Index Profile Of Fiber Research Articles

A Direct Formula for Ultra-Large Effective Area Fibers Design With Top-Hat Intensity Profile

In this paper, we present a new refractive index profile, in simple easy to use equation form, which allows the design of large mode area (LMA) single mode (SM) optical fibers with the special property of supporting “perfect top-hat” mode profiles. The few parameters of this formula define the refractive index profile of such fibers. We show the effect the parameters of the refractive index profile have on the desired mode field. By applying this direct formula, we avoid the use of complex inverse refractive index reconstruction methods, or time-consuming iterative design processes. We demonstrate this formula with a number of example designs of LMA SM optical fibers with perfect flat-top electric field profile and an effective mode area (Aeff) size that in some cases exceeds the 4800 μm 2 . We expect such LMA SM top-hat fiber design to be useful for the mitigation of non-linear effects and catastrophic optical damage, as well as for achieving uniform intensity deposition on the target (material, biological tissue, and so on) in high-power applications. The results presented here are testing the validity of the refractive index profiles for non-ideal designs so as we can determine the tolerance to manufacturing such fibers.

Design of silica optical fibers with enlarged core diameter for a few-mode fiber optic links of onboard and industrial multi-Gigabit networks

This work presents alternative fast and simple method for design refractive index profile of silica multimode optical fibers (MMFs) providing effective mode bandwidth improvement under laser-based multi-Gigabit data transmission and few-mode regime operation in comparison with commercially available MMFs. Optimized profile equalizes delays of selected particular order guided modes being the main mode components of multi-Gigabit network transceiver laser excited optical signal transferred over proposed MMF in a few-mode regime. We present some results of refractive index profiles synthesis for MMFs with core diameters 50 and 100 μm under various combinations of the reference mode delay and the first iteration profile grade parameter as well as corresponding to these samples curves of differential mode delay spectral characteristics computed over “O”-band

Design of Arbitrary Shape Higher Order Mode Electric Field in Optical Fibers for High Power Applications

In this paper, we present a new and efficient technique for the exact reconstruction of large mode area (LMA) higher order mode (HOM) optical fibers by using arbitrary shape HOM electric field profiles. One known strategy to achieve LMAs for high power optical applications is by using optical fibers supporting multimode operation, and engineering these fibers such that they operate on just a single transverse mode. Although the fundamental mode is preferred in most circumstances, there is an increasing interest in operating on a single HOM instead since these can have interesting dispersion characteristics and also significantly higher ability to scale mode areas. An issue with the use of HOMs in high power applications is that often they demonstrate regions of high field intensity across the core. This leads to problems with optical damage at lower values of effective area than might otherwise be expected. In order to avoid this problem, we offer designs of optical fibers supporting mode-flattened HOM electric fields. We develop a new inverse transmission line technique for calculating directly and accurately the refractive index profiles of such fibers from knowledge of the desired HOM electric field. We demonstrate this algorithm with a number of example reconstructions of LMA HOM optical fibers supporting prescribed mode-flattened electric field profiles with ultralarge effective mode areas We expect such fiber designs to be useful in the mitigation of nonlinear effects and in thermal and damage management.

Adaptive simultaneous algebraic reconstruction technique for retrieving refractive index profiles of optical fiber

An efficient adaptive simultaneous algebraic reconstruction technique (ASART) to calculate optical fiber refractive index profiles is proposed based on phase difference curves obtained by digital holography technique. We develop adaptive relaxation parameter (ARP) on simultaneous algebraic reconstruction technique (SART) to increase the convergence speed and improve the reconstruction accuracy. A formula of ARP is derived mathematically and multilevel scheme (MLS) is used to increase convergence speed in the first iteration. Experimental results show the proposed ASART convergences over 40% faster than SART and achieve significantly higher reconstruction accuracy. Experimental verification shows that ASART is more efficient than SART and filtered back projection in image reconstruction, especially with few projection views. The running time of ASART is much shorter than that of SART, and ASART needs fewer iteration numbers to obtain the same reconstruction effects. In addition, it can be used to measure optical fibers with various diameters that cannot be measured with S14 refractive index profiler (S14).

Modeling of single mode optical fiber having a complicated refractive index profile by using modified scalar finite element method

A numerical method based on modified scalar finite element method (SC-FEM) is presented and programmed on MATLAB platform for optical fiber modeling purpose. We have estimated the dispersion graph, mode cut off condition, and group delay and waveguide dispersion for highly complicated chirped type refractive index profile fiber. The convergence study of our FEM formulation is carried out with respect to the number of division in core. It has been found that the numerical error becomes less than 2 % when the number of divisions in the core is more then 30. To predict the accurate waveguide dispersion characteristics, we need to compute expression $$\frac{{{\text{d}}^{2} \left( {\text{vb}} \right)}}{{{\text{dv}}^{2} }}$$ numerically by the FEM method. For that the normalized propagation constant b (in terms of $$\beta$$ ) should be an accurate enough up to around 6 decimal points. To achieve this target, we have used 1 million sampling points in our FEM simulations. Further to validate our results we have derived the higher order polynomial expression for each case. Comparison with other methods in calculation of normalized propagation constant is found to be satisfactory. In traditional FEM analysis a spurious solution is generated because the functional does not satisfy the boundary conditions in the original waveguide problem, However in our analysis a new term that compensate the missing boundary condition has been added in the functional to eliminate the spurious solutions. Our study will be useful for the analysis of optical fiber having varying refractive index profile.

Millimeter-long fiber Fabry-Perot cavities

We demonstrate fiber Fabry-Perot (FFP) cavities with concave mirrors that can be operated at cavity lengths as large as 1.5 mm without significant deterioration of the finesse. This is achieved by using a laser dot machining technique to shape spherical mirrors with ultralow roughness and employing single-mode fibers with large mode area for good mode matching to the cavity. Additionally, in contrast to previous FFPs, these cavities can be used over an octave-spanning frequency range with adequate coatings. We also show directly that shape deviations caused by the fiber's index profile lead to a finesse decrease as observed in earlier attempts to build long FFP cavities, and show a way to overcome this problem.

Raman scattering enhancement characteristic of NbCl5- and Nb2O5-doped silica fibers

Two kinds of Nb-doped silica fibers, an NbCl5-doped fiber and an Nb2O5-doped fiber, are fabricated and characterized in this Letter. First, the refractive index profiles of both fibers are obtained, and then their Raman spectra are measured with 785 nm exciting light. The Nb-doped fibers’ Raman spectra are compared with a conventional GeO2-doped single-mode silica fiber that is prepared with the same method and under the same conditions. As a result, the Raman gain coefficients of the Nb-doped silica fiber core are obtained. The experimental results show that Nb2O5 doping can enhance the Raman scattering intensity of the optical fibers.

Improvement of refractive index profiling of a small-core single-mode fiber under partially coherent light excitation

The refractive index profile of a non-bending small-core single-mode fiber was first reconstructed from the measured guided mode intensity profile and its spatial derivatives. By combining a rotating diffuser with a coherent laser source, the resulting partially coherent light source overcomes the speckles on the guided mode image of a straight fiber, and the corresponding refractive index profile was successfully reconstructed. Furthermore, guided mode images of a bent fiber with a fiber coil at midway were also measured under different coherency light excitations for comparison. The slight asymmetry of the reconstructed index profile of a bent fiber measured under coherent light excitation was greatly improved when measured under partially coherent light excitation. The generated additional leaky modes propagating partly in both core and cladding induced by the effects of the fundamental core mode deformation at the intermediate fiber bending structure and the mode transition at the bent-to-straight fiber section were averaged out with a low coherence transformed light source.

A NOVEL BRILLOUIN OPTICAL TIME-DOMAIN REFLECTOMETER DEMODULATING METHOD BASED ON A SLOW-LIGHT MACH-ZEHNDER INTERFEROMETER

□ A novel demodulating method based on a Gaussian index profile fiber Bragg grating slow-light Mach-Zehnder interferometer to demodulate the frequency shift of a Brillouin optical time-domain reflectometer is proposed and demonstrated. The slow-light was generated with a Gaussian index profile fiber Bragg grating, and transmission spectra and group index spectra characteristics of the grating were obtained through theoretical analysis and numerical simulation. With the slow-light Mach-Zehnder interferometer used, the phase sensitivity and relative power sensitivity can reach up to 0.0132 rad/MHz and 0.0144/MHz, respectively. These results were improved to 133 times and 22.4 times, respectively, which were as large as values based on a double-pass Mach-Zehnder interferometer.

Bent induced refractive index profile variation and mode field distribution of step-index multimode optical fiber

The effect of bending of step-index optical fiber on its refractive index profile and the mode field distribution were investigated. An enhanced slab model is suggested in this investigation. A qualitative study has been done on a bent step-index optical fiber. A very small radius of bending curvature (R) has been reached, practically R is 9.25mm. In this case a dramatic change of the refractive index profile has been observed with an induced birefringence. The refractive index profile is recovered from the interferograms which were generated by Mach–Zehnder interferometer. The interferogram has been analyzed using advanced image analyses software. We have proposed another approach to calculate the refractive index profile of bent optical fiber. In this approach the fiber is divided into layers and slabs, simultaneously. The induced refractive index profile variation of the bent optical fiber, for parallel and perpendicular components of the light beam, is calculated considering the refraction of the light beam traversing the fiber. The mode field distribution and mode numbers in these two directions of polarizations are determined for both straight and bent fibers.

Distributed Strain and Temperature Measurement by Brillouin Beat Spectrum

A novel distributed strain and temperature measurement method based on Brillouin beat spectrum (BBS) in a complex index profile fiber are proposed. The BBS corresponds to the optical interaction of different acoustic modes. For a large-effective-area fiber (LEAF), the first peak of BBS is contributed by the first and second acoustic modes, while the second peak in BBS is contributed by the first and third accoustic modes. Through determining power changes in the peaks of BBS due to strain and temperature variation along a LEAF, the distributed strain and temperature can be measured by the homodyne Brillouin optical time-domain reflectometry (BOTDR) without scanning the Brillouin spectrum. The strain and temperature at the end of a 4.5-km LEAF are measured at 3-m spatial resolution in 140 s.

Brillouin Spectrum in LEAF and Simultaneous Temperature and Strain Measurement

The triangle refractive index profile of LEAF fiber (a non-zero dispersion shifted fiber) makes it much more sensitive to temperature and strain. Owing to its high stimulated Brillouin scattering (SBS) threshold for long distance distributed sensors, we studied the Brillouin spectrum characteristics of LEAF under different strain and temperature conditions. The results are compared with those of SMF-28. Based on the linear relationship between the four peaks' linewidth/peak frequency and strain/temperature, we achieved a strain error of 37 με and a temperature error of 1.8 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> C with a spatial resolution of 4 m for simultaneous temperature and strain measurement.

Explicit finite difference solution of the power flow equation in W-type optical fibers

Using the power flow equation, we have calculated spatial transients of power distribution and a steady-state distribution that are due to coupling of guided to leaky modes in W-type optical fibers (doubly clad fibers). A numerical solution has been obtained by the explicit finite difference method. Results show that power distribution in W-type optical fibers depends on both the intermediate layer width and the coupling strength. W-shaped index profile of optical fibers is effective in reducing modal dispersion and therefore in improving the fiber bandwidth. We have also shown that explicit finite difference method is effective and accurate for solving the power flow equation in W-type optical fibers.

Effective Supercontinuum Generation by Using Highly Nonlinear Dispersion-Shifted Fiber Incorporated with Si Nanocrystals

The dispersion-shifted fiber (DSF) incorporated with Si nanocrystals (Si-NCs) having highly nonlinear optical property was fabricated to investigate the effective supercontinuum generation characteristics by using the MCVD process and the drawing process. Optical nonlinearity was enhanced by incorporating Si nanocrystals in the core of the fiber and the refractive index profile of a dispersion-shifted fiber was employed to match its zero-dispersion wavelength to that of the commercially available pumping source for generating effective supercontinuum. The non-resonant nonlinear refractive index, n2, of the Si-NCs doped DSF measured by the cw-SPM method was measured to be 7.03 x 10(-20) [m2/W] and the coefficient of non-resonant nonlinearity, gamma, was 7.14 [W(-1) km(-1)]. To examine supercontinuum generation of the Si-NCs doped DSF, the femtosecond fiber laser with the pulse width of 150 fs (at 1560 nm) was launched into the fiber core. The output spectrum of the Si-NCs doped DSF was found to broaden from 1300 nm to wavelength well beyond 1700 nm, which can be attributed to the enhanced optical nonlinearity by Si-NCs embedded in the fiber core. The short wavelength of the supercontinuum spectrum in the Si-NCs doped DSF showed shift from 1352 nm to 1220 nm for the fiber length of 2.5 m and 200 m, respectively.

New transverse techniques for characterizing high-power optical fibers

Novel transverse techniques for measuring the refractive index profile and spontaneous emission of high-power optical fibers are described. These techniques are particularly attractive for measuring fiber samples incorporating axial variations, such as mode transformers, gratings, fusion splices, tapers, taps, or couplers. Computerized tomography of spontaneous emission is demonstrated as the first nondestructive method for estimating the spatial distribution of gain in a rare earth-doped fiber, which can be particularly useful when exploiting a spatially inhomogeneous dopant profile.

A New Approach for Representing Photonic Crystal Fiber Index Profile to Determine their Optical Characteristics

A genetic algorithm is implemented to represent the different shapes of Photonic Crystal Fiber (PCF) profile; this is due to the fact that such fibers have special structure. A novel approach is suggested which differs from the usual fibers. By applying this new approach, more realistic representations of their profiles are drawn and hence highly accurate results are obtained including propagation and dispersion characteristics.

A New Approach for Representing Photonic Crystal Fiber Index Profile to Determine their Optical Characteristics

A genetic algorithm is implemented to represent the different shapes of Photonic Crystal Fiber (PCF) profile; this is due to the fact that such fibers have special structure. A novel approach is suggested which differs from the usual fibers. By applying this new approach, more realistic representations of their profiles are drawn and hence highly accurate results are obtained including propagation and dispersion characteristics.

Investigation of refractive index profile and mode field distribution of optical fibers using digital holographic phase shifting interferometric method

In this paper a digital holographic phase shifting interferometric method is used to characterize the graded index (GR-IN) optical fibers. Off-axis digital holographic Mach–Zehnder like arrangement in aid of phase shifting tool is applied. Numerical reconstruction of phase shifted holograms is applied to calculate the optical phase difference distribution in the image plane, and then the optical phase differences across GR-IN fibers are extracted considering image enhancement and noise reduction steps. Also, a simple algorithm is presented to modify the position of the extracted optical phase differences across the fibers to be perpendicular to x-axis, so that it becomes easy to calculate the mean optical phase differences along the fiber. The mean optical phase differences in combination with multilayer model are applied to calculate the refractive index profiles across GR-IN optical fibers. An analytical model is presented to predict the mode distribution associated with the effective indices and the propagation coefficient of the parabolic refractive index profile GR-IN fiber.

Intermodal group velocity dispersion of few-mode fiber

The intermodal dispersion of few-mode fiber limits the propagation distance of mode division multiplexing (MDM). We numerically investigate the propagation constant and group velocity of few-mode fibers. The refractive index profile of few-mode fibers should be designed to achieve long and dense MDM transmissions with digital coherent receivers.

Study on measurement of refractive index profile of GI-POF by light scattering

This paper is devoted to the study on measurement of refractive index profile of graded-index polymer optical fiber (GI-POF) by light scattering. Using Generalized Airy theory and Debye series of an inhomogeneous cylinder, the scattering intensity distributions are obtained of Airy structure of rainbows for different refractive index profile. The results show that positions of Airy peaks depend closely on refractive index profile of GI-POF. Since each order of rainbow penetrates it to different depths, such methods could be used to provide information of the refractive index profile of GI-POF. For GI-POF with given diameter, positions of Airy peaks of rainbows are simulated as a function of refractive index profile, which can be used to inverse unknown parameters of refractive index profile. The least square method is used in inversion of refractive index profile with the given refractive index of the cladding. The results obtained agree with theoretical values with high precision. The method has the advantages of non-instructive and on-line measurement, and can be used for the measurement of other inhomogeneous droplets.