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We report microwave spectroscopy of Josephson junctions chains made from an epitaxial Al/InAs heterostructure. The chains exhibit superinductance, with characteristic wave impedance exceeding . The planar nature of the junctions results in a large plasma frequency, with no measurable deviations from ideal dispersion up to . Internal quality factors decrease sharply with frequency, which we describe with a simple loss model. The possibility of a loss mechanism intrinsic to the superconductor-semiconductor junction is considered.

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