Correct for: 
	...of the mirror coatings on gravitational wave dectors
	a tight focusleads-> focus leads
	...fits into a cuvette which for convenient -> which provides convenient
	...external translation state,before mirror -> external translation stage, before the mirror
	...far detuned form -> far detuned from
	CQED -> cavity QED

Add reference for LG basis 
Add this paragraph to the conclusion, but I'm not sure if it is convincing.
	At this cavity length, we observe the transverse-mode fre-
	quency spacing of 40(5) MHz, which is within the same
	order of magnitude as the estimated atom-cavity cou-
	pling strength of 20 MHz. As a result, the presented
	cavity design can be employed to probe the atomic dy-
	namics in the regime of multi-mode strong coupling cav-
	ity QED