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Principles of Nonlinear Optics (Wiley Series in Pure and Applied Optics) (Hardcover)
by Y. R. Shen (Author) "Physics would be dull and life most unfulfilling if all physical phenomena around us were linear..." (more)
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Nonlinear Optics, Second Edition (Hardcover)
by Robert W. Boyd (Author) "Nonlinear optics is the study of phenomena that occur as a consequence of the modification of the optical properties of a material system by the..." (more)
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Fig. 1: Spatial walk-off: the intensity distribution of a beam in an anisotropic crystal propagates in a direction which is somewhat different from that of the wave vector.
Spatial walk-off
Definition: the phenomenon that the intensity distribution of a beam in an anisotropic crystal drifts away from the direction of the wave vector
For a laser beam propagating in an isotropic medium, the transverse intensity distribution propagates along the beam axis as defined by the medium k vector.
In anisotropic (and thus birefringent双折射晶体) crystals, this is not necessarily the case: it can occur that the intensity distribution drifts away from the direction defined by the k vector, as illustrated in Fig. 1, where the gray lines indicate wavefronts and the blue color the region with optical intensity. This phenomenon, called spatial walk-of, birefringent walk-off or Poynting vector walk-off , is associated with some finite angle ρ (called walk-off angle走离角) between the Poynting vector (能流传播方向)and the k vector(波前传播方向). The Poynting vector defines the direction of energy transport, while the k vector is normal to the wavefronts.
Spatial Walk-Off in Nonlinear Interactions
Spatial walk-off is encountered in nonlinear frequency conversion schemes based on critical phase matching in nonlinear crystals. Its consequence is that the waves interacting within a focused beam lose their spatial overlap during propagation, because those waves with extraordinary polarization experience the walk-off, while this is not the case for those with ordinary polarization. (Note that birefringent phase matching necessarily involves beams with both polarization states.)
In effect, the useful interaction length and thus the conversion efficiency can be limited, and the spatial profile of product beams may be broadened and the beam quality reduced(倍频光束质量下降).
Unfortunately, it is no solution simply to work with more strongly focused beams, requiring a shorter interaction length, because the spatial walk-off becomes more important for smaller beam radii.(进一步聚焦,可以缩短基波与非线性晶体作用长度,但是这对于补偿走离效应无济于事) The problem gets reduced, however, for high optical intensities, which allow for good conversion within a short length.
The phenomenon of spatial walk-off is directly related to that of a finite angular phase-matching bandwidth. The equation above shows that a large walk-off angle occurs in situations with a strong angular dependence of the extraordinary refractive index. In such cases, the phase-matching conditions also strongly depend on the propagation angle, and phase matching becomes incomplete when using tightly focused beams, having a large beam divergence.
It is possible to achieve a kind of walk-off compensation [1] by using two subsequent nonlinear crystals which are oriented so that the walk-off directions are opposite to each other. There is then still walk-off within these crystals, but its overall effect can be strongly reduced.
Spatial walk-off can be avoided altogether by using a noncritical phase matching scheme. This, however, generally requires operation of the crystal at a temperature which is not by coincidence close to room temperature.
[ 本帖最后由 t0y 于 2008-1-2 17:26 编辑 ] |
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