In Japanese, あとで
is a combination of the noun 後（あと）
(behind), and the particle で
(with). When these words are linked, they form an adverbial phrase which is used to express ‘after’, or ‘later’. As with で
’s standard meaning of ‘with’, あとで
is simply highlighting that something will happen, ‘with’ the ‘after/behind’ part of something.
To use あとで
, attach it to the end of any past-tense verb, noun followed by の
, or verb followed by のは
You can study after you finish eating. (With the time after eating)
I will go to the party after work. (With the time after work)
Since it’s fine to make the copies later, please call the boss right now. (With the time after calling the boss)
The reason that 後（あと） is translated as both ‘after’, and ‘behind’, is because sequences of events in Japanese behave similarly to a train. When the head of the train (one action) passes a specific point, there are still potentially many carriages (other actions) coming ‘after’, or ‘behind’ it.
may also be used to alter the meaning of an entire phrase, by appearing at the front. This nuance is just that (A) will happen (at some point) after now.