# How to derive equation (upper bound for the period to-wavelength, grating)

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:

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