Directional imbalance of Bloch surface waves for ultrasensitive displacement metrology

Precise position sensing and nanoscale optical rulers are important in many applications in nanometrology, gravitational wave detection and quantum technologies. Several implementations of such nanoscale displacement sensors have been recently developed based on interferometers, nanoantennas, optical field singularities and optical skyrmions. Here, we propose a method for ultrasensitive displacement measurements based on the directional imbalance of the excitation of Bloch surface waves by an asymmetric double slit, which have low propagation loss and provide high detected intensity. The directionality of excitation changes dramatically with a sub-nanometric displacement of the illuminating Gaussian beam across the slit and can be used for displacement and refractive index metrology. We demonstrate a theoretical intensity ratio of the BSW excitation in opposite directions exceeding 890, which provides a displacement sensitivity of up to 2.888 nm^-1 with a resolution below 0.5 nm over a 100 nm linearity range. Experimentally, a directional intensity ratio more than 90 has been achieved, with a displacement sensitivity of 0.122 nm^-1 over a 300 nm linearity range, resulting in a resolution below 8 nm for a 600 nm illumination wavelength. The proposed facile configuration may have potential applications in nanometrology and super-resolution microscopy.