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# Lesson 12 – Analyzing 2D Photonic Crystals

## Analyzing 2D Photonic Crystals Introduction

The tutorial demonstrates analysis of 2D photonic crystal using PWE Band solver. First we create a lattice model of dielectric cylinders (permittivity=8.9) suspended in air. We then proceed with a simple simulation on a predefined k-vector path and result analysis. Finally we discuss the meaning of the Domain Origin in the PWE dialog box. Step   …

## 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…

## PWE Band Solver Parameters

Open PWE Parameters dialog box (Simulation->PWE Band Solver Parameters…). By default the PWE solver should be set to 2D Solver, TE polarization, no inversion symmetry. The Lattice vectors should use defaults, i.e. the mesh (#Steps a, #Steps c) should be set to 16×16. Also make sure the Domain origin is set to (0,0,0). Set number…

## Simulation Results

When finished with editing band solver parameters click Run… to start the simulations. A simulation windows will be launched and simulation starts. You will be notified in the Notification tab window at the bottom about progress of the simulations. The engine first reports on the permittivity averaging process, then on the progress of calculations for individual…

## Inversion Symmetry and Domain Origin

In case the simulated unit cell or supercell structure has inversion symmetry the operator matrix in the eigenvalue problem becomes a real symmetric matrix. This can be used to achieve significant savings in storage and as well as speed improvement. The inversion symmetry in the design is not detected automatically but user can notify the…

## 2D Hexagonal Lattice

We are now going to verify band structure of 2D hexagonal lattice as reported in reference [1]. At this point you might want to save the current file under different name. The photonic structure we want to analyze consists of a hexagonal pattern of air holes in dielectric with permittivity 13. We have defined all…

## Rotated 2D Lattice

Occasionally you might use a lattice to build a more complicated 2D layout design. In such design the lattice might also be rotated. You do not have to create a new layout to analyze the lattice. Use the Default Lattice Vectors and Domain Origin to set the computational domain and to capture the correct periodicity.…

## References

[1]   Joannopoulos, J.D., Meade, R.D., Winn, J.N., “Photonic Crystals, Molding the flow of light”, Princeton University Press 1995