Theoretical and experimental evaluation of the modal field shift and the associated transition loss in perturbed index-profile single-mode optical fiber with application of Fizeau interferometry

Fizeau micro-interferometry is applied to evaluate some parameters of a curved single-mode optical fiber. The field shift of the fundamental mode and the associated transition loss in a perturbed index-profile fiber due to bending are determined. The preceding fiber parameters are determined as a function of the shift of multiple-beam Fizeau fringes. For a curvature range between 0.13 and 0.053 mm(-1), a range of field shift between 0.44 and 0.21 microm is determined. A fraction of the transition loss ranging between 0.0056 and 0.028 is calculated within the same curvature range. Because our method has high index resolution and spatial resolution, it shows good agreement with theory. The results and the agreement with theory indicate that the use of multiple-beam Fizeau fringes is a promising technique that is capable of determining with high accuracy some guidance parameters of the optical fibers.     

Surface plasmon resonance in a bent single-mode fiber with a metallized cladding experimental research

The processes of surface plasmon resonance excitation in a bent single-mode optical fiber with a metallized cladding have been studied experimentally. It is shown that, for a certain combination of the bending radius of an optical fiber and the thickness of a metal film, a strong coupling between the fundamental and plasmon–polariton mode is achieved through a whispering gallery mode supported by the fiber cladding, which leads to the formation of a resonance dip with a depth of ~30 dB or more in the transmission spectrum of an optical fiber loop. The position of the dip depends strongly on the ambient refractive index, which provides the possibility of refractometric measurements with a spectral sensitivity of ~5 μm/RIU and a resolution of ~4 × 10^–6. Limits of measurement of the refractive index are determined by the operating spectral range and the bending radius of the optical fiber and are 1.42–1.44 for the setup used.     

Theory and measurement of Young's modulus radial profiles of bent single-mode optical fibers with the multiple-beam interference technique

Multiple-beam Fizeau fringes in transmission have been applied to the study of the nonlinear stress-strain relationship due to bending in the cladding of single-mode optical fibers. The present study yields a relation between the variation of refractive indices of bent single-mode fibers, represented by the fringe shift, and the nonlinear radial change of Young's modulus along the fiber cross section. Experimentally, the study confirms the nonlinear asymmetric stress-strain relation across the fiber cross section. This relation is due to the asymmetric distribution of the compression and tensile stresses over the fiber cross section rather than to the shift in the centroid (neutral axis).     

Influence of bending on power distribution in step-index plastic optical fibers and the calculation of bending loss

A means of calculating optical power distribution in bent multimode optical fibers is proposed. It employs the power-flow equation approximated by the Fokker-Planck equation that is solved by the explicit finite-difference method. Conceptually important steps of this procedure include (i) dividing the full length of the bent optical fiber into a finite number of short, straight segments; (ii) solving the power equation for each segment sequentially to find its output distribution; and (iii) expressing that output distribution in rotated coordinates of the subsequent segment along the curved fiber to determine the input distribution for that subsequent segment and thus enable the calculation of the power flow and output distribution for it. The segment length and bend-induced perturbation of output angles are determined by geometric optics. The resulting power distributions are given at different cross sections along the curved fiber axis. They vary with the radius of fiber curvature and launch conditions. Results are compared to those for straight fiber. Bending loss is calculated as well.     

Bending effect on fiber acousto-optic mode coupling

The acousto-optic effect in a bent fiber is studied experimentally and numerically by using the scalar finite-element method. The resulting transmission spectra show that new mode-coupling peaks appear due to the breaking of the mode spatial symmetry. The strength of new peaks increases as the fiber-bending curvature increases with a redshift or blueshift in wavelength, strongly depending on the orientation of fiber bending with respect to the acoustic-wave vibration direction.     

Power losses in bent and elongated polymer optical fibers

This study performs experimental and numerical investigations into the power losses induced in bent, elongated polymer optical fibers (POFs). The theoretical analysis is based on a three-dimensional elastic-plastic finite-element model and makes the assumption of a planar waveguide. The finite-element model is used to calculate the deformation of the elongated POFs such that the power loss can be analytically derived. The effect of bending on the power loss is examined by considering seven different bend radii ranging from 10 to 50 mm. The results show that bending and elongation have a significant effect on the power loss in POFs. The contribution of skew rays to the overall power loss in bent, elongated POFs is not obvious at large radii of curvature but becomes more significant as the radius is reduced.     

Bending loss of elliptical-hole core circular-hole holey fibers bent in arbitrary bending directions

A holey fiber having a core with an elliptical-hole lattice structure, which is referred to as an elliptical-hole core circular-hole holey fiber (EC-CHF), can be easily designed as a single-polarization fiber by using the fundamental space-filling modes of the core and cladding lattices. However, because the guided mode in an EC-CHF has a polarization that arises from the large geometric anisotropy of the core lattice, the influence of the bending direction on the bending loss is a crucial issue for the practical implementation of EC-CHFs. Here, the bending losses of an EC-CHF bent in arbitrary angular orientations with respect to the core cross section are calculated numerically using the equivalent anisotropic step-index circular fiber model for a real EC-CHF, and the influence of the bending direction of the fiber on the bending loss is discussed.     

Numerical analysis of bent waveguides: bending loss, transmission loss, mode coupling, and polarization coupling

A rigorous, full-vectorial and computationally efficient finite-element-based modal solution, together with junction analysis and beam propagation approaches have been used to study bending loss, transition loss, mode coupling, and polarization coupling in bent optical waveguides. The waveguide offset and their widths have been optimized to reduce the transition loss and the mode beating.     

Optical time-domain reflectometry of bent plastic optical fibers

Optical time-domain reflectometry (OTDR) signals of step-index plastic optical fibers (POF's) and graded-index POF's were measured with a laser diode and an avalanche photodiode. When bent step-index and graded-index POF's were used, the OTDR signal behavior differed. The OTDR signal of the bent graded-index POF's had a step that corresponds to a curvature loss, but the step-index POF's had a spike signal at a bend, which indicated the occurrence of backscattering. The peak intensity was proportional to the square of the curvature. The refractive-index variation of the bent step-index POF's was measured, and the dependence of the peak intensity on the curvature was shown to agree with that predicted by the scattering from the refractive-index perturbation.     

Graded-index fiber lens proposed for ultrasmall probes used in biomedical imaging

The quality and parameters of probing optical beams are extremely important in biomedical imaging systems both for image quality and light coupling efficiency considerations. For example, the shape, size, focal position, and focal range of such beams could have a great impact on the lateral resolution, penetration depth, and signal-to-noise ratio of the image in optical coherence tomography. We present a beam profile characterization of different variations of graded-index (GRIN) fiber lenses, which were recently proposed for biomedical imaging probes. Those GRIN lens modules are made of a single mode fiber and a GRIN fiber lens with or without a fiber spacer between them. We discuss theoretical analysis methods, fabrication techniques, and measured performance compared with theory.     

Power losses in deformed graded-index polymer optical fibers

We investigate the power losses in bent and elongated graded-index polymer optical fibers (GI POFs). The variations of power losses in deformed GI POFs for various radii of curvature and elongations are measured. A simple tensile test result is used to calculate the average plastic energy density (APED) in a deformed GI POF at various elongations. The results indicate that the APED accumulated in a deformed GI POF can be considered as a key index to study the power loss in POF. Based on the experimental results, a curve-fitted equation is proposed to estimate the power loss using the APED for various radii of curvature. The maximum difference between the proposed equation and the experimental results is less than 3% for the deformed GI POFs.     

Analysis of characteristics of bent rib waveguides

With a perfectly matched layer boundary treatment, a semivectorial finite-difference method is used to calculate the eigenmodes of a single-mode (SM) or multimode (MM) bent rib waveguide. A detailed analysis is given for the dependence of the bending losses (including the pure bending loss and the transition loss) on geometrical parameters of the bent rib waveguide such as the rib width, the rib height, and the bending radius. The characteristics of the higher-order modes are analyzed. It is shown that the bending loss of the fundamental mode can be reduced effectively by increasing the width and height of the rib. For an integrated device, undesired effects due to the higher-order modes of a MM bent waveguide can be removed by appropriate choice of the geometrical parameters. An appropriately designed MM bent waveguide is used to reduce effectively the bending loss of the fundamental mode, and a low-loss SM propagation in a MM bent waveguide is realized when the bending losses of the higher-order modes are large enough.     

The measurement of the relative density of homogeneous fluids bymeans of an optical technique

A transducer that uses an intensity-modulated optical method to measure the relative density of homogeneous fluids is described. An optical fiber is used in a special way as a refractometer, measuring index of refraction, which has a direct relationship with relative density. The method relies on the optical power loss exhibited by a fiber bent beyond a critical radius. For such a fiber the critical angle of reflection is a function of the refractive index of the surrounding medium. The latter will therefore determine the amount of leakage, which can be measured and related to the value of relative density     

Bend sensing with long-period fiber gratings in capillaries embedded in structures

Bend responses of an LPG inscribed with a CO₂ laser in a conventional single-mode fiber are investigated in an arrangement, where the LPG is inserted into a thin silica capillary bonded to a steel strip. The curvature of the strip, laid on two supports and bent with a micrometer driver in the middle between the supports, decreases linearly with distance from the center of bending to the supports. Experiments are done for a very large range of bend deflections with the LPG in three positions shifted with respect to the center of bending, and two distinct opposite rotational orientations with respect to the plane of bending. Responses obtained for the above positions and orientations are greatly different and some of them show features which have not been reported for LPGs bent with a constant curvature and smaller deflections. They are, particularly, maxima and minima of the central wavelength's shift along with reversals of its direction, or the reappearance of a previously vanished attenuation band with increasing magnitude of bending. Also, it is found that the responses depend not only on the average curvature of the bent LPG, but also on the particular dependence of the curvature along the LPG's length. Some of the results obtained cannot be satisfactorily explained at the present level of knowledge, and a more thorough theoretical analysis is needed.     

Minimizing bend loss by removing material inside the caustic in bent single-mode fibers

By removing the cladding on the outside of a bent single-mode optical fiber and exposing a surface at a radius smaller than that of the radiation caustic, the leaky nature of the propagating mode is almost suppressed, and bend loss is effectively eliminated. The practical realization of this effect is described, and a loop with a bend radius of 0.50 mm on standard telecommunications fiber is demonstrated with negligible loss.     

Foundations for low-loss fiber gradient-index lens pair coupling with the self-imaging mechanism

A fiber-optic collimator that emits a Gaussian beam with its beam waist at a certain distance after the exit face of the lens is labeled a self-imaging collimator. For such a collimator, the waist of the emitted Gaussian beam and its location are partly dependent on the properties of the gradient-index (GRIN) lens. Parameters for the self-imaging collimator are formulated in terms of the parameters of a GRIN lens (e.g., pitch, core refractive index, gradient index, length) and the optical wavelength. Next, by use of the Gaussian beam approximation, a general expression for the coupling power loss between two self-imaging-type single-mode fiber (SMF) collimators is, for the first time to our knowledge, derived as a function of three types of misalignment, namely, separation, lateral offset, and angular tilt misalignment. A coupling experiment between two self-imaging collimators with changing separation distance is successfully performed and matches the proposed self-imaging mechanism coupling loss theory. In addition, using a prism, lateral offset, as well as angular tilt, misalignments are experimentally simulated for a two self-imaging collimator coupling condition by a single collimator reflective test geometry. Experimental results agree well with the proposed loss formulas for self-imaging GRIN lenses. Hence, for the first time to our knowledge, the mathematical foundations are laid for employing self-imaging-type fiber collimators in SMF-based free-space systems allowing optimal design for ultra-low-loss coupling.     

Fabrication method of ultra-small gradient-index fiber probe

Fabrication method and device of ultra-small gradient-index(GRIN) fiber probe were investigated in order to explore the development of ultra-small probes for optical coherence tomography(OCT) imaging.The beamexpanding effect of no-core fiber(NCF) and the focusing properties of the GRIN fiber lens were analyzed based on the model of GRIN fiber probe consisting of single-mode fiber(SMF),NCF and GRIN fiber lens.A stereo microscope based system was developed to fabricate the GRIN fiber probe.A fiber fusion splicer and an ultrasonic cleaver were used to weld and cut the fiber respectively.A confocal microscopy was used to measure the dimensions of probe components.The results show that the sizes of probe components developed are at the level of millimeter.Therefore,the proposed experimental system meets the fabrication requirements of an ultra-small self-focusing GRIN fiber probe.This shows that this fabrication device and method can be employed in the fabrication of ultrasmall self-focusing GRIN fiber probe and applied in the study of miniaturized optical probes and OCT systems.     

Controlled growth of single-walled carbon nanotubes for unique nanodevices

The controlled growth of bent and horizontally aligned single-walled carbon nanotubes (SWNTs) is demonstrated in this study. The bent SWNTs growth is attributed to the interaction between van der Waals force with substrate and aerodynamic force from gas flow. The curvature of bent SWNTs can be tailored by adjusting the angle between gas flow and step-edge direction. Electrical characterization shows that the one-dimensional resistivity of bent SWNTs is correlated with the curvature, which is due to strain induced energy bandgap variation. Additionally, a downshift of 10 cm(-1) in G-band is found at curved part by Raman analysis, which may be resulted from the bending induced carbon-carbon bond variation. In addition, horizontally aligned SWNTs and crossbar SWNTs were demonstrated. To prove the possibility of integrating the SWNTs having controllable morphology in carbon nanotube based electronics, an inverter with a gain of 2 was built on an individual horizontally aligned carbon nanotube.     

Dependence of bending losses on cladding thickness in plastic optical fibers

Our main goal is to provide a comprehensive explanation of the existing differences in bending losses arising from having step-index multimode plastic optical fibers with different cladding thickness and under different types of conditions, namely, the variable bend radius R, the number of fiber turns, or the fiber diameter. For this purpose, both experimental and numerical result of bending losses are presented for different cladding thicknesses and conditions. For the measurements, two cladding thicknesses have been considered: one finite and another infinite. A fiber in air has a finite cladding thickness, and rays are reflected at the cladding-air interface, whereas a fiber covered by oil is equivalent to having an infinite cladding, since the very similar refractive index of oil prevents reflections from occurring at the cladding-oil interface. For the sake of comparison, numerical simulations based on ray tracing have been performed for finite-cladding step-index multimode waveguides. The numerical results reinforce the experimental data, and both the experimental measurements and the computational simulations turn out to be very useful to explain the behavior of refracting and tunneling rays along bent multimode waveguides and along finite-cladding fibers.     

Birefringence measurements in gradient-index rod lenses

Stress birefringence can be found in gradient-index (GRIN) materials because they contain a variation in composition. GRIN glass fabricated by ion exchange may contain stress from two different processes. These include a size difference between the exchange and the diffusing ions and a variation in the thermal-expansion coefficient across the gradient region. The optical properties of the stressed material are polarization dependent, and therefore image quality is directly affected. We examine birefringence in GRIN rod lenses that have lengths more than ten times greater than their diameters. The effects are more easily observed in long rod lenses because of the large optical path lengths.