Phase-Sensitive Multimode Parametric Amplification in a Parabolic-Index Waveguide

We show that multiple spatial modes or images can be amplified by an optical parametric amplifier based on a graded-index waveguide, and that the modal gains can be equalized by using a superposition of several pump modes. We present a coupled-mode model of such an amplifier and develop gain equalization techniques for both 1- and 2-D cases. In the former case, we find that ~ 20 modes can be amplified with a relatively low gain ripple by a superposition of four pump modes. In the latter case, over 250 modes can be similarly amplified by a superposition of 4×4 = 16 pump modes.