Equilibrium Mode Distribution Research Articles

Launch Light Design for Coupling Loss Measurement of Step-Index Multimode Fiber Connections

Measurement of coupling loss using step-index multimode fiber connections that are used in multi-gigabit optical communication systems must be accurate and precise to meet rigorous system specifications. We propose a launch light design for performing coupling loss measurement with reproducibility for step-index plastic cladding silica fibers. In the proposed design, the modal power distribution of the launch light is represented by the encircled angular flux (EAF). Specifically, the lower-order mode and the higher-order mode sides of the EAF boundary conditions were systematically calculated. The EAF boundary conditions were designed using our developed flowchart, which is composed of an optical model design, a performance review, and a model redesign based on the equilibrium mode distribution obtained from round-robin tests. The validity of the EAF boundary conditions was confirmed by optical design computing simulation and experiment. Under practical conditions wherein the misalignment range of a fiber connection is 40 μm or less in the lateral direction offset and 100 μm or less in the axial direction offset, the EAF boundary conditions of the launch light were determined such that the connection loss was 2.0 dB or less and the variation in loss due to modal power distribution variations was ±0.20 dB or less. The use of the launch light that meets the determined EAF boundary conditions allows for sufficient measurement reproducibility in verifying that the connection losses meet the system requirements. The alignment tolerance thus achieved is suitable for practical purposes.

Influence of mode coupling on three spatially multiplexed channels in multimode graded index plastic optical fibers

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.

Spatial division multiplexing in nine-core graded index plastic optical fibers

We propose a spatial division multiplexing in a new designed multimode multicore graded index plastic optical fiber with nine cores arranged in an octagonal array. The influence of mode coupling on two-channel spatial division multiplexing capability in each of nine cores 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 in each of nine cores with a minimal crosstalk between two neighbor spatial optical channels. Two spatial channels in the proposed nine-core graded index plastic optical fiber can be employed with a minimal crosstalk up to the fiber length of 5 m, which is about 18% of the coupling length (fiber length where equilibrium mode distribution is achieved). Such characterization of multicore graded index plastic optical fibers should be considered in designing a multicore optical fiber transmission system for space division multiplexing.

Improvement of transmission characteristics of step-index multimode fibers using variable mode controller

The mode dispersion induced in step-index multimode fibers significantly deteriorates the transmission characteristics and bandwidth. To overcome this existing problem, we suppressed the delay of the transmission signal through mode redistribution realized by applying a torsional stress to a fiber using a variable mode controller (VMC). By suppressing the transmission delay, the transmission characteristics and bandwidth of the fiber set in the VMC have been improved. The mode of the fiber set in the VMC achieves an equilibrium mode distribution by mode redistribution. Therefore, the near- and far-field patterns of the VMC were largely stable.

Influence of wavelength on equilibrium mode distribution and steady state distribution in W-type plastic optical fibers

Wavelength dependence of equilibrium mode distribution (EMD) and steady state distribution (SSD) in W-type plastic optical fibers (POFs) is investigated in this paper for parametrically varied width of the fiber’s intermediate optical layer and refractive index of the outer cladding. We have shown that with increasing the wavelength EMD and SSD are achieved at shorter W-type POF lengths. This is explained by the rise of the leaky mode losses with increasing wavelength. This facilitates tailoring W-fibers to a specific application at hand at different wavelengths.

Influence of mode coupling on angular division multiplexing in seven-core plastic optical fibers

We propose an angular division multiplexing in new designed multicore plastic optical fiber with seven cores arranged in a hexagonal array. The influence of mode coupling on two-channel angular division multiplexing capability in each of seven cores is investigated by solving the power flow equation. Our numerical results show that mode coupling significantly limits the fiber length at which the angular division multiplexing can be realized in each of seven cores with a minimal crosstalk between two neighbor angular optical channels. Two angular channels in the proposed seven-core plastic optical fiber can be employed with a minimal crosstalk up to the fiber length which is about 20% of the coupling length (fiber length where equilibrium mode distribution is achieved). Such characterization of multicore optical fibers should be considered in designing a multicore optical fiber transmission system for space division multiplexing.

Mode coupling in bent and twisted step-index plastic-clad silica fibers

The state of mode coupling in bent and twisted step-index plastic-clad silica fibers is investigated in this article by the numerical solving of the time-independent power flow equation. The coupling length Lc at which the equilibrium mode distribution is achieved and the length zs of the fiber required for achieving the steady-state mode distribution are obtained. It was found that the bent and twisted step-index plastic-clad silica fiber investigated in this work shows a much stronger mode coupling than the straight plastic-clad silica fiber. As a result, the coupling lengths where equilibrium mode distribution is achieved, and the lengths of fiber required for achieving a steady-state mode distribution for bent and twisted fibers, are much shorter than corresponding lengths for straight fibers.

Wavelength dependence of equilibrium mode distribution and steady state distribution in W-type plastic-clad silica fibers

Abstract Wavelength dependence of equilibrium mode distribution (EMD) and steady state distribution (SSD) in W-type plastic-clad silica fibers (PCSFs) is investigated in this paper for parametrically varied width of the fiber’s intermediate optical layer and refractive index of the outer cladding. We have shown that the W-type PCSF has better transmission characteristics at longer infrared wavelengths. This is explained by the rise of the leaky mode losses with increasing wavelength. This facilitates tailoring W-fibers to a specific application at hand in the infrared wavelength region.

Mode coupling and its influence on space division multiplexing in step-index plastic-clad silica fibers

Abstract The state of mode coupling in step-index plastic-clad silica fibers is investigated in this article by numerical solving of the time-independent power flow equation. The coupling length Lc at which the equilibrium mode distribution is achieved and the length (zs) of the fiber required for achieving the steady-state mode distribution are obtained. It was found that the plastic clad silica fiber investigated in this work showed a much weaker mode coupling than the plastic-clad silica fibers investigated in earlier works. We have also shown that mode coupling significantly limits the fiber length at which the space division multiplexing (SDM) can be realized with a minimal crosstalk between the neighbor optical channels.

Influence of mode coupling on three, four and five spatially multiplexed channels in multimode step-index plastic optical fibers

We investigate the influence of mode coupling on space division multiplexing capability of three multimode step-index plastic optical fibers with different strengths of mode coupling. Results show that mode coupling significantly limits the fiber length at which the space division multiplexing can be realized with a minimal crosstalk between the neighbor optical channels. Three, four and five spatially multiplexed channels in the investigated multimode step-index plastic optical fibers can be employed with a minimal crosstalk up to the fiber lengths which are about 7%, 5% and 3% of the corresponding coupling lengths (fiber length where equilibrium mode distribution is achieved), respectively. Such characterization of optical fibers should be considered in designing an optical fiber transmission system for space division multiplexing.

Mode coupling in multimode step-index plastic-clad silica fibers with corrugated surfaces

The state of mode coupling in step-index plastic-clad silica fibers with corrugated surfaces is investigated in this article using the power flow equation. The coupling coefficient in this equation was obtained using our previously reported method. This enabled us to obtain the length of the corrugated piece of the fiber at which equilibrium mode distribution is achieved as well as the length at which a steady state distribution is established. It was found that the plastic-clad silica fibers with corrugated surfaces showed much stronger mode coupling than plastic-clad silica fibers without corrugated surfaces. Consequently, the equilibrium as well as steady state mode distributions were achieved at shorter fiber lengths in plastic-clad silica fibers with corrugated surfaces than in the same type of optical fibers without corrugated surfaces.

Encircled Angular Flux Representation of the Modal Power Distribution and Its Behavior in a Step Index Multimode Fiber

The optical properties of inline optical components inserted at the input to a multimode optical fiber (MMF) strongly affect the propagating modal power distribution (MPD). To realize stable systems with predictable reproducible performance and to encourage widespread use of MMF systems, improvements to the system design process and to the characterization process need to be made and new interface standards need to be defined. To this end, we have developed a new reproducible MPD measurement and representation together with its theoretical definition. By modifying the encircled flux (EF) representation, which is based on the near-field pattern of a graded-index multimode optical fiber (GI-MMF), we define the encircled angular flux (EAF) for step-index multimode optical fibers (SI-MMFs) based on their far-field patterns (FFPs). Using a SI-MMF, which is used for low cost short distance interconnects, as an example, we show the changes in the MPD along the fiber, reveal an unusual insertion loss-increasing phenomenon due to the evanescent tails of the core modes extending into the cladding, and characterize the equilibrium mode distribution (EMD) in the fiber. The EAF representation enables these phenomena to be quantified. We also propose an EAF template that consists of the target EMD and its tolerance. If device system designers use the EAF template to set the launch conditions, they can perform a fair assessment of the components, and they can design the system performance even if some components are replaced with others from a different supplier manufactured by a different method. We call this concept “Total MPD Management.”

Statistical analysis of intrinsic and extrinsic coupling losses for step-index polymer optical fibers

The intrinsic and extrinsic coupling losses of step-index polymer optical fibers are statistically examined by Monte Carlo simulations. In contrast to most existing models that linearly scale individual losses, a comprehensive analytic coupling loss model is used that also considers the interdependencies between mismatches in numerical aperture and core diameter, as well as radial and longitudinal offsets. As a typical example, the coupling losses of A4a.2 step-index multimode fibers are analyzed for an equilibrium mode distribution. The results show considerably less conservative coupling loss estimations than with traditional models, improving link power budgeting.

Mode coupling in glass optical fibers and liquid-core optical fibers by three methods

We test Slemon and Wells's function and recently reported Hurand et al.'s (Appl. Opt., 50, 492–499, 2011) function for calculation of coupling characteristics in step-index optical fibers against experimental measurements and against calculations by a related method that is based on the power flow equation. Compared are the coupling length Lc (which is the fiber length where the equilibrium mode distribution is achieved) and length zs (where steady-state distribution is achieved) in three step index glass optical fibers as well as a liquid core optical fiber. The two functions, while simpler to apply being just algebraic formulas, are less accurate over a wide range of numerical apertures. It is also shown that fibers with same coupling coefficient can have much different coupling characteristics.

EQUILIBRIUM MODE DISTRIBUTION IN W-TYPE GLASS OPTICAL FIBERS

Power flow equation is used to calculate equilibrium mode distribution in W-type glass optical fibers. It has been shown how the coupling length for achieving the equilibrium mode distribution in W-type glass optical fibers varies with the depth and width of the intermediate layer and coupling strength for different widths of launch beam distribution. W-type optical fibers have shown effectiveness in reducing modal dispersion and bending loss.

Mode coupling in low NA plastic optical fibers

Using the power flow equation and experimental measurements, investigated in this article is the state of mode coupling in low NA (0.3) step-index plastic optical fibers for laser beam launch. Results show the coupling length L c at which the equilibrium mode distribution is achieved and the length z s of the fiber required for achieving the steady-state mode distribution. Numerical results obtained using the power flow equation agree well with experimental measurements. • The state of mode coupling in low NA (0.3) step-index plastic optical fibers is investigated. • The coupling length L c at which the equilibrium mode distribution is achieved is obtained. • The length z s of the fiber required for achieving the steady-state mode distribution is also determined.

EQUILIBRIUM MODE DISTRIBUTION IN W-TYPE GLASS OPTICAL FIBERS

Power flow equation is used to calculate equilibrium mode distribution in W-type glass optical fibers. It has been shown how the coupling length for achieving the equilibrium mode distribution in W-type glass optical fibers varies with the depth and width of the intermediate layer and coupling strength for different widths of launch beam distribution. W-type optical fibers have shown effectiveness in reducing modal dispersion and bending loss.

An Analytic Connector Loss Model for Step-Index Polymer Optical Fiber Links

The authors report on an analytic connector loss model for step-index polymer optical fibers (SI-POF). The model describes the non-linear dependencies for combinations of the most important intrinsic and extrinsic influence parameters like Fresnel reflections, mismatches in numerical aperture (NA) and core diameters, as well as lateral, longitudinal and angular offsets. As connector losses strongly depend on the mode distribution, expressions for the mode-dependent coupling efficiencies for the various influence parameters are derived. This way, the model can handle any rotationally symmetric mode distribution including the uniform mode distribution (UMD) and the equilibrium mode distribution (EMD) in the steady-state. It is shown that for step-index fibers, lateral and longitudinal offsets can be handled in a similar way, which reduces the overall effort for the mathematical description. For the typical case of identical fibers, the authors also derive easy-to-apply approximations for a combination of lateral and longitudinal offsets under UMD and EMD conditions. The results are in good agreement with ray-tracing simulations and are evaluated for the cases of identical fibers and the worst case parameter constellation for the SI-POF in the IEC A4a.2 fiber class.

Influence of width of launch beam distribution on equilibrium mode distribution in W-type glass optical fibers

Power flow equation is used to calculate spatial transients and equilibrium mode distribution in W-type glass optical fibers (doubly clad fibers with three layers). A numerical solution has been obtained by the explicit finite difference method. For the first time, we have shown how the coupling length for achieving the equilibrium mode distribution in W-type glass optical fibers varies with the depth and width of the intermediate layer and coupling strength for different widths of launch beam distribution. Such characterization of these fibers is consistent with their manifested effectiveness in reducing modal dispersion and bending loss.

Equilibrium mode distribution and steady-state distribution in 100–400 μm core step-index silica optical fibers

Using the power flow equation, the state of mode coupling in 100-400 μm core step-index silica optical fibers is investigated in this article. Results show the coupling length L(c) at which the equilibrium mode distribution is achieved and the length z(s) of the fiber required for achieving the steady-state mode distribution. Functional dependences of these lengths on the core radius and wavelength are also given. Results agree well with those obtained using a long-established calculation method. Since large core silica optical fibers are used at short distances (usually at lengths of up to 10 m), the light they transmit is at the stage of coupling that is far from the equilibrium and steady-state mode distributions.