|
Dielectric, ohmic-loss-free, finite photonic crystals (PCs) may sustain the propagation of highly confined surface waves that propagate bound to the interface of the bulk structure and the free space. For many years the dielectric photonic crystals surface states have been treated as a subsidiary effect related to the inevitable finite size of the PCs in realistic implementations. However, in the recent years it has been realized that the features of the dielectric surface states and their impact to the wave exit from the photonic crystal structure render the relevant structures suitable components for a variety of applications, including optical spectroscopy, sensing, intercomponent coupling, etc. In this work we present the design of a silicon-based PC component that couples the modes that propagate through the bulk structure into outgoing, free space propagating beams with high directionality. In addition to previous works involving silicon-based PCs for beam collimation in the near infrared and optical regime, we demonstrate here, that the (frequency depended) emission angle of the generated beams can be controlled by properly engineering the PC termination. Thus the component may serve as a beam steering structure or a de-multiplexer in the optical telecommunications wavelength band (~1.5 μm).
Our design takes into account the state-of-the-art nano-fabrication technology and all the constraints arising from the treatment of silicon-based periodic media in this frequency regime. It consists of air holes drilled through an infinite silicon slab, arranged in a standard hexagonal lattice with periodicity α = 320 nm. Within the bulk photonic crystal we assume a line-defect waveguide that leads to the PC-air interface, where a properly designed termination layer of air holes is imprinted. The termination is designed to induce surface states at the PC-air interface with desirable dispersion and spatial characteristics. The line-defect waveguide is an area of unperforated silicon slab and it is chosen since it is a widely used scheme for guiding energy through the reflective photonic crystals; therefore, our design is compatible with the majority of the silicon-based PCs circuit components. By properly designing the interfacial termination layer we can tailor the properties of the non-radiating, dark, surface states in order to adapt and match the waveguide propagating modes and the free-space modes. As a result, we demonstrate a silicon-based photonic crystal structure that provides (a) the generation of well-defined and highly directional beams at the exit of the photonic crystal structure; (b) efficient beam multiplexing, i.e., the formation of two well defined beams that exhibit sufficiently high spectral isolation, as well as sufficiently high spatial separation. In particular we present two design approaches; the first is able to generate two beams at the operation wavelengths λ1 = 1.37 μm and λ2 = 1.5 μm, with high spatial separation defined by the emission angles φ1 = +20 deg and φ2 = -23 deg and the second generates two beams at λa = 1.42 μm and λb = 1.52 μm with emission angle φa = +1 deg and φb = 23 deg. The wavelengths of operation, as well as the emission angle, can be engineered at will.
|
