We established a theoretical model for a single knot-ring resonator and investigated the transmission spectrum by Jones matrix. The numerical results show that two orthogonal polarization modes of knot-ring, which are originally resonated at the same wavelength, will split into two resonant modes with different wavelengths. The mode splitting is due to the coupling between the two orthogonal polarization modes in the knot-ring when the twisted angle of the twist coupler is not exactly equal to 2mπ (m is an integer). It is also found that the separation of the mode splitting is linearly proportional to the deviation angle δθ with a high correlation coefficient of 99.6% and a slope of 3.17 nm/rad. Furthermore, a transparency phenomenon analogous to coupled-resonator-induced transparency was also predicted by the model. These findings may have potential applications in lasers and sensors.
Sensing the nanometric displacement of a micro-/nano-fiber induced by optical forces is a key technology to study optical forces and optical momentum. When the gap between a micro-/nano-fiber and glass substrate becomes down to micrometer scale or less, a white light interference was observed. The gap changes when optical force arising from the propagating pump light along the micro-/nano-fiber causes a transversal nanometric displacement of a micro-/nanofiber, resulting in movement of the interferometric fringes. Therefore this movement of the interferometric fringes can be used to sense the nanometric displacement of the micro-/nano-fiber induced by optical forces. Experimental results show that the resolutions of this method can reach 7.27nm/pixel for tilted angle 0.8<sup>o</sup> between the micro-/nano-fiber and substrate. It is concluded that the white light interferometry method is suitable for measuring the weak optical force.