Most likely this is due to the co-called "late-time instability" issue. FDTD is a weakly stable algorithm. any numerical errors can trigger this instability, such as single precision of the numerical data. You may search only for more information.
The late-time instabiity usually occurs for long simulation. You may check if you really need that long simulation. and if this nonlinear simulation involves gain, please significantly increase "autoshuoff max".
You may also need to add 3 profile monitors (xy, yz,and xz plane) and record data inside PML, and movie moitors. and then check where the diverge begis. It might be from PML. So you can modify the PML types and number of layers.
I particular, the custom source should turn on gradually to not excite higher frequencies unexpected. You can use a time monitor and check its spectrum to see if there is a resonance.
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