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By Jean-Claude Diels
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Although very particular details is gifted, the authors give you the details in an easily-read and concise structure, with transparent verbal descriptions, figures, and bibliographic references on the finish of every bankruptcy. this article is written on the point of senior undergraduate scholars in physics, chemistry or engineering, yet offers abundant descriptions for these much less mathematically prone. it's definitely a welcome boost to ones reference library. Raymond F. Lanzsafame, Photomedicine and Laser surgical procedure
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Extra info for Ultrashort Laser Pulse Phenomena. Fundamentals, Techniques, and Applications on a Femtosecond Time Scale
Sample text
26 Fundamentals If the propagation of short pulses is computed over long distances, the cumulative error introduced by neglecting the right-hand side of Eq. 88) may be significant. In those cases, a direct numerical treatment of the second-order wave equation is required. Further simpUfications are possible for a broad class of problems of practical interest, where the dielectric constant changes slowly over frequencies within the pulse spectrum. In those cases, terms with n > 3 can be omitted too {V = 0), leading to a greatly simplified reduced wave equation: S(rj^^)--k';-^£iri,^) = 0.
It is sometimes expressed in fs^ |im~^ A positive GVD corresponds to d^k dQ^ 0. 4. Gaussian Pulse Propagation For a more quantitative picture of the influence that GVD has on the pulse propagation we consider the Hnearly chirped Gaussian pulse of Eq. 33) entering the sample. To find the pulse at an arbitrary position z, we multiply the field spectrum, Eq. 35), with the propagator exp (-i^k^^Q^zj as done in Eq. 121) AQ is a complex amplitude factor which we will not consider in what follows and TGO describes the pulse duration at the sample input.
The dependence of a dispersive parameter can be given as a function of either the frequency Q or the vacuum wavelength X. 2 ~ (2;rc)2 y dX^ -^1^) d^ dO? {ITTCY d}? ) or the wavelength dependence n(X) of the index of refraction. The derivatives of the propagation constant used most often in pulse propagation problems, expressed in terms of the index n, are: The second equation, Eq. 116), defining the GVD is the frequency derivative of \lvg. Multiplied by the propagation length L, it describes the frequency dependence of the group delay.