How thin can a microfiber be and still guide light?

For the adiabatically deformed optical fiber the intermode transmission amplitudes and loss vanish exponentially with the characteristic length of the fiber's nonuniformity. For this reason smoothly deformed optical fiber tapers can have very small losses. However, losses dramatically increase with a thinning of the microfiber down to a diameter much smaller than the radiation wavelength. The theory of nonadiabatic intermode transitions is briefly discussed and, by using this theory, the problem of the smallest diameter of a microfiber that can transmit evanescent radiation is studied. It is shown that even for an extremely high uniformity of microfiber the ability of light transmission does not leave much space for microfiber thinning: the propagating mode vanishes at a threshold value of the microfiber's diameter, that is smaller than the radiation wavelength by only an order of magnitude.