Use of analyte-modulated modal power distribution in multimode optical fibers for simultaneous single-wavelength evanescent-wave refractometry and spectrometry

A new method is described for the simultaneous determination of absorbance and refractive index of a sample medium. The method is based on measurement of the analyte-modulated modal power distribution (MPD) in a multimode waveguide. In turn, the MPD is quantified by the far-field spatial pattern and intensity of light, i.e., the Fraunhofer diffraction pattern (registered on a CCD camera), that emerges from a multimode optical fiber. Operationally, light that is sent down the fiber interacts with the surrounding analyte-containing medium by means of the evanescent wave at the fiber boundary. The light flux in the propagating beam and the internal reflection angles within the fiber are both affected by optical absorption connected with the analyte and by the refractive index of the analyte-containing medium. In turn, these angles are reflected in the angular divergence of the beam as it leaves the fiber. As a result, the Fraunhofer diffraction pattern of that beam yields two parameters that can, together, be used to deduce refractive index and absorbance. This MPD based detection offers important advantages over traditional evanescent-wave detection strategies which rely on recording only the total transmitted optical power or its lost fraction. First, simultaneous determination of sample refractive index and absorbance is possible at a single probe wavelength. Second, the sensitivity of refractometric and absorption measurements can be controlled simply, either by adjusting the distance between the end face of the fiber and the CCD detector or by monitoring selected modal groups at the fiber output. As a demonstration of these capabilities, several weakly absorbing solutions were examined, with refractive indices in the range from 1.3330 to 1.4553 and with absorption coefficients in the range 0-16 cm-1. The new detection strategy is likely to be important in applications in which sample coloration varies and when it is necessary to compensate for variations in the refractive index of a sample.     

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.     

Thermooptic coupler for multimode optical fibers

The detailed theory is presented together with design considerations and recent experimental results for an electronically controllable directional coupler for multimode optical fibers. The device, based on plastic-clad silica fiber, is of exceptionally simple construction and compact size and is highly reliable. A theoretical model of the coupler is described and compared with actual device performance. The coupling can be varied from -4 to -28 dB with an excess loss of <0.2 dB over the entire coupling range, in agreement with theory. Improvements in the present device design are also discussed.     

Vortex optical Magnus effect in multimode fibers

A theoretical and experimental analysis is made of the optical Magnus effect in multimode optical fibers excited by a laser beam whose wavefront has a pure screw dislocation and carries the topological charge ±l, where l is the azimuthal quantum number. It is found that the angular rotation of the plane of propagation of a local wave depends on the magnitude and sign of the topological charge and changes qualitatively when the circulation of the polarization is reversed. The phase mechanism is attributed to spin-orbit interaction in the photon ensemble. It is demonstrated experimentally that the optical Magnus effect in a few-mode fiber for the CP₁₁ mode at the beat length is observed as a rotation of the axis of the pure edge dislocation field through an angle proportional to the beat length. Pis’ma Zh. Tekh. Fiz. 23, 76–81 (August 26, 1997)     

Method for calculating the coupling coefficient in step-index optical fibers

A simple method is proposed for determining the mode coupling coefficient D in step-index multimode optical fibers. It only requires observation of the far-field output pattern for one fiber length with the input light launched centrally along the fiber axis (theta(0)=0). For illustration, the coupling coefficient determined by this simple method for a step-index plastic optical fiber was used to calculate the coupling length L(c) at which the equilibrium mode distribution is achieved, and length z(s) at which the steady-state distribution is achieved. Our results are in good agreement with experimental results reported earlier.     

Mode coupling in strained and unstrained step-index plastic optical fibers

Using the power-flow equation, we have examined the state of mode coupling in strained and unstrained step-index plastic optical fibers. The strained fibers show much stronger mode coupling than unstrained fibers of the same types. As a result, the coupling lengths where equilibrium mode distribution is achieved and the lengths of fiber required for achieving a steady-state mode distribution for strained fibers are much shorter than the corresponding lengths for unstrained fibers.     

Numerical and experimental study of microfluidic devices in step-index optical fibers

Microfluidic devices composed of microslits in step-index optical fibers are thoroughly investigated. Numerical simulations are performed to explain scattering and power loss in such devices. Experimental results based on microslits fabricated by femtosecond laser processing corroborate theoretical data. Dependency of the device performance on the refractive index of fluid in the slit is further utilized to construct a refractive index sensor and an in-fiber attenuator.     

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.     

Kramers-Kronig analysis of infrared reflection spectra with perpendicular polarization

The application of Kramers-Kronig analysis for reflection spectra from a single interface with perpendicular (s) polarization has been studied theoretically with regard to a phase correction term. The errors in phase shift and complex refractive index obtained by the use of Kramers-Kronig analysis have been examined for such techniques as external, internal, and total internal reflection spectroscopies by the use of spectral simulation and the complex refractive index based on dispersion theory. The advantages and disadvantages of the various measurement techniques used to obtain the complex refractive index of a sample material have been compared. It is concluded that the external reflection technique can be used until the sample thickness becomes too thin to provide the edge shape necessary to avoid the detection of reflection from the back surface. The total internal reflection technique should be used only for a thin-film sample because knowledge of the refractive index at some frequency is required and bcause this technique may yield larger errors than the other techniques in the complex refractive index obtained by the use of Kramers-Kronig analysis.     

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.     

Influence of numerical aperture on mode coupling in step-index plastic optical fibers

Using the power-flow equation, we have examined the state of mode coupling in step-index plastic optical fibers with different numerical apertures. Our results confirm that the coupling rates vary with the coupling coefficient of the fibers as the dominant parameter, especially in the early stage of coupling near the input fiber end. However, we show that the fiber's numerical aperture has a significant influence on later stages of this process. Consequently, equilibrium mode distribution and steady-state distribution are achieved at overall fiber lengths that depend on both of these factors. As one of our examples demonstrates, it is possible for the coupling length of a high-aperture fiber to be similar to that of a low-aperture fiber despite the three-times-larger coupling coefficient of the former.     

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.     

Solution of mode coupling in step-index optical fibers by the Fokker-Planck equation and the Langevin equation

The power-flow equation is approximated by the Fokker-Planck equation that is further transformed into a stochastic differential (Langevin) equation, resulting in an efficient method for the estimation of the state of mode coupling along step-index optical fibers caused by their intrinsic perturbation effects. The inherently stochastic nature of these effects is thus fully recognized mathematically. The numerical integration is based on the computer-simulated Langevin force. The solution matches the solution of the power-flow equation reported previously. Conceptually important steps of this work include (i) the expression of the power-flow equation in a form of the diffusion equation that is known to represent the solution of the stochastic differential equation describing processes with random perturbations and (ii) the recognition that mode coupling in multimode optical fibers is caused by random perturbations.     

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.     

In-line optical fiber sensors based on cladded multimode tapered fibers

The use of uniform-waist cladded multimode tapered optical fibers is demonstrated for evanescent wave spectroscopy and sensors. The tapering is a simple, low-loss process and consists of stretching the fiber while it is being heated with an oscillating flame torch. As examples, a refractive-index sensor and a hydrogen sensor are demonstrated by use of a conventional graded-index multimode optical fiber. Also, absorbance spectra are measured while the tapers are immersed in an absorbing liquid. It is found experimentally that the uniform waist is the part of the taper that contributes most to the sensor sensitivity. The taper waist diameter may also be used to adjust the sensor dynamic range.     

Launching light from semiconductor lasers into plane-ended multimode optical fibers

A systematic and detailed study of launching light from semiconductor lasers into plane-ended multimode optical fibers has been carried out--we believe for the first time. Three different semiconductor lasers and four multimode fibers having numerical apertures in the 0.16-0.40 range were used. Simple theoretical models developed for the launching efficiency eta give good agreement with experimental results. We show how erroneous results can be obtained when considering only the stimulated emission of the lasers in calculating eta. The dependence of eta on axial, lateral, and angular misalignments is also investigated and explained qualitatively with ray optics.     

Stress optical fiber sensor using light coupling between two laterally fused multimode optical fibers

A stress optical fiber sensor was manufactured and tested. It uses light coupling between two parallel and laterally fused, all-silica multimode optical fibers along a cladding length of a few centimeters. This sensor is dedicated to the measurement of high values of stress. A theoretical model was developed using the mode coupling and the perturbation theory to calculate the global coupling coefficient of light. A serial optical fiber sensor network interrogated by the time-division multiplexing method was realized and tested. The major applications of this sensor are control and monitoring of civil engineering structures and concretes.