  Spin is a fundamental degree of freedom, whose existence was proven by Dirac
for an electron by imposing the relativity to quantum mechanics, leading to the
triumph to derive the Dirac equation. Spin of a photon should be linked to
polarisation, however, the similar argument for an electron was not applicable
to Maxwell equations, which are already Lorentz invariant. Therefore, the
origin of polarisation and its relationship with spin are not completely
elucidated, yet. Here, we discuss propagation of coherent rays of photons in a
graded-index optical fibre, which can be solved exactly using the
Laguerre-Gauss or Hermite-Gauss modes in a cylindrical or a Cartesian
coordinate. We found that the energy spectrum is massive with the effective
mass as a function of the confinement and orbital angular momentum. The
propagation is described by the one-dimensional ($1D$) non-relativistic
Schr\"odinger equation, which is equivalent to the $2D$ space-time Klein-Gordon
equation by a unitary transformation. The probabilistic interpretation and the
conservation law require the factorisation of the Klein-Gordon equation,
leading to the $2D$ Dirac equation with spin. We applied the
Bardeen-Cooper-Schrieffer (BCS)-Bogoliubov theory of superconductivity to a
coherent ray from a laser and identified a radiative
Nambu-Anderson-Higgs-Goldstone mode for recovering the broken symmetry. The
spin expectation value of a photon corresponds to the polarisation state in the
Poincar\'e sphere, which is characterised by fixed phases after the onset of
lasing due to the broken $SU(2)$ symmetry, and it is shown that its azimuthal
angle is coming from the phase of the energy gap.
