Adiabatic invariance in GRIN channel waveguides and its use in 3-dB cross couplers

We have extended the local normal mode approach of Burns and Milton to derive the condition for adiabatic invariance in graded-index channel waveguides. The results show that in spite of the index-grading and 2-D confinement, the inequality describing the adiabatic condition is basically the same as that for step-index slab waveguides. To verify the predictions of the theory, we have fabricated, using ion exchange in glass, a cross coupler with two asymmetric input channel waveguides and two symmetric output guides. The experimental results show equal output power (3.0 +/- 0.1 dB) from the two symmetric guides when either of the two unequal guides is excited, demonstrating excellent agreement with the theory.