Lost is Lost...

Photon travels in a helical path.  Its phase is understood to be its relative position along its circular path.  For every \(\lambda\) distance along its direction of travel, the photon completes one full revolution, a phase of  \(2\pi\).  The following diagram shows how destructive and constructive interference might occur through collisions.

Over a longitudinal distance of  \(\cfrac{\lambda}{2}\), the photon along it circular path reverses direction completely.  In this direction, it can collide with another photon at zero phase,

\(m_pc-m_pc=0\)

Momentum is zero after the collision and the kinetic energy is completely lost.

This is consistent with the conventional understanding of destructive interference.  In this case, a \(\pi\) phase difference or a optical path difference of  half a wavelength can result in such destructive collisions.

In this model however,  there is no gain in energy during constructive interference.  It is unlikely to have collision, as both photons have the same velocity.

The lost energy during destructive interference does not re-appear during constructive interference.