We show that light confined in a circularly polarized fundamental mode of a nanofiber has a finite angular momentum, with both spin and orbital components. We derive exact analytical expressions for the angular momentum and its spin and orbital components. We show that the spin component is dominant when the fiber radius is small or large compared to the light wavelength. For intermediate fiber radii, a substantial orbital component appears, which is absent in the two limits mentioned above. The orbital component is maximized when the fiber radius is about one-fourth of the light wavelength.
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