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- ItemUltrashort optical pulse propagation in terms of analytic signal(New York, NY : Hindawi, 2011) Amiranashvili, Sh.; Demircan, A.We demonstrate that ultrashort optical pulses propagating in a nonlinear dispersive medium are naturally described through incorporation of analytic signal for the electric field. To this end a second-order nonlinear wave equation is first simplified using a unidirectional approximation. Then the analytic signal is introduced, and all nonresonant nonlinear terms are eliminated. The derived propagation equation accounts for arbitrary dispersion, resonant four-wave mixing processes, weak absorption, and arbitrary pulse duration. The model applies to the complex electric field and is independent of the slowly varying envelope approximation. Still the derived propagation equation posses universal structure of the generalized nonlinear Schrdinger equation (NSE). In particular, it can be solved numerically with only small changes of the standard split-step solver or more complicated spectral algorithms for NSE. We present exemplary numerical solutions describing supercontinuum generation with an ultrashort optical pulse.
- ItemMathematical fundamentals of modern linear optics(New York, NY : Hindawi, 2012) Gitin, A.V.All known quantum-mechanical approaches to wave and statistical optics are united into a single theory, using Feynman's path integral as a fundamental principle. In short-wave approximations, this principle, the Fourier transformations, and concepts of the theory reproduce Fermat's principle, the Legendre transformations, and concepts of Hamilton's optics and radiometry in a one-to-one fashion.