In this example, we will use MODE' EME solver to study the effect of adding a phase shift to the Bragg grating to create a resonance peak within the stopband. This design can be used as a filter in an integrated optics circuit, as well as a sensor for biological sensing applications.

## Background

In this Bragg grating design, a phase shift is introduced at the center of the device to create a Fabry-Perot cavity with mirrors formed by the gratings on each side. This phase shift will lead to a sharp resonance peak within the stop band of the transmission spectrum.

## Simulation Setup

The setup for the phase-shifted Bragg grating in shift_Bragg_eme.lms is similar to that of the waveguide Bragg grating example, with a few modifications required to accommodate the cavity region at the center of the grating,

Under the EME setup tab, we define 5 cell groups for the EME solver, 2 for the input and output waveguides, 1 for the center phase shift region and 2 for the gratings on each side. Note that 2 cells are used for cell groups 2 and 4, 1 for each waveguide width. For the initial simulation, we will use 10 modes for each cell group in the EME calculation. Symmetry is used here to reduce the number of modes required for this calculation.

To set the periodicity of the grating, we will define 2 periodic groups under the "periodic group definition" table, 1 for the gratings on each side of the cavity. This means that cell groups 2 and 4 will be propagated 100 times, and the final length of the device will be 66.32um.

Since EME is a frequency-domain method, we will need to run 1 simulation for each wavelength of interest. The script shift_period_sweep.lsf will calculate the results at each wavelength and plot the transmission spectrum of the phase-shifted Bragg grating.

## Simulation Results

The transmission spectrum of the phase-shifted Bragg grating with 100 pairs of gratings on each side of the cavity is shown below. One can see the sharp resonance peak in the middle of the stop band, which is consistent with the experimental results in [1].

The script shift_period_sweep.lsf can also calculate the spectrum for a different number of grating periods. Since scanning the number of periods does not require re-calculating the modes, one can obtain the transmission spectrum for an arbitrary number of grating periods with very little additional computation time. The figure below shows the transmission for the same Bragg grating with different numbers of grating periods. One can see that the resonance peak becomes sharper as the number of periods increases, but eventually disappears when the number of periods is very large.

### Related publication

1. P. Prabhathan, et al., “Compact SOI nanowire refractive index sensor using phase shifted Bragg grating", Optics Express, Vol. 17, No. 17, 2009

### See also

Bragg Grating Initial Design with FDTD