Multimode Step Index Research Articles

Step and graded-index core-based polymer multimode interference splitters for photonic integrated circuits

This paper demonstrates step-index (SI) and graded-index (GI) core-based multimode interference (MMI) splitters realized with polymer materials for photonic integrated circuits (PICs). These SI and GI index-based MMI splitters guide the input light through the multimode waveguide following the self-imaging principles and demonstrate the multiple outputs with the same uniformity when the self-imaging length is obtained. We numerically design and develop (1 ×5) MMI splitters using the beam propagation method (BPM), and we use the RSoft CAD BeamPROP solver for the structural design and waveguide characterization. The structures of the SI and GI MMI splitters are optimized by investigating the structural parameters, particularly the width and length of the multimode waveguide and the core spacing between the output ports with the maximum uniform intensity at the self-imaging length. We also compare the structural design and optical properties of the SI and GI MMI waveguides. The excess losses of the SI MMI splitter are 1.09 and 1.12 dB for transverse electric (TE) and transverse magnetic (TM) modes, respectively, while for the GI MMI splitter, the losses are 0.57 dB and 0.56 dB for TE and TM modes, respectively at 1.55 µm. The power splitting efficiency for the SI MMI splitter is 77%, and for the GI MMI splitter, it is 88%. We also investigate the polarization dependence loss (PDL) for both MMI splitters, and the losses for the SI and GI MMI splitters are 0.024 dB and 0.004 dB, respectively.

Calculation of the Coupling Coefficient in Step-Index Multimode Polymer Optical Fibers Based on the Far-Field Measurements

Using the power flow equation (PFE), this article investigates mode coupling in step-index (SI) multimode (MM) polymer optical fiber (POF). This equation’s coupling coefficient was initially fine-tuned so that it could appropriately reconstruct previously recorded far-field (FF) power distributions. The equilibrium mode distribution (EMD) and steady-state distribution (SSD) in the SI MM POF were found to be obtained at lengths Lc = 15 m and zs = 41 m, respectively. These lengths are substantially shorter than their glass optical fiber counterparts. Such characterization of the investigated POF can be used in its employment as a part of the communication or sensory system. Namely, the POF’s bandwidth is inverse linear function of fiber length (z−1) below the coupling length Lc. However, it has a z−1/2 dependence beyond this equilibrium length. Thus, the shorter the coupling length Lc, the sooner transition to the regime of slower bandwidth decrease occurs. It is also important to be able to determine a modal distribution at a certain length of the POF employed as a part of optical fiber sensory system.

Mode Coupling and Steady-State Distribution in Multimode Step-Index Organic Glass-Clad PMMA Fibers

Mode coupling and power diffusion in multimode step-index (SI) organic glass-clad (OGC) PMMA fiber is examined in this study using the power flow equation (PFE). Using our previously proposed approach we determine the coupling coefficient D for this fiber. When compared to standard multimode SI PMMA fibers, the multimode SI OGC PMMA fiber has similar mode coupling strength. As a result, the fiber length required to achieve the steady-state distribution (SSD) in SI OGC PMMA fibers is similar to that required in standard SI PMMA fibers. We have confirmed that optical fibers with a plastic core show more intense mode coupling than those with a glass core, regardless of the cladding material. These findings could be valuable in communication and sensory systems that use multimode SI OGC PMMA fiber. In this work, we have demonstrated a successful employment of our previously proposed method for determination of the coupling coefficient D in multimode SI OGC PMMA fiber. This method has already been successfully employed in the previous research of mode coupling in multimode SI glass optical fibers, SI PMMA fibers and SI plastic-clad silica optical fibers.

Theoretical Investigation of Bandwidth in Multimode Step-Index Silica Photonic Crystal Fibers

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.

Treatment of Mode Coupling in Step-Index Multimode Microstructured Polymer Optical Fibers by the Langevin Equation.

By solving the Langevin equation, mode coupling in a multimode step-index microstructured polymer optical fibers (SI mPOF) with a solid core was investigated. The numerical integration of the Langevin equation was based on the computer-simulated Langevin force. The numerical solution of the Langevin equation corresponded to the previously reported theoretical data. We demonstrated that by solving the Langevin equation (stochastic differential equation), one can successfully treat a mode coupling in multimode SI mPOF as a stochastic process, since it is caused by its intrinsic random perturbations. Thus, the Langevin equation allowed for a stochastic mathematical description of mode coupling in SI mPOF. Regarding the efficiency and execution speed, the Langevin equation was more favorable than the power flow equation. Such knowledge is useful for the use of multimode SI mPOFs for potential sensing and communication applications.

Theoretical Investigation of the Capacity of Space Division Multiplexing with Multimode Step-Index Air-Clad Silica Optical Fibers

We studied the effect of mode coupling on the space division multiplexing (SDM) capabilities of multimode step-index (SI) air-clad silica optical fibers by numerically solving the power flow equation. Mode coupling considerably reduces the length of these fibers at which space division multiplexing may be achieved with minimal crosstalk between neighboring optical channels, according to the findings. Up to 120 m and 30 m, respectively, the two and three spatially multiplexed channels in the investigated multimode step-index silica optical fibers can be used with low crosstalk. When building a space division multiplexing-based optical fiber transmission system, such characterization of optical fibers should be taken into account.

Comparison of Several Characteristics of Single Mode Step-Index (SMSI), Multimode Step-Index (MMSI), and Multimode Graded-Index (MMGI) Fibers for Optical Communication Systems

Abstract: Optical fiber is a medium that made by silica or plastic, and widely used in transmitting information over longer distance especially in communication system. There are three types of fiber optic used in this project which are single mode stepindex (SMSI), multimode step-index (MMSI), and multimode graded-index (MMGI) in optical communication system. There are three objectives in this project in order to get the suitable optical fibers in the communication system. First objective is to simulate the result by using Excel and Origin software. The data and the formula of fiber optics will be key in through Excel software while the graph will be analyzed by using Origin software. The second objective is to compare the different types of fiber optics in communication system by comparing the several of their characteristics such as numerical aperture (NA), acceptance angle (θ(a)) and propagation constant (β). The performance of all types fiber optics are analyzed from the result using the standard communication wavelength of 1550 nm. The core diameter for SMSI, MMSI, and MMGI are 9, 200 and 50 μm respectively while the cladding diameter for SMSI and MMGI is 125 μm and 240 μm for MMSI. This diameter also been analyzed by using the standard value for optical communication system. Then, the comparison between SMSI, MMSI and MMGI will be made to choose the more suitable for optical communication system based on their characteristics. From the results, MMSI and MMGI give best performance compared to SMSI. After that, the third objective is to make the comparison between MMSI and MMGI in term of intermodal dispersion to compare the efficiencies of fiber optics. MMGI give the better result in terms of efficiencies for communication system compared to MMSI. Keyword: Single Mode Step-Index (SMSI), Multimode Step-Index (MMSI), Multimode Graded-Index (MMGI), Communication System, Excel and Origin Software

Power efficient Space Division Multiplexing–Wavelength Division Multiplexing system using multimode EDFA with elevated refractive index profile

SummarySpace division multiplexing (SDM) is an endowment technology to increase the collective bandwidth of multimode transmission in wavelength division multiplexing (WDM) system. In this paper, four wavelength signals from 229.6 to 232.6 THz are transmitted. For each wavelength, three linearly polarized (LP) modes are multiplexed using SDM. These 12 LP modes are transmitted through four parallel Multimode Step Index (MSI) fibers and received by four optical network units (ONUs). A multimode erbium doped fiber amplifier (MMEDFA) with elevated refractive index profile (ERIP) is used as preamplifier to this SDM–WDM system. This ERIP is complying with ITU‐T G.651.1 standard fiber in dispersion performance. The pumping power of 10 mW is adequate for this MMEDFA which is very low and cost effective. LP modes are transmitted, and performance of proposed transmission system is evaluated in terms of spatial electric fields, pumping power requirement, output optical power, and bit error rate (BER).

Effect of optical fiber core diameter on Brillouin scattering loss

This paper reports the effect of core diameter of optical fiber cables on stimulated Brillouin scattering loss, which is one of the major loss characteristics of an optical fiber communication system. Analysis of this loss characteristic at three windows of the operating wavelength of a laser has been carried out through a numerical approach. Among different types of optical fiber cables, multi-mode step index silica fiber, multi-mode graded index silica fiber and plastic fibers have been considered for the numerical analysis. The numerical analysis has been performed using MATLAB in this research work. Through the comparative analysis, it has been ascertained that the Brillouin scattering loss is not only affected by the operating wavelength, but also by the core diameter of the different type of the cable. From the investigation of the comparative analysis, it is revealed that Brillouin scattering loss declines with the application of multi-mode graded index silica fiber. However, in the plastic fiber category, plastic step index fiber offers better performance.

Absolute spectral backscatter measurements of large-core multimode PMMA polymer optical fibers.

To our knowledge, we are the first to measure the absolute value of the backscattering coefficient of a standard 1 mm core-diameter, multimode (MM) step-index (SI) polymethylmethacrylate (PMMA) polymer optical fiber (POF) for the spectral range of 450 nm to 700 nm. Our optical time domain reflectometer (OTDR) setup consists of a femtosecond supercontinuum laser with an acousto-optical filter as a tunable light source with short pulses and a time-correlated single-photon counting system as a receiver with a high dynamic range. The backscattering coefficient is calculated from the ratio between the energy within the fiber end reflex and the distributed backscattering level. We also measured the spectral attenuation with our OTDR setup and compared it with a standardized measurement method. At the attenuation minima within the measured spectral range the backscattering level of a 1 ns pulse is about -46dB at 520 nm, -48dB at 570 nm, and -51 dB at 650 nm. We were also able to show by the observed wavelength dependence that Rayleigh scattering causes a majority of the scattering.

Design of Step-Index Multimode Optical Fiber

In this paper, a step-index fiber with core index 1.445 5 1 7 and cladding index 1.443 1 5 7 has been designed and studied. Multimode operation is achieved by using a fiber with core radius 25 μm operating at a wavelength of 1.3 μm. The mode parameters (effective refractive index, phase constant, fractional modal power in the core and cutoff wavelength) were calculated using RP fiber calculator (PRO version 2020). The shapes of the intensity and amplitude distribution of linearly polarized guided modes were shown.

Observation of strong mode coupling in multimode step index silica optical fibers with fluorinated thermoplastic polymer cladding

Using the power flow equation, the state of mode coupling in step index multimode silica optical fiber with fluorinated thermoplastic polymer cladding is investigated in this work. Coupling coefficient is determined by employing our previously reported calculation method. The silica optical fiber with fluorinated thermoplastic polymer cladding shows much stronger mode coupling than the all plastic-clad silica fibers investigated in earlier works. Consequently, it takes much shorter fiber length for the equilibrium mode distribution or steady state distribution to develop (faster launch beam narrowing), which is of great interest in employing silica optical fiber with fluorinated thermoplastic polymer as a part of telecommunication, medical and sensory system.

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.

Reciprocity-induced symmetry in the round-trip transmission through complex systems.

Reciprocity is a fundamental principle of wave physics and directly relates to the symmetry in the transmission through a system when interchanging the input and output. The coherent transmission matrix (TM) is a convenient method to characterize wave transmission through general media. Here, we demonstrate the optical reciprocal nature of complex media by exploring their TM properties. We measured phase-corrected TMs of forward and round-trip propagation in a single polarization state through a looped 1 m-long step-index optical multimode fiber (MMF) to experimentally verify a transpose relationship between the forward and backward transmission. This symmetry impedes straightforward MMF calibration from proximal measurements of the round-trip TM. Furthermore, we show how focusing through the MMF with digital optical phase conjugation is compromised by system loss since time reversibility relies on power conservation. These insights may inform the development of new imaging techniques through complex media and coherent control of waves in photonic systems.

Investigation of mode coupling in low and high NA step index plastic optical fibres using the Langevin equation

By employing the Langevin equation, we have examined a mode coupling in low and high NA step index plastic optical fibres. The numerical integration of the Langevin equation is based on the computer-simulated Langevin force. The solution matches the experimental data reported previously. We have shown that by solving the Langevin equation (stochastic differential equation) one can treat a mode coupling in multimode low and high NA step index plastic optical fibres, which is the result of fibre's intrinsic random perturbations.

All fiber optic hetero-core spliced multimode single mode multimode filter

We report here the transmission characteristics of a step index multimode–single mode–multimode fiber (MSM) optic integrated system. Owing to a good coupling between the fibers, the designed system reveals band-elimination filter characteristics. The variability of the stop-bandwidth for this system is incurred by altering the length and core diameter of the mid-single mode fiber. The observed stop band in the range of 80 nm, having good consistency with numerical results, is found to be dependent on the length of the mid-single mode fiber (SMF). Further, the core diameter of the SMF is also varied to tune the band eliminated output from the proposed MSM structure, which results in a narrow bandwidth of 50 nm, giving a margin of 30 nm with respect to the former. The attained results possess higher potential in the field of optical communications, such as a trimmer, etc.

Encircled Angular Flux: A New Measurement Metric for Radiating Modal Power Distributions from Step-Index Multimode Fibers

Step-index multimode fiber (SI-MMF) has been used in many fields and industries, including the automotive and railroad industries. Although the modal power distribution (MPD) of SI-MMF greatly influences its transmission characteristics, we rarely discuss the MPD dependency of systems and components composed of the fiber because there is no measurement metric to define MPD. Under the circumstances, encircled angular flux (EAF), which is a new metric for defining the MPD in SI-MMF, has been developed. Here, the EAF measurement method and a measurement apparatus for fθ imaging, which is the standardized EAF measurement method of the International Electrotechnical Commission, are reported. Using the apparatus, we analyzed the MPD in a hard polymer cladding fiber. We examined the measurement tolerances of the apparatus, which has sufficient tolerances of ±0.5 mm or more in all axes within a variation of ±15% at the EAF of 95%. We also investigated the measurement reproducibility of the apparatus and showed that the apparatus has sufficient reproducibility as indicated by the standard deviation of 0.008° based on repeated measurements. We showed that insertion loss was caused by higher mode radiation at connections.

Highly nonlinear Pb2P2O7-Nb2O5 glasses for optical fiber production

In this study we present the production and characterization of Pb2P2O7–Nb2O5 glasses and optical fibers. The dependence of Nb2O5 content on thermal, structural and optical properties were investigated by thermal analysis (DSC), Raman spectroscopy, UV–Visible absorption, M-Lines and Z-scan techniques. Glass transition temperature (Tg) increased linearly with Nb2O5 content up to 60mol%, while thermal stability against crystallization (ΔT) reached a maximum value of 225°C at 40mol% of Nb2O5. Raman spectra showed a significant structural change by the insertion of NbO6 octahedral units in the glass network. The increase of Nb2O5 concentration shifts the glasses absorption edge to lower energies, and also increases the linear refractive indexes (n0) due to the high polarizability of niobium atoms and formation of non-bridging oxygen. Similarly to n0, an increase in the positive values of nonlinear refractive indexes was observed using Z-Scan technique with increase of Nb2O5 content, based on structural changes caused by the replacement of Pb2P2O7 instead Nb2O5. The average of n2 values at 500–1500nm raised from 2.2×10−19 to 3.8×10−19m2/W, when the Nb2O5 content was increased from 10 to 60mol%. Lastly, a core-cladding preform was produced by suction method and the optical fiber drawn. The sample containing 40mol% of Nb2O5 was used for presenting the highest thermal stability against crystallization and n0 values >2 from green to near-infrared wavelengths. Multimode step index fiber with good core circularity and concentricity was produced and the optical losses were determined by cut-back method at visible and near-infrared ranges.

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.”

多模阶跃光纤纤芯传导模式的快速求解

多模阶跃光纤纤芯传导模式的快速求解