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Lesson 11 – Analyzing 1D Photonic Crystals (Bragg Gratings)

Analyzing 1D Photonic Crystals (Bragg Gratings) Introduction

The simplest photonic crystal consists of alternating layers of material with different dielectric constants. Such multilayer structures have been widely studied and are frequently referred to as Bragg gratings. In this tutorial we design simple Bragg Grating that consists of alternating layers with permittivity contrast 1/13 as discussed and analyzed in [1]. We will show…

Define the Lattice Structure

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 Lessons 1 through to Lesson 9. We start investigating system of equally…

PWE Band Solver Parameters

Open PWE Parameters dialog box (Simulation->PWE Band Solver Parameters…) Figure 4: PWE parameters dialog box Unless stated otherwise use default values. In the Solver group select 1D, TE Polarization. Domain parameter group gives you the option to modify the lattice vectors, mesh size as well as simulation center. Select Use defaults in ‘Lattice Vectors’ group. The…

Run Simulation and View Results

When finished with editing band solver parameters click Run… to start the simulations. A simulation window will be launched and simulation starts. You will be notified in the output window at the bottom (Notification tab) about progress of the simulations. After the simulation is finished the graph is populated with set of eigenfrequencies of individual k-vectors.…

Bragg Grating with Layers of Different Width

Thanks to the parameterized design we can easily verify other published results as well as point out other features of PWE band solver. Let’s change a variable to 0.2 to simulate grating with alternating layers of different widths. The layer of the high permittivity (waveguides) will be 0.2a thick, whereas the air layer will be…

Off-Axis Propagation

In the previous examples we intentionally selected propagation direction (k-vector) normal to the multilayer structures. Changing the polarization from TE to TM we are getting the same results, which confirm that the TE/TM modes are degenerate. In case of an off-axis propagation the k-vector has a component parallel to the Bragg layers, and the degeneracy of…

References

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