2D Rectangular Lattice of Dielectric Cylinders

Note:

• For the details on how a lattice can be created, please refer to Lesson 3— Photonic crystal and photonic band gap simulation and Lesson 9—FDTD Band Solver.
• For the details on how material and waveguide profile can be created, please refer to lesson 1 to lesson 9
• To define the variable, please input the variable name in the Initial Properties dialog box. Click “OK” to access the Variables and Function dialog box to define the values.

We are going analyze 2D photonic crystals with rectangular and hexagonal lattices as reported in reference [1]. Start defining necessary materials and channel profiles in the Profile Designer. Two tables below show the materials and channels needed for the project, next to proposed names and lattice, in which they are used. For the following exercise we will employ only 2D materials and channels.

Table 1

Table 2

After creating the materials and channels specify the dimensions of the wafer as 10×10 microns and wafer material as eps1_0 (air). Create a 2D rectangular lattice of dielectric cylinders with permittivity 8.9 suspended in air, with radius of 0.2a where a is the lattice constant of the square lattice.

On the waveguide toolbar select the PBG Crystal Structure and click on the layout. Open the lattice properties by double clicking on the empty lattice structure. In the Crystal Lattice Properties dialog box set the Origin as (1,-4), in Lattice Properties select Type as 2D Rectangular and set both #A and #C to 8. We will build the lattice parameterized so that it is easy to change physical dimensions later on. Define a variable called ‘a’ and set it to 1. It will be our lattice constant. You can do so either from the Crystal Lattice Properties box by clicking any field which contains fx symbol or from the designer (Simulation >> Edit Parameters). As the basis vectors are in unit length by default, by setting Scale in Lattice Dimensions group to ‘a’ the lattice constant of the lattice is expressed by scale in microns.

In ‘Atom Waveguides in Unit Cells’ group add new elliptical waveguide with major and minor radius set to 0.2a and profile ‘Chan8_9’. Now the lattice is defined.

To test the parameterized lattice go to ‘Simulation->Edit Parameters…’ and change ‘a’ variable value to e.g. 1.5, click ok and you will see that the whole lattice has the lattice constant of 1.5, and cylinders have radius of 0.2a. Set scale to its original value 1.0.