why quarter wavelength for directional coupler?

for directional couplers which is nothing but two parallel microstrips adjacent to each other, I can't understand why it has to be quarter wavelength.

My guess is that since coupling is merely interacting with the other microstrip through E, H fields, there isn't any need to be quarter wavelength. The longer, then more coupling will occur and more power will be transferred.

But every google search that I look up, it says that directional couplers use quarter wavelength but it doesn't say why. What is wrong with my guess?

Your understand of theory is right: it does not have to be 1/4 wavelength for a directional coupler.

In general, coupling will change with frequency. If you make the coupler 1/4 wavelength, you can reach a nice bandwidth where coupling does not change too much.

Next to the coupling, you should also consider the matching:

For microstrip direct. coupler, the value of 1/4*wavelength is explained in http://kilyos.ee.bilkent.edu.tr/~mic...ler/theory.htm in the middle.

hmm.. your answer kind of answers some part of my question but it also confuses me again on the other.

okay you said the length doesn't necessary have to be quarter wavelength to provide good coupling.
despite this, you still mention that the coupler is 'good' to have a length equal to quarter wavelength. Even though the purpose of configuring the length is to get a nice BW of relatively high coupling for a frequency range of interest,

still, even in the graph that you've shown, the 'nice BW' range seems to repeat along frequency.

I wanted to know if why coupling repeats by frequency and I assume that this has to do something with the length of the TL.
for example, when the frequency is a multiple of the fundamental frequency that has a quarter wavelength equal to the given TL length, then the coupling is increased.
how can I explain this repeating tendency?
why is coupling enhanced when the current frequency's quarter wavelength is a 1/N (N=integer) of the TL length?

True, but that's independent of the coupler length, as explained in the document that you linked: