Does light exit a single mode fiber in the same angle it enters?

Question

If I have a laser beam of width larger than the core of the single mode fiber, and I use a lens to focus the light such that the entrance of the fiber sits at the focal point of the lens, does the fiber emit light in a cone of light with equal incident and exit angles?

Lets say I've been careful to choose my lens such that the incoming cone of laser light has a narrower angle than the maximum angle of acceptance, then is the angular/spatial structure of my light field preserved?

Answer 1

No - the reflections inside the fiber will result in light propagating in the entirety of the single mode, which does not "remember" the angle at which the light entered the fiber.

See also this question and associated answers.