This quasi-classical theory is the first to contain such a large number of the features required to model a photon. The model uses Maxwell?s equations that not only embody relativity but contain elements of quantum theory. Conventional localised wave-packets cannot explain quantisation or the non-local behaviour of a photon. Standard methods for quantising Maxwellian modes using the harmonic oscillator formalism at angular frequency w, have the unsatisfactory feature that the Schr?dinger frequencies (M+?)w (integer M) have no clear physical significance and do not explain why, in a dispersive wave-guide, experiments indicate no difference between the velocity of single photons (M=1) and classical groups (M >>1). With this motivation, novel solutions to Maxwell?s classical equations in a dispersive system such as a circular guide are considered in a relativistic format. A helical twist with an arbitrary angular frequency W can modulate an arbitrary classical mode (angular frequency w, group velocity vg) provided that the helical velocity vh equals vg. Pairs of waves with modal and helical frequencies (w, W) and (w, -W) can trap one temporal period, (2p/w), of the underlying mode given that W = (M+?)w : the ?Schr?dinger? frequencies. The value of M is found to have no effect on group velocity or polarisation. A relativistic format shows how to create stable resonant wave-packets where conventional retarded waves overlap unconventional advanced waves. Energy is postulated to be carried only in the region of overlap and follows a ?Planck?s law? where the energy is proportional to the helical modulation frequency. Causality is never violated. Standard concepts of promotion and demotion have the clear physical meaning of increasing or decreasing the helical frequency. Advanced waves enable phase and polarisation to be predicted along all possible future paths and may help to explain the outcomes of experiments on delayed-choice interference and entanglement.
