Multi-distance surface-emitting beam profile calculation method based on the FDTD method and the diffraction theory

A hybrid method to calculate a multi-distance beam profile emitted perpendicular from a surface of a photonic crystal (PhC) is proposed here based on the finite-domain time-difference (FDTD) method and the diffraction theory. Although the FDTD method is available to calculate a near-field emitted from the PhC, it needs too many voxels to calculate mid- and far-fields. Thus, the diffraction theory is additionally applied to obtain the mid- and far-fields using the near-field calculated by the FDTD method. A surface-emitting quantum cascade laser (QCL) that consists of a PhC and an edge-emitting laser source is fabricated to demonstrate the validity of the hybrid method. A measured beam profile of the QCL agrees with that calculated using the hybrid method, which validates applicability of the method to a surface-emitting device.