Methods and apparatuses for photonic filtering using nonuniform lattice filters

An apparatus for photonic filtering, comprising:

• a plurality of directional coupler-differential delay devices connected in series, wherein each of the directional coupler-differential delay devices includes a directional coupler section and a differential delay section, wherein each directional coupler section has a corresponding coupling constant, and wherein a first of the plurality of directional coupler-differential delay devices is constructed to receive a pump and a signal;
• and
• an end-stage directional coupler connected in series to a last of the plurality of directional coupler-differential delay devices, wherein the end-stage directional coupler includes an input port, a through port, and a cross port, wherein the end-stage directional coupler is constructed to receive the pump and the signal at the input port,
• wherein the end-stage directional coupler has another coupling constant,
• wherein coupling constants respectively corresponding to the directional coupler sections and the other coupling constant corresponding to the end-stage directional coupler are based on:
• (i) a total number (n) of directional coupler sections in the plurality of directional coupler-differential delay devices,
• (ii) a uniform coupling constant for an n-stage uniform lattice filter, and
• (iii) a number (j) denoting an integer, where j is between 1 and n+1,
• wherein at least one of the coupling constants respectively corresponding to a plurality of directional coupler sections and the other coupling constant corresponding to the end-stage directional coupler are different, and
• wherein the signal is output on the through port of the end-stage directional coupler, and the pump is output on the cross port of the end-stage directional coupler.