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The recent development of subwavelength photonic and phononic crystals showsthe possibility of controlling wave propagation at deep subwavelength scales.Subwavelength bandgap phononic crystals are typically created using a periodicarrangement of subwavelength resonators, in our case small gas bubbles in aliquid. In this work, a waveguide is created by modifying the sizes of thebubbles along a line in a dilute two-dimensional bubbly crystal, therebycreating a line defect. Our aim is to prove that the line defect indeed acts asa waveguide; waves of certain frequencies will be localized to, and guidedalong, the line defect. The key result is an original formula for thefrequencies of the defect modes. Moreover, these frequencies are numericallycomputed using the multipole method, which numerically illustrates our mainresults.

Subwavelength guided modes for acoustic waves in bubbly crystals with a line defect