Comparative study of coupling to symmetric and antisymmetric cladding modes in long-period fiber gratings

We analyse the influence of coupling to symmetric and antisymmetric cladding modes in arc-induced Long-Period Fiber Gratings for temperature and strain sensing. The origin of this difference in energy coupling is related to the fabrication process of these gratings and depends on the electric arc discharge conditions, which modulates the refractive index and geometry of the optical fiber. Finally, results demonstrate the performance of different cladding modes excited in arc-induced LPFGs to temperature and strain applications and, in addition, indicate which coupling might be appropriate to certain sensing applications.     

Minimization of temperature effects of high-birefringent elliptical fibers for polarimetric optical-fiber sensors

The temperature dependence of polarization-maintaining fibers is a problem in polarimetric optical-fiber sensors. We report a novel method for making a temperature-insensitive, polarization-maintaining fiber, which may be used for the sensing part in a polarimetric strain sensor. The fiber has a double-clad elliptical core with built-in stresses in the core and cladding regions. To minimize the temperature sensitivity, the built-in stresses are balanced with the refractive-index differences and the core ellipticity properly chosen. The temperature and strain sensitivities of the fiber are calculated. A practical design and some potential applications of such a temperature-insensitive fiber with a high strain sensitivity are presented.     

Comparative study of dispersion characteristics of uniaxial crystalline optical fiber under the extreme cases of helix pitch angles

Some special cases of dispersion characteristics of a uniaxial crystalline optical fiber with a helical winding on the core-cladding boundary are investigated theoretically. In the present case, the optical fiber is doubly unconventional: (i) in the choice of uniaxial crystalline optical fiber and (ii) in the choice of sheath helix between the core and cladding. Field components, boundary conditions, and eigenvalue equations for HE and EH modes are obtained. We consider two special cases, i.e. ψ = 0° and ψ = 90° to obtain simpler eigenvalue equations which contain Bessel and modified Bessel functions and their derivatives. The nature of the dispersion curve remains unaffected with the anisotropy and only cutoff frequency is lowered for the positive uniaxial crystals. The helix pitch angle does not affect the modal cutoffs but it effectively controls the number of guided modes. This property has promising importance in long-distance communication where only a few modes are desired to be guided in order to minimize the inter-modal dispersion.     

Substrate geometry-dependent nonlinear absorption of carbon nanotubes deposited onto D-shaped optical fibers

The effect of single-wall carbon nanotubes (SWNTs) on nonlinear optical absorption of D-shaped fibers with versatile the remaining length of the cladding region and the interaction length are investigated. The optical absorption based on SWNTs is induced by the energy bandgap in SWNTs. The bandgap energy depends on the tube diameter of SWNTs. After fabricating versatile D-shaped fiber, SWNTs are deposited on the polished surface of D-shaped fibers. The cladding region of single mode fibers is removed by a side-polishing technique and the D-shaped fiber is obtained. In the D-shaped fiber, the cladding region is thin enough to induce the evanescent field coupling of core mode to the other modes of the SWNT-overlay. The nonlinear absorption based on the SWNTs-overlay is changed by the remaining length of cladding region and the interaction length because the coupling strength of evanescent field strongly depends on the different remaining lengths of the cladding region and the interaction lengths as well.     

Acoustic modes in optical fiberlike waveguides

A perturbation analysis of guided and leaky modes in fiber acoustic waveguides with core and cladding parameters that are slightly different is presented. The perturbing parameter is the shear-velocity difference between the core and cladding material epsilon(s). Acoustic fields and eigenvalues are expanded in power series of epsilon (s)(1/2) for radial and flexural modes and in powers of epsilon(3) for torsional modes. Expansion of leaky longitudinal modes is also in terms of epsilon(s), but the nature of perturbation analysis for these modes is somewhat different from that of guided modes. Zero-order solutions for all types of modes are obtained, and some important higher-order effects are discussed. Common features of optical and acoustic modes in weakly guiding fibers are addressed. It is shown that with respect to zero-order solutions of guided modes, optical and acoustic fibers have identical propagation characteristics. Exact and zero-order propagation characteristics for several lower-order shear-type modes are calculated and compared.     

Acoustic wave propagation in piezoelectric fibers of hexagonalcrystal symmetry

An exact analysis is presented for acoustic wave propagation in cladded acoustic fibers having a core and an infinite thick cladding both made of piezoelectric hexagonal crystal of 6 mm point group symmetry. The crystalline Z axes of both the core and cladding coincide with the fiber axis. A general dispersion equation is derived for all the acoustic modes propagating along the fiber axis. Two simpler and independent equations which represent the dispersion relations of torsional and radial-axial modes can be separated from the general dispersion equation. It has been found that the radial-axial and general flexural modes are piezoelectrically active while the torsional modes are not. Approximate dispersion relations for pure guided modes in weakly guiding weakly piezoelectric fibers which are much simpler than the exact ones are also given. Numerical results are only presented for pure guided modes. Exact and approximate dispersion curves of several lower order pure guided flexural, radial-axial and torsional modes in a weakly guiding ZnS fiber are compared and they are in good agreement     

Coupling characteristics of cladding modes in tilted optical fiber bragg gratings

We have studied both theoretically and experimentally the effect of grating tilting on the coupling between the fundamental core mode and the cladding modes in an optical fiber Bragg grating. The coupling is shown to be very sensitive on the tilting angle. It is also shown that tilting angle has to be minimized in fibers with designs to suppress the coupling between the fundamental core mode and the cladding modes. We have also studied the single, strong loss peak accompanying the Bragg reflection peak in depressed-cladding fibers, thus showing a good agreement between behavior that is measured and that is predicted theoretically.     

Comparative study of mid-infrared fibers for modal filtering

We compare the filtering capabilities of two infrared fibers developed to achieve a high rejection ratio of the higher order modes in order to obtain compact modal filters devoted to stellar interferometry. Two types of double-clad fibers are studied: a fiber with a second thin absorbing cladding and a fiber with a second thick absorbing cladding closer to the fiber core; both are single mode around the CO(2) band (10.6 μm). We present the single-mode spectral domain and the nulling capabilities of both fibers for different fiber lengths, comparing simulations with experimental results. We show that the filtering capabilities are improved when the absorbing clad is closer to the fiber core, as the propagation distance needed to filter out these modes is shorter. Thus, to obtain high rejection ratios in compact devices, an absorbing cladding close to the core of the fiber is compulsory in order to suppress cladding modes that could eventually recouple into the waveguide. We present an empirical model that allows determining the minimum filter length, considering only one effective leaky mode with low attenuation, which considerably simplifies the theoretical studies.     

Characteristics of a long-period fiber grating with reduced cladding for refractive index sensing

The sensitivity to surrounding refractive index (SRI) of a long-period fiber grating (LPFG) can be effectively improved by decreasing the cladding radius. When the cladding is reduced, a three-layer model is necessary to evaluate the effective refractive index (ERI) of the core mode. A variation of SRI can induce a greater resonant wavelength shift when the core mode is coupled to a higher-order cladding mode. However, as the cladding is reduced further, the highest-order cladding mode would be cut off, i.e. the number of cladding modes that a given fiber structure can support would be less; thus, the higher-order cladding modes that can be used for higher sensitivity are limited. Hence, the implementation of high sensitivity for SRI sensing with cladding-reduced LPFGs is dependent on the proper combination of cladding radius and cladding mode order. Based on the vector coupled-mode theory, the transmission spectrum and sensitivity are numerically analyzed with respect to the cladding radius, which shows that the SRI sensitivity of the HE₁₂ mode with cladding radius a ₂?=?20?µm is 32 times as high as that with a ₂?=?62.5?µm and the SRI resolution is available to the order of 10^?7.     

Design of Long-Period Fiber Grating Refractometric Sensors With Linear Response by a Genetic Algorithm

A new method for the design of optical fiber refractometric sensors based on nonuniform long-period fiber gratings (LPFGs) is presented. A specialized genetic algorithm (GA) with properly designed operators is a fundamental element of this method and performs the theoretical synthesis of a necessary nonuniform LPFG period profile. Such a profile yields a linear response of the sensor to the refractive index of the external medium. A distinctive feature of the designed LPFG is a linear gradient of the core and cladding refractive index along the grating length. Also, a new mathematical model of nonuniform LPFGs is presented, the model permits to take into account the effect of some LPFG sections of a lower and others of a higher cladding refractive index than that of the external medium. The application of both the design method and the mathematical model is illustrated with a numerical example.     

Propagation and coupling of hybrid modes in twisted fibers

The first-order paraxial approximation is used to obtain the distributions of the electric and magnetic fields for the core and cladding hybrid fiber modes. The coupling coefficients of these modes are found for fibers subject to twist. The longitudinal electric field component determines the mode coupling in twisted fibers. It is shown that in the first-order paraxial approximation the cladding hybrid modes propagating in a twisted fiber rotate along the direction of the twist at the same rate as the core mode, independently of the azimuthal and radial mode numbers. Four hybrid modes constituting one linearly polarized mode have different longitudinal components, and the corresponding cladding-mode resonances of a long-period fiber grating undergo different shifts owing to different mode self-coupling coefficients. This results in the removal of mode degeneracy and splitting of resonances of long-period gratings in twisted fibers.     

Measurement of CO2-laser-irradiation-induced refractive index modulation in single-mode fiber toward long-period fiber grating design and fabrication

We report a new method to measure the CO(2)-laser-irradiation-induced refractive index modulation in the core of a single-mode optical fiber for the purpose of design and fabrication of long-period fiber gratings (LPFGs) without applying tension. Using an optical fiber Fabry-Perot interferometer, the laser-induced axial refractive index perturbation was measured. We found that the CO(2)-laser-irradiation-induced refractive index change in the fiber core had a negative value and that the magnitude was a sensitive function of the laser exposure time following almost a linear relation. Under the assumption of a Gaussian-shaped refractive index modulation profile and based on the first two terms of Fourier series approximation, the measured refractive index perturbations were used to simulate the LPFG transmission spectra. LPFGs with the same laser exposure parameters were fabricated without applying tension, and their spectra were compared with those obtained by simulations.     

Superstructured fiber-optic contact force sensor with minimal cosensitivity to temperature and axial strain

In this work a new superstructured, in-fiber Bragg grating (FBG)-based, contact force sensor is presented that is based on birefringent D-shape optical fiber. The sensor superstructure comprises a polyimide sheath, a stress-concentrating feature, and an alignment feature that repeatably orients the sensor with respect to contact forces. A combination of plane elasticity and strain-optic models is used to predict sensor performance in terms of sensitivity to contact force and axial strain. Model predictions are validated through experimental calibration and indicate contact force, axial strain, and temperature sensitivities of 169.6 pm/(N/mm), 0.01 pm/με, and -1.12 pm/°C in terms of spectral separation. The sensor addresses challenges associated with contact force sensors that are based on FBGs in birefringent fiber, FBGs in conventional optical fiber, and tilted FBGs. Relative to other birefringent fiber sensors, the sensor has contact force sensitivity comparable to the highest sensitivity of commercially available birefringent fibers and, unlike other birefringent fiber sensors, is self-aligning with respect to contact forces. Unlike sensors based on Bragg gratings in conventional fiber and tilted Bragg gratings, the sensor has minimal cosensitivity to both axial strain and changes in temperature.     

Highly sensitive fiber loop ringdown strain sensor using photonic crystal fiber interferometer

A highly sensitive strain sensor is demonstrated by introducing a photonic crystal fiber (PCF) Mach-Zehnder interferometer (MZI) in a cavity ringdown fiber loop as a sensing element. The MZI is fabricated by splicing a short length of PCF between two single-mode fibers with collapsed air holes over a short region at two splicing points, which allows coupling between core and cladding modes inside the PCF. By measuring the decay constants of the fiber ringdown loop under different applied strains, a high strain sensitivity of ~0.21 μs?1/εm and a minimum detectable strain of ~3.6 με are obtained. As a benefit from the ultralow thermal dependence of PCF, the maximum temperature-induced measurement error could be reduced to ~0.24 με.     

Simultaneous measurement for liquid level and refractive index based on all-fiber modal interferometer

A simple fiber sensor capable of simultaneous measurement of liquid level and refractive index (RI) is proposed and experimentally demonstrated. The sensing head is an all-fiber modal interferometer manufactured by splicing an uncoated single-mode fiber with two short sections of multimode fiber. The interference pattern experiences blue shift along with an increase of axial strain and surrounding RI. Owing to the participation of multiple cladding modes with different sensitivities, the height and RI of the liquid could be simultaneously measured by monitoring two dips of the transmission spectrum. Experimental results show that the liquid level and RI sensitivities of the two dips are 245.7 pm/mm, ?38 nm/RI unit (RIU), and 223.7 pm/mm, ?62 nm/RIU, respectively. The approach has distinctive advantages of easy fabrication, low cost, and high sensitivity for liquid level detection with the capability of distinguishing the RI variation simultaneously.     

Analysis of weakly guiding cladded acoustic fibers of hexagonal crystal symmetry

An approximate analysis of the weakly guiding cladded acoustic fiber consisting of a core and infinite thick cladding both with hexagonal crystal symmetry is presented. The crystalline Z axis is parallel to the fiber axis. Weak guidance conditions require that the stiffness constants of the core are slightly less than those of the cladding, and the density of the core and cladding are almost the same. Approximate dispersion and cutoff equations are derived for all pure guided modes. Dispersion curves of several lower-order guided torsional, radial-axial and flexural modes are evaluated using both exact and approximate formulas and they are in good agreement. A simple approximate dispersion equation for leaky (longitudinal-type) modes is also obtained.     

Analysis of cladded acoustic fibers of hexagonal crystal symmetry

A cladded acoustic fiber consisting of a core and an infinite thick cladding both having a hexagonal crystal symmetry is analyzed. The crystalline Z axes of both core and cladding are parallel to the fiber axis. Dispersion equations and field distributions for all modes are derived, and previously reported results for the isotropic case are retrieved. Numerical results for a few lowest-order pure guided torsional, radial-axial and flexural modes are shown. Material considerations are discussed.     

Modeling of the loss and mode coupling due to an irregular core-cladding interface in step-index plastic optical fibers

The core-cladding boundary in step-index plastic optical fibers is imperfect. Surface irregularities locked in during the manufacturing process couple the guided modes by reflecting them in directions that deviate unpredictably from the expected directions. This causes an additional loss as the multiple reflections from surface elements with directions randomized around the nominal for the cylinder transfer the power to the radiation modes that are carried away from the core into the cladding. We model such loss and mode coupling by ray tracing. The irregular core-cladding interface is represented by nominally cylindrical surface elements with orientations randomly perturbed around two geometric axes. The results show mode coupling and relative loss per unit fiber length caused by the core-cladding interface irregularities. The loss is high close to the input fiber end where mode coupling is intense. It drops farther along the fiber as mode coupling slows down and stabilizes where the equilibrium mode distribution is reached.     

A readout scheme providing high spatial resolution for distributed fluorescent sensors on optical fibers

Optical fiber sensors using fluorescent probes distributed along the fiber cladding are of great interest for monitoring physical and chemical properties in their environment. The location of an emitting fluorophore along a fiber can be determined by measuring the time delay between a short, exciting laser pulse propagating in the fiber core and the returning fluorescence pulse. However, fluorescence lifetimes limit the spatial resolution, since a minimum separation of the fluorophores is required to resolve returning light pulses. For many applications, a closer spacing of sensor regions is desirable. We present a new method for the readout of closely packed fluorescent chemosensors located in the cladding of an optical fiber. By using a second fiber as an optical delay line, the minimum spacing between adjacent sensor regions can be well below the fluorescence lifetime limit. Since the coupling between the two fibers is evanescent, the attenuation of the excitation pulse is low, making long arrays of sensor regions feasible. This is particularly important since the one-dimensional combinatorial chemistry method developed by us allows for efficient preparation of diverse linear arrays. Detection sensitivities of 10(-7) mol/L are demonstrated, with the potential for significant improvement.