Divergence angle of light exiting a nano-etched single mode fiber

[melnop]

I am working with a single mode fiber at 830 nm with a NA of 0.12 (http://www.thorlabs.com/thorcat/19600/P3-830A-FC-2-AutoCADPDF.pdf). One end has a fiber tip coated in silver with a small hole of 200 nm diameter to essentially create a point source. My advisor told me that the fiber has a few modes when the light traveling through is shorter than 830 nm. I know that the acceptance angle may be calculated easily for a normal fiber, but I'm not sure how the small hole will affect things.

How could I calculate the cone of light that is coming out of the silvered end?

(I have included a diagram for clarity)

 

[rigetFrog]

http://en.wikipedia.org/wiki/Diffraction#Single-slit_diffraction

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