Graded-index Optical Fiber Research Articles

Power over fiber system using high-power laser source operating at 1470 nm with maximum power 2.0 W for powering to distance up to 5855 m

We report on the properties of the Power over Fiber (PoF) system using a High-Power Laser Source (HPLS) operating at 1470 nm with an optical power of up to 2.0 W. Graded-index and step-index optical fibers with a core diameter of 50 µm were used for transmission and two types of Photovoltaic Power Converters (PPCs) were used for optical power to electricity conversion. We experimentally demonstrated the powering to a distance of 5855 m, where we achieved the electric power of 44.4 mW and estimated the possibility of powering to distances longer than 9000 m with the input optical power of 15 W, where we expect to achieve the delivery of the electric power around 150 mW.

High-gain far-detuned nonlinear frequency conversion in a few-mode graded-index optical fiber

We present theoretical and experimental evidence of high-gain far-detuned nonlinear frequency conversion, extending towards both the visible and the mid-infrared, in a few-mode graded-index silica fiber pumped at 1.064 μm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu \\hbox {m}$$\\end{document}, and more specifically achieving gains of hundreds of dB per meter below 0.65 μm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu \\hbox {m}$$\\end{document} and beyond 3.5 μm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu \\hbox {m}$$\\end{document}. Interestingly, our findings highlight the potential of graded-index fibers for enabling high-gain wavelength conversion into the strong-loss spectral region of silica. Such advancements require an accurate interpretation of intramodal and intermodal four-wave mixing processes.

On the maximization of entropy in the process of thermalization of highly multimode nonlinear beams.

We present a direct experimental confirmation of the maximization of entropy which accompanies the thermalization of a highly multimode light beam, upon its nonlinear propagation in standard graded-index (GRIN) optical fibers.

Dirac equation for photons in a fibre: Origin of polarisation

Spin is a fundamental degree of freedom, which was discovered by Dirac for an electron in his relativistic quantum mechanics, known as the Dirac equation. The origin of spin for a photon is unclear because Maxwell's equations in a vacuum are Lorentz invariant without introducing the concept of spin. Here, the propagation of coherent rays of photons in a graded-index optical fibre is considered to discuss the origin of polarisation for photons using exact solutions of the Laguerre-Gauss and Hermite-Gauss modes. The energy spectrum is massive, and the effective mass is a function of the confinement and orbital angular momentum. The propagation is described by the one-dimensional (1D) non-relativistic Schrödinger equation, which is equivalent to the 2D space-time Klein-Gordon equation by a unitary transformation. The probabilistic interpretation and the conservation law require the factorisation of the Klein-Gordon equation, leading to the 2D Dirac equation with spin. The spin expectation values of photons correspond to the polarisation state on the Poincaré sphere. As an application of the theory, a polarisation interferometer is proposed, whose energy spectrum shows a Dirac cone in the Stokes parameter space.

Asymmetries Caused by Nonparaxiality and Spin–Orbit Interaction during Light Propagation in a Graded-Index Medium

Spin–orbit coupling and nonparaxiality effects during the propagation of vortex vector light beams in a cylindrical graded-index waveguide are investigated by solving the full three-component field Maxwell’s equations. Symmetry-breaking effects for left- and right-handed circularly polarized vortex light beams propagating in a rotationally symmetric graded-index optical fiber are considered. The mode-group delay in a graded-index fiber due to spin–orbit interaction is demonstrated. A scheme for observing the temporal spin Hall effect is proposed. It is shown that the relative delay times between vortex pulses of opposite circular polarizations of the order of 10 ps/km can be observed in graded-index fibers for high-order topological charges.

An asymmetric graded indexed helical structured optical fibre for enhanced optical delays

Optical fibres are generally used to provide a guided path to optical signals. Optical fibres are classified as multi-mode or single-mode fibres. Multi-mode graded index (GRIN) optical fibres have been prevalent in short-range optical networks, while single-mode GRIN fibres are used for long-range links. Another potential application of optical fibre is the optical delays in numerous applications, such as quantum computing, network buffering, data synchronization, pattern correlation, etc. This paper conceptualizes a novel application of an asymmetric GRIN optical fibre for possible enhanced optical delays. An asymmetric GRIN parabolic profile with helical structure geometry has been proposed for this task. A detailed analysis has been presented to investigate the effects of various parameters of the proposed geometry. Further, a guided propagation has also been demonstrated with the help of ray optics and the Helmholtz wave equation to assess the feasibility of the proposal. The presented investigations revealed that the geometrical length of the proposed structure is significantly compact compared with the traditional GRIN fibre, proving it beneficial for optical delays.

Rayleigh–Jeans thermalization vs beam cleaning in multimode optical fibers

Classical nonlinear waves exhibit, as a general rule, an irreversible process of thermalization toward the Rayleigh–Jeans equilibrium distribution. On the other hand, several recent experiments revealed a remarkable effect of spatial organization of an optical beam that propagates through a graded-index multimode optical fiber (MMF), a phenomenon termed beam self-cleaning. Our aim here is to evidence the qualitative impact of disorder (weak random mode coupling) on the process of Rayleigh–Jeans thermalization by considering two different experimental configurations. In a first experiment, we launch speckle beams in a relatively long MMF. Our results report a clear and definite experimental demonstration of Rayleigh–Jeans thermalization through light propagation in MMFs, over a broad range of kinetic energy (i.e., degree of spatial coherence) of the injected speckle beam. In particular, the property of energy equipartition among the modes is clearly observed in the condensed regime. The experimental results also evidence the double turbulence cascade process: while the power flows toward the fundamental mode (inverse cascade), the energy flows toward the higher-order modes (direct cascade). In a 2nd experiment, a coherent laser beam is launched into a relatively short MMF length. It reveals an effect of beam cleaning driven by an incipient process of Rayleigh–Jeans thermalization. As discussed through numerical simulations, the fast process of Rayleigh–Jeans thermalization observed in the 1st experiment can be attributed due to a random phase dynamics among the modes, which is favored by the injection of a speckle beam and the increased impact of disorder in the long fiber system.

(Invited) Spatiotemporal soliton stability in multimode fibers: A Hamiltonian approach

We introduce a Hamiltonian approach to study the stability of three-dimensional spatiotemporal solitons in graded-index multimode optical fibers. Nonlinear light bullet propagation in these fibers can be described by means of a Gross–Pitaevskii equation with a two-dimensional parabolic potential. We apply a variational approach, based on the Ritz optimization method, and compare its predictions with extensive numerical simulations. We analytically find that, in fibers with a pure Kerr self-focusing nonlinearity, spatiotemporal solitons are stable for low energies, in perfect agreement with numerical simulations. However, above a certain energy threshold, simulations reveal that the spatiotemporal solitons undergo wave collapse, which is not captured by the variational approach.

Multimode Optical Fiber Beam-By-Beam Cleanup

We introduce and experimentally demonstrate the concept of all-optical beam switching in graded-index multimode optical fibers. Nonlinear coupling between orthogonally polarized seed and signal beams permits to control the spatial beam quality at the fiber output. Remarkably, we show that even a few-mode control beam whose power is about ten times lower than that of the total beam may substantially enhance the quality of an intense, highly multimode signal beam. We propose a simple geometrical representation of the beam switching operation, whose validity is quantitatively confirmed by the experimental mode decomposition of the output beam. All-optical switching of multimode beams may find important applications in high-power beam delivery and fiber lasers.

Radiation-resistant graded-index multimode optical fibers based on fluorosilicate glass

Using the MCVD-technology, radiation-resistant multimode optical fibers based on fluorosilicate glass with a gradient refractive index profile were developed. Radiation-induced attenuation (RIA) of light in the fibers was compared with the literature data on analogous fibers manufactured by the PCVD-technology. It was found out that RIA in the MCVD-fibers at the wavelength λ=1310 nm under γ-irradiation at the doses of up to 10 kGy is 1-2 dB/km (19-29%) lower than RIA in the Super RadHard fiber produced by the PCVD-technology and previously supposed to have a record-high radiation resistance. Keywords: radiation-induced attenuation of light, RIA, graded-index multimode optical fiber, radiation resistance.

Amplification of whispering gallery microlaser emission using dye-doped graded-index polymer optical fiber

PMMA-based Rhodamine-640 perchlorate doped microring embedded hollow polymer optical fiber (MEHPOF), as well as graded-index polymer optical fiber (GIPOF), were fabricated. At a threshold pump pulse energy (PPE) of 0.23 mJ, a whispering gallery mode lasing was observed from the MEHPOF. The quality factor and free spectral range of the fabricated microcavity were found to be 3.69×103 and 0.25 nm respectively. The lasing modes from the MEHPOF were amplified using a GI fiber doped with the same gain material. The maximum gain achieved from the experiment is 17.5 dB. The optimum length of the amplifier fiber for maximum gain was found to be 8 cm.

Sapphire Fiber Fabry-Perot Sensors With High Fringe Visibility

It is difficult for sapphire fiber Fabry-Perot (FP) sensors to generate high quality interference fringes because their highly multimode property. In this paper, we report a sapphire fiber FP strain sensing system with high fringe visibility, realized by the use of a self-made fiber collimator. The collimator is made by a quarter-period graded index optical fiber (GIOF) fused to a single mode fiber (SMF). In the contrast experiment, no effective signal was collected from a sensing system without the fiber collimator. While adding a fiber collimator into the sensing system, high visibility interference fringes were collected. The fringe visibility is 49.37% when the FP cavity length is 341.1 μm, and 20.09% when the cavity length is 1343.3 μm. The effective range of the cavity is over 1000 μm. Strain experiment at room temperature shows the measuring range is 10037 μϵ with relative error of 0.37% while the gauge length is 100 mm. High temperature experiment was also carried out and the result shows that the sensor can work at 1300 °C. This method is expected to be helpful for decreasing the difficulty of fabricating high fringe visibility sapphire fiber FP sensors, and increasing the measuring range.

Effect of Kerr nonlinearity on signal and pump intensities in EDFA comprising single-mode step index fiber: Estimation by a simple but accurate mathematical formalism

The paper presents simple but accurate analytical expressions for the estimation of variation of signal and pump intensity with normalised radial distance in case of erbium doped fiber amplifier. Choosing two typical single-mode step index fibers in our investigation, we hereby predict the said variations relating to both pump and signal in presence as well as absence of Kerr nonlinearity. The stated formulation uses power series expression for the fundamental modal field of graded index optical fiber as derived by Chebyshev formalism. Method of iteration is applied for the prediction of concerned parameters in presence of Kerr type nonlinearity. Our results have been shown to be agreeing excellently with the numerical exact ones in absence and also in presence of Kerr nonlinearity. Exact results in case of Kerr nonlinearity are determined using the cumbersome finite element method. It is noteworthy that execution of our proposed method requires very less computation and as such it will be remarkably user friendly for researchers and technologists associated with nonlinear optical engineering.

Multimode soliton collisions in graded-index optical fibers.

In this work, we unveil the unique complex dynamics of multimode soliton interactions in graded-index optical fibers through simulations and experiments. By generating two multimode solitons from the fission of an input femtosecond pulse, we examine the evolution of their Raman-induced red-shift when the input pulse energy grows larger. Remarkably, we find that the output red-shift of the trailing multimode soliton may be reduced, so that it accelerates until it collides with the leading multimode soliton. As a result of the inelastic collision, a significant energy transfer occurs between the two multimode solitons: the trailing soliton captures energy from the leading soliton, which ultimately enhances its red-shift, thus increasing temporal separation between the two multimode solitons.

Continuous spatial self-cleaning in GRIN multimode fiber for self-referenced multiplex CARS imaging.

We demonstrate how spatial beam self-cleaning and supercontinuum generation in graded-index multimode optical fibers can be directly applied in multiplex coherent anti-Stokes Raman Scattering (M-CARS) spectroscopy. Although supercontinuum generation causes pump depletion mainly in the center of the beam, the partial recovery of the pump brightness due to self-cleaning may enable self-referenced M-CARS, with no additional delay lines to synchronize pump and Stokes waves. As a proof-of-principle, we report examples of imaging of single chemical compounds and polystyrene beads. The new scheme paves the way towards simpler M-CARS systems based on multimode fiber sources.

Design guidelines for collimating or focusing graded-index fiber tips.

Graded-index optical fiber probes suitable for focusing or collimating the output of an optical fiber at a wavelength of 1.3 µm have become an enabling technology in optical coherence tomography imaging applications for in vivo bioimaging. Such fiber tips however remain uncommon in other photonics applications. This paper provides the first numerical study of graded-index fiber tips covering a broad range of wavelengths spanning from the UV to short-infrared. The wavelength dependency and the influence of probe geometry on performance characteristics such as far-field divergence angle, spot size and working distance are analyzed. The paper yields easily accessible design guidelines for the fabrication of collimating or focusing fiber tips. Fiber collimators have considerable potential for use in free-space systems and could benefit a range of devices such as variable attenuators, dynamic wavelength equalisers and large 3D optical cross-connect switches, whereas focusing fiber tips have applications in high-resolution imaging.

Error-free PAM-4 transmission by a high-speed plastic optical fiber without forward error correction.

This Letter reports, to the best of our knowledge, the first study in which error-free four-level pulse-amplitude modulation (PAM-4) transmission has been achieved using a graded-index plastic optical fiber (GI POF) without the use of forward error correction (FEC) techniques, at a high data rate (>50Gb/s), for short-reach applications (10 m). The GI POF that is developed has the characteristic microscopic heterogeneities in the fiber core material, which provide distinct mode coupling and significantly stabilize PAM-4 data transmission. The results of the study in this Letter indicate that the GI POF achieves highly stable PAM-4 transmission without the need for the current FEC techniques, which seriously increase the communication delay and power consumption of the transmission systems. Our GI POF material is paving the way for "material changes the system" approaches for achieving unprecedented optical interconnects in real time at a high speed and with low power consumption.

Depolarization of Light in Optical Fibers: Effects of Diffraction and Spin-Orbit Interaction

Polarization is measured very often to study the interaction of light and matter, so the description of the polarization of light beams is of both practical and fundamental interest. This review discusses the polarization properties of structured light in multimode graded-index optical fibers, with an emphasis on the recent advances in the area of spin-orbit interactions. The basic physical principles and properties of twisted light propagating in a graded index fiber are described: rotation of the polarization plane, Laguerre–Gauss vector beams with polarization-orbital angular momentum entanglement, splitting of degenerate modes due to spin-orbit interaction, depolarization of light beams, Berry phase and 2D and 3D degrees of polarizations, etc. Special attention is paid to analytical methods for solving the Maxwell equations of a three-component field using perturbation analysis and quantum mechanical approaches. Vector and tensor polarization degrees for the description of strongly focused light beams and their geometrical interpretation are also discussed.

Surface plasmon resonance biosensor using inverted graded index optical fiber

A new type of surface plasmon resonance biosensor based on inverted graded index optical fiber is presented. To allow the exciting of the surface plasmons, the cladding is removed and a thin film of gold is coated on the inverted graded index core at this region. This sensor can measure the refractive index (RI) of biomaterials in the range of 1.36–1.48. The simulation results show that the proposed biosensor has a maximum sensitivity of about 7000 nm/RI unit (RIU) and the average figure of merit is 48 RIU−1. The simplicity of the design and its high sensitivity make it a good candidate for low-cost RI sensors suitable for biomaterials.

X-ray computed tomography using partially coherent Fresnel diffraction with application to an optical fiber.

A reconstruction algorithm for partially coherent x-ray computed tomography (XCT) including Fresnel diffraction is developed and applied to an optical fiber. The algorithm is applicable to a high-resolution tube-based laboratory-scale x-ray tomography instrument. The computing time is only a few times longer than the projective counterpart. The algorithm is used to reconstruct, with projections and diffraction, a tilt series acquired at the micrometer scale of a graded-index optical fiber using maximum likelihood and a Bayesian method based on the work of Bouman and Sauer. The inclusion of Fresnel diffraction removes some reconstruction artifacts and use of a Bayesian prior probability distribution removes others, resulting in a substantially more accurate reconstruction.