Passive stabilization of low-power laser beams in soft hydrogels with parabolic-index profile for optogenetic neural stimulation: a phase analysis.

Optogenetic stimulation of deep brain regions is limited by rapid light divergence in soft tissue, mechanical damage from rigid optical fibers, and the impracticality of active beam control systems that require external power. This study introduces a passive, biocompatible solution based on soft parabolic-index hydrogels that stabilize the phase of propagating Gaussian beams without any external energy. Using beam propagation method simulations and phase-resolved analysis, we demonstrate three main findings: first, the proposed hydrogel maintains periodic focusing and defocusing cycles along the propagation path. Second, the transverse wavenumber becomes discrete and quantized, which confirms preservation of spatial coherence. Third, the optical phase undergoes periodic resetting to its initial value after each oscillation cycle, ensuring predictable beam focus at regular intervals. Furthermore, we show that the phase-intensity correlation stabilizes rapidly after initial propagation, and that the phase accumulation rate can be tuned by adjusting the gradient coefficient of the hydrogel. These findings establish that graded-index hydrogels can function as passive, implantable optical waveguides for delivering phase-stable, focused light to precise neural targets. This technology directly resolves the three major obstacles in optogenetic neural stimulation devices: light delivery, tissue damage, and reliance on external power.