BER evaluations for multimode beams in underwater turbulence

Abstract

In underwater optical communication links, bit error rate (BER) is an important performance criterion. For this purpose, the effects of oceanic turbulence on multimode laser beam incidences are studied and compared in terms of average BER (<BER>), which is related to the scintillation index. Based on the log-normal distribution, <BER> is analysed for underwater turbulence parameters, including the rate of dissipation of the mean squared temperature, the rate of dissipation of the turbulent kinetic energy, the parameter that determines the relative strength of temperature and salinity in driving index fluctuations, the Kolmogorov microscale length and other link parameters such as link length, wavelength and laser source size. It is shown that use of multimode improves the system performance of optical wireless communication systems operating in an underwater medium. For all the investigated multimode beams, decreasing link length, source size, the relative strength of temperature and salinity in driving the index fluctuations, the rate of dissipation of the mean squared temperature and Kolmogorov microscale length improve the <BER>. Moreover, lower <BER> values are obtained for the increasing wavelength of operation and the rate of dissipation of the turbulent kinetic energy in underwater turbulence.     

Rotation of multimode Gauss-Laguerre light beams in free space

An iterative algorithm is presented for calculating diffractive phase optical elements that form light beams which are an effective superposition of a small number of nonradially symmetric Gauss-Laguerre modes with a prescribed energy contribution from each mode. Pis’ma Zh. Tekh. Fiz. 23, 1–6 (September 12, 1997)     

Generating function approach for creation of coherent multimode beams by diffractive optics

Tailored compositions of transverse modes provided by mathematical generating functions are exploited for the synthesis of multimode laser beams in free space. We show that analytical equations which are available for the generating functions provide physical insight into modal phase and power balance in multimode coherent light beams. Multimode coherent beams were created by methods of diffractive optics implementing the generating functions. Experimental and computer simulated results demonstrate a good match.     

Miniature multimode monolithic flextensional transducers

Traditional flextensional transducers classified in seven groups based on their designs have been used extensively in 1-100 kHz range for mine hunting, fish finding, oil explorations, and biomedical applications. In this study, a new family of small, low cost underwater, and biomedical transducers has been developed. After the fabrication of transducers, finite-elements analysis (FEA) was used extensively in order to optimize these miniature versions of high-power, low-frequency flextensional transducer designs to achieve broad bandwidth for both transmitting and receiving, engineered vibration modes, and optimized acoustic directivity patterns. Transducer topologies with various shapes, cross sections, and symmetries can be fabricated through high-volume, low-cost ceramic and metal extrusion processes. Miniaturized transducers posses resonance frequencies in the range of above 1 MHz to below 10 kHz. Symmetry and design of the transducer, polling patterns, driving and receiving electrode geometries, and driving conditions have a strong effect on the vibration modes, resonance frequencies, and radiation patterns. This paper is devoted to small, multimode flextensional transducers with active shells, which combine the advantages of small size and low-cost manufacturing with control of the shape of the acoustic radiation/receive pattern. The performance of the transducers is emphasized.     

Modal dynamics in multimode fibers

The dynamics of modes and their states of polarizations in multimode fibers as a function of time, space, and wavelength are experimentally and theoretically investigated. The results reveal that the states of polarizations are displaced in Poincaré sphere representation when varying the angular orientations of the polarization at the incident light. Such displacements, which complicate the interpretation of the results, are overcome by resorting to modified Poincaré sphere representation. With such modification it should be possible to predict the output modes and their state of polarization when the input mode and state of polarization are known.     

Two-dimensional model for three-dimensional index-guided multimode plasmonic waveguides and the design of ultrasmall multimode interference splitters

We demonstrate that a three-dimensional (3D) index-guided multimode plasmonic waveguide can be approximated to a two-dimensional (2D) lossy slab waveguide by using an effective-index method. It is found that this 2D approximation is more accurate when the width of the multimode waveguide increases. Such a 2D approximation can be used for a quicker and more efficient design of complicated multimode plasmonic devices. 1 x N ultrasmall multimode interference splitters based on multimode surface plasmon waveguides are designed by using this 2D model and the designs are validated with a 3D finite-difference time-domain method.     

A classification for multimode simultaneous buckling

The elastic post-buckling behaviour of a structure under the influence of a quasistatic load is considered. A criterion for the classification of simultaneous buckling in m modes is given. This is based on a study of the system under the influence of linear perturbations and makes use of a simplified approach using polar coordinates. A complete classification for threefold branching of generic cubic potentials is given and verified with a simple structural model.     

Neural network-based multimode fiber-optic information transmission

A new technique for transmitting information through multimode fiber-optic cables is presented. This technique sends parallel channels through the fiber-optic cable, thereby greatly improving the data transmission rate compared with that of the current technology, which uses serial data transmission through single-mode fiber. An artificial neural network is employed to decipher the transmitted information from the received speckle pattern. Several different preprocessing algorithms are developed, tested, and evaluated. These algorithms employ average region intensity, distributed individual pixel intensity, and maximum mean-square-difference optimal group selection methods. The effect of modal dispersion on the data rate is analyzed. An increased data transmission rate by a factor of 37 over that of single-mode fibers is realized. When implementing our technique, we can increase the channel capacity of a typical multimode fiber by a factor of 6.     

Design of a phase-locked multimode SAW oscillator

A 60-100 MHz multimode SAW (surface acoustic wave) oscillator with comb spacing Deltaf=10 MHz used a low-loss SPUDT (single-phase unidirectional transducer) comb filter in conjunction with two varactor-based control elements and two feedback loops, for mode selection and stability enhancement over long dwell times. The end aim is to reduce close-in phase noise over that of the unlocked oscillator, corresponding to improved intermediate-term time-domain stability. Frequency deviation was less than 20 Hz over two hours in each of the five comb modes.     

Experimental study of bent multimode optical waveguides

Bend losses of bent multimode waveguides have been experimentally studied. The results experimentally verify a simple analytical expression based on ray optics that can be used to determine bend losses in bent multimode waveguides. We have also shown that bend-induced losses in such multimode optical waveguides are wavelength independent.     

Modal decomposition technique for multimode fibers

We propose a new solution for modal decomposition in multimode fibers, based on a spectral and spatial imaging technique. The appearance of spurious modes in the spectral and spatial processing of the images at the output of the fiber under test when it has more than two modes is demonstrated theoretically. The new method, which allows us to identify spurious modes, is more accurate, simpler, and faster than previously reported methods. For demonstration, measurements in a standard step-index multimode fiber and a small-core microstructured fiber are carried out successfully.     

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.     

Shannon capacity calculation on multimode fibres

As the ultimate transmission performance of installed multimode fibres is uncertain, there is a need to understand the practical maximum capacity limit that a multimode fibre can support. The authors therefore present a new model to determine the worst-case Shannon capacity limit for multimode fibres. Detailed calculations are reported for fibre-distributed-data-interface (FDDI)-grade and OM1 fibres for operation using serial transmission with a single wavelength near 1310 nm. The method is also applicable to FDDI-grade, OM1, OM2 and OM3 fibres at all wavelengths of operation. The Shannon capacity limit of a multimode fibre is calculated for 220 m link lengths, assuming a link power budget consistent with the IEEE 10GBASE-LRM Gigabit Ethernet standard. It is shown that the Shannon capacity for non-optimised and optimised transmission spectra are at least 42 and 52 Gb/s, respectively.     

Studying semiconductor lasers with multimode rate equations

After the summation over terms that describe interactions between carriers and photons of various diode modes is worked out, implicit-form analytical solutions to the multimode rate equations of a semiconductor laser are obtained within the framework of the mean field approximation. With emphasis on the threshold region, several laser characteristics of importance, such as the carrier density, photon density, and output spectral width, have been investigated theoretically and experimentally.     

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.