The Wikipedia article on Radiation Pressure gives an equation for the pressure on a perfect reflector produced by a beam of photons with an energy flux $E_f$ (in units of power/area) as
where $\theta$ is the angle of incidence between the incoming photon beam and the surface normal of the reflector, and $c$ is the speed of light. Maximum pressure is at normal incidence, and it drops to zero at 90° when the incidence is perpendicular to the surface normal.
The $cos^2(\theta)$ behavior can be understood as follows; the component of the photon's momentum perpendicular to the surface scales as $cos(\theta)$, and the projected cross-sectional area of a flat surface exposed to the incoming light also varies as $cos(\theta)$. Together they result in the $cos^2(\theta)$ behavior.
However, Wikipedia's article Solar Sail mentions both the simple $cos^2(\theta)$ shape and also a more complicated, "realistic" shape with the form
$$0.349 + 0.662cos(2\theta) - 0.11cos(4\theta)$$
and states that realistically the force drops to zero at around 60° rather than at 90°.
An actual square sail can be modeled as: F = F0 (0.349 + 0.662 cos 2θ − 0.011 cos 4θ) / R2 Note that the force and acceleration approach zero generally around θ = 60° rather than 90° as one might expect with an ideal sail.(18)
I don't understand how the square shape of the sail has anything to do with the pressure, and I don't understand why it would go to zero near 60°. Reference (18) is given as Space Sailing, Jerome Wright (1992), Gordon and Breach Science Publishers, Appendix B.
I've pasted that expression into an internet search and I see that it is repeated in many places, with similarly worded text, but so far I have not found any explanation for why it is supposed to better represent the performance of a solar sail.
Question: What is the physics behind this approximate expression? Why would the pressure drop from maximum to zero at about 60°? Would a square shape have anything to do with it at all?
Beyond 60° the expression goes negative; are we supposed to clip it at zero, rather than there being an attractive force due to negative photon pressure, or does this represent a known physical phenomenon? Under some conditions light can be used as an attractive force as in the case of a laser trap, but that usually involves either a strong gradient, or tuning to a specific resonance. In this case the light is uniform and the interaction is non-resonant.
In the plot below, the simple $cos^2(\theta)$ behavior is shown by the thick solid (blue) curve as a function of incident angle $\theta$, and the more complex expansion is shown by the thinner solid (green) curve. Zero is indicated by the dashed (black) line.