Study on the Dispersion of the Light-Focusing Glass Fiber Lens (Selfoc Lens)

Abstract

Dispersion of Selfoc lens originates from the wavelength dependence of the refractive index on axis N₀ and a constant A, where refractive index distribution is expressed as N=N₀ (1-A/2r²).
So far N₀ and A can not have been measured separately. Here, we proposed a new method of measuring A and N₀ separately.
First, A can be determined by making the parallel incident beam focus on the output end surface of Selfoc lens whose length is set up to a quarter of its periodic length.
Namely the length of Selfoc lens (Z₀) is measured under this condition, and A can be derived from the relation A= (π/2Z₀) ².
Secondly, we measured a distance (S) between the spot and the output end surface of Selfoc lens whose length (Z) is set up to shorter than a quarter of the periodic length. We found, then N₀ from N₀=1/S√A tan √AZ.
We measured A and N₀ for various wavelengths, and derived dispersion of A and N₀ separately.
We found the relation between A and λ (wavelength) such as, A= (A₂+B₂/λ²) / (A₁+B₁/λ²) R², where R is the radius of the Selfoc lens.