I read in a paper that when one etches a fiber to a very sharp tip (say 100nm), as light propagates down the fiber, it will begin to leak out of the fiber at a certain critical diameter. In other words, the tapered tip gets to a tube width through which the final mode of the fiber can no longer enter. Maybe I don't understand this process very well, but I'm really interested in understanding how to compute the cutoff diameter of the fiber.
For example, if I have a fiber of known cladding/core materials, can I determine the cutoff diameter?
By adiabatically etching a fiber you actually get a tapered tip fiber which is used to insert (or collect) light from smaller waveguides e.g. chip facets. Since you re downsizing the cladding as well the core-cladding system now must include air so you have air-cladding-core. Due to the high index contrast (and always assuming adiabatic transitions) you can get light to squeeze to the tip's dimensions, effectively minimizing the spot size. At some point onwards however the size of the tip becomes comparable to the wavelength. In that case the spot size actually increases with most light now travelling in the surrounding air.
You can either simulate this using software or try to calculate the normalised cut-off frequency of the fieber system you want
http://www.winnerscience.com/fibre-optics/v-number-or-cut-off-frequency-or-normalized-frequency-in-optical-fibers/
May be in a fiber there's a balance of light transmitted and light reflected. In view of maximum transferring is important there is a "continuity" in glass material, independent from the respective diameters. ...... You can obtain this using fused splicing. I have made this, with fiber of different diameter.....
I think, this kind of taper is different from the fusing tapered fiber, for the fusing tapering fabricated fiber tips, the core and cladding will squeeze simultaneously, and for the fusing tapering fabricated taper tip, its light mode field will squeeze or enlarge depends on the taper ratio, you can read some published papers or book "Optical Fiber Splicing (Springer) to find the exact explain. As the optical fiber taper is some kind of complicated, its optical character depends on many parameters, for the cut off diameter, I rarely saw people said so, from most of the paper i have read, they just using the software directly calculate and simulate it.
Thanks for the replies guys. I should clarify that my tips are very small, and the cladding is effectively gone from the area that I'm referring to. There is some leakage due to the loss of cladding, but the majority of the loss occurs almost at the tips, at where I believe this cutoff diameter is. I will dig further.
As Alexandros Kapsalis says, as the diameter is reduced, the energy remains guided by the cladding, the spot size increases to infinity as the the cladding diameter tends to zero. Interestingly before Charles Kao and George Hockham proposed single-mode optical fibre for communications using a core and cladding, they explored single-material ultra thin dielectric guides as a way of overcoming the high losses of current glasses (most of the the energy propagated in the surrounding air). The cylindrical glass fibres were so thin they floated away and could not be handled physically or supported without attenuation, but thin film planar guides looked slightly more promising as they could be supported at the edges, and made to guide in two dimensions by applying a helical twist. Here's a photo (~1964) of bend loss measurements being made on a thin film planar guide: http://www.goforich.co.uk/lr/earlydays/content/_1180_2_large.html
Thankfully, the losses of glass and silica were reduced enabling the clad fibres we use today.
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