Fiber Refractive Index Profile Research Articles

Improved evaluation model for macro-bending loss and power variation in single-mode fiber

It is challenging to calculate the macro-bending loss of optical fiber when the bending radius is reduced to sub-millimeter levels, based on Marcuse's theory and its derivative theories. Furthermore, these theories are limited in their ability to assess the distribution and changes of the optical field within the fiber, focusing solely on the analysis of loss. To overcome these limitations, we proposed an evaluation model which can simultaneously provide results for both macro-bending loss and power variation in a bent single-mode fiber. Our model achieves this by conformally transforming the fiber's refractive index profile of the axis section according to the bending radius. The ratio of output power to input power exhibits oscillation with changes in the bending radius, thereby resolving the issue of inability of Marcuse's theory to obtain an oscillation loss curve for sub-millimeter bending radii. The proposed model was validated by finite element method. We also obtained the internal power variation along the axial distance of the bent fiber through this model. This research improves the current fiber macro-bending loss evaluation model and lays a foundation for further studies on bend-insensitive fibers and the design of sub-millimeter bending sensors.

The optical fiber refractive index profile measurement based on phase-correct quantitative phase microscopy

The optical fiber refractive index profile measurement based on phase-correct quantitative phase microscopy

Electrooptic control of the modal distribution in a silicate fiber.

We demonstrate the use of the electrooptic effect to control the propagation constant of the guided modes in silicate few mode fibers with internal electrodes. The electrooptic effect induces a perturbation of the fiber's refractive index profile that controls intermodal interference. To increase the electrooptic effect the silicate fibers are poled. The response time is in the nanosecond range.

Designing High-Performance Multimode Fibers Using Refractive Index Optimization

The rich design landscape of optical fibers offers many opportunities for refractive index optimization. In particular, the refractive index profiles of multimode fibers (MMFs) and multicore fibers (MCFs) govern the behavior of spatial and polarization modes, including their bandwidth, mode count, mode coupling, modal dispersion, chromatic dispersion, and mode-dependent loss. In this article, we obtain update equations to optimize the shapes of fiber refractive index profiles for various applications using gradient descent. Starting with an initial fiber designed according to standard best practices, our methods iteratively modify the refractive index profile to improve upon the initial design. Interestingly, we see that optimization can sometimes yield large improvements in key fiber properties, such as a 20-fold reduction in the root-mean-square modal group delay spread, even though the index profile is changed very little from the initial design. We show that our methods can be used to tailor the mode coupling, modal dispersion and chromatic dispersion properties to desired values, and that optimization can be successfully applied over a large bandwidth. We provide illustrative design examples, including an optimization of a graded-index MMF with low group delay spread for long-haul mode-division-multiplexed transmission. Our algorithms can be used to design novel fibers or optimize existing fibers for next-generation transmission systems.

Development of a Method for Measuring the Optical Fiber Refractive Index Profile

Development of a Method for Measuring the Optical Fiber Refractive Index Profile

Modelling and record technologies of address fibre Bragg structures based on two identical ultra-narrow gratings with different central wavelengths

Address fiber Bragg structures (AFBS) make it possible to effectively solve the problem of sensors interrogation and multiplexing in multi-sensor networks with microwave photonic processing of information. Based on the method of inverse Fourier transform, a mathematical model of the optical fiber refractive index profile was constructed to form 2λ-FBG AFBS with two FBG with identical spectral responses at separated wavelengths. As the initial parameters for the construction of the mathematical model, the desired spectral profile of 2λ-FBG AFBS was specified, including the reflection coefficient and the width of the transmission band of its two identical ultra-narrow-band gratings and the separation between them. On the basis of the study of the mathematical model, the possibility of selecting the necessary values of the refractive index and the laws of its modulation is shown, allowing the spectral profile of 2λ-FBG AFBS to be formed so that they can be used as a sensitive element, transforming information from optical range to radiofrequency one. The analysis of the formation and recording methods for 2λ-FBG AFBS was carried out. To implement given structures, the technology, using of an ultraviolet argon laser, the classic phase masks with sequential recording of several arrays with precise movement and strain of the fiber were chosen. Further paper deals with issues of interrogation of the developed structures and principles of measurement system construction on their basis.

Optical Fiber Refractive Index Profiling by Iterative Optical Diffraction Tomography

A non-destructive iterative interferometric tomographic technique is proposed for imaging fibers with high refractive index contrast, complex structures, and/or large optical path differences. Both simulation and experimental results demonstrate that this technique enables the reconstruction of fiber refractive index profiles accurately and robustly with sub-wavelength resolution.

Multi-parameters of spun optical fibers measured by digital holographic tomography

Digital holographic tomography (DHT) technology is efficiently utilized to measure optical fiber structure profile. A Mach-Zender off-axis holographic interferometer is used to get fiber wavefront, an angular spectrum reconstruction algorithm is applied to obtain optical path difference (OPD) curves. With an adaptive simultaneous algebraic reconstruction technique (ASART), we obtain a fiber refractive index profile and non-circularity. In fiber wavefront measuring, errors are inevitably caused by measurement accuracy and fiber position offset as fiber rotating. In order to improve fiber structure profile reconstruction accuracy, we propose a novel algorithm to eliminate measuring errors of OPD curves including value drift and position drift, which obviously improves the reconstruction quality. With ASART, we analyze the structure parameters of single-mode spun fiber with various spinning pitches, including refractive index profiles and the fiber non-circularity. The results show that as the shortening of fiber spinning pitch, the refractive index dip in the fiber core is deeper and both cladding non-circularity and core non-circularity are less.

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).

Mode Coupling Effects in Ring-Core Fibers for Space-Division Multiplexing Systems

An optical fiber with weak mode coupling is desirable for future ultrahigh capacity space-division multiplexing (SDM) systems because mode coupling in an optical fiber results in extrinsic loss of the fiber and crosstalk between guided optical modes. To study the feasibility of a ring-core fiber (RCF) for SDM systems, in this paper, we investigate the mode coupling in the RCF supporting five or seven guided mode groups (MGs) at a wavelength of 1550 nm. For this purpose, the coupled mode/power theory with identified spatial power spectrum of random perturbations of fiber axis is used to estimate the bend loss/crosstalk of the RCF due to microbending. It is shown that based on the identified parameters for the spatial power spectrum in the 5/7-MG RCF, the estimated bend loss/crosstalk of the RCF agrees well with experimental results. In addition, the impact of the gradient parameter α and refractive index contrast Δ of the fiber refractive index profile on bend loss and crosstalk of the RCF is explored. Simulation results indicate that the Δ instead of the α significantly affects bend loss and crosstalk of the RCF. The magnitude improvement in bend loss by increasing the Δ is dependent on the spatial power spectrum.

Measurement of the focusing constant of gradient-index fiber lens and its application in developing GRIN fiber probes

The curve-fitting algorithm is adopted to measure the focusing constant of a gradient-index (GRIN) fiber lens, which is used to further design ultra-small GRIN fiber probes. Firstly, the refractive index profile of a GRIN fiber lens is acquired by using the Optical Fiber Refractive Index Profile tester. And the focusing constant of the GRIN fiber lens is obtained by means of the curve-fitting algorithm of quadraticpolynomial. Secondly, the measured focusing constant is used to design ultra-small GRIN fiber probes with different focusing properties. Thirdly, according to the designed optical probe models, GRIN fiber probe samples have been fabricated and tested. Finally, comparative analysis is conducted between the theoretical focusing performance parameters and the experimentally measured values. The results show that, in the given condition, the fitted value of the focusing constant of GRIN fiber lens and the theoretical focusing performance parameters of GRIN fiber probes, respectively agree well with the nominal value provided by the manufacturer and the experimentally measured data. Therefore, the proposed methods of measuring the focusing constant of GRIN fiber lens and its application in designing GRIN fiber probes are validated and feasible to further developing ultra-small GRIN fiber probes requiring specific optical focusing performance.

Signals of an intermodal fiber interferometer induced by laser frequency modulation

Signals of an intermodal fiber interferometer induced by laser optical frequency modulation are studied. Dependences of signal amplitudes and spectra on the laser frequency deviation are examined theoretically and experimentally for various optical fibers. It is established that the sensitivity of the intermodal fiber interferometer to the laser frequency variation essentially depends on the fiber refractive index profile. The minimal sensitivity corresponds to graded-index (α ≈ 2) multimode optical fibers. Step-index optical fibers (α = ∞) are more sensitive to the laser frequency variation by more than a factor of 100.

SMS Fiber Sensor Utilizing a Few-Mode Fiber Exhibits Critical Wavelength Behavior

We experimentally demonstrate the existence of a critical wavelength in the 1.4-1.6-μm optical communication window for the single-mode-multimode-single-mode (SMS) fiber sensor utilizing a few-mode fiber (FMF). Peaks near the critical wavelength exhibit higher sensitivity to temperature or strain. A theoretical analysis of this SMS structure shows that the critical wavelength behavior is mainly governed by the fiber refractive index (RI) profile with no significant effect from material dispersion. There is only one critical wavelength in the range where the LP <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">02</sub> mode of the FMF is supported. Small alterations of the fiber RI profile can tune the critical wavelength.

Multi-Wavelength Optical Fiber Refractive Index Profiling by Spatially Resolved Fourier Transform Spectroscopy

A non-destructive technique to measure an optical fiber's refractive index profile with sub-¿m spatial resolution over a wavelength range spanning more than one octave (from 480 to 1040 nm) in a single measurement is described. Data showing the variation of refractive index with wavelength for several fiber types is presented.

Automatic determination of refractive index profile of fibers having regular and/or irregular transverse sections considering the refraction of light rays by the fiber

A new model, using non-destructive two- and/or multiple-beam interferometric techniques, is suggested for measuring the refractive index profile of fibers having regular and/or irregular cross-sectional shape taking into consideration the refraction of the light rays by the fiber. The proposed model is applied for three different fibers having different cross-sectional shapes and different refractive index profiles. These fibers are PPT, homogeneous fiber, with circular cross-section, graded index optical fiber of circular cross-sectional shape and Dralon fiber of irregular cross-section. To validate the proposed model it is used, firstly, to calculate the index profile for a standard PPT fiber. Secondly, the calculated results for the irregular Dralon fiber and GR-IN optical fiber are compared with that calculated using other conventional method. From this comparison, we recommend that the refraction must be taken into account to obtain accurate results especially for birefringent fibers and graded index optical fibers.

Automatic determination of refractive index profile, sectional area, and shape of fibers having regular and/or irregular transverse sections

A new method based on a mathematical model and a computer program is suggested to determine the refractive index profile of fibers having regular and/or irregular transverse sectional shape. Microinterferogram of both multiple-beam Fizeau fringes and the duplicated image from two-beam interference microscope are used for the determination of refractive index profile, cross-sectional area and shape of three different types of fibers. To confirm the suggested model, the calculated area and the shape of the transverse section of these fibers are compared with those results obtained using conventional methods.

Interferometric studies on the influence of temperature on the optical and dispersion parameters of GRIN optical fibre

Opto-thermal device attached to automate Fizeau interferometer is used to investigate the influence of temperature on opto-thermal properties of multimode graded-index (GRIN) optical fibre in the range from 27 to 54 °C. The effect of temperature on the refractive index profile of fibre is studied. The optical parameters and the opto-thermal coefficient of this fibre are determined. Also the variation of oscillation and dispersion energies, zero dispersion wavelengths, coupling efficiency, normalised frequency, number of propagation modes with the temperature and the material dispersion with the wavelength at different temperatures are calculated. Microinterferograms are given for illustration.

Segmented-clad fiber design for inherently gain-flattened L/sup +/-band TDFA

We present here an efficient design for high gain, inherently gain-flattened L/sup +/-band thulium-doped fluoride fiber amplifier (TDFA), based on a novel segmented clad fiber refractive index profile. Detailed simulations show that the designed amplifier is able to achieve 20-dB gain, with /spl plusmn/0.7-dB gain ripple over 40-nm bandwidth (1600-1640) nm. Performance comparisons of the proposed module with an L/sup +/-TDFA based on conventional W-fiber designs and on a conventional step-index fiber have also been carried out.

Mode dispersion and delay characteristics of optical waveguides using equivalent TL circuits

A new analysis leading to an exact and efficient algorithm is presented for calculating directly and without numerical differentiation the mode dispersion characteristics of cylindrical dielectric waveguides of arbitrary refractive-index profile. The new algorithm is based on the equivalent transmission-line (T-L) technique. From Maxwell's equations, we derive an equivalent T-L circuit for a cylindrical dielectric waveguide. Based on the TL-circuit model we derive exact analytic formulas for a recursive algorithm which allows direct calculation of mode delay and dispersion. We demonstrate this technique by calculating the fundamental mode dispersion for step, triangular, and linear chirp optical fiber refractive index profiles. The accuracy of the numerical results is also examined. The proposed algorithm computes dispersion directly from the propagation constant without the need for curve fitting and subsequent successive numerical differentiation. It is exact, rapidly convergent, and it results in savings for both storage memory and computing time.

Refractive-index profiling of azimuthally asymmetric optical fibers by microinterferometric optical phase tomography

Accurate nondestructive refractive-index profiling is needed in the modeling, design, and manufacturing of optical fibers and fiber devices. Most profile measurement techniques cannot correctly characterize fibers with small or irregular refractive-index variations over their cross sections. Microinterferometric optical phase tomography (MIOPT) is a technique that allows measurement of fiber refractive-index profiles exhibiting such variations. We present the first demonstration, to our knowledge, of MIOPT. The profile of a polarization-maintaining fiber is measured by MIOPT and shown to be in agreement with (destructive) fiber end-face measurements. MIOPT is also applied to the limiting case of a symmetric single-mode fiber.