Hybrid Longitudinal-Transverse Propagating Electric Fields in Photonic Crystal Waveguides
In a uniform, source-free, and unbounded medium, Maxwell's equations require electromagnetic waves to be purely transverse. However, when a beam of light is tightly focused or strongly confined, a longitudinal field component can emerge. Strong longitudinal fields enable many novel phenomena and applications, including single molecule detection, near-field imaging, and high-resolution photolithography. Although the behavior of the longitudinal electric (LE) field component of the electromagnetic field in ordinary waveguides is well established, judicious nanostructuring offers unprecedented control over its strength as well as spatial and spectral distribution. Here, we demonstrate a full-vectorial theory and experimental results showing that for specially designed waveguides, such as one-dimensional antislot photonic crystal (PhC) waveguides, the LE field can hybridize with the transverse electric (TE) field in the waveguide and can be subsequently decomposed into independent polarizations through far field imaging. When the in-plane mirror symmetry of a PhC unit cell is broken, coupling between LE and TE modes produces two hybrid LE-TE modes and opens a new photonic bandgap. The LE-TE composition of the hybrid modes and the width of the resulting bandgap can be tuned by changing the rotation angle of the antislot within the unit cell. We show that a 45-degree antislot orientation with respect to the propagation direction yields hybrid modes with the largest LE field contribution and the widest geometry-induced bandgap. Such engineered PhC waveguides enable new on-chip photonic functionalities, including in-plane angle-invariant dipole coupling in quantum systems, higher-order polarization-division multiplexing, and enhanced control of light flow.