Special theory of relativity for a graded index fibre

Frontiers in Physics

Physics

Shinichi Saito¹ 

[1] null;

关键词: Stokes parameters;    Poincaré sphere;    polarisation;    spin angular momentum;    SU(2);    coherent state;   

DOI  :  10.3389/fphy.2023.1225387

 received in 2023-05-19, accepted in 2023-07-18,  发布年份 2023

来源: Frontiers

【 摘 要 】

The speed of light (c) in a vacuum is independent of the choice of frames to describe the propagation, according to the theory of relativity. We consider how light is characterised in a material, where the speed of light is different from that in a vacuum due to the finite dielectric constant. The phase velocity in a material is smaller than c, such that the speed of a moving frame can be larger than the phase velocity, such that the frame can move faster than the speed of light in a material. Consequently, an unusual Doppler effect is expected, and the wavelength in the moving frame changes from the red-shift to the blue-shift upon increasing the speed of the frame. The corresponding energy of the light also changes sign from positive to negative, while momentum is always positive, leading to the changes of signs for the phase velocity and the helicity. In a graded index fibre, where the exact solution is available, even more complicated phenomena are expected, due to the finite effective mass of photons. Upon the increase of the energy gap, generated by optical confinements and optical orbital angular momentum, the effective mass of photons increases. If the gap is large enough, momentum starts to change the sign upon increasing the frame velocity, while the energy of photons is always positive. In this case, the phase velocity diverges if momentum is in agreement with the fame velocity. Contrary to the unusual behaviours of the phase velocity, the group velocity is always below c. This thought experiment might be useful for considering insight into the polarisation state of light.

【 授权许可】

Unknown   
Copyright © 2023 Saito.