. 15

VI. DISCUSSION AND CONCLUSION

The paper reviews structured light in turbulence and presents theoretical and experimental tools alongside new illustrative results. Practical hurdles still constrain structured-light free-space optical links to kilometer-scale distances, making translation from laboratory demonstrations to real-world links a central challenge.

VI. DISCUSSION AND CONCLUSION

  • The review introduces a theoretical and experimental toolkit and reports in-house results on vector modes, correction, real-world beam types, and turbulence memory.The cited real-world turbulence results include a 150 m link and implications for signal processing.Source: §VI · p. 15
  • The paper provides a balanced account of open questions and uses illustrative examples to support the tutorial-style review.Source: §VI · p. 15
  • Practical hurdles have so far restricted structured-light free-space optical links to kilometer-scale distances.The discussion frames moving laboratory demonstrations into real-world conditions as necessary for extending distance and information capacity.Source: §VI · p. 15
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