Guiding, bending and splitting of electromagnetic waves in photonic crystal waveguides

Burak Temelkuran

Department of Materials Science and Engineering & Research Laboratory of Electronics,
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 USA

Mehmet Bayindir and Ekmel Ozbay

Department of Physics, Bilkent University, Bilkent, 06533 Ankara, Turkey

We have investigated the guiding, bending and splitting of electromagnetic (EM) waves in three different types of waveguides built around layer-by-layer photonic crystal structures at microwave frequencies: planar waveguide, coupled cavity waveguide and highly confined hallow waveguide.

Introducing an air gap between two photonic crystal walls, we observed full transmission of the guided electromagnetic (EM) waves within the stop-band frequencies of the photonic crystal through this planar waveguide structure. We used two different methods to explain the guidance of the EM wave: The first approach was to use the phase difference, introduced by the guide, to calculate the dispersion relation. In the second method, calculating the effective width of the guide from the reflection-phase measurements of the photonic crystal walls, we used a planar waveguide theory to achieve the same dispersion relation. The results of both methods were in good agreement with each other, and were powerful in predicting the frequencies at which the guidance starts and ends. We then coupled the output of this planar waveguide into a second planar waveguide, which was perpendicular to the first. The EM wave, making a 90 degrees turn through the guides, resulted in an average transmission of 10 dB below the incident signal, within the stop-band frequencies of the photonic crystal.

The eigenmode splitting due to coupling between the evanescent defect modes was observed experimentally and well explained by the classical wave analog of the tight-binding (TB) method in the solid state physics. Forming the cavities by removing a single rod from each unit cell of a layer-by-layer dielectric photonic crystal, we were able to extract the TB parameters from the experimental results. We used these coupled cavities to demonstrate a new type of waveguiding mechanism in three-dimensional photonic crystals. In this waveguide, photons propagate through strongly localized high-Q cavities via hopping. High transmission of the electromagnetic waves, nearly 100%, is observed for various waveguide structures even if the cavities are placed along an arbitrarily shaped path. The dispersion relation of the waveguiding band is obtained from transmission-phase measurements, and this relation is well explained within the tight-binding photon picture.

We constructed another waveguide structure by removing rods, where in this case, the hallow region formed by the removed rod was used as the waveguide. Full transmission of the EM waves was observed for straight and bended waveguides. We also investigated the power splitter structures in which the input EM power could be efficiently divided into the output waveguide ports. The experimental results, dispersion relation and photon lifetime, were analyzed with a theory based on the tight-binding photon picture.

We proposed and demonstrated two other methods to split electromagnetic waves based on the waveguide structures described above. By measuring transmission spectra, it was shown that the guided mode in a coupled-cavity waveguide can be splitted into the coupled-cavity or planar waveguide channels without radiation losses. The flow of electromagnetic waves through output waveguide ports can also be controlled by introducing extra defects into the crystals.

Since the Maxwell's equations have no fundamental length scale, our microwave results can easily be extended to the visible spectrum, where these results may provide important tools for designing photonic crystal based optoelectronic components.