The bandwidth of multimode W-type microstructured plastic optical fibers (mPOFs) is analyzed using the time-dependent power flow equation (TD PFE). The results demonstrate that increasing the wavelength enhances the bandwidth in W-type mPOFs, depending on the inner cladding width and the launch beam distribution width. We observed that bandwidth improves with thinner and shallower inner cladding, as well as a narrower centrally launched beam. This characterization aligns with the fibers’ effectiveness in increasing bandwidth, allowing for the customization of various W-type optical fibers for specific applications at different wavelengths.

Up to now, there have been no commercial simulation tools accessible for researching the transmission properties of multimode microstructured optical fibers (MOFs). In order to avoid this problem, this study uses the time-independent power flow equation (TI PFE) numerical solution to examine the wavelength dependency of the equilibrium mode distribution (EMD) and steady state distribution (SSD) in multimode graded-index microstructured polymer optical fibers (GI mPOF) with a solid core. We showed that the lengths zs at which an SSD is obtained in GI mPOF and the coupling length Lc necessary to create an EMD are shorter at λ = 568 nm than they are found to be at λ = 633 nm. The lengths Lc and zs stay constant when the wavelength decreases further from λ = 568 to 522 and then to 476 nm. As a result, it is anticipated that a faster bandwidth enhancement in the tested GI mPOF will take place at wavelengths around λ = 568 nm as opposed to λ = 633 nm. Such a bandwidth improvement is not brought about by additional wavelength reduction. The study’s findings can be used in communication and sensory systems that use multimode GI mPOFs at different wavelengths.

This study employs a novel physics-informed neural network (PINN) approach, the standard explicit finite difference method (EFDM) and unconditionally positivity preserving FDM to tackle the one-dimensional Sine–Gordon equation (SGE). Two test problems with known analytical solutions are investigated to demonstrate the effectiveness of these techniques. While the three employed approaches demonstrate strong agreement, our analysis reveals that the EFDM results are in the best agreement with the analytical solutions. Given the consistent agreement between the numerical results from the EFDM, unconditionally positivity preserving FDM and PINN approach and the analytical solutions, all three methods are recommended as competitive options. The solution techniques employed in this study can be a valuable asset for present and future model developers engaged in various nonlinear physical wave phenomena, such as propagation of solitons in optical fibers.

Multimode polymer optical fibers (POFs) are considered to be the best choice for short-distance communication lines due to their advantageous properties. One must pay close attention to POFs’ most crucial transmission property, bandwidth (BW), which affects the fibers’ transmission capacity. The improvement of POF transmission qualities, particularly BW, which is its most crucial property, has been the subject of many researches during the past few decades. Both experimental and theoretical approaches have been used to address this issue. Up to now, there were no commercial simulation tools available for studying the transmission characteristics of multimode optical fibers. To overcome this problem, the modal continuum approach is employed to characterize light transmission in various kinds of multimode optical fibers. This modal continuum approach, which uses the time-dependent power flow equation (TD PFE), plays the most important role in the theoretical approaches. The PFE is the most comprehensive because it takes into account attenuation, mode coupling and modal dispersion, which significantly affects the BW. It can also be modified to accommodate various refractive index profiles, including step-index (SI), W-type index and graded index (GI) profiles. This review analyzes the pertinent literature related to the use of modal continuum-based models for BW modeling in conventional and microstructured multimode POFs. An overview of methodologies for optical fiber analysis with a focus on modal continuum approximation, and solutions to the TD PFE for various multimode fiber types, is provided.

The time-dependent power flow equation (TD PFE) is used to theoretically examine the wavelength dependency of the bandwidth in a multimode graded-index microstructured polymer optical fiber (GI mPOF) with a solid core. The TD PFE is numerically solved using the explicit finite difference method (EFDM) and physics-informed neural networks (PINNs). Our numerical results show that the bandwidth decreases with an increasing wavelength from 476 to 522 and finally to 568 nm. With further increasing of the wavelength from 568 to 633 nm, the bandwidth increases. In this way, we have demonstrated that the maximum bandwidth of the analyzed GI mPOF in the analyzed wavelength region is obtained at 633 nm. Such bandwidth behavior is a consequence of the different influences of the analyzed wavelengths on the parameters that characterize the refractive index distribution and the maximum propagating principal mode number of the analyzed GI mPOF. We also showed that, when the radial offset of the incident light beam increases, the bandwidth decreases. This results from a greater modal dispersion when higher guided modes are excited. As a result, based on the observations reported in this work, it is simpler to modify the GI mPOF for a particular application at various wavelengths. (c) 2024 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.

We employed a novel physics-informed neural networks (PINN) to tackle (1+1) dimensional Sine-Gordon equation (SGE). A test problem with known analytical solution is numerically solved to demonstrate the effectiveness of the PINN, and compared to standard explicit finite difference method (EFDM) and Chen-Charpentier et al.’s finite difference method (CCFDM). Although the three methods used show good agreement, our research shows that the EFDM results accord with the analytical solution the best. Given the consistent agreement between the numerical results obtained by all three methods and the analytical solution, all three methods are recommended as competitive options. The methods employed in this study can be a valuable asset for present and future model developers engaged in various nonlinear physical wave phenomena, such as solitons evolution or soliton interaction as well as optical pulses propagation in nonlinear media, including optical fibers.

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We investigate mode coupling in a multimode graded-index microstructured polymer optical fiber (GI mPOF) with a solid core by solving the time-independent power flow equation (TI PFE). Using launch beams with various radial offsets, it is possible to calculate for such an optical fiber the transients of the modal power distribution, the length Lc at which an equilibrium mode distribution (EMD) is reached, and the length zs for establishing a steady-state distribution (SSD). In contrast to the conventional GI POF, the GI mPOF explored in this study achieves the EMD at a shorter length Lc. The earlier shift to the phase of slower bandwidth decrease would result from the shorter Lc. These results are helpful for the implementation of multimode GI mPOFs as a part of communications and optical fiber sensory systems.

The investigation of the bandwidth in multimode graded-index microstructured polymer optical fiber (GI mPOF) with a solid core is proposed using a modal diffusion approach. For a variety of launch radial offsets of multimode GI mPOF, bandwidth is reported by numerically solving the time-dependent power flow equation (TD PFE) using the explicit finite difference method (EFDM) and physics-informed neural networks (PINN). The decline in bandwidth with fiber length becomes slower at fiber lengths close to the coupling length Lc at which an equilibrium mode distribution (EMD) is attained, showing that mode coupling enhances bandwidth at longer fiber lengths. As fiber length is increased, bandwidth approaches complete independence from radial offset, suggesting the steady-state distribution (SSD) has been reached. We compare multimode GI mPOF performance in terms of bandwidth with that of traditional multimode GI POFs made of the same material. Higher bandwidth performance and quicker bandwidth improvement are displayed by the GI mPOF. To enhance fiber performance in GI mPOF links, such a fiber char-acterization can be used.

By solving the time-independent power flow equation (TI PFE), we study mode coupling in a multimode W-type microstructured polymer optical fiber (mPOF) with a solid-core. The multimode W-type mPOF is created by modifying the cladding layer and reducing the core of a multimode singly clad (SC) mPOF. For such optical fiber, the angular power distributions, the length Lc at which an equilibrium mode distribution (EMD) is achieved, and the length zs for establishing a steady state distribution (SSD) are determined for various arrangements of the inner cladding's air-holes and different launch excitations. This information is useful for the implement of multimode W-type mPOFs in telecommunications and optical fiber sensors.

This paper investigates wavelength dependence of equilibrium mode distribution and steady-state distribution in W-type (double-clad) microstructured polymer optical fibers (mPOFs) with a solid core for parametrically varied refractive index and width of the intermediate layer (IL) (inner cladding) by solving the time-independent power flow equation (TI PFE). In the case of wider IL, independent of wavelength, the lengths for establishing the equilibrium mode distribution and steady-state distribution are larger. We have demonstrated that the wavelength has no effect on these lengths for IL’s width that is larger. These lengths drop in a wavelength-dependent manner as the IL's width decreases. Equilibrium mode distribution and steady-state distribution occur at shorter optical fiber lengths as the depth of the IL diminishes, which is due to the similarly declining number of leaky modes. The smaller the depth of the IL, the shorter the fiber length is required for completion of the coupling process. These programmable characteristics allow double-clad W-type mPOFs to be easier customized for a particular use in optical fiber sensors and communications at various wavelengths.

Solving the time-dependent power flow equation (PFE) provides a useful method to study the transmission bandwidth of step-index silica photonic crystal fibers (SI SPCFs). The transmission bandwidth of these kinds of fibers is determined for different air-hole structures (different numerical apertures (NAs)) and different distribution widths of the Gaussian launch beam. The results indicate that the lower the NA of SI SPCFs, the higher the bandwidth (for example, for a lower NA of SI SPCFs, a bandwidth that is eight times larger is obtained at a fiber length of 3500 m). The narrower launch beam at short fiber lengths results in a wider bandwidth. The longer the fiber (>300 m), the much less the effect of the launch beam width on the bandwidth. The bandwidth becomes independent of the width of the launch beam distribution at the fiber length at which a steady-state distribution (SSD) is reached. These results are useful for some potential applications, such as high capacity transmission optical fiber systems.

We investigate the state of mode coupling in a multimode step-index plastic photonic crystal fiber (SI PPCF) with a solid-core by solving the time-independent power flow equation. For various arrangements of air-holes, and therefore a different numerical apertures (NAs), as well as a different widths of launch beam distribution, the length Lc for achieving equilibrium mode distribution (EMD) and length zs at which a steady state distribution (SSD) is established are determined for such fiber. We show that the larger the air holes in the cladding (higher NA), the longer length of the fiber it takes for the modal distribution-transients to reach their equilibrium and steady state. This is as a consequence of the greater participation rate of higher-order modes in higher-aperture photonic-crystal fibers. In contrary, in the case of a wide launch that excites more guiding modes, these lengths shorten. This is because the energy of a wide launch beam is more uniformly distributed among guided modes in the fiber, thus the EMD and SSD are reached at shorter distances than for a narrow launch beam. Such information is of interest for application of multimode photonic crystal fibers in telecommunication and fiber optic sensors.

By solving the time-dependent power flow equation, we present a novel approach for evaluating the bandwidth in a multimode step-index polymer photonic crystal fiber (SI PPCF) with a solid core. The bandwidth of such fiber is determined for various layouts of air holes and widths of Gaussian launch beam distribution. We found that the lower the NA of SI PPCF, the larger the bandwidth. The smaller launch beam leads to a higher bandwidth for short fibers. The influence of the width of the launch beam distribution on bandwidth lessens as the fiber length increases. The bandwidth tends to its launch independent value at a particular fiber length. This length denotes the onset of the steady state distribution (SSD). This information is useful for multimode SI PPCF applications in telecommunications and optical fiber sensing applications.

We propose a new method for investigation the state of mode coupling in a multimode step-index silica photonic crystal fiber (SI SPCF) with a solid-core by solving the time-independent power flow equation. For various arrangements of air-holes (different numerical apertures (NAs)), as well as a different widths of launch beam distribution, the length Lc for achieving equilibrium mode distribution (EMD) and length zs at which a steady state distribution (SSD) is established are determined for such fiber. We obtained that the larger the air holes in the cladding (higher NA), the longer length of the fiber it takes for the modal distribution-transients to reach their equilibrium and steady state. In the case of a wide launch that excites more guiding modes, these lengths shorten. Such information is of interest for application of multimode SI SPCFs in telecommunication and fiber optic sensors.

The bandwidth and steady-state loss of multimode W-type plastic-clad silica optical fibers are investigated by solving the time-dependent power flow equation. The results show how the bandwidth of W-type plastic-clad silica optical fibers can be enhanced by shifting from the red to the infrared wavelength region for different intermediate layer widths and refractive indices of the outer cladding. Such characterization of these fibers is consistent with their manifest effectiveness in reducing modal dispersion and increasing bandwidth.

By solving the power flow equation, we investigate the influence of mode coupling on space division multiplexing capability of three multimode step-index silica optical fibres with a different strengths of mode coupling. Results show that mode coupling significantly limits the length of these fibres at which the space division multiplexing can be realized with a minimal crosstalk between the neighbour optical channels. This is most pronounced in silica optical fibres with the strongest mode coupling. The two and three spatially multiplexed channels in the investigated step-index silica optical fibres can be employed with a minimal crosstalk up to the fibre lengths of few hundred of meters and few tens of meters, respectively. These lengths are much shorter than kilometer lengths at which these fibres are usually employed without space division multiplexing. Such characterization of optical fibres should be considered in designing an optical fibre transmission system for space division multiplexing.

A method is proposed for predicting the evolution of the power distribution along graded-index plastic optical fibers. This method is verified against our recently reported measurements. The strong influence of mode coupling on the power distribution is demonstrated on a specific graded-index plastic fiber to illustrate the influence of mode coupling in applications, such as data transmission, power delivery, and sensing systems.

The influence of mode coupling on three-channel spatial division multiplexing capability in multimode graded index plastic optical fibers is investigated by solving the power flow equation. Our numerical results show that mode coupling significantly limits the fiber length at which the spatial division multiplexing can be realized with a minimal crosstalk between three neighbor spatial optical channels. Three spatial channels in the multimode graded index plastic optical fiber can be employed with a minimal crosstalk up to the fiber length of 3.5 m, which is about 12.5% of the coupling length (fiber length where equilibrium mode distribution is achieved). Such characterization of multimode graded index plastic optical fibers should be considered in designing an optical fiber transmission system for space division multiplexing, particularly for small office networking.

Transmission characteristics (bandwidth and steady state loss) of multimode W-type glass optical fibers are investigated by solving the time-dependent power flow equation. Results show how the bandwidth in W-type glass optical fibers can be enhanced by shifting from the red to infrared wavelength region for different depths and widths of the intermediate layer as well as for different launch excitations. Such characterization of these fibers is consistent with their manifested effectiveness in reducing modal dispersion and bending loss.