Focusing properties of linear phase-conjugate array

Phase conjugation generates a backpropagating field that refocuses on the original source, rendering it an effective technique for sound source localization. In addition, linear arrays are widely used in underwater source localization. Therefore, investigating the focusing properties of a linear phase-conjugate array is crucial. This study analyzes the backpropagating field produced by phase-conjugate arrays, proposing indicators for focus bias (FB), focal point size (FS), and sidelobe interference (SLI) to quantitatively characterize these properties. Numerical simulations of the focusing properties of monopole phase-conjugate (PCM), dipole phase-conjugate (PCD), and perfect phase-conjugate (PCP) arrays for a single-frequency point source are conducted to evaluate the effects of array aperture, element spacing, source-to-array distance, and source bias on the different focusing properties of each array. The results indicate that focus bias and focal point size are primarily associated with the array angular aperture (determined by array aperture, source-to-array distance, and source bias); element spacing is the primary factor influencing sidelobe interference. Under identical array configurations, the focus bias of the three phase-conjugate arrays is similar, while the PCM array exhibits the smallest focal spot size, and the PCD array displays the least sidelobe interference.