Numerical evaluation of the impulse response of multimode optical fibers

Abstract

A numerical technique based on ray optics is presented that provides the impulse response of multimode optical fibers having arbitrary smooth index profiles and arbitrary material dispersion. The variation of dn/dλ ₀ as a function of n when the dopant concentration varies is obtained from Fleming⁽¹⁾ measurements on bulk samples. This technique is applied to germania-doped multimode fibers with power-law profiles and various values of Δ ≡ Δn/n Previous results⁽²⁾ are shown to be invalid when Δ ? 0.005. By successive approximations, optimum profiles that minimize the impulse response widths for quasi-monochromatic sources are found. For these optimum profiles, the quasi-monochromatic root-mean-square (rms) impulse response width is found to be of the order of 150 Δ²nsec/km, in agreement with a recent analytical result.⁽³⁾     

Wavelength dependent propagation in optical multimode fibers

Under various assumptions concerning the wavelength dependence of the refractive index of a fiber whose radial dependence is not an “a priori” known function of r, a method is described to obtain a closed form expression for the flight time of a ray in a multimode fiber. Consequently, the refractive index n(r) is shown to be the solution of a differential equation. Thus, for these selected profiles, we avoid the problem of the high precision required in the calculation of the flight time of a ray, a problem that arises frequently if the impulse response is to be reconstructed from a large number of rays, and transpose it to the determination of a single function of r, namely the refractive index.     

Parallel-beam impulse response of multimode fibres: numerical results

Impulse responses are calculated for parallel-beam injection into fibres having-type profiles with a varying from 1 to 8. The responses obtained exhibit characteristic features which can guide the interpretation of experimental investigations of such fibres. The ray model is used and leaky-mode attenuation is taken into account. Finally, the dependence of the transmitted power on the injection angle is investigated, suggesting a possible functional relation to the index profile.     

Rigid reed-type routing switch for multimode optical fibers

Abstract

A mechanical switch developed earlier for routing light in multimode optical fibers has been improved by reducing its cubic volume, insertion loss, switching time, and required switching power. Using an immersion fluid, an insertion loss below 0.5 dB was realized. The switching time is shorter than 13 msec, and the required switching power less than 16 mW.     

Ray theory of the impulse response of randomly bent multimode fibres

A ray theory based on the time-independent Fokker-Planck equation and the integration of time along ray trajectories provides analytical expressions for the average arrival time and spread of optical pulses propagating in randomly distorted, multimode, optical fibres. A clear physical picture emerges from the theory. The analytical expressions obtained for t and t ² coincide with the ones obtained by Olshansky from coupled-mode theory. The t ³ and t ⁴ moments of the impulse response are also calculated. Simple closed-form formulae are given for the step-index slab. The coupling between all modes is effectively taken into account in our ray theory.On leave of absence at the Laboratoire des Signaux et Systèmes.     

Rigid reed-type routing switch for multimode optical fibers

A mechanical switch developed earlier for routing light in multimode optical fibers has been improved by reducing its cubic volume, insertion loss, switching time, and required switching power. Using an immersion fluid, an insertion loss below 0.5 dB was realized. The switching time is shorter than 13 msec, and the required switching power less than 16 mW.     

An estimation of the baseband transfer function of multimode optical fibers

This paper discusses an alternative criterion for estimating the baseband transfer function of multimode optical fibers. The optical fibers having little mode conversions show that the baseband frequency characteristics are affected strongly by the launching condition of an input optical pulse. In the criterion presented here, the baseband transfer function in such fibers is estimated by considering the launching condition that excites all fiber modes uniformly in amplitudes. In order to obtain such a transfer function, the actual responses affected by the launching conditions are measured together with the modal power distributions for different kinds of launching conditions. A numerical procedure is then presented that enables us to derive the baseband transfer function independently of modal power distributions. Experimental results at λ x= 633 nm and 856 nm are presented for step index fibers (0.1 and 0.2 km long) having a core radius of 30 pm (its refractive index is 1.452) and a refractive index difference of 0.7%.     

An estimation of the baseband transfer function of multimode optical fibers

This paper discusses an alternative criterion for estimating the baseband transfer function of multimode optical fibers. The optical fibers having little mode conversions show that the baseband frequency characteristics are affected strongly by the launching condition of an input optical pulse. In the criterion presented here, the baseband transfer function in such fibers is estimated by considering the launching condition that excites all fiber modes uniformly in amplitudes. In order to obtain such a transfer function, the actual responses affected by the launching conditions are measured together with the modal power distributions for different kinds of launching conditions. A numerical procedure is then presented that enables us to derive the baseband transfer function independently of modal power distributions. Experimental results at λ x= 633 nm and 856 nm are presented for step index fibers (0.1 and 0.2 km long) having a core radius of 30 pm (its refractive index is 1.452) and a refractive index difference of 0.7%.     

Mid-infrared radiation transmission through fluoride glass multimode optical fibers

Measurement of the transmission laser radiation from Q-switched and free-running Er:YAG lasers operating at 2.94 μm through fluoride glass multimode optical fibers of 448, 465 and 620 μm core diameter were performed. Attenuation measurements were obtained as a function of the laser energy input, of the bending angle and of the radius of curvature. The fibers exhibited low attenuation under straight and bent conditions. The output beam quality was also studied using the appropriate beam profiler. The output beam profiles showed a central multi-spiked energy distribution.     

Aperture properties of multimode conical optical fibers (focons)

The problem on the propagation of meridional rays in conical optical fibers (focons) has been considered in terms of the geometric optics model. A sine condition for the ray parameters at reflection points has been obtained. A general equation that relates the geometric size of a focon with the ray parameters at the entrance and exit of the focon has been deduced. The equation is valid for all physically possible taper angles of a focon. The aperture properties of two types of focons (hollow and dielectric) have been analyzed. The entrance and exit aperture angles appear to be piecewise continuous or piecewise smooth functions of the parameters, which is related to the discreteness of the number of ray reflections. The main properties of the considered types of focons with typical values of the parameters have been illustrated by numerical calculations of the aperture angles.     

高功率脉冲激光对阶跃折射率多模光纤损伤机理

 理论分析和模拟仿真研究了激光点火系统中光纤端面损伤、光纤初始输入段损伤和光纤内部损伤机理。结果显示：端面损伤主要是由光纤端面的杂质和缺陷引起；光纤初始输入段损伤是由光束的初次反射造成光纤局部激光能量密度增大引起的；光纤内部体损伤主要由于激光自聚焦效应引起损伤和光纤受到的意外应力产生微小碎片，吸收激光能量，引起光纤局部损伤。给出了激光点火系统中提高光纤损伤阈值的一般方法，主要包括光纤端面处理、设计合理的激光注入耦合装置。     

Stimulated Brillouin scattering phase conjugating properties of long multimode optical fibers

This paper describes and characterizes a detailed experiment that proves the phase conjugating properties of stimulated Brillouin scattering in multimode fibers (km of length), a problem still in debate in the literature, by studying the random aberrations correction abilities of this nonlinear interaction. Detailed qualitative and quantitative evaluation of aberration correction, by using the M² beam propagation ratio as a criterion to assess beam quality of the beams, proves the phase conjugation via SBS in long MM fibers. A new parameter to characterize the efficiency of the SBS phase conjugation process is proposed and conditions to obtain a complete healing of distortions (complete phase conjugation) are discussed.     

Nanosecond laser-induced surface damage of optical multimode fibers and their preforms

High-power optical multimode fibers are essential components for materials processing and surgery and can limit the performance of expensive systems due to breakdown at the end faces. The aim of this paper is the determination of laser-induced damage thresholds (LIDT) of fibers (FiberTech) and preforms (Heraeus Suprasil F300). Preforms served as models. They were heated up to maximum temperatures of 1100, 1300 and 1500°C and cooled down to room temperature at rates of 10 K min⁻¹ (oven) and ∼10⁵ K min⁻¹ (quenched in air) to freeze in various structural states simulating different conditions similar to a drawing process during the production of fibers. Single- and multi-pulse LIDT measurements were done in accordance with the relevant ISO standards. Nd:YAG laser pulses with durations of 15 ns (1064 nm wavelength) and 8.5 ns (532 nm) at a repetition rate of 10 Hz were used. For the preforms, LIDT values (1-on-1) ranged from 220 to 350 J/cm² (1064 nm) and from 80 to 110 J/cm² (532 nm), respectively. A multi-pulse impact changed the thresholds to lower values. The LIDT (1064 nm wavelength) of the preforms can be regarded as a lower limit for those of the fibers.     

Time impulse response and time frequency response of optical pupils

We define the time impulse response of optical pupils and relate this function to the optical characteristics of the pupils. Then we link the time impulse response to the spatial impulse response of the pupil.     

Planar optical coupling elements for multimode fibers with two-step ion migration process

An electric field assisted two-step ion migration process in soda-lime glass plates has been used to produce optical couple waveguides with semicircular and circular cross sections. The radius and the numerical aperture of the guides are approximately the same as those of the graded index multimode fibers. A new coupler structure, the edge reflecting element, which could be used as an integrated demultiplexer in wavelength division multiplexing, has been fabricated. The loss spectrum of the waveguides is analyzed and a theoretical treatment of the ion concentrations is given.     

Nanosecond laser damage resistance of differently prepared semi-finished parts of optical multimode fibers

Optical multimode fibers are applied in materials processing (e.g. automotive industry), defense, aviation technology, medicine and biotechnology. One challenging task concerning the production of multimode fibers is the enhancement of laser-induced damage thresholds. A higher damage threshold enables a higher transmitted average power at a given fiber diameter or the same power inside a thinner fiber to obtain smaller focus spots.In principle, different material parameters affect the damage threshold. Besides the quality of the preform bulk material itself, the drawing process during the production of the fiber and the preparation of the fiber end surfaces influence the resistance. Therefore, the change of the laser-induced damage threshold of preform materials was investigated in dependence on a varying thermal treatment and preparation procedure.Single and multi-pulse laser-induced damage thresholds of preforms (F300, Heraeus) were measured using a Q-switched Nd:YAG laser at 1064 nm wavelength emitting pulses with a duration of 15 ns, a pulse energy of 12 mJ and a repetition rate of 10 Hz. The temporal and spatial shape of the laser pulses were controlled accurately.Laser-induced damage thresholds in a range from 150 J cm⁻² to 350 J cm⁻² were determined depending on the number of pulses applied to the same spot, the thermal history and the polishing quality of the samples, respectively.     

Use of multimode optical fibers for fiber-based coherent anti-Stokes Raman scattering microendoscopy imaging

A multimode fiber (MMF) was used for both delivery of excitation lasers and collection of returned coherent anti-Stokes Raman scattering (CARS) signals in a CARS microendoscopy prototype imaging system. We demonstrated a polarization-based scheme for suppression of four-wave mixing (FWM) signals in delivery fibers. Our experimental results showed that this polarization-based FWM-suppressing scheme can dramatically reduce FWM signals generated in MMFs, and MMFs can be used to produce CARS images in this microendoscopy system. The proposed MMF-based CARS microendoscopy imaging system with the polarization-based FWM-suppressing scheme offers a potential platform for building fiber-based CARS microendoscopes that can effectively suppress FWM background noises.     

All propagation modes of large-core multimode optical fibers with an arbitrary core profile

Plastic optical fibers are typical large-core multimode optical fibers. High-bandwidth graded-index plastic optical fibers, which support a great number of propagation modes compared with conventional silica-glass multimode optical fibers, were developed in the 1990s. However, because they support a great number of propagation modes, their modal analyses have been limited to the WKB analysis. We obtain all the propagation modes of a convex-index large-core multimode optical fiber by use of the finite-element method, which has a strong advantage for arbitrary core profiles.