The demand to increase bandwidth and capacity in telecommunications has become absolutely necessary. In particular, academia, social media, business affairs, and government Administration have been impacted by Internet networks [1]. As a result, new techniques such as spatial domain multiplexing (SDM) and orbital angular momentum (OAM) are urgently needed to address this issue. SDM combines multiple channels in the same wavelength band into a single channel using different spatial paths or positions. This is the new technique of Multiple-Input Multiple-Output (MIMO) communication systems to improve reliability and increase data rates [2–4]. Orbital angular momentum (OAM) is a property of light that describes the rotational movement of a light beam about its propagation axis. OAM has potential applications in areas such as optical communication, quantum information, and microscopy due to its ability to carry multiple independent information channels in a single beam of light. The value of OAM can be quantized, and by using different values of OAM, multiple light beams can be transmitted simultaneously, providing increased capacity for data transfer [5–8]. In addition, OAM is a physical structure layer used to multiplex the signals that are transported by light. The basic principle works based on multiplexing different signals according to their orthogonality states. The OAM has a helical wavefront based on circular polarization in two components. This unique property could offer an unlimited channel for data transmission [7–9]. However, this technique has suffered some losses related to the gap spacing between free space and optical fiber, optical scattering from micro-particles in the atmosphere, and mode coupling in the guided media, scrambling the wavefronts of OAM modes destroys orthogonality, increasing crosstalk [10–15]. As the topological charges increase, the beam divergence intensifies, and the receiver aperture should be designed to maintain the size of the beams. In this contribution, the effect of BER and power losses has been investigated and characterized to maintain the minimum losses possible and maximize the capacity of the OAM/SDM G-PON optical network.

SDM achieves spatial multiplexing by controlling the entry initiation angles, increasing the bandwidth of the optical fiber [16]. This technique is achieved by launching individual light channels into optical fibers with different angles. Each channel spirals across the fibers based on their input angle. The output end angles of the SDM channel are dependent on the input angles. These MIMO channels traverse the length of the fibers without interfering with each other. The screen projection of the light density at the end of the fiber exit appears as a concentric circle. Spatial filtering techniques are utilized at the end of the fiber output for eliminating multiplex and treating individual channels [17]. The SDM can maximize optical fiber data transmission by working in synchronization with various multiplexing technologies and using a mixed architecture [18–20].

The potential of carrying data on OAM modes, multiplexing it, transmitting it over SDM, and de-multiplexing it is proposed.OAM mode could carry data in huge capacity [21, 22]. This platform, called OAM-SDM technology, is demonstrated in Figure 1. The Single Mode Fiber (SMF) is the transmission channel between each channel and the Beam Separator Module (BSM). SDM carrier fiber represents the multimode optical fiber that carries the helical propagation of the SDM system. On the right-hand side of Figure 1, the detection circuit is represented by the demultiplexing technique that starts with De-BSM and the detector circuit. This technique has greatly improved communication systems. OAM wavefront is doughnut-shaped with zero intensity at its center. This characteristic is a proposed method to identify OAM beams and their topological charge. However, the most common method to express OAM in its topological charge is the interference method in terms of the Gaussian beam profile [23].

Scientists have proposed different types of optical fiber to enhance the coupling of OAM. As the refractive index profile, this type must be a ring shape to match OAM modes, high contrast between core and clad to ameliorate the separation between the channels, and the smooth interface between core and cladding (i.e., the preferred profile of graded index). These criteria could enhance the capacity transmission and efficiency of SDM platform technology. SDM or BSM multiplexer employs a spatial filter to link each input channel with a helical wavefront at the end of the output optical fiber. So the signal could be independently captured and processed. The SDM has a different configuration of the optical components, such as taper waveguide, diode optical source, and other optical bulk, etc. Researcher Murshid et al. have suggested a novel configuration of SDM as (CAD) analyses made by an array of lenses then de-multiplexed to a separated detector [16]. Another type of SDM has been proposed by Murshid et al. [24] that employs the hollow core of an array waveguide for gradually separating the signal as an SDM function and then enhancing the coupling between the waveguide and detector.

The structure of the OAM/SDM system is illustrated in Figure 2. Geometrical losses occur when the transmitted beam is spread between the transmitter and receiver [25]. This can happen when the beam’s spot size is larger than the aperture of the receiver, resulting in energy loss. The formula that governs this phenomenon can be expressed as:

$$G_L=\frac{D_r^2}{{[D_t+\left(\mathrm{L\theta }\right)]}^2}$$(1)where: θ presents the divergence angle in (mrad), and L presents the distance connection in (mm). The losses of the geometrical path of the free space optics (FSO) connection depend on several parameters, such as the size of the optical beam of transmitter D (Fig. 2), the divergence angle θ, and the optical path length. The transmitter and receiver have quantifiable aperture sizes determined during manufacturing. When planning any FSO link, the geometric path loss must be considered. This loss is a fixed value for a particular FSO deployment scenario and should always be considered. Unlike the loss caused by factors like rain attenuation, fog, haze, or scintillation, the geometric path loss does not vary with time.

Different sources of the loss in the optical system could be affected in free space as defects of the lens and other optical elements; for example, a lens could be transmitted 95% of light and reflect or absorb the rest of light. This loss depends on the quality and characterization of the equipment. Therefore, this value of the loss could be obtained from the manufacturer.

The absorption and diffusion effect of infrared light present the molecular attenuation that appears in the terrestrial atmosphere. This phenomenon affects the beam of light and then directly impacts the transmission distance. Many types of this attenuation, such as carbon dioxide, water, and ozone, make the absorption of molecules a selective phenomenon. The total attenuation is a summation of free space attenuation in the gap and the geometric loss. Total attenuation for a combination guided and free space optical communication system is given by the following

$$\mathrm{Total} \mathrm{Attenuation}=\frac{D_r^2}{{\left[D_t+\left(\mathrm{L\theta }\right)\right]}^2}\left[\exp \left(-\beta L\right)\right]$$(2)where β is the total scattering coefficient (unit: 1/Km).

Several parameters are considered when calculating the OAM/SDM G-PON optical link budget, such as geometric loss, link margin received power and Bit Error Rate (BER). Due to the medium’s attenuation and total loss, the received power is less than the transmitted power. In the basic free-space channel, the optical field generated at the transmitter propagates only with an associated beam spreading loss. Therefore, the received power in the OAM/SDM G-PON system can be determined by calculating the difference between transmitted power through the transmission medium and the total loss of the medium using the mathematical formula in equation (3)

$$P_r={\mathrm{TP}}_{\mathrm{t}}-\mathrm{Total} \mathrm{Loss}.$$(3)

For any path we have:

$$R= \frac{P_r}{P_i}$$(4)

$$T=\frac{P_t}{\mathrm{Pi}}$$(5)where R is the reflection coefficient, T is the transmission coefficient and both are related to each other in the form R + T = 1

$$T=\frac{n_t\cos \left({\theta }_t\right)}{n_i{\cos (\theta }_i)}{t}^2$$(6)

$$T=\frac{{2n}_i\cos \left({\theta }_i\right)}{n_i{\cos (\theta }_t)+n_t\cos ({\theta }_t)}{t}^2$$(7)where n_i, θ_i, and n_t, θ_t are the refractive indices and angles of the incident and transmit planes, respectively. T₁ and T₂ present the transmission coefficient for the input and output ends. Further, it could be estimated using equation (6), where the single-mode optical fiber (SMOF) T₁ = 0.96.

The schematic diagram of the experimental setup is shown in Figure 3, the number of light sources is three, which were taken from passive optical network (PON) cards (SFP V-SOL) in the optical line terminal (G-PON, V-SOL OLT), and the DS/US data rate is 2.4/1.2 GBps and splitting ratio up to 128, G.652 single-mode optical fibers and (62.0/125) MM-1.8 × 3.7 multi-mode fibers (MMF) are used to build the OAM/ SDM G-PON. For the light source’s geometry, the first path’s gap length (SMF-to-MMF) is set to L = 3 cm length, and θ₁ = 5, 10, 13, 16, 19. The OAM side consisted of three biconvex lenses with focal length = 3 cm. On the receiver side, the output of the MMF is connected to a 1 × 4 PLC splitter with an insertion loss of less than 7.6 dB. Then, the output of the splitter is connected to the optical spectrum analyzer (Mini OSA), and the output is launched into the computer for signal processing using OSA analyzer software. The SDM technology implies special coupling techniques between the SMF and MMF to generate an OAM ring and develop a helical propagation path. This OAM rings, and helical propagation can be achieved only for specific values of L and θ. The whole process depends on calculating the gap length between the SMF and MMF as a function of topological charge. The topological charge is determined based on the SMF’s small radius (r), the mode’s wavelength, and the incident angle, as shown in equation (8). The gap length L is determined using geometrical (ray) optics depending on the direct distance (X), as explained in equation (9), from the center of the end face of the focusing lens to the center of the MMF

$$l=\frac{2\pi r}{\lambda }\tan \left(\theta \right)$$(8)

$$L=\sqrt{r^2+X^2}$$(9)

The evaluation of the OAM/SDM G-PON system is calculated based on the eye diagram that has been obtained from the spectrum analyzer Figure 4. The eye diagram is used to evaluate the performance of the OAM/SDM system. The first channel is launched into the MMF at θ₁ = 5 with respect to the MMF fiber axis, and the second channel is at approximately θ₁ = 10. The blue trace represents the eye of the channel at θ₁ = 5, and the pink trace is the eye for the channel at θ₁ = 10. Since the eye diagram opening is very clear and can be recognized, the quality of the received signal of each channel is acceptable. The eye diagram does not show signs of inter-symbol interference ISI and discernible crosstalk. The vertical axis of the eye diagram is measured on an mV scale and represents the amplitude of the response with low additive noise. The opening of the eye diagram represents the eye width, which can be used to study and investigate the timing synchronization and jittering effects of the SDM system. The maximum eye amplitude is 280 mV, and the eye width is equal to 80 psec. All tested channels show no signs of a chaotic appearance generated by reflection or intermittent degradation. The presence of an OAM optical beam is confirmed experimentally by placing a thin test wire in front of the output of the (62.5/125) MM-1.8 × 3.7 MMF. The test wire appears to block part from the output ring; instead of the shadow of the test wire appearing as a straight line cutting through the optical rings, it shows a tilt either in the clockwise or the counterclockwise directions. This tilt in the shadow of the test wire confirmed that the helically propagating optical beam inside the fiber carries the OAM beam. The helical propagation of the OAM optical beam is a function of the gap distance between the optical source and the MMF and launching angles [26–28]. The illustration and schematic diagram of the shadow of the test wire approach and the OAM rings are shown in Figure 5. The electromagnetic field representing light can carry angular momentum, demonstrating the amount of dynamic rotation in the optical signal. This dynamic rotation of the angular momentum of the light beam is divided into spin angular momentum and orbital angular momentum [27]. The spin angular momentum depends on the polarization of light while the OAM depends on the topological charge, where any two OAM modes with different topological charge numbers do not interfere.

The experimental results indicated the effect of the path loss, and the angle of OAM has been carefully taken. The results showed an increase in loss when the path length increased, especially at the gap of free space. Moreover, the incident angle also contributed to increasing the losses.

This section first processed the free space path (gap) between the multi-mode and single-mode optical fiber. Table 1 presents the percentage ratio of path loss for three wavelengths. In addition, Figure 6 represents the path loss of the SMOF-MMOF part of the system.

The path loss was studied using multimode optical fiber at each incident angle for three wavelengths (1330 nm, 1490 nm, 1550 nm). The results are illustrated in Table 2 and Figure 7.

This path represents the free space path between the output of multi-mode optical fiber to the photodetectors. Table 3 and Figure 8 list the path loss percentage ratio values.

The total path loss has been evaluated from equation (2). This parameter presents the multiplication of all losses. The results are illustrated in Table 4 as a percentage value in dBm units. The overall path losses are illustrated in Figure 9

$$\mathrm{TPL}=\mathrm{LSMF}-\mathrm{MMF}+\mathrm{LMMF}+\mathrm{LMMF}-\mathrm{PD}$$(10)

Both SNR and BER are used to assess the quality of communication systems. BER performance depends on the average received power, the scintillation strength, and the receiver noise. With an appropriate design of aperture averaging, the received optical power could be increased, and the effect of the scintillation can be dumped under the effect of the gap in the OAM/SDM system, the correlation between the optical SNR and BER are expressed as in Figure 10 and 11 [28]:

An estimate for BER can be obtained by approximating the noise density of nj with a Gaussian distribution, which gives:

$$\mathrm{BER}=\frac{\mathrm{erfc}\left(I_1-I_{\mathrm{th}}\right)}{4\left(\sqrt{2}{\sigma }_1\right)}+\frac{\mathrm{erfc}\left(I_{\mathrm{th}}-I_0\right)}{4\left(\sqrt{2}{\sigma }_1\right)}$$(11)where erfc is the complementary error function, I₀ and I₁ are the average currents, and σ₁ and σ₀ are the RMS noise currents for the “0” and “1” bits, respectively. BER is expressed as the number of bit errors per unit of time. Bit synchronization errors and distortion, interference, and noise are factors. BER is usually expressed as a percentage. It can be automatically detected and displayed experimentally or using the above formula after getting the input data from experimental outcomes. The evaluation of BER as a function of Eb/No (dB) is shown in Figure 10. The results represent the performance of the OAM/SDM G-PON system at different coupling angles. Changing the coupling angle results in fluctuation in the system’s performance in terms of BER.

Therefore, to test the characterization of the system for real applications, Figures 10 and 11 are chosen to represent the system behavior under different values of θ. BER as a function of Eb/No dB BER was a criterion that could be used to measure the system’s preference by evaluating the number of errors in the digital communication system where the value was expressed as a ratio or percentage. It is often used as a performance metric to evaluate the system’s quality. Eb/No (energy per bit to noise power spectral density ratio) measures the signal-to-noise ratio (SNR) of a digital communication system. It is typically expressed in decibels (dB) and is used to evaluate the system’s quality under different noise conditions. As a function of Eb/No, BER is usually represented by a graph, with the horizontal axis showing the Eb/No in dB and the vertical axis showing the BER. The BER curve typically starts at a low value of BER at high values of Eb/No and increases as Eb/No decreases. The BER curve is often used to determine the minimum Eb/No required to achieve a certain BER. It is worth mentioning that the slope of the BER curve is related to the modulation scheme used in the system. For example, BPSK (Binary Phase Shift Keying) will perform better than QPSK (Quadrature Phase Shift Keying), and so on.

This paper proposed an OAM/SDM multiplexing architecture for a G-PON multi-optical communication system. The outcomes showed the path length effect as a function of total power and the BER. Furthermore, the impact of the coupling angle has been carefully taken into account, and the performance of the SDM has been approved as a function of coupling efficiency. It is concluded that OAM multiplexing is a technique that utilizes the orbital angular momentum of light to increase the capacity of a single optical fiber in optical communication networks. When combined with space-division multiplexing (SDM) and implemented in a G-PON system, it can provide higher data rates, lower costs, and better scalability than traditional PON systems. The architecture of an OAM/SDM G-PON system typically includes a central office and several optical network units connected via optical fibers, with the use of wavelength division multiplexing and OAM multiplexer/demultiplexer (OAM-MUX/DEMUX) units to multiplex and demultiplex the OAM and SDM channels. The OAM/SDM G-PON system can provide better capacity and scalability than the traditional PON system.