Power and radiance scaling in Coherent Beam Combination Generally, it's said that for incoherent laser beam combining, the intensity scales with N (where N = # of lasers), whereas the intensity scales with $N^2$ for coherent combining.
$$I_{array,incoherent}=N*I_{single}$$
$$I_{array,coherent}=N^2*I_{single}$$
 Why? Because in coherent combining, the amplitudes add up, and the intensity scales with the square of the amplitude.
However, things seema bit more nuanced and I feel like I've read some confusing info while delving deeper into the theory, which I'll elaborate on below. Imagine two methods of coherent combining:
Method A -->  "Side-by-side", or "tiled", combining. N lasers are placed in an array with fill factor 1, all in phase.

Method B --> "Filled-aperture" combining. N lasers are combined using 50/50 beamsplitters and using the 100% constructive interference from one output when the phase is just right.

What I don't understand stems from the following paper:
https://www.ll.mit.edu/news/Fan_LaserBeamCombining.pdf
states that:

Another way to look
  at the nonideality of CBC systems is to recognize that, for the
  ideal phasing of an array of N elements, the on-axis far-field
  intensity will be N times higher than for the same array with no
  fixed phase relations (incoherent) among the elements [3]. This can be simply understood by recognizing that the radiance of the incoherent array is at best that of a single element and that an ideally phased system will have a radiance of N times this amount.

This suggests that if the far-field intensity is a factor N higher for incoherent combining (compared to a single source), it should be $N*N=N^2$ higher for coherent combining. Directly after, it reads

As a note, it has been often stated that the on-axis intensity of
  CBC systems scales as $N^2$ (e.g., see [4]), which appears to be
  at odds with the stated brightness scaling. The on-axis intensity
  does scale as $N^2$, but only if the emitting aperture grows proportional
  to N. If instead the aperture size is constrained to a fixed
  size, then the on-axis intensity scales only as N.

For method A (tiled), I can see how the emitting aperture grows (due to the array) and that the intensity scales indeed with $N^2$. However, for method B (filled-aperture), one of the characteristics is that the aperture size remains constant. 
Then, does this indeed mean that using this coherent combining method, you'll really only get a factor N rather than $N^2$ higher intensity?
(If so, what happened to the square of the amplitude? Is there any way to increase the area to get the $N^2$ dependency?)


Some considerations that I felt fit not in the question, but might be useful:
For Method A, I'd say the total beam power scales with N (lasers). Due to the reduced divergence, the final on-axis intensity then scales with $N^2$. (One factor N due to the nr of lasers, one due to the reduced divergence)  
For Method B, I'd say the total beam intensity scales with $N^2$ (lasers, constructive interference) and the divergence is unaffected, resulting also in an on-axis intensity of $N^2$, rather than the N suggested above.
Extra: If the intensity ($W/m^2$) scales with $N^2$ increases, and the beam area remains the same, I'd still expect an $N^2$ dependency for the power as well, even though you can't 'make' extra power?
 A: Asking the question, trying to explain my thoughts and the direction CuriousOne pushed me in with his comments made me think that I understand it now, so I'll try to go ahead and answer my own question:
YES, both method A and method B will increase the power of the final beam by a factor N.
ONLY method A will increase the final intensity of the beam with a factor $N^2$: One factor is due to the power, another factor is due to the reduced divergence.
Where I thought methods A and B were different, but with similar end effects, I think I was wrong: Method A is better if you're looking for high intensity.
As to my confusion on how the intensity of a beam can scale with $N^2$ whereas the power can not (even when the beam stays the same size): I had lost sight of the second leaving the beamsplitter:  
Imagine a 1W laser hitting a 50/50 beam splitter. Each side has a 0.5W output. Coherently combining a second 1W laser will result in a single 2W output and one "0W" output. So yes, from 0.5W to 2W is indeed a factor $N^2$, but no power was generated since this power was 'taken' from the other output. While the power of that specific beam increased by a factor $N^2$, the power of the system increased with only a factor N.
