Orbital angular momentum multiplexed photonic crystal multimode fiber–free-space optics link under fog-induced attenuation: design and performance analysis

1 Introduction

To keep up with the unprecedented rise in global data traffic, new spatial, spectral and polarization degrees of freedom are being explored for multiplexing in conventional optical communication infrastructure. Free-space optical (FSO) links have gained much research momentum in the past few years as a high-capacity line-of-sight (LOS) solution for the last mile access, backhaul, and fast deployment cases, due to its inherent physical layer security, immunity to electromagnetic interference, and large unlicensed bandwidth [1, 2]. Atmospheric conditions like haze, fog, rain and turbulence, however, have a significant impact on the performance of FSO, causing attenuation, scintillation and beam wander, which in turn reduces the quality factor (Q-factor) and leads to an increase of the bit error rate (BER) with propagation distance [3, 4]. Meanwhile, single-mode or few-mode fiber connections are also facing capacity challenges, and, as a complementary technique to wavelength-division multiplexing (WDM) and polarization-division multiplexing (PDM), spatially structured light and mode-division multiplexing (MDM) are being considered [5].

Orbital angular momentum (OAM) of light is one of the most powerful spatial degrees of freedom, with each mode having an azimuthal index that in principle can have arbitrary integer values, and a helical phase structure [6]. OAM modes have the advantage of being orthogonal to each other, and are not bound by the state space of the light field, which makes them ideal for mode-division multiplexing, allowing several data streams to be carried over the same wavelength and polarization [7]. Well-defined radial and azimuthal modes, called Laguerre–Gaussian (LG) beams, exist naturally in free space and guided media to realize such OAM modes [8]. It has been demonstrated experimentally that OAM multiplexing can significantly increase the aggregate capacity of FSO links, especially in conjunction with other multiplexing dimensions as WDM and PDM, which is a promising scalable pathway for achieving beyond terabit data rates [9–11].

One of the major problems which arise in practical OAM communication systems is the purity of the mode and suppression of intermodal coupling during generation, propagation and detection, particularly when a mode is communicated from a guided channel to an unguided channel [12]. The presence of OAM modes creates crosstalk, capacity loss and complexity in digital signal processing (DSP), as in conventional step-index or graded-index multimode fibre (MMF), OAM modes easily couple into the linearly polarized (LP) modes, which causes orthogonality to be lost [13]. To overcome these shortcomings, photonic crystal fiber (PCF) has become a very flexible technology for the design of refractive index profiles and confinements that can simultaneously support multiple OAM modes over a large wavelength window [14, 15]. However, the number of OAM modes supported, the effective index separation, the confinement loss and the mode purity of PCF structures can be appropriately designed to support tens to hundreds of OAM modes with large effective index separation, low confinement loss, and high mode purity, which make them promising candidates for OAM based mode-division multiplexing in fiber links [16–18].

Hybrid fiber–FSO architectures are especially attractive for extending high-capacity optical backbones to the more difficult deployment environments, such as the case of extending fiber lines to maximize available capacity while maintaining the ability to cross physical fiber deployment limitations or cost [19, 20]. These systems feature a short-reach fiber link, which can be either guided link or unguided link, to launch a guided OAM or LG-mode signal into the FSO channel, or to launch an unguided signal into a guided OAM or LG-mode link, providing flexible reconfigurability and high bandwidth over a combined guided-unguided path. On the other hand, the transmission characteristics of these hybrid links rely on the atmospheric characteristics of the FSO link as well as the modal characteristics of the fiber link. The influence of spatial structure modification due to atmospheric turbulence in OAM and LG beams may result in modal crosstalk, power modulation in modes, and eventually Q-factor reduction and BER penalty at the receiver [21, 39]. Fog is by far the worst weather for FSO because of the strong Mie scattering caused by the droplets whose size is comparable to the optical wavelength, causing severe attenuation and rapid decrease in link range with decreasing visibility [3].

In recent research, the effects of clear air, haze, thin fog and heavy fog on the received power, Q-factor and BER of a single mode link have been quantifying [22, 23]. The results presented in these works all demonstrate that higher levels of atmospheric attenuation reduce the achievable FSO range, decrease the Q-factor, and increase BER beyond acceptable levels for error-free operation for a given transmit power and aperture configuration. Design of PCFs has been mostly parallel and directed towards the number of supported OAM modes, to a larger index difference, >10⁻⁴, and to optimize dispersion and confinement loss, but without taking into account integrated fiber–FSO links [24]. To this end, a systematic design and the performance evaluation of such integrated PCF based multimode fiber–FSO systems that make use of OAM multiplexing under realistic fog conditions and for practical link distances are still needed.

In this work, an integrated MMF-FSO link is studied that utilizes OAM multiplexing of four LG modes (LG 0 0 , LG 2 0 , LG 4 0, and LG 6 0) over a fixed 100 m MMF link with a variable FSO link. The optimization of the structural parameters of a specially designed PCF in MATLAB using finite element method (FEM) to support these LG modes with a minimum confinement loss and a sufficient separation of the effective index [25, 26]. The PCF parameters thus obtained are then fed into a PCF system model that is implemented in an OptiSystem software and is used to simulate the entire OAM-multiplexed MMF–FSO link. The proposed framework combines the MMF design based on PCF with a realistic FSO channel model, which considers the attenuation caused by the weather, to reflect the combined effects of the guided-wave and free-space propagation on system performance. The FSO section of the link is being modelled under four representative weather conditions: clear, light, medium and heavy fog. The attenuation coefficient is tailored for each condition to simulate typical visibility values reported in the literature [27, 28], with the end goal of evaluating the combined MMF–FSO system over realistic deployment scenarios. The performance metrics studied in this work are the Q factor and the log of the BER as a function of the FSO range, both of which give a complete picture of signal quality and reliability. The higher order LG modes have larger beam radius and more complex ring structures that may be beneficial for multiplexing but results in greater degrees of beam divergence and sensitivity to misalignment/cross-talk over long FSO paths.

In the present study, the effect of the FSO range and the attenuation caused by the weather on the important metrics of the system is studied without alleviating the effects of the mode by including a large number of modes and by increasing the length of the fiber segment. Such a combined view is key to designing real-life OAM-based hybrid links where the fiber section and FSO section cannot be optimized separately. To our best knowledge, few publications have reported a combined design and performance analysis of a PCF-based MMF directly coupled into an FSO link and subjected to various fog conditions, measured in terms of Q-factor, BER and eye diagrams [29, 30]. A lot of the existing FSO studies ignore the presence of fog and the OAM studies are mostly based on PCF in guided wave transmission.

In the present contribution, we make an effort to overcome this challenge by (i) designing a PCF structure to support suitable confinement characteristics of the desired modes LG 0 0 , LG 2 0 , LG 4 0, and LG 6 0, (ii) embedding the designed structure into a complete model of OAM-multiplexed MMF-FSO system implemented in MATLAB and OptiSystem [31], and (iii) systematically quantifying the impact of clear, light fog, medium fog and heavy fog conditions on the possible achievable FSO range for a given target Q-factors and BER. The knowledge acquired from this research work would be beneficial for the practical implementation of OAM multiplexed hybrid FSO (H-FSO) link in foggy environment and it also shows the importance of combining PCF design with OAM link design to achieve reliable and high capacity optical wireless system.

2 System design

2.1 Proposed system architecture

The proposed integrated MMF-FSO system is designed to simultaneously transport four independent data channels, each modulated at 20 Gbps using non-return-to-zero on-off keying (NRZ-OOK). This data rate provides a balance between high per-channel capacity and manageable transmitter and receiver bandwidth, resulting in an aggregate transmission rate of 80 Gbps. NRZ-OOK was selected because of its simple implementation, low receiver complexity, and compatibility with intensity-modulation/direct-detection optical links. The system block diagram is illustrated in Figure 1. At the transmitter, a pseudo-random binary sequence (PRBS) generator feeds an NRZ pulse shaper, which drives a Mach–Zehnder modulator (MZM) driven by a continuous-wave (CW) laser [32]. The CW laser outputs the fundamental Gaussian beam LG 0 0 mode, and each of the four LG modes LG 0 0 , LG 2 0 , LG 4 0, and LG 6 0 carries a separate 20 Gbps data stream. The four independently modulated beams are combined using a mode-division multiplexer (MDM MUX) and launched into the PCF-based MMF segment of 100 m length. A 100 m PCF-MMF length was selected to represent a practical short-reach feeder link while limiting fiber-induced modal coupling and propagation loss, thereby allowing the influence of the FSO channel to be evaluated more clearly. After propagation through the PCF–MMF, the multiplexed beam enters a FSO channel whose length is varied under four weather conditions: clear, light fog, medium fog, and heavy fog. At the receiver end, an MDM demultiplexer (MDM DEMUX) separates the individual LG-mode channels, each of which is subsequently detected by a PIN photodiode, filtered through a low-pass filter (LPF), and evaluated in terms of bit-error-rate (BER) and Q-factor. The operating wavelength of 1,550 nm was selected because it lies within the low-loss optical communication window, is compatible with widely available fiber and FSO components, and permits higher eye-safe transmit power than shorter wavelengths.

2.2 Simulation parameters

Table 1 summarizes the complete set of simulation parameters employed in the MATLAB FEM analysis and the OptiSystem link simulation. The parameters span the transmitter, PCF geometry, FSO channel model, and receiver configuration.

TABLE 1. Simulation parameters used in MATLAB - FEM and OptiSystem link modeling.

2.3 Laguerre Gaussian beam theory and mode profiles

The spatial degree of freedom is exploited by utilizing the azimuthal phase structure of LG beams generated at the transmitter. In cylindrical coordinates r , ϕ , z the electric field distribution of an LG mode propagating along the z-axis is mathematically described by Equation 1 [6, 8]:

U p l r , ϕ , z = C w z 2 r w z l L p l 2 r 2 w 2 z exp − r 2 w 2 z exp ⁡ i l ϕ exp − i k r 2 2 R z exp i 2 p + l + 1 ζ z exp ⁡ − i k z (1)

Here C represents the normalization constant, p = 0 , 1 , 2 , … is the radial index, l is the azimuthal index, L p l is the associated Laguerre polynomial, w z is the beam radius, R z is the wavefront curvature, and ζ z = arctan ⁡ z / z R is the Gouy phase where z R is the Rayleigh range.

For the proposed system, four representative modes, LG₀ ⁰, LG₂ ⁰, LG₄ ⁰, and LG₆ ⁰, were selected to examine the effect of progressively increasing mode order while maintaining a manageable system configuration. Because the radial index is zero (p = 0) for all selected channels, the spatial intensity profile is solely governed by the topological charge l. The defining characteristic of the OAM beam is the helical phase term, given by Equation 2:

ψ O A M ϕ = exp i l ϕ (2)

Because the chosen modes possess distinct topological charges (l = 0 , 2 , 4 , 6), they are strictly orthogonal [7]. This orthogonality prevents inherent inter-modal crosstalk during multiplexing, defined analytically by the inner product of their electric fields over the transverse plane (Equation 3):

∬ U p 1 , l 1 r , ϕ U p 2 , l 2 * r , ϕ r d r d ϕ = δ p 1 p 2 δ l 1 l 2 (3)

The theoretical spatial characteristics of the generated optical channels are visually corroborated in Figure 2 [33], which illustrates the simulated transverse intensity and phase profiles for the LG 0 0 , LG 2 0 , LG 4 0, and LG 6 0 modes. As governed by the spatial intensity distribution, the fundamental LG 0 0 mode (l = 0) exhibits a standard Gaussian spot with peak intensity at the beam axis. In contrast, the higher-order modes (l = 2 , 4 , 6) display the characteristic annular (“doughnut') intensity distribution resulting from the phase singularity at the center (r = 0). As the topological charge l increases, the radius of this maximum intensity ring correspondingly expands. Furthermore, the accompanying phase profiles visually confirm the presence of the helical phase term exp i l ϕ. While the LG 0 0 mode maintains a continuous phase front, the LG 2 0 , LG 4 0, and LG 6 0 modes clearly depict an azimuthal phase variation of 2 π l, representing the distinct quantized twists of the orbital angular momentum that ensure strict inter-modal orthogonality during propagation.

2.4 PCF design for OAM mode guidance

The PCF used as the multimode fiber segment in the proposed system is designed to support all four LG modes with low confinement loss, high mode purity, and adequate effective refractive index (ERI) separation to prevent intermodal coupling during propagation. The structural and modal parameters of the PCF are derived analytically and numerically in MATLAB using the finite element method (FEM) [24–26], and the optimized values are subsequently imported into OptiSystem for full link simulation.

The proposed PCF has a simple ring-core structure. The central air core helps form the annular field distribution required for OAM guidance, while the surrounding high-index P₂O₅-doped ring confines the modes and reduces leakage into the silica cladding. The structure was modeled using a two-dimensional cross-section with micrometer-scale dimensions. The central air-core radius was defined as r 0 − Δ r, where r 0 = 11.5 μ m and Δ r = 0.35 μ m, giving an air-core radius of 11.15 μ m. The doped annular ring extends up to a radius of r 0 + t ring, where t ring = 0.8 μ m, resulting in an outer ring radius of 12.30 μ m. Thus, the effective ring thickness measured from the air-core boundary is approximately 1.15 μ m. The silica refractive index was calculated from the Sellmeier equation as n silica = 1.4375 at the operating wavelength of 1.99 μ m, while the P₂O₅-doped ring was assigned a higher refractive index of n ring = 2.30. The outer computational domain radius was set to 30 μ m, with an additional 2 μ m outer layer used in the geometry. Figure 3 illustrates the proposed PCF cross-section, consisting of a silica background with a central air core, a high-index P₂O₅-doped annular ring, and periodically arranged air holes in the cladding. The corresponding finite-element mesh used for modal analysis is shown in Figure 3b. This annular-ring, air-core guiding geometry follows design principles established for ring-core and air-core OAM-supporting fibers reported in the literature [14, 16, 18, 34–36].

2.5 FSO channel modeling

After propagation through the PCF link, the signal is launched into the FSO channel. The total received optical power P R at the FSO receiver is governed by the Friis transmission equation modified for atmospheric losses [37] (Equation 4):where P T is the transmitted power, η T and η R are the optical efficiencies of the transmitter and receiver antenna, D T and D R are the transmitter and receiver aperture diameters, θ is the beam divergence angle, Z is the FSO propagation range and α is the atmospheric attenuation coefficient (in dB/km).

P R = P T η T η R D R D T + θ Z 2 10 − α Z 10 (4)

The propagation loss due to atmospheric conditions follows the Beer-Lambert law [3, 39]. The atmospheric transmittance h Z is described by Equation 5:where β a t m is the total atmospheric extinction coefficient. Under fog conditions, Mie scattering is the dominant attenuation mechanism. Mie scattering occurs because fog-droplet sizes are comparable to the optical wavelength, causing light to be scattered away from the receiver aperture and thereby reducing the received optical power. The empirical Kim and Kruse models define the fog attenuation coefficient [4, 27, 28, 38] β f o g as a function of visibility V (in km) and operating wavelength λ (in nm):

h Z = exp − β a t m Z (5)

β f o g = 3.91 V λ 550 − q (6)

The size distribution of the scattering particles dictates the parameter q. Based on the Kim model, q is defined conditionally relative to atmospheric visibility [4, 38]:

q = 1.6 , V > 50 k m 1.3 , 6 < V ≤ 50 k m 0.16 V + 0.34 1 < V ≤ 6 k m V − 0.5 , 0.5 < V ≤ 1 k m 0 , V ≤ 0.5 k m (7)

Furthermore, geometrical spread induces a power penalty L g e o (in dB) over distance, expanding the beam beyond the receiver aperture [10] (Equation 8):where A R = π D R 2 2 is the receiver collection area.

L g e o = 10 ⁡ log 10 4 A R π θ Z 2 (8)

To evaluate the link’s end-to-end performance at the PIN photodetector, the Signal-to-Noise Ratio (SNR) is modeled by accounting for both thermal noise and shot noise [32]. The SNR is given by Equation 9:where R λ is the photodiode responsivity. The thermal noise variance σ t h 2 and shot noise variance σ s h 2 are respectively described by Equations 10, 11: where k B is the Boltzmann constant, T is the absolute temperature, B e is the effective electrical bandwidth of the low-pass filter, R L is the load resistance, and q e is the elementary electron charge.

S N R = R λ P R 2 σ t h 2 + σ s h 2 (9)

σ t h 2 = 4 k B T B e R L (10)

σ s h 2 = 2 q e R λ P R B e (11)

Assuming an OOK modulation scheme processed through the 3 R regenerator, the BER is derived from the statistical distribution of the received signal and noise, expressed using the complementary error function [32] (Equation 12):

B E R = 1 2 e r f c Q 2 (12)

The Q-factor, which serves as a primary metric alongside log (BER) to quantify system degradation over the FSO range Z, is defined as the difference in the expected mean values (μ 1 , μ 0) of the ‘1′and ‘0′bits normalized by their respective standard deviations (σ 1 , σ 0) [32] (Equation 13):

Q = μ 1 − μ 0 σ 1 + σ 0 (13)

These theoretical models are integrated using a co-simulation methodology between MATLAB (for modal and dispersion analysis of the PCF) and OptiSystem (for link-level BER, Q-factor, and eye diagram evaluation) to validate the end-to-end performance under clear weather and varied fog conditions.

3 Results and discussion

3.1 Analysis of PCF performance

Figure 4a shows the variation of the real part of the effective refractive index, Re n eff, for different P 2 O5 ring thicknesses, R t. For all investigated values of R t, Re n eff decreases almost linearly as the wavelength increases from 1.50 μ m to 1.60 μ m, indicating stable dispersive behavior of the guided mode. With increasing R t, Re n eff shifts upward from approximately (1.4481) to (1.4487) at 1.50 μ m, and from (1.4473) to (1.4480) at 1.60 μ m. This trend confirms stronger modal overlap with the high-index P 2 O5-doped annular ring. Figure 4b presents the corresponding imaginary part, Im n eff, which remains very small overall, confirming weak leakage from the guided mode. However, the leakage response is more sensitive to R t; the R t = 0.86 μ m case shows pronounced peaks, reaching approximately 2.02 × 10 − 10 near 1.59 μ m, whereas R t = 0.88 μ m maintains the lowest Im n eff across most of the wavelength range. Therefore, R t = 0.88 μ m provides the most favorable balance between enhanced effective index and reduced leakage loss.

Figure 5a shows the wavelength-dependent effective mode area, A eff, for different P 2 O5 ring thicknesses. For all values of R t, A eff increases gradually with wavelength from 1.55 μ m to 1.60 μ m, indicating progressive modal spreading at longer wavelengths. At 1.55 μ m, A eff increases from 156.27 μ m 2 for R t = 0.80 μ m to a maximum of 228.30 μ m 2 for R t = 0.86 μ m, while at 1.60 μ m it rises from 162.97 μ m 2 to 240.10 μ m 2. This confirms that the ring thickness strongly controls the modal expansion inside the hollow-core region. Figure 5b presents the confinement loss response over 1.50 – 1.60 μ m. The loss shows a non-monotonic dependence on wavelength due to leakage sensitivity and modal interaction with the ring boundary. Among the investigated cases, R t = 0.86 μ m exhibits the highest loss peak of approximately 6.93 × 10 − 3 dB / m near 1.59 μ m, whereas R t = 0.88 μ m provides the lowest loss over most of the band, reaching a minimum of 1.44 × 10 − 9 dB / m near 1.57 μ m. Therefore, although R t = 0.86 μ m gives the largest effective area, R t = 0.88 μ m is more favorable for low-loss guidance.

Figure 6a shows the mode purity variation for different P 2 O5 ring thicknesses, R t. The mode purity remains high over the full wavelength range and decreases only slightly from about (0.9667) at 1.50 μ m to about 0.9605 – 0.9608 at 1.60 μ m, indicating stable single-mode-like guidance with increasing wavelength. The effect of R t is relatively weak; however, thicker rings provide a marginally higher purity, with R t = 0.88 μ m giving the highest value of approximately (0.9668) at 1.50 μ m. Figure 6b presents the propagation constant, β, which decreases nearly linearly with wavelength for all R t values. For example, β decreases from approximately 6.07 × 10 6 rad / m at 1.50 μ m to 5.68 × 10 6 rad / m at 1.60 μ m, mainly due to the wavelength-dependent phase accumulation. The curves almost overlap, showing that R t has only a minor influence on β, although a slight upward shift is observed for larger ring thicknesses.

Figure 7a presents the chromatic dispersion, D, for different P 2 O5 ring thicknesses. All curves remain in the negative-dispersion region over 1500 – 1600 nm, while D becomes less negative as the wavelength increases. For R t = 0.80 μ m, D changes from approximately − 11.87 to − 8.56 ps / nm · km, whereas for R t = 0.88 μ m, it varies from about − 15.27 to − 11.55 ps / nm · km. This indicates that increasing the ring thickness generally enhances the magnitude of negative dispersion, with the thicker P 2 O5 ring offering stronger dispersion control. Figure 7b shows the corresponding group-velocity dispersion, β 2, which remains positive throughout the investigated wavelength range and gradually decreases with increasing wavelength. The β 2 value decreases from 14.18 to 11.63 p s 2 / km for R t = 0.80 μ m, while the highest values are obtained for R t = 0.88 μ m, decreasing from 18.24 to 15.70 p s 2 / km. The opposite signs of D and β 2 are consistent with their inverse dispersion relationship, and the results confirm that the doped ring thickness provides an effective tuning parameter for dispersion engineering in the proposed PCF.

Figure 8a shows the third-order dispersion, β 3, for different P 2 O5 ring thicknesses. The β 3 response remains mostly positive over the investigated wavelength range, indicating a weak but controllable higher-order dispersion contribution. For R t = 0.80 μ m, β 3 changes from − 3.49 × 10 − 3 p s 3 / km at 1500 nm to 9.22 × 10 − 3 p s 3 / km at 1600 nm, with a maximum of about 4.74 × 10 − 2 p s 3 / km near 1552 nm. For thicker rings, β 3 remains positive throughout the band, with R t = 0.84 μ m giving one of the strongest and most stable responses, ranging from about 3.03 × 10 − 2 to 4.42 × 10 − 2 p s 3 / km. Figure 8b presents the fourth-order dispersion, β 4, which increases almost linearly with wavelength and changes sign from negative to positive. The zero-crossing point shifts toward longer wavelength as R t increases, moving from about 1552 nm for R t = 0.80 μ m to around 1585 nm for R t = 0.88 μ m. This tunable sign transition of β 4, together with the controlled β 3 behavior, confirms that the P 2 O5 ring thickness is an effective parameter for higher-order dispersion engineering in the proposed PCF.

3.2 FSO link performance under clear-sky conditions

Figure 9 reports the log (BER) and Q-Factor analysis as a function of FSO range for clear-sky conditions [32]. When the FSO range is 3 km, the log (BER) of all four channels is below −18, Q-factor is between 8.72 dB and 8.83 dB, and the mode orthogonality is preserved after passing through the PCF segment of 100 m, which indicates negligible FSO atmospheric attenuation and excellent performance. When the range increases all metrics are degraded monotonically: for the range of 5 km the Q-factor is close to 6.74–6.87 dB, and at the maximum simulated range of 7 km the Q-factor is 4.56–4.73 dB with log (BER) of −5.60 to −5.97 dB. The clear sky performance is acceptable in all four channels at 7 km based on the Q ≥ 4 dB criterion, which demonstrates multi-kilometer operation under clear sky conditions. Channel 1 (LG 0 0) always has the best Q and lowest BER, and Channel 3 (LG 4 0) always has the worst Q and highest BER. The inter-channel Q-factor spread is less than 0.18 dB at 7 km, which indicates low inter-modal crosstalk from the PCF-MMF segment. Eye diagrams are narrow at 7 km, but are still visible for all channels.

3.3 FSO link performance under light fog

In light fog conditions (Figure 10), the range that can be achieved is reduced to sub-1.5 km scale and the link is evaluated by steps of 43.75 m from 1,050 m to 1,400 m [22, 38]. The Q-factor is between 8.05 and 8.20 dB over the four channels at 1,050 m, which is similar to what has been obtained at about half this distance with clear sky conditions, thus supporting the additional Mie-scattering penalty caused by the fog droplets. At 1,400 m, the Q-factor falls to 4.70–5.09 dB and log (BER) rises to between −5.91 and −6.77. At 1,400 m, all four channels meet the requirement of Q ≥ 4 dB with Channel 1 (LG 0 0) having the largest Q value of 5.09 dB. The degradation in channel 3 (LG 4 0) is the highest (4.70 dB at 1,400 m) but is still greater than 4 dB, so the achievable range for light-fog is at least 1,400 m for all channels. This is a ∼78% decrease in range when compared to the clear-sky case.

3.4 FSO link performance under medium fog

The results are shown in Figure 11 for medium fog, with the range varying from 700 m to 1,000 m with increment 37.5 m [29, 31]. The difference in attenuation coefficient compared to light fog can be seen immediately. At 700 m the Q-factor is 8.27–8.47 dB, which is just slightly better than what was found at 1050 m in light fog. The link degrades rapidly, reaching Q-factors of 3.83–4.20 dB and log (BER) of −4.20 to −4.88 at 1,000 m. At 1,000 m, Channel 1 (LG 0 0) achieves Q = 4.20 dB (above threshold), but Channels 2, 3, and 4 fall to Q = 3.95, 3.83, and 3.87 dB respectively just below the 4 dB threshold. At medium fog condition, the fog range Q ≥ 4 dB is about 925–960 m, which is about 86% less than clear-sky conditions. At 1,000 m, eye diagrams exhibit much more closure than in the previous scenarios, and noticeable amplitude noise and jitter can be seen.

3.5 FSO link performance under heavy fog

Since there is a significant Mie-scattering attenuation of dense fog, the link was evaluated from 550 m to 750 m in steps of 25 m (Figure 12) [23, 30]. The Q-factor at 550 m is in a range from 8.28 dB to 8.56 dB, which is generally comparable to other fog situations. At the maximum simulated range of 750 m, the Q-factor falls to 4.58–4.85 dB with log (BER) between −5.64 and −6.23. All four channels have Q > 4 dB at 750 m in heavy fog with Channel 1 (LG 0 0) having Q = 4.85 dB and Channel 3 (LG 4 0) having Q = 4.58 dB is the weakest performance at the longest range in heavy fog. The heavy fog range (Q ≥ 4 dB) is about 700–750 m, 89% of the clear-sky range. This is in line with the results of the other three weather scenarios examined, confirming that the distance penalty caused by heavy fog is the highest of all four weather scenarios. The eye diagrams provide a visual indication of the received signal quality. A larger vertical eye opening indicates better separation between the logical “1” and “0” levels and a greater tolerance to amplitude noise, while a wider horizontal opening indicates lower timing uncertainty.

3.6 Comparative analysis and discussion

The summary of maximum simulated range, channel wise maximum Q factor and log (BER), and estimated Q > 4 dB operating range for all 4 weather conditions are summarized in Table 2. This threshold analysis is more suitable for fog impaired FSO links as compared to the conventional BER = 10⁻⁹ criterion, because at practical link distances, strong Mie scattering makes the conventional BER threshold unattainable except in the clearest of the conditions [40].

TABLE 2. Summary of maximum simulated FSO range, channel-wise Q-factor and log (BER) spread, and estimated operating range at Q ≥ 4 dB for all weather conditions.

There are two patterns in the full data set. First, the achievable FSO range would decrease drastically with the decline in visibility, between about 78% in light fog, 86% in medium fog, and 89% in heavy fog, showing the disproportionate effect of the fog-induced Mie scattering, described by Equations 6, 7, on the link budget. This non-linear contraction is due to the exponential relationship between atmospheric transmittance and range and attenuation coefficient.

Second, the performance gap between the four multiplexed LG channels is relatively low throughout, with typical inter-channel crosstalk Q-factor performance of 0.3–0.4 dB for the longest measured distance for each weather condition, suggesting that the performance of the PCF-based MMF segment is still very suitable for keeping inter-channel crosstalk as a dominant impairment. For all four OAM channels, range-dependent atmospheric attenuation is the limiting factor for all weather.

The fundamental channel LG 0 0 has the most graceful degradation with range in this limited spread for all four weather conditions. This is due to the smaller radius of the beam and lower divergence compared to higher order modes; the larger beam footprint of LG 2 0 , LG 4 0, and LG 6 0 modes make them slightly more susceptible to geometric spreading loss and fog-induced scattering, resulting in marginally lower performance.

4 Conclusion

In this paper, we have discussed a systematic design and end-to-end performance analysis of an 80 Gbps aggregate capacity OAM-multiplexed PCF based MMF–FSO hybrid link over 4 LG channels (LG 0 0 , LG 2 0 , LG 4 0, and LG 6 0). The FEM is used to optimize the PCF to obtain high mode purity (∼0.967), low confinement loss (as low as 1.44 × 10 − 9 dB/m at the optimized ring thickness of 0.88 μm), and anomalous chromatic dispersion which is favorable for OAM mode propagation. Optimized values of the PCF parameters are added to a full link simulation using co-simulation between MATLAB and OptiSystem. Four atmospheric conditions are investigated, and the criterion used is Q ≥ 4 dB. All four channels meet the Q ≥ 4 dB criteria at the maximum simulated FSO range of 7 km under clear-sky conditions, and do not drop below this threshold until about 1,350–1,400 m (∼78% range reduction) under light fog conditions. Channel 1 (LG 0 0) is the only channel able to marginally meet the criterion in the medium fog (Q ≥ 4 dB) range, which is about 925–960 m (∼86% reduction). At heavy fog, the critical value of Q is at least 4 dB, and all channels keep above the threshold at about 700 m–750 m which corresponds to 89% reduction. The inter-channel Q-factor spread is within 0.3–0.4 dB for all weather conditions, verifying that the attenuation due to fog is the main limiting factor rather than crosstalk between the different channels of the PCF-MMF segment. The LG 0 0 channel always performs better than the higher order modes because of its lower beam divergence and geometric spreading loss. This work offers quantitative deployment instructions for OAM-multiplexed hybrid fiber–FSO systems in foggy conditions and confirms the performance of the co-simulation set-up integrating MATLAB with OptiSystem for the design of the hybrid guided-wave and free space links. Adaptive power control, spatial diversity and error correction schemes will be studied in future for further expanding the Q ≥ 4 dB operating range for dense fog.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Footnotes

Edited by: Abhishek Sharma, National Institute of Technology, Hamirpur, India

Reviewed by: Iqbal Singh, Southern Illinois University Edwardsville, United States

Rittwick Mondal, Sidho Kanho Birsha University, India