Sure, a diverging spherical wavefront of the corresponding radius is actually the perfect match for a conical waveguide (and the only one), even better than a flat wavefront is for an OS waveguide. There is no doubt about that. That's the reason I would like to try this out. Now I'm searching for any drawbacks. There must be some as I don't see this being done - actually I have never seen this done like that. Either it is too brilliant or too dumb
A converging wave front at the exit, a plane wave, or a diverging wave front can all be made by varying the path lengths in the phase plug from inner and outer portions of the diaphragm, regardless of whether the diaphragm is annular or dome shaped.
Drawbacks to your “in horn” rather than “in driver” phase plug proposal:
1)The level of machining (fractions of a millimeter) to make a good high frequency phase plug is such that incorporating it into the horn itself would not be cost effective for manufacturing.
2) Each different pattern horn would require a complete redesign of the phase plug portion.
3) Each section of the phase plug as illustrated is a “beamy” very high frequency horn, and as such would have HF “fingering” as multi-cell horns do.
4) Diffraction effects would be worse than standard phase plugs, as the slit exit dimensions are larger and spaced further apart.
Dave Gunness 2005 AES Convention paper “Improving Loudspeaker Transient Response with Digital Signal Processing”
https://web.archive.org/web/2012051...m/info/EAW/Technical_Papers/NT_Whitepaper.pdf
section 3.1 gives some insight into problems inherent in phase plug design.
Art