Non-interferometric measurement of geometric phase through stimulated second harmonic generation

The geometric phase (GP), arising from the evolution of states like polarization on the Poincaré sphere, is conventionally measured using interferometry. However, the interferometric techniques often suffer from instability, causing GP to be masked by dynamic phase contributions. Here, we propose a non-interferometric approach based on stimulated second harmonic generation (S-SHG) for GP measurement. Using a 1064 nm continuous-wave pump and two-stages SHG, we achieved S-SHG in the second crystal using the seed SHG (9.3 mW) and undepleted pump (0.52 W) of the first crystal. By exploiting the phase-sensitive nature of the S-SHG, we mapped the GP arising from the rotation of the half-waveplate, θH, placed between two quarter-waveplates oriented at 45° to the horizontal onto the S-SHG power. The S-SHG power varies sinusoidally with θH, and the variation increases by 2 times for the GP induced in the pump beam as compared to the seed beam, resulting in enhanced sensitivity. The measured GP value agrees with Jones calculus and interferometric measurement. We measured S-SHG amplification to be high (18×) for low seed (1 mW) and high pump (0.81 W) powers, making the current S-SHG technique suitable for imaging biological samples with low illumination, avoiding thermal damage.