6. JOSA-B Tutorial Paper

6.1. Introduction

Dr Christian Wolff and colleagues have used NumBAT throughout their 2021 SBS tutorial paper Brillouin scattering—theory and experiment: tutorial published in J. Opt. Soc. Am. B. This set of examples works through their discussions of backward SBS, forward Brillouin scattering, and intermodal forward Brillouin scattering.

As the calculations in this paper used NumBAT with essentially the same code in these tutorials, we do not bother to include the original figures.

6.1.1. Example 1 – Backward SBS in a circular silica waveguide

Figure 15 in the paper shows the fundamental optical field of a silica 1 micron waveguide, with the gain and other parameters shown in Table 2. The corresponding results generated with sim-josab-01.py are as follows:

_images/EM_E_field_01.png

Fundamental optical mode fields.

_images/AC_field_28.png

Elastic mode with largest SBS gain.

_images/josab_01-gain_spectra.png

Gain spectrum for the silica waveguide.

6.1.2. Example 2 – Backward SBS in a rectangular silicon waveguide

Figure 14 in the paper calculates the backwards SBS properties of a rectangular \(450x200\) nm silicon waveguide. The corresponding results generated with sim-josab-02.py are as follows:

_images/josab_02a-gain_spectra.png

The fields and gain parameters are as follows:

_images/EM_E_field_00.png

Fundamental optical mode fields.

_images/AC_field_02.png

Fundamental elastic mode fields for mode 2.

_images/AC_field_06.png

Fundamental elastic mode fields for mode 6.

We can reproduce Fig. 13 showing the elastic dispersion of this waveguide silicon waveguide using sim-josab-02b-acdisp.py.

_images/josab_02b-disp-qnu.png

Acoustic dispersion diagram with modes categorised by symmetry as in Table 1 of “Formal selection rules for Brillouin scattering in integrated waveguides and structured fibers” by C. Wolff, M. J. Steel, and C. G. Poulton https://doi.org/10.1364/OE.22.032489

6.1.3. Example 3 – Forward Brillouin scattering in a circular silica waveguide

Figure 16 and Table 3 examine the same waveguides in the case of forward Brillouin scattering.

These results can be generated with sim-josab-03.py and sim-josab-04.py.

Let’s see the results for the silica cylinder first:

_images/josab_03-gain_spectra.png

Gain spectrum for forward SBS of the silica cylinder.

_images/EM_E_field_011.png

Fundamental optical mode field.

_images/AC_field_061.png

Elastic mode of maximum gain.

_images/AC_field_12.png

Elastic mode of second highest gain.

6.1.4. Example 4 – Forward Brillouin scattering in a rectangular silicon waveguide

The corresponding results for the silicon waveguide can be generated with sim-josab-04.py:

_images/josab_04-gain_spectra.png

Gain spectrum for forward SBS of the silicon waveguide.

_images/EM_E_field_001.png

Fundamental optical mode field.

_images/AC_field_062.png

Elastic mode of maximum gain.

6.1.5. Example 5 – Intermodal Forward Brillouin scattering in a circular silica waveguide

For the problem of intermodal FBS, the paper considers coupling between the two lowest optical modes. The elastic mode of highest gain is actually a degenerate pair:

_images/josab_05-gain_spectra.png

Gain spectrum for intermodal forward SBS of the silica waveguide.

_images/EM_E_field_002.png

Fundamental optical mode field.

_images/EM_E_field_012.png

Second order optical mode field.

_images/AC_field_063.png

Elastic mode field of maximum gain.

6.1.6. Example 6 – Intermodal Forward Brillouin scattering in a rectangular silicon waveguide

Finally, the silicon waveguide generates extraordinarily high gain when operated in an intermodal configuration:

_images/josab_06-gain_spectra.png

Gain spectrum for intermodal forward SBS of the silicon waveguide.

_images/EM_E_field_003.png

Fundamental optical mode field.

_images/EM_E_field_02.png

Second order optical mode field.

_images/AC_field_021.png

Elastic mode field of maximum gain.