Determining the relationship between the refractive-index difference of a coiled single-mode optical fiber and its bending radius by a mode-image analysis method

In this experiment, we wrap a single-mode optical fiber around various sizes of cylindrical acrylic tubes, forming a series of manually controllable birefringent optical fibers. We launch linearly polarized external-cavity feedback wavelength-tunable visible diode laser light into the stressed birefringent fiber and capture simultaneously the fiber cross-sectional images of two orthogonally polarized modes under various wavelengths by a Wollaston prism polarizer. Through image analysis, we can obtain the two orthogonally polarized light intensities and calculate the phase difference of the two orthogonally polarized modes in the fiber core. By examining the variations of the phase difference with the optical wavelength, we can thus obtain the refractive-index difference of the birefringent fiber. Then by successively changing the size of the acrylic tube, we demonstrate that the refractive-index difference of a coiled fiber varies with its bending radius in a square inverse law. This experiment can reveal precisely the variations in the birefringence of a coiled fiber by a home-made wavelength-tunable diode laser and a mode-image analysis method, providing an advanced teaching kit in the optics laboratory.