if | δ$_{LL}$ | ∼ Q a ≫ 1, the uniform Lorentz LF is suppressed when the laser is tuned closely to the exact atomic resonance, δ ≈ 0, reaching its minimum intensity The LF in this case is effectively “pushed out” by the lattice atoms. Interestingly, a huge LF enhancement is reached at a red-shifted frequency, at δ ≈ δ$_{LL}$ < 0, where Note that Eqs. (8), (10), and (11) are very similar to the corresponding equations for 1D arrays of atoms which were discussed in [1, 2]. The only difference is that the relation between δ$_{LL}$ and Q a there was δ$_{LL}$ = − Q a if E$_{in}$ is parallel to the array (and dipoles are aligned “head-to-tail”) and δ$_{LL}$ = Q a / 2 if E$_{in}$ is perpendicular to the array (and dipoles are aligned “side-to-side”), assuming the NNA [see, e. g., Eq. (3.4) of Ref. [2]]. Here, within the NRA, δ$_{LL}$ does not depend on the incident field polarization in the lattice plane. Quite naturally, its value (9) lies in-between the two values for the 1D array, because mutual orientations of different pairs of dipoles in the lattice vary between the two extremes. The frequency dependence of a spatially uniform LF, like in Eq. (8), and the associated Lorentz shift are long known phenomena. Similar effect was also observed experimentally in alkali vapors [15]. The unusual new phenomenon is that in ordered low-dimensional structures there are spatially varying solutions, which we call locsitons [1], that emerge at some values of Q in addition to the uniform LF. We will look for the locsitons in the form of 2D plane-wave excitations of the LF: where q is the normalized wave vector of the locsiton. By substituting E$_{L}$ = ¯ E$_{L}$ + Δ E$_{L}$ into Eq. (7) we obtain the dispersion relation for the wave vector q in an integral form: where ψ is the polar angle of q counted from the direction of E$_{in}$ in the lattice plane. Using the standard expansion of trigonometric functions with a harmonic argument into Bessel functions [see, e. g., Eq. (21.8-25 a ) in Ref. [16]], | ¯ E$_{L}$ | 2 min ≈ | E$_{in}$ | 2 1 + δ 2 LL . (10) | ¯ E$_{L}$ | 2 max ≈ (1 + δ 2 $_{LL}$) | E$_{in}$ | $^{2}$. (11) Δ E$_{L}$ ∝ exp( i q · r /l a ) , (12) 1 + 3 Q 4 π ∫ π 0 (3 cos 2 θ + 1) cos[ q cos( θ − ψ )] dθ = 0 , (13) cos( q sin φ ) = J$_{0}$ ( q ) + 2 ∞ ∑ m =1 J$_{2}$ m ( q ) cos(2 mφ ) , (14) 10