Finite-element modal analysis of large-core multimode optical fibers

Plastic optical fibers that are a typical large-core multimode optical fiber support a great number of modes compared with conventional silica-glass multimode optical fibers. So far the WKB method hasbeen used for most of the modal analyses of these fibers because of a great number of guided modes. We describe the accurate eigenmodal analysis of large-core multimode optical fibers with the finite-element method (FEM) and compute the propagation constants of all LP modes. In addition, the FEM has a strong advantage for arbitrary core profiles whereas the WKB method is not suitable fornonmonotonic profiles. To demonstrate the advantage, we apply the FEM to the fiber having sinusoidal fluctuations.     

Kramers-Kronig analysis of molecular evanescent-wave absorption spectra obtained by multimode step-index optical fibers

Spectral distortions that arise in evanescent-wave absorption spectra obtained with multimode step-index optical fibers are analyzed both theoretically and experimentally. Theoretical analysis is performed by the application of Kramers-Kronig relations to the real and the imaginary parts of the complex refractive index of an absorbing external medium. It is demonstrated that even when the extinction coefficient of the external medium is small, anomalous dispersion of that medium in the vicinity of an absorption band must be considered. Deviations from Beer's law, band distortions, and shifts in peak position are quantified theoretically as a function of the refractive index and the extinction coefficient of the external medium; the effect of bandwidth for both Lorentzian and Gaussian bands is also evaluated. Numerical simulations are performed for two types of sensing sections in commonly used plastic-clad silica optical fibers. These sensors include an unclad fiber in contact with a lower-index absorbing liquid and a fiber with the original cladding modified with an absorbing species. The numerical results compare favorably with those found experimentally with these types of sensing sections.     

Free-space optical relay for the interconnection of multimode fibers

We present results from a system that shows that multimode fibers can be used for both the input and the output of a free-space optical system. The system consists of plastic microlenses integrated with plastic optomechanical components that are suitable for low-cost fabrication and assembly. Such a system opens up opportunities to construct large repeaters and switches for multigigabit ethernet applications by integration with two-dimensional arrays of optoelectronic devices. We demonstrate a 2.5-Gbit/s transmission rate by using commercial vertical-cavity surface-emitting lasers coupled to 62.5-mum core fibers. We consider the design constraints and the capabilities of custom optical modules suitable for mass production.     

High numerical aperture in multimode microstructured optical fibers

Microstructured or "air-clad" fibers, with air holes surrounding a large core, have recently demonstrated much wider light-acceptance angles than conventional fibers. An original and accurate method is presented for determining the numerical aperture of such fibers using leaky modes. The dependence on length, wavelength, and various microstructure dimensions are evaluated for the first time for a class of fibers that exhibit exceptionally high numerical apertures. These results show excellent agreement with published measurements on similar fibers and verify that bridge thicknesses much smaller than the wavelength are required for high numerical apertures.     

One-step measurement of optical fields in multimode circular fibers

We propose to determine the optical field in multimode circular fibers by using a one-step method that measures the Wigner distribution function of a section of the field in the fiber. This method allows an estimation not only of the power carried by each mode but also of the relative phases of different modes in the fiber. An additional measurement with the same setup can even determine the propagation constants of different modes. An example is provided, and the connection of this method of field recovery to the coupling coefficient between fibers and light sources is also discussed.     

Broadband parallel-fiber optical link for short-distance interconnection with multimode fibers

In a multimode step-index fiber the propagation angle of a beam is conserved over short distances even if the fiber is bent slightly. This behavior can be exploited for a multiplexed signal transmission by the assignment of different channels to different propagation angles [angle-division multiplexing (ADM)]. Thus parallel transmission can be achieved. Because each channel occupies only a subrange of the fiber's numerical aperture, modal dispersion is reduced compared with single-channel transmission through the same fiber. The transmission properties of an ADM-based transmission line are analyzed for short propagation distances. Passive all-optical setups for multiplexing and demultiplexing operations are proposed. Cross-talk measurements are shown for a transmission with a length of 8 m and 13 multiplexed channels.     

Modal power decomposition of beam intensity profiles into linearly polarized modes of multimode optical fibers

We calculate the modal power distribution of a randomly and linearly polarized (LP) multimode beam inside a cylindrical fiber core from knowledge of spatial-intensity profiles of a beam emitted from the fiber. We provide an exact analysis with rigorous proofs that forms the basis for our calculations. The beam from the fiber end is collimated by a spherical lens with a specific focal length. The original LP-mode basis is transformed by the spherical lens and forms another orthogonal basis that describes the free-space beam. By using this basis, we calculate the modal power distribution from the mutual-intensity profile. This is acquired by adopting a well-known mutual-intensity-profile-retrieving technique based on measurements of the intensity patterns several times after two orthogonal cylindrical lenses with varying separation. The feasibility of our decomposition algorithm is demonstrated with simulations.     

Influence of depth of intermediate layer on optical power distribution in W-type optical fibers

For different depth and width of the intermediate layer, a power flow equation is used to calculate spatial transients and steady state of power distribution in W-type optical fibers (doubly clad fibers with three layers). A numerical solution has been obtained by the explicit finite difference method. Results show how the power distribution in W-type optical fibers varies with the depth of the intermediate layer for different values of intermediate layer width and coupling strength. We have found that with increasing depth of the intermediate layer, the fiber length at which the steady-state distribution is achieved increases. Such characterization of these fibers is consistent with their manifested effectiveness in reducing modal dispersion and improving bandwidth.     

Numerical analysis of modal dispersion in graded-index plastic optical fibers

Modal dispersion properties of a fabricated plastic optical fiber are numerically calculated through a finite-element method. The modal index, group delay, impulse response, and output pulse shape are compared with those for the power-law profile plastic optical fiber; the influence of index profile deviations from the power-law profile is described. It is shown that index profile fluctuations in the actual index profile strongly affect the group delays, even though they are relatively small. On the other hand, they have little effect on the modal indices.     

Segmented chirped grating for coarse wavelength division demultiplexing with multimode optical fibers

A chirped grating segmented into partitions each having a constant blaze angle to use in a demultiplexer for coarse wavelength division multiplexing with multimode optical fibers is developed. Its designed configuration utilizes a resonance region to achieve high diffraction efficiency and large dispersion. The width, blaze angle, and diffraction order of each partition were optimized by vector diffraction analysis. The diffraction loss of the manufactured grating was less than 1.5 dB, and polarization-dependent loss was less than 0.6 dB within a wavelength width of at least 70 nm. It is confirmed that a demultiplexer with the developed chirped grating had a wide passband and low cross talk.     

Design and performance of thin cylindrical diffusers created in Ge-doped multimode optical fibers

Cylindrical fiber diffusers have become common tools for various medical therapies. However, their large outer diameters and short lengths restrict their clinical application in some newly developed light therapies. Here, a 250-microm outer-diameter diffuser with an active length that exceeds 5 cm is presented. Diffusers are created in photosensitive optical fibers with outer cladding diameters of 140 microm by use of a structured beam from an excimer laser. Predetermined emission profiles can be achieved. Photometric characteristics, including longitudinal, polar, and azimuthal emission diagrams, were determined by use of a goniometer to assess the light-emission performance of the diffuser. Longitudinal isotropy of better than +/- 10% was achieved. Polar and azimuthal emissions were within +/- 15% of those of an ideal linear Lambertian emitter. Polar uniformity could be improved by an insignificant increase in the outer diameter by use of a diffusing recoating compound. The residual leakage of light at the distal end of the diffuser can be as little as 1%. Other physical parameters tested include minimal bending radius after recoating (< 5 mm) and maximum power handling (> 1.0W cm(-1)). All materials employed were biocompatible.     

Numerical aperture of optical fibers based on high-purity As2S3 glass: Unsteady-state modal distribution

The numerical aperture of core-clad multimode optical fibers with the core made from high-purity As₂S₃ glass is measured by a far-field technique using a cw CO laser (5.3-6.3 μm). The lengths at which a steady-state modal distribution is reached are determined for optical fibers with metallic coatings, tetrafluoroethylene/difluoroethylene copolymer coatings, or immersion. Various factors affecting the numerical aperture of fibers with an unsteady-state modal distribution are examined.     

Bandwidth estimation for multimode optical fibers using the frequency correlation function of speckle patterns

In this paper we present a new method for estimating the bandwidth of multimode optical fibers based on the frequency correlation function of the speckle patterns generated by the interference of fiber modes. This technique, which does not require a pulse or signal generator, can be utilized to estimate the bandwidth of a multimode fiber using a relatively short length of fiber. By applying this method to a test fiber we obtained a bandwidth of approximately 36 MHz km which is in relatively good agreement with the approximately 44-MHz x km bandwidth measured by a conventional pulsed technique.     

Impact and vibration detection in composite materials by using intermodal interference in multimode optical fibers

An optical fiber sensor based on the intermodal interference principle is integrated in a composite material to detect impacts and vibrations. Six fibers are integrated at the top of a carbon/epoxy composite panel so as to form a grid into the structure. Spectral and temporal responses to impacts and acoustic vibrations of the sensor are compared with a piezoelectric accelerometer. The tests proved the facility of integration and the high sensitivity of the device. The location of impacts is performed with this arrangement by measuring the arrival times of the front waves to the fibers.     

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.     

Power loss, modal noise and distortion due to microbending of optical fibers

Theoretical and experimental investigations are described for determining the transmission characteristics of a multimode fiber with microbending for coherent and partially coherent illumination. The measured values of the average excess power loss are shown to be in close agreement with the theory. Also, an estimate of the excess transient loss due to mode coupling is found to be in good agreement with previously published data. Mode-mode interference is shown to be the cause of temporal fluctuations in the microbending loss, from which expressions for modal noise and baseband/subcarrier nonlinearity are derived on a statistical basis. For a given overall loss, the results show that many uniformly distributed small amplitude microbends cause much less modal noise and distortion than a few large amplitude microbends.     

Launching light from semiconductor lasers into multimode optical fibers having hemispherical ends and taper-with-hemisphere ends

The plane ends (PE) of various multimode optical fibers have been transformed into (a) hemispherical ends (HE) and (b) taper-with-hemisphere ends (TE) by using a microtorch and also a CO2 laser for HE only. We confirmed that the launching efficiency eta from semiconductor lasers into multimode fibers is much greater than TE and HE compared with PE, with TE being the most efficient. A rigorous comparison between these three launching arrangements is reported here for the first time together with detailed analysis of similar published work. The effect of various misalignments is also investigated and compared for the three fiber terminations.     

Spectropolarimetry of multimode quartz fibers in the infrared

Results are presented of experimental spectropolarimetric investigations of multimode fiber-optic waveguides with core diameters between 65 and 404 μm in the infrared (0.8, 1.3, and 1.55 μm). A theoretical explanation is proposed for the results. Pis’ma Zh. Tekh. Fiz. 24, 75–80 (December 12, 1998)