Mechanics and refractive power optimization of tunable acoustic gradient lenses

Tunable acoustic gradient index (TAG) lenses create tunable multiscale Bessel beams. These lenses are fluid-filled cylindrical cavities within which an acoustic radial standing wave is excited. This standing wave modulates the density, and thereby the refractive index within the lens. Spatial gradients in the refractive index can be used for lensing. A predictive model for the steady-state fluid mechanics behind TAG lenses driven with a sinusoidal voltage signal is presented here. The model covers inviscid and viscous regimes in both the resonant and off-resonant cases. The density fluctuations from the fluidic model are related to refractive index fluctuations. The entire model is then analyzed to determine the optimal values of lens design parameters for greatest lens refractive power. These design parameters include lens length, radius, static refractive index, fluid viscosity, sound speed, and driving frequency and amplitude. It is found that long lenses filled with a fluid of high refractive index and driven with large amplitude signals form the most effective lenses. When dealing with resonant driving conditions, low driving frequencies, smaller lens radii, and fluids with larger sound speeds are optimal. At nonresonant driving conditions, the opposite is true: High driving frequencies, larger radius lenses, and fluids with low sound speeds are beneficial. The ease of tunability of the TAG lens through modifying the driving signal is discussed, as are limitations of the model including cavitation and nonlinearities within the lens.