a method of delivering guided radiation arriving via a first transparent medium having a first refractive index into a second transparent medium having a second refractive index that is smaller than the first refractive index , comprising : providing a transparent radiation delivery waveguide capable of admitting concentrated radiation and having a longitudinal axis and a third refractive index substantially equal to or greater than the first refractive index and adapted to guide the radiation along the longitudinal axis . the waveguide having a tapered radiation delivery portion of non - circular cross - sectional shape . mounting the waveguide in optical contact with the first transparent medium so that the radiation delivery portion projects inside the second transparent medium .