The script produces the plot below which includes points representing the zone-folded lightline for the cladding material (n=1.45). With the default settings in the simulation file, the sweep named Bandstructure will calculate the bandstructure for kx = 0-0.5. Although this coupling mechanism is very weak, it will contribute to the loss over propagation distances of a large number of periods. In addition, there may be some weak coupling at a wavelength of 1550nm to the Si substrate with the SiO2 cladding n=1.45 only 1 micron thick. Thus PC waveguide modes near the large 'second order' band gap may have radiation components that contribute to loss. It should be noted, however, that the true period of the waveguide is 693 nm. However, when the wavevector is 2π/(period/2) = 2*2π/period, we expect to see a large bandgap. When the guide wavevector, k, equals 2π/period, there will be a barely observable bandgap.

We can expect to see results that are nearly equivalent to a waveguide that is periodically modulated at a pitch of period/2=346.5nm. Therefore the structure is 'nearly periodic' with a pitch of period/2. Apart from the lateral shift, there is no difference between the first row of holes and the second one. However, if we consider the microstructure along the direction of propagation of the waveguide, the 2D PC consists of alternating rows of holes, each row shifted laterally to the next. Since a = 400 nm, we have a period of approximately 693 nm. The waveguide is periodic in the direction of propagation, with period = a * sqrt(3), where a is the photonic crystal lattice constant. Analysisīefore calculating the bandstructure, we will consider the type of results we expect. This allows us to easily create a narrowband source when we want to selectively excite the fundamental mode only. The dipole cloud object that we use in this simualtion does not set the properties of the dipoles so that we are able to set them directly by modifying the global source properties.

We use a different dipole cloud than the one in the Object library. The 100 nm thick Si layer is on a 1 μm thick layer of SiO 2. The holes are filled with SiO 2 and the cladding above the waveguide core is also SiO 2.

The waveguide is composed of a rectangular a Si 3N 4 rectangular core (1μm width and 400nm thickness), shown in green, on a 100 nm thick layer of Si with a triangular PC lattice of lattice constant a = 400 nm and hole diameter 260 nm. The waveguide has been drawn up in the simulation file waveguide3D.fsp, and is shown in the figure above. In this example we calculate the bandstructure and mode loss of the waveguide structure described in K. When photonic crystals are used to make waveguides, the calculation of the photonic bandstructure becomes a 1 dimensional problem since the waveguide structure is only periodic in the direction of propagation.

Lumerical fdtd examples