As part of a project I'm working on this term, I ran these Google Scholar n-grams for a professor. (They aren't the first or even the most impressive ones I've run, but they are the ones that I'm most behind on sharing.)
The first corpus is a broad overview of the frequency of the use of the term "American empire" in Google's corpus of American English.
|"American empire", corpus: American English, 1850-2008|
What emerges is a somewhat surprising pattern: There's a long decline over the nineteenth century, a blip following the acquisition of an actual American empire in 1898, and then a long plateau following the United States' inadvertent victory in World War I.
The decline that set in after the height of Vietnam War guilt is reversed almost immediately by the events of September 11, which sent discussions of "American empire" to an all-time high (that's right, even eclipsing the period of time when we stole--there's no other nice word for it--Hawai'i, Puerto Rico, the Philippines, and Guam!).
|"American empire", corpus: American English, 1968-2008|
(Note that although this chart and the subsequent one include the case-sensitive "American Empire" in addition to "American empire," the trend lines for all are essentially the same.) Here, we again see the same post-9/11 jump (and an odd post-World War II blues jump in the proper noun "American Empire"). (Note that the British were much less concerned about Vietnam as an exercise in American empire-building.)
|"American Empire" and "American empire", corpus: British English, 1968-2008|
|"American Empire" and "American empire", corpus: English, 1800-2008|
|"Roman Empire", "British Empire", "Ottoman Empire", corpus: English, 1800-2008|