In this approach, the two necessary sub-crystals are a TM sub-crystal having a large TM PBG and a TE sub-crystal having a large TE PBG. The sub-crystals can be periodic or aperiodic. Since the dominant TM and TE PBGs of assembled crystals mainly arise from the different sub-crystals, they should be essentially independent of each other. Importantly, this offers the possibility to separately tune the TM and TE PBGs by altering the respective sub-crystals and make them overlap to generate a composite structure with a larger, complete PBG than previously known structures. These assembled crystals can be fabricated using a number of techniques including photolithography, nanoimprint lithography, electron beam lithography (EBL), and multiple exposure interference lithography (MEIL). Furthermore, it is straightforward to introduce purposeful defects in these crystals to generate optical devices. For example, two-photon direct laser writing can be used to introduce regions that can act as wave guides, filters, etc.