Partially etched phase-transforming optical element
An optical element includes a substrate, an intermediate layer, a topmost layer, and a contiguous multitude of recessed and non-recessed areal regions. The intermediate layer is formed over a top surface of the substrate and has a refractive index n I . The topmost layer is formed directly on the intermediate layer and has a refractive index n T where n T ≠n I . The intermediate and topmost layers are substantially transparent over an operational wavelength range that includes a design wavelength λ 0 . A subset of areal regions has a largest transverse dimension less than about λ 0 . Each non-recessed areal region includes corresponding portions of the intermediate and topmost layers. Each recessed areal region extends entirely through the topmost layer and at least partly through the intermediate layer. A fill medium fills the recessed areal regions. The areal regions are variously sized and distributed transversely across the optical element.
1. An optical element comprising:
a substrate;
an intermediate layer formed over a top surface of the substrate and having a refractive index n I ;
a topmost layer formed directly on the intermediate layer and having a refractive index n T where n T ≠n I ;
a contiguous multitude of recessed and non-recessed areal regions;
a planar reflector formed over the topmost layer so as to cover the multitude of non-recessed areal regions and enclose the multitude of recessed areal regions; and
a fill medium enclosed within each recessed areal region by the reflector, wherein:
the intermediate and topmost layers are substantially transparent over an operational wavelength range that includes a design wavelength λ 0 ;
the areal regions of the multitude are variously sized and distributed transversely across the optical element, the multitude of areal regions includes a non-empty subset of the areal regions having a largest transverse dimension less than about λ 0 , each non-recessed areal region of the multitude includes corresponding areal portions of the intermediate and topmost layers, each recessed areal region of the multitude extends entirely through the topmost layer and at least partly through the intermediate layer, and the multitude of recessed areal regions includes a first non-empty subset of the recessed areal regions that extend entirely through the intermediate layer; and includes a second non-empty subset of the recessed area regions that extend only partially through the intermediate layer; and
the fill medium is substantially transparent over the operational wavelength range and has a refractive index n F where n F ≠n I ≠n T .
2. The optical element of claim 1 , wherein:
the optical element is structurally arranged so as to receive on at least a portion of the contiguous multitude of areal regions an incident optical signal, within the operational wavelength range, and to transmit or reflect at least a portion of the incident optical signal as a phase-transformed optical signal that is transformed substantially according to a specified effective phase transformation function φ eff (x, y) that varies as a function of transverse two-dimensional position coordinates x and y across the optical element; and
the topmost layer has a substantially uniform thickness d T ;
the intermediate layer has a substantially uniform thickness d I ; and
the refractive indices n T , n I , and n F , the thicknesses d T and d I , and arrangement of the variously sized and distributed areal regions of the multitude result in the areal regions of the optical element are configured to collectively impart onto the phase-transformed optical signal the effective phase transformation φ eff (x, y).
3. The optical element of claim 1 , wherein:
the intermediate layer comprises silicon nitride and the topmost layer comprises silicon dioxide; or
the intermediate layer comprises polycrystalline silicon and the topmost layer comprises silicon nitride.
4. The optical element of claim 1 , wherein the topmost layer provides better impedance matching of the non-recessed areal regions to the fill medium compared to non-recessed areal regions made entirely of a material of the intermediate layer without a material of the topmost layer.
5. The optical element of claim 1 , wherein each recessed areal region of the multitude extends entirely through the topmost and intermediate layers.
6. The optical element of claim 5 , wherein:
the intermediate layer is formed directly on the top surface of the substrate; and
the substrate exhibits an etch rate smaller than an etch rate exhibited by the intermediate layer.
7. The optical element of claim 5 , further comprising a bottom layer formed over the top surface of the substrate, wherein:
the intermediate layer is formed directly on the bottom layer; and
the intermediate layer exhibits an etch rate smaller than an etch rate exhibited by the bottom layer.
8. The optical element of claim 5 , further comprising a bottom layer formed directly on the top surface of the substrate, wherein:
the intermediate layer is formed directly on the bottom layer;
each recessed areal region of the multitude further extends entirely through the bottom layer; and
the substrate exhibits an etch rate smaller than an etch rate exhibited by the intermediate layer and the bottom layer.
9. The optical element of claim 1 , wherein:
the substrate is substantially transparent over the operational wavelength range; and
the optical element is structurally arranged so as to receive on at least a portion of the contiguous multitude of areal regions an incident optical signal propagating through the substrate and to reflect the phase-transformed optical signal to propagate through the substrate.
10. The optical element of claim 1 , wherein:
the topmost layer has a substantially uniform thickness d T ;
the intermediate layer has a substantially uniform thickness d I ; and
N T , d T , n I , d I , n F , and the variously sized and distributed areal regions of the multitude result in one or more improved performance parameters of the optical element, relative to a reference optical element that is arranged so as to impart the effective phase transformation φ eff (x, y) with areal regions variously sized and distributed transversely across the reference optical element in the same transverse arrangement as the optical element and with non-recessed areal regions of the reference optical element that include only a single material.
11. The optical element of claim 10 , wherein the one or more improved performance parameters include at least one of:
reduced or minimized overall reflectivity;
increased or maximized overall optical throughput;
increased or maximized focusing efficiency when the optical element is arranged to function as a lens;
transmissivity;
polarization dependence;
linear or circular birefringence; or
angular dependence.