Theoretical investigation on super-resolution refractive index measurement with parity detection

The refractive index measurements based on traditional wave optical methods are mainly depended on intensity and wavelength detection strategies. Interference spectrometers are widely used as the most ideal wavelength detecting devices. Interference spectrometers measure the signal intensity, analyze the change of fringe numbers and the corresponding optical path difference by means of optical power meter, and then calculate the wavelength of signal light. Therefore, its essence is still based on intensity detection. However, the resolution of interference signal in intensity detection is restricted by classical diffraction limit, thus its resolution is difficult to further improve. In order to solve this bottleneck, parity detection which could break through the classical resolution limit and realize super-resolution refractive index measurement is proposed in this paper. According to the quantum detection and estimation theory, the expressions for signals and their corresponding sensitivities of refractive index measurement with parity and intensity detections were derived respectively and their numerical comparison analysis was carried out. In addition, the effects of loss on resolution and sensitivity of the output signal were investigated. Numerical results show that the resolution of parity detection is ${\text{2{\text{π}}}}\sqrt N$ times that of intensity detection, achieving super-resolution refractive index measurement. Moreover, the optimal sensitivity reaches the refractive index measurement shot noise limit ${\lambda \mathord{\left/ {\vphantom {\lambda {\left( {2{\text{π}} l\sqrt N } \right)}}} \right. } {\left( {2{\text{π}} l\sqrt N } \right)}}$. The loss reduces the sensitivity and resolution of the signal. The resolution of the parity detection signal is consistently better than that of intensity detection except for the very large loss and very low photon number. Finally, the physical essence of the super-resolution refractive index measurement is analyzed from the detection means itself.