5. JOSA-B Tutorial Paper¶
5.1. 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.
5.1.1. 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 simo-josab-01.py are as follows:
Fundamental optical mode fields.¶
Elastic mode with largest SBS gain.¶
Gain spectrum for the silica waveguide.¶
5.1.2. 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 simo-josab-02.py are as follows:
The fields and gain parameters are as follows:
Fundamental optical mode fields.¶
Fundamental elastic mode fields.¶
We can reproduce Fig. 13 showing the elastic dispersion of this waveguide
silicon waveguide using simo-josab-02b-acdisp.py.
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¶
5.1.3. 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 simo-josab-03.py and simo-josab-04.py.
Let’s see the results for the silica cylinder first:
Gain spectrum for forward SBS of the silica cylinder.¶
Fundamental optical mode field.¶
Elastic mode of maximum gain.¶
Elastic mode of second highest gain.¶
5.1.4. Example 4 – Forward Brillouin scattering in a rectangular silicon waveguide¶
The corresopnding results for the silicon waveguide can be generated with simo-josab-04.py:
Gain spectrum for forward SBS of the silicon waveguide.¶
Fundamental optical mode field.¶
Elastic mode of maximum gain.¶
5.1.5. 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:
Gain spectrum for intermodal forward SBS of the silica waveguide.¶
Fundamental optical mode field.¶
Second order optical mode field.¶
Elastic mode field of maximum gain.¶
5.1.6. 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:
Gain spectrum for intermodal forward SBS of the silicon waveguide.¶
Fundamental optical mode field.¶
Second order optical mode field.¶
Elastic mode field of maximum gain.¶
