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 continuous-wave pump and two-stage SHG, we achieved S-SHG in the second crystal using the seed SHG and undepleted pump 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, placed between two suitably oriented quarter-waveplates, onto the S-SHG power to measure GP with a sensitivity better than 26 μW/mrad. The measured GP value agrees with Jones' calculus and interferometric measurement. Furthermore, we found that the sensitivity of GP measurement is high for phase-modulation to pump beam and a high S-SHG amplification at low seed power, establishing the suitability of the S-SHG scheme for imaging biological samples with low illumination, avoiding thermal damage. Such a generic scheme can be implemented using any nonlinear crystal and laser (cw to ultrafast), establishing its potential for various applications.