Plana holographic multiplexer/demultiplexer utilizing photonic bandgap quasi-crystals with low intrinsic loss and flat top passband

A method for creating a planar waveguide for performing multiplexing and/or demultiplexing operations comprising the steps of:

• determining a two-dimensional profile of refraction index function A(x,y), wherein A(x,y) represents a linear superposition of modulation functions, each modulation function corresponding to a distinct subgrating;
• applying a binarization process to A(x,y) to generate a two-dimensional binary function B(x,y) representing a plurality of binary features;

A method for performing apodization of a binary function representing a plurality of binary features within a two-dimensional structure comprising the steps of:

• determining an apodization function g(r);
• and, adjusting the density of binary structures such that an average density of binary structures at a distance r is proportional to g(r).

A planar waveguide, wherein the planar waveguide may be utilized for multiplexing and/or demultiplexing operations comprising:

• a photonic bandgap quasi-crystal (“PBQC”), wherein the PBQC is synergetic and includes a plurality of binary features, wherein each binary feature generates constructive interference on average for a plurality of wavelengths

A method of demultiplexing comprising:

• receiving a composite signal comprising a superposition of optical signals;
• providing the composite signal to an optical planar waveguide, wherein the optical planar waveguide is comprised of a photonic bandgap quasi-crystal (“PBQC”), the PBQC being synergetic and including a plurality of features, wherein each feature generates constructive interference on average for a plurality of wavelengths and wherein the PBQC achieves a demultiplexing of the optical signals to generate a plurality of optical signals;
• receiving each of the plurality of optical signals at a respective output port..

A method of multiplexing comprising:

• receiving a plurality of optical signals;
• providing each of the plurality of optical signals a respective input port of an optical planar waveguide, wherein the optical planar waveguide is comprised of a photonic bandgap quasi-crystal (“PBQC”), the PBQC being synergetic and including a plurality of features, wherein each feature generates constructive interference on average for a plurality of wavelengths and wherein the PBQC achieves a multiplexing of the optical signals to generate a composite signal comprising a superposition of the optical signals;
• receiving the composite signal at an output port.