I am currently reading the paper entitled "Antireflection behavior of silicon subwavelength periodic structures for visible light" [P. Lalanne & G Michael Morris, Nanotechnology 8, 53 (1997)].

On the first page, they write:

To suppress Fresnel reflections for randomly polarized light, we consider 2D SWS '(Subwavelength structured)' surfaces. The free parameters of the design are the period $\Lambda$, the grating profile and the depth. The period is related to the smallest wavelength $\lambda_{min}$ so that, for a given angle of incidence $\theta_i$, the SWS surface acts as a zero$^\mathrm{th}$-order filter by reflection. If the reflected zero$^\mathrm{th}$ order alone is to propagate in the incident medium of refractive index equal to 1, the upper bound for the period to-wavelength ratio $\Lambda$/$\lambda_{min}$ is simply equal to 1/(1+sin($\theta_i$)).

I would like to know how they derived this, more specifically, why for $m=0$ (zero$^\mathrm{th}$ order) and an incident medium equal to $n=1$ (refractive index), we have:

$$\frac{\Lambda}{\lambda_{min}} = \frac{1}{1+\sin(\theta_i)}$$


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