A new treatment of the well-known Sommerfeld solution of the problem of plane-wave diffraction from a perfectly conducting half-plane is reported. We show, in both theory and experiment, that the diffraction field (E-polarization) can be represented as a superposition of real physically existing waves, in contrast to geometrical and boundary waves postulated in Sommerfeld's representation. Our representation includes two pairs of wave components: one pair propagates along the direction of the incident wave, and the other in a mirror-reflected direction. Each wave pair consists of a plane-wave component with an amplitude half that of the incident wave and a nearly plane-wave component with an infinitely extended edge dislocation. On the basis of the proposed interpretation, all features of the half-plane diffraction are explained.
Due to recent demonstrations of cooling by anti-Stokes fluorescence the optical geometries under which the cooling efficiency can be optimized are investigated. Since the cooling efficiency is proportional to the absorbed power of radiation, and in previously reported cooling experiments a single pass configuration was mostly used, two schemes for enhancing the absorbed power are compared: placing the cooling medium within the laser resonator and multipassing through an externally located medium. The point of departure in this comparative study is the intracavity circulating intensity, described in terms of the laser gain coefficient and the sum total of losses due to reflections, scatter, and absorption due to the presence of a cooling medium. Substituting measured values of the gain and loss factors for a practical cw pumped dye laser system, a comparison in cooling efficiencies between the two schemes is made for a range of optical densities of the cooling medium. The gain and loss coefficients of a dye laser are measured by introducing a varying loss mechanism by means of an acousto-optic modulator inside the cavity. For high optical densities (>0.1) it was found that when extrapolating the pump power to the dye laser up to 10 W the same cooling power can be achieved with an extra-cavity configuration using relatively few passes as with the intracavity configuration. For low optical densities (<0.01) the number of passes required for equivalent cooling power exceeds 10 and the intracavity configuration becomes a more efficient means for laser cooling.
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