By Pauling L.
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Additional info for A New Crystal for Wave-Length Measurements of Soft X-Rays
14) ω The nonlinear term χe describes an interaction potential which couples the particles together. This interaction potential is attractive when χe is positive, as it is in most Kerr media, and the value of the potential is V (xv − xv ) = −¯ hχe δ(x − x ) . 15) There is a subtlety here, which is that this type of frame transformation (commonly used in nonlinear optics) is not a relativistic one, even though v can be relativistic. In fact, it is simply a useful mathematical transformation - there is no observer travelling at v, and all results must therefore be transformed back to the laboratory frame before they can be interpreted literally.
The much more complex case of nonlinear interactions in atom optics will be treated in the last section. 1 Fiber optics Hamiltonian The optical fiber treated will be a single-transverse mode fiber with dispersion and nonlinearity. Since boundary effects are usually negligible in experiments, it is useful to first take the infinite volume limit, which effectively replaces a summation over wave-vectors with the corresponding integral. The effect of a transverse mode structure will also be included, to show how the simplified theory is applicable in real three-dimensional fibers.
We use coordinates, as is common in nonlinear optics, where the time-origin changes with position1 , so that: τ = (t−x/v)/t0 , ζ = x/x0 . This generates a so-called propagative form of the equations, and typically requires a slowly-varying envelope approximation, where vt0 /x0 1. For example, typical parameters might be: t0 ∼ 1ps, x0 ∼ 100m, vt0 /x0 ∼ 10−4 . If dispersion is large, then the full space-time equations must be utilized. The ‘semi-classical’ technique is derived from the Wigner representation, and gives symmetrically ordered operator correlations.
A New Crystal for Wave-Length Measurements of Soft X-Rays by Pauling L.