A new annular-core optical fiber is useful, inter alia, for stabilizing
the behavior of an optical attenuator based on a Long Period Grating
(LPG) against fluctuations in the polarization of the fundamental optical
signal. The fiber dimensions and .DELTA.n are selected such that when a
LPG of some period is used to couple fundamental-mode radiation in the
fiber into higher-order modes, the wavelength of peak coupling into an HE
mode is removed by at least 30 nm from the wavelength of peak coupling
into the nearer of a TE mode or a TM mode.