In this example, we use the 2.5D FDTD propagation method ('varFDTD' solver) in MODE to study the PC waveguide described in O.V.(Alyona) Ivanova et al.
To accurately model this device, the complex scattering and interference effects from the high index contrast photonic crystal must be precisely modeled. This typically requires a rigorous (but relatively slow) technique like 3D FDTD. In this example, we show that it is also possible to obtain accurate results using the MODE' 2.5D varFDTD propagation method, which is much more efficient and only requires the simulation time and memory of 2D FDTD.
The following instructions briefly describe how to setup this simulation. Initially, you may want to skip this section and proceed to "Results and Discussions" using the completed simulation file PhC_waveguide_L1.lms.
The waveguide described in O.V.(Alyona) Ivanova et al. is deposited on a glass substrate with refractive index 1.445. The core has refractive index sqrt(12.1) ~ 3.5 with a thickness of 220nm. The hole radius is 135nm, and the modified hole radius is 170nm. The period 'a' is 440nm. The input/output waveguide width is sqrt(3)*a. The upper cladding is air. This is a typical one-line defect (L1) PhC waveguide.
To set up the simulation in MODE, start by creating a new blank simulation. Next, open the "Material database"
, click the Add button and select "Dielectric", set the index parameter to 1.445, and then click the Color column to choose the color you like. Finally, name the newly created material "Substrate".
Click the Structure button
and choose Rectangle
, set the name to "SiO2", x and y span = 20um, z max 0 and z min=-9um, and set the material property to "Substrate". Then add a central core layer "Core" thickness 220nm, length 18*440nm, width 20um. The width of the input and output waveguides should be sqrt(3)*440nm. Next, add a circle and array it as required to create the PC array (see Arrays of objects for more detail on how to use the "array" function). Set the material property to 'etch'. To form the PhC waveguide, delete unused holes and the central row of the holes, and modify the holes above and below the central row. You can group the array of holes into a structure group.
Add a varFDTD simulation region and set the span to 15 by 12 by 6 um (x,y, z), set the polarization to "E mode (TE)", set x0 and y0 in the core region (this point will be used to calculate the vertical slab mode, so you should not specify a location on top of the etched holes). The location of the 4 test points will not effect the simulation. Set the simulation time to 20000fs, as this device has strong resonances and the fields will require longer to decay. Un-select the 'Clamp values to physical material properties" option, set the Bandwidth setting to Broadband.
Add a mode source and set the wavelength range from 1.3 to 2.0 um. The fundamental TE mode that will be injected by this source is mostly Ey polarized. Due to the symmetry of the mode and structure, set the Y-min boundary condition to anti-symmetry. This will make the simulation run 2x faster. All other boundaries should be set to PML. Add an Effective Index monitor, a transmission monitor "T" and reflection monitor "R", as well as a profile monitor "Profile" with only 3 monitoring frequency points.
Results and discussions
First, we can look at the effective index monitor data.
These effective index values are generated by collapsing the vertical dimension based on the methods described in 2.5D FDTD propagation method. One can see that the core index has an effective index of around 2.8. Next, we can plot the transmission and reflection spectra:
One can see that there is a stop-band from approximately 1.52um to 1.65um, which are comparable to the published results.
O. V. (Alyona) Ivanova, Remco Stoffer, Lasse Kauppinen, and Manfred Hammer, "Variational Effective IndexMethod for 3D Vectorial Scattering Problems in Photonics: TE Polarization"