Pseudoreversibility condition for minimizing radiation loss at discontinuities of coupled waveguides

A design condition is derived for lossless discontinuities of coupled waveguides by finding solutions, which satisfy time reversibility of guided modes. The derived condition is used as a bound for minimizing radiation loss. Even when there is strong coupling between guided modes, the radiation loss can be minimal. A comparison between different grating designs in a 2 * 2 backward coupler demonstrates that two coherently coupled gratings can significantly reduce radiation loss, as compared to a single grating.