A general formula giving cutoff frequencies of modes in an optical fiber having an arbitrary refractive-index profile is derived from the stationary expression of the propagation constant. It is found that the cutoff frequency is inversely proportional to the square root of the overlap integral of the refactive-index and mode-power profiles. From this general formula, an approximate formula for actual calculation is derived, which is relatively accurate when applied to lower order modes. The single-mode condition (cutoff frequency of LP₁₁ mode) can be calculated with a good accuracy using this approximate formula. The single-mode limits computed for some practical nonuniform-core profiles show good agreement with rigorous values.

A new acousto-optic tunable filter utilizing collinear acousto-optic interaction along the direction near to the optic axis is proposed and demonstrated by using LiNbO₃ crystal. This near axis interaction lowers the driving frequency and also expands the angular aperture in the ordinary plane. The acousto-optic figure of merit M₂ (p²/ρv³) of this filter is 7.510^-18 sec³/g and tuning from 700 nm to 420 nm can be obtained by changing the acoustic frequency from 56 MHz to 119 MHz. At 514.5 nm the filter bandwidth of 1.1 nm and the angular aperture of about 6 in the ordinary plane have been obtained.

The performance of the tapered velocity coupler for single mode fibers is investigated theoretically and experimentally. An improved analytical solution convenient for analyzing and designing the tapered velocity couplers is derived. The mode cross-talk in the tapered region and the mode conversion loss due to the discontinuity at the ends of the fibers are measured and are compared with the theoretical results. Simultaneous shaping of the multiple single mode fibers into tapered structure is successfully realized and a low loss splicing (less than 0.2 dB) is achieved either by using adhesives or by the thermal fusion technique.