In this lesson we check that the layer peeling algorithm can reconstruct an unknown
grating with knowledge of only the reflection coefficient. In the first step, we select a
typical grating with chirp and apodization and calculate its reflection coefficient. This
spectrum is then exported to a text file. In the next step, OptiGrating is run again and
the spectrum file imported. The layer peeling algorithm is applied to the imported
spectrum to reconstruct the original grating.

Step
1File > Open. Choose file Ex1a.ifo.
2Select the Profile tab to see the details of this grating.

Optical Grating - Profile tab

  •  It has a linear chirp of 0.2 nm, and a gaussian apodization with FWHM = 0.5.
3Select the Power tab to see the reflection and transmission spectra.

Optical Grating - Reflection and transmission spectra

Note: You can press Calculate to calculate the spectrum again, if desired.

4Click on Spectrum in the Single Fiber drop down menu, then click on the graph in the main window to active it.
5Select Tools > Export Complex Spectrum and select the Reflection button as shown below:

Optical Grating - Export Complex Spectrum

6Click Export.
7In the Save As dialog box, find a suitable place and name for your data file.
8Close Ex1a.ifo.
Step
1Now, open a new project with File > New > Single Fiber.
2Choose Calculation > Inverse Scattering Solver to get the Inverse Problem Solver dialog box.
3Select the From File checkbox.
4Navigate to the place where you left the file with the reflection spectrum.  Open the file.

Optical Grating - Inverse Problem

5We suppose that the original length of the grating is known, so enter 50000 μm in the Length box. (Feel free to experiment with different lengths.)

  • The original spectrum was generated with a profile having 100 segments. It is not necessary that the reconstruction have the same number, here it is set to 1000.
6 Click on the Causality button to test this spectrum.

Optical Grating - Test this spectrum

  • Since this spectrum was generated from a real grating, it displays exactly the causal property of being zero for negative argument.
7 Click Close.
8Click Start in the Inverse Problem Solver dialog box to begin the
reconstruction.
9Click on Spectrum to enable all tabs.
10 Select the Profile tab to see the reconstructed profile.

Optical Grating - Reconstructed profile

  • The apodization appears to be a similar shape as the original grating.
11To see the chirp more clearly, right click the mouse in the Profile window and select Chirp Period.

Optical Grating - Chirp Period.

. . . to get the following:

Optical Grating - the chirp

  • The chirp is linear and shifts by 0.2 nm, like the original grating.
12Select the Power tab to compare the reflectivities, one from the imported complex spectrum and the other from the calculated response of the reconstructed grating.

Optical Grating - Reconstructed grating