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The etching effect on the bandwidth of acoustooptic coupling between core and cladding modes in a single-mode (SM) fiber was investigated experimentally and theoretically. It was found that when the fiber diameter is etched down to a critical value, extremely broadband acoustooptic tunable filter (AOTF) could be achieved. We demonstrated an ultra-broadband acoustooptic filter with -3-dB bandwidth of 362 nm and dynamic range of >14 dB, which is the broadest bandwidth of AOTF on SMF up to now. The results point to potential realization of a new class of high efficient, fast, all-fiber variable optical attenuator.