Numerical Aperture Limits on Efficient Ball Lens Coupling of Laser Diodes to Single-Mode Fibers With Defocus To Balance Spherical Aberration

The potential capabilities and limitations of single ball lenses for coupling laser diode radiation to single-mode optical bers have been analyzed; parameters important to optical ber communications were specically considered. These parameters included coupling eciency, eective numerical apertures , lens radius, lens refractive index, wavelength, magnication in imaging the laser diode on the ber, and defocus to counterbalance spherical aberration of the lens. Limiting numerical apertures in object and image space were determined under the constraint that the lens perform to the Rayleigh criterion of 0.25-wavelength units (Strehl ratio = 0.80) with de-focus compensation to balance spherical aberration of the lens. The spherical aberration-defocus balance to provide an optical path dierence of 0.25 wavelength units was shown to dene a constant coupling eciency (i.e., 0.56). The relative numerical aperture capabilities of the ball lens were determined for a set of wavelengths and associated ber-core diameters of particular interest for single-mode optical ber communication. The results support continuing efforts in the optical ber communications industry to improve coupling links within such systems with emphasis on manufacturing simplicity, system packaging exibility, relaxation of assembly alignment tolerances , cost reduction of optoelectronic components, and long term reliability and stability.