[georgeburdell]

Could you explain, or maybe point to a good textbook with a chapter on the subject, why the coupling efficiency to the second waveguide on the directional coupler peaks at a certain intermediate waveguide length? I have a PhD, just not in photonics.

[alvesjnr]

I'll try an ELI5:

When the light propagates in a waveguide as the one used in my circuit, the E and H components of the EM wave are not fully confined to the waveguide, but part of it stays outside the waveguide. If you put two waveguides close to each other and makes the light travel to the first waveguide, part of the EM field of the light will also see the second waveguide.it makes part of the ligh couple to the second waveguide. As the wave travels, more and more light couples to the second waveguide. If you engineer it well, at some point 50% of the light will be confined in each waveguide. At this point you separate both WG and you have a 50:50 coupler.

[georgeburdell]

Yes I know that the mode isn't perfectly confined in the waveguide, but Figure 4(b) of the article shows the coupling efficiency to the second waveguide going down as the length of the intermediate waveguide gets longer past some critical value. That's the part that gets me.

[mmmBacon]

Pretty decent introduction if you have some physics background with some basic optical/E&M theory (PhD won’t help otherwise) is Silicon Photonics Design by Chrostowski.