By H. A. Buchdahl
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Extra info for An Introduction to Hamiltonian Optics
Microscopic formulation is in terms of total charge density ρ, [C/m3 ], including free and bound charges, and total current density vector J, [A/m2 ], which similarly includes free and bound currents, including the charges and currents at the atomic level. ∇ · E = ρ/ε0 , ∇×E=− ∂B , ∂t ∇ × B = µ0 ε0 ∇ · B = 0. e. bound charges and currents have been factored out. To do this, additional fields need to be defined: the displacement field vector D, [C/m2 ], ✐ ✐ ✐ ✐ ✐ ✐ “K16119” — 2014/11/12 — 9:30 — page 5 — #29 ✐ ✐ 5 Introduction and the magnetic field vector H.
This may be done under the assumption that the nonlinear terms are much smaller than the linear terms for any displacement. 1 The potential energy stored in a spring is calculated by finding the work necessary to stretch the spring a distance x from its equilibrium or un-stretched length. From Hooke’s Law, the spring force equals F = −ks x, where ks is the spring constant. Consequently, the work done (and therefore the stored potential energy) is Ue = − F dx = ks xdx = 1 ks x 2 . e. 82) and by replacing the driving field with λE(t).
Raman and his coworkers who demonstrated the effect, and after whom the effect is named the Raman effect. A. Franken and coworkers who were the first to report observation of optical second harmonic generation . However, it is without question that both results have contributed significantly, and it is very difficult, if possible at all, to define the most important result. In addition, there are many other results, not directly within nonlinear optics, that have made it possible to make significant advances within the field.