Spherical harmonics large radii

Here the unit vector n and radius vector R have opposite directions. The volume V is surrounded by the surface S as well as a spherical surface with infinitely large radius. In deriving this equation we assume that the potential U p) is a harmonic function, and the Green s function is chosen in such a way that allows us to neglect the second integral over the surface when its radius tends to an infinity. The integrand in Equation (1.117) contains both the potential and its derivative on the spherical surface S. In order to carry out our task we have to find a Green s function in the volume V that is equal to zero at each point of the boundary surface ... 

Output resonance is reached (for a droplet with a fixed radius) when specific wavelengths within the inelastic emission profile correspond to MDR s with different n,t values. For those wavelengths, the droplet can be envisioned as an optical cavity with a large Fresnel number and Q-factors which are dependent on the specific n and I values. The portion of the inelastic radiation detected is that allowed to "leak" out of the droplet cavity. However, it is the internal field distributions of the electromagnetic waves at X, and X, which are best described by spherical harmonic functions and not by plane waves as in the case of an extended medium, that affect the nonlinear optical interactions. Such interactions in droplets can be illustrated by several well known examples in nonlinear spectroscopy of liquids in an optical cell. 

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