[A response to Andrew Shields' comment]
Poetry is the art of writing emotions down, just as philosophy is the art of writing concepts down. In 1879, Frege published his Begriffsschrift, normally translated as "conceptual notation", a formalism that was supposed to make the connection between thoughts perspicuous. It was not intended to describe how we actually think, it was not a delineation of some natural "language of thought", rather it was an artificial simulation of thought, intended to be more precise than our ordinary thought processes. Likewise poetry is an Ergriffsschrift, an "emotional notation", an attempt to make the connections between our feelings intense. It does not stimulate genuine feelings, but artificial ones, which foster greater precision in our emotional apparatus and, therefore, a finer range of genuine feeling in the long run.
In making a poem, I don't "express emotion", I write the emotion down. I don't communicate a feeling to the reader but offer the reader an occasion for greater precision in feeling, through the intensity of the emotion. So there is certainly something "emotional" about the process of writing a poem, just as there is something conceptual about philosophizing. But it is true that I do not, at the time of writing feel the emotion. In an important sense (and this is something T.S. Eliot emphasized) the poem is intended to free us from feelings (and personality). More precisely, as Heidegger said of philosophical questioning into concepts, poetry "prepares a free relationship" to the emotion.
This freedom can of course itself be felt. It is the exhilaration that is familiar to us as literary pleasure, what Nabokov called "aesthetic bliss". It is not, to be sure, the possible bliss that comes from feeling the emotion that is the ostensible theme of the poem. That feeling, after all, may be altogether painful.