Beam-bending in spatially variant photonic crystals at telecommunications wavelengths

Formulation of Iterative Finite-Difference Method for Generating Large Spatially Variant Lattices

“…For brevity, the following formulation focuses on eqn (6) as the basic building block for the update equation and then applied by inspection to the other equations. Eqn ( 6) can be approximated by a central finitedifference to the i − 1 side or a central finite-difference to the i + 1 side…”

“…The algorithm for spatial variance introduces geometrical changes to the PhC in a way that makes the PhC smooth, continuous, and free of unintentional defects [4] while retaining the geom-etry of the unit cells so that electromagnetic response is maintained. Most approaches to incorporate spatial variance in SCPCs [5][6][7] do so in either planar SCPCs or with devices in which the third dimension is not spatially varied. The method described in [3] suffers from the major drawback of being memory inefficient due to its reliance on large full storage matrices and computationally expensive lower-upper (LU) decomposition operations, thus limiting the size of spatially variant lattices (SVLs) that can be generated.…”

Multiscale multiphase 3D printing of photonic devices and sensors for system health monitoring

“…DLW uses polymers to build photonic platforms with 3D geometries and thus offers better options as mode converters for broadband in-plane coupling 2 . Devices fabricated using IP Dip, a photoresist commonly used in DLW report low coupling losses owing to the 3D geometries as well as the intrinsic properties of the polymer-IP-Dip, has a propagation loss of 0.78 dB/mm at 1550 nm and essentially zero absorption coefficient at visible and near infrared wavelengths 3,4 . 3D printed polymer couplers include tapered waveguides that offer in-plane coupling 5 and geometries that exploit out-of-plane total internal reflection to offer additional tolerance in mechanical alignment 2 .…”