They are trying to explain the resonant cavity thrusters , controversial propelling engines.
It seems to me that the paper you quote confuses photons with light waves, attributing a real space wave nature to the photon. From their fig1:
Our reasoning is that when light waves combined with opposite phases, the photons do not vanish for nothing but continue propagating and carrying momentum.
The light wave emerges from a confluence of photons, elementary particles described by quantum electrodynamics. Individually they have energy equal to h*nu and momentum h/lamda . That is all, there are no real phases measurable for an individual photon.
Momentum is a vector quantity and in a classical particle is uniquely defined in direction too. In a quantum mechanical particle where a wavefunction in space gives the probability density for the location of the "particle" the uncertainty in the location spatially will give an uncertainty to the individual photon direction. True the photon does not "vanish", it changes direction and manifests from the dark fringes to the bright fringes during interference.
This blog entry by Lubos helped me understand how the classical beam emerges from the quantum mechanical individual photons. Hand waving: the classical beam emerges from the addition in space of the individual photon complex wave functions , which carry the electromagnetic potential A information in their complex manifestation. As photon-photon interactions are much repressed the potentials in their complex form add spatially and all the various classical interference patterns appear. It is how the quantum mechanical position uncertainty is quantified mathematically, for the given frequency, which is not random but controlled by each photon's wave function; this generates the interference patterns , the addition of probability density amplitudes have the sinusoidal dependence, not the photon in space.
As others have observed in standing waves, by construction, the photon momenta add up to zero beam momentum, as the classical beam emerges from photons propagating backwards and forwards . Any opening will destroy the balance and momentum will be carried off by the photons in the beam.
Their basic premise seems to be out dated and wrong, italics mine:
Field theory, when manipulating photons as virtual particles, has been subject to reservations, because its follows from perturbation theory.19,20 Instead, the old atomistic tenet makes sense to us by regarding the quanta of light as indivisible and indestructible basic building blocks of nature.
I am not commenting on whether the particular controversial drive works or not, but on the explanation offered by the authors assuming it does. From the wiki article there seems to be doubt on the experimental side too.