Partially etched phase-transforming optical element

A method for making an optical element, the method comprising:

• (A) spatially selectively etching a material layer comprising a first optical medium to remove the first optical medium from selected volumes of the material layer, the material layer being supported by or part of a substantially solid substrate;
• and
• (B) filling with a second optical medium the selected volumes of the material layer from which the first optical medium is removed, thereby forming a transmissive layer of the optical element with the transmissive layer supported by the substrate,
• wherein:
• (a) the first and second optical media are substantially transparent over an operational wavelength range including a design vacuum wavelength λ0 and are characterized by differing respective first and second wavelength-dependent bulk refractive indices n1(λ) and n2(λ), and the first optical medium comprises a substantially solid material;
• (b) the transmissive layer comprises the first and second optical media arranged as a contiguous multitude of discrete volumes, including a non-empty subset of volumes of the multitude having a largest transverse dimension less than about λ0, wherein each discrete volume comprises either the first optical medium or the second optical medium, but not both;
• (c) the optical element is structurally arranged so as to receive an optical signal, within the operational wavelength range, and to transmit or reflect at least a portion of the incident optical signal transformed substantially according to a specified effective phase transformation function φeff(x,y) that varies as a function of two-dimensional position coordinates x and y along the transmissive layer;
• (d) the discrete volumes of the multitude are variously sized and distributed in the transmissive layer so as to impart on the transmitted or reflected portion of the incident optical signal the effective phase transformation φeff(x,Y);
• (e) the multitude of discrete volumes includes (i) multiple discrete volumes of the first optical medium that each extend entirely through the transmissive layer, (ii) multiple discrete volumes of the second optical medium that each extend entirely through the transmissive layer, (iii) multiple discrete volumes of the first optical medium that each extend only partly through the transmissive layer, and (iv) multiple discrete volumes of the second optical medium that each extend only partly through the transmissive layer;
• (f) the contiguous multitude of discrete volumes is arranged so that:
• (i) any locally perpendicular straight-line path extending through the transmissive layer passes through only the first optical medium, through only the second optical medium, or through only one discrete volume of each of the first and second optical media;
• (ii) the discrete volumes of the multitude are distributed on the transmissive layer according to local thicknesses d1(x,y) and d2(x,y) through the first and second optical media, respectively, along the locally perpendicular straight-line path through a given position (x,y);
• and (iii) the transmissive layer includes areal regions for which d1(x,y)≠0 and d2(x,y)=0, areal regions for which d1(x,y)=0 and d2(x,y)≠0, and areal regions for which d1(x,y)≠0 and d2(x,y)≠0;
• and
• (g) one or both transverse dimensions of each areal region that corresponds to a discrete volume of the second optical medium that extends only partly through the transmissive layer and for which d1(x,y)≠0 and d2(x,y)≠0 are less than one or both transverse dimensions of each areal region that corresponds to a discrete volume of the second optical medium that extends entirely through the transmissive layer and thereby includes at least a portion thereof for which d1(x,y)=0 and d2(x,y)≠0.