Many academic subjects that were taught previously in the framework of theoretical physics moved to engineering. These include courses in electromagnetics, statics and dynamics, heat and mass transfer, mechanics of solids, nuclear power, and courses that branch from these, like fiber optic communications thermodynamics. However, the mathematical foundation in engineering education has remained substantially unchanged during this transition period, typically peaking at the level of linear algebra, vector calculus and integral transforms. As a result many undergraduate engineering courses are built in such a way as to avoid tensor analysis and tensor calculus, as if such mathematical constructs are beyond the capacity of the undergraduate student to understand. We show that this not the case.
A four-channel soliton system design is described that represents an improvement on a previous study (Opt. Express, 2007). In that study, a bit-rate-length (BL) product in excess of 2.0×1015 baud/km from a dense-dispersion-managed (DDM) dual-soliton system was achieved through numerical experimentation. Similar to the dual-soliton design, a combination of polarization multiplexing and wavelength-division multiplexing is employed. Numerical experiments with four soliton channels, each carrying 80 Gb/s, are carried out over 10,000 km. As system parameters are optimized, the Q=6 threshold distance attained is 9150 km, yielding a BL product of 2.9×1015 baud/km.
As electromagnetics, photonics, and materials science evolve, it is increasingly important for students and practitioners in the physical sciences and engineering to understand vector calculus and tensor analysis. This book provides a review of vector calculus. This review includes necessary excursions into tensor analysis intended as the reader's first exposure to tensors, making aspects of tensors understandable to advanced undergraduate students. This book will also prepare the reader for more advanced studies in vector calculus and tensor analysis.
A transmission-line model of a two-stage all-fiber soliton-effect femtosecond-pulse compressor is designed using comprehensive simulation tools. The compressor is predicted to have compression factors as high as 24, with low peak power (<0.5 nJ pulse energy at a 180-fs pulse width) and high repetition rate (~40 GHz) without many of the disadvantages of heretofore-designed compressors. Prior optical pulse compressors are primarily based on solid state lasers or fiber Bragg gratings. Solid state lasers are relatively large, have high pulse energies (~10 nJ), and lack the precision needed for many applications, such as in medical diagnosis and treatment. Fiber Bragg grating compressors are limited in attainable compression factors and intensity levels and have restricted use with other fiber Bragg gratings. Other fiber compressors face third-order dispersion (TOD), self-steepening (SS), intrapulse stimulated Raman scattering (ISRS), and higher order dispersion (HOD), which limits their use. The suggested design addresses a requirement for the modeling of an all-fiber optical pulse compressor that answers the preceding objections. The designed compressor, has no third-order or higher order dispersion, and is not affected by ISRS and SS effects, which can otherwise reduce the quality of the compressed pulses.
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