Engineering chromatic response using cascaded metasurfaces
To overcome the problem of a diffractive surface having a large, and often excessively large, amount of chromatic aberration, an optical system can use multiple cascaded or sequential diffractive surfaces that, combined, have a reduced amount of chromatic aberration. The optical system can be designed such that all rays traversing the optical system and passing through the diffractive surfaces have an equal optical path length. In the design process, the sets of rays are identified, and the designs of the diffractive surfaces are selected to produce the angular deviations to produce the identified ray paths. In one example, an achromatic lens formed as two annular optical surfaces can receive a collimated incident beam, redirect rays helically at the first surface toward the second surface, and redirect the rays at the second surface toward a focal point. The azimuthal redirection can decrease with increasing distance away from a central axis.
1. An achromatic bilayer metasurface beam deflector, comprising:
at least one body that is substantially transparent at a wavelength,
the at least one body having a first optical surface,
the first optical surface including a first pattern formed from first sub-wavelength elements that are sized smaller than the wavelength,
the at least one body having a second optical surface opposite and substantially parallel to the first optical surface,
the second optical surface including a second pattern formed from second sub-wavelength elements that are sized smaller than the wavelength,
the first optical surface and the second optical surface including respective phase distributions that are configured to deflect rays along paths of equal optical group length (OGL), and
the OGL for a path between a first point on the first optical surface and a second point on the second optical surface being defined as a product of a group refractive index of the body and a distance between the first point and the second point, added to a distance between the second point and an image point.
2. The optical element of claim 1 , wherein the first pattern and the second pattern are configured such that the at least one body is configured to function as an achromatic beam deflector.
3. The optical element of claim 1 , wherein the first pattern and the second pattern are configured such that the at least one body is configured to function as an achromatic doublet metalens.
4. The optical element of claim 1 , wherein the first pattern and the second pattern are configured such that the at least one body is configured to function as a triplet chromatic corrector.
5. The optical element of claim 1 , wherein the first pattern and the second pattern are configured such that the at least one body is configured to function as a triplet metalens.
6. The optical element of claim 1 , wherein the first pattern and the second pattern are configured such that the at least one body is configured to function as a triplet corrector, the triplet corrector being a Type I corrector or a Type II corrector.
7. The optical element of claim 1 , wherein the first pattern and the second pattern are configured such that the at least one body is configured to function as a metalens triplet based on a corrector, the corrector being a Type I corrector or a Type II corrector.
8. The optical element of claim 1 , wherein the first pattern and the second pattern are configured such that the at least one body is configured to function as a super-dispersive beam deflector.
9. The optical element of claim 1 , wherein the first pattern and the second pattern are configured such that the at least one body is configured to function as a beam deflector having positive dispersion.
10. The optical element of claim 1 , wherein the first pattern and the second pattern are configured such that the at least one body is configured to function as an afocal triplet.
11. The optical element of claim 1 , further comprising a triplet lens, wherein the first pattern and the second pattern are configured such that the at least one body is configured to function as an afocal triplet that increases a dispersion of the triplet lens or changes a sign of a dispersion of the triplet lens.
12. An achromatic lens, comprising:
a first optical surface including a first pattern formed from sub-wavelength elements, the first pattern extending over a first annular area that surrounds a first central location, the first pattern configured to receive an incident beam, the incident beam including light rays that are all parallel to one another, the first optical surface further configured to angularly divert each light ray in the incident beam by a first angular diversion to form a helical internal beam, the first angular diversion varying from ray-to-ray for at least two light rays in the incident beam; and
a second optical surface oriented parallel to the first optical surface, the second optical surface including a second pattern formed from sub-wavelength elements, the second pattern extending over a second annular area that surrounds a second central location, the first and second central locations defining a central axis, the second pattern configured to receive the helical internal beam and angularly divert each light ray in the helical internal beam by a second angular diversion to form an exiting beam, the second angular diversion varying from ray-to-ray for at least two light rays in the helical internal beam such that the all the light rays in the exiting beam are angled to intersect the central axis at a focal point of the achromatic lens.
13. The achromatic lens of claim 12 , wherein the first and second optical surfaces are planar.
14. The achromatic lens of claim 13 , wherein the light rays in the incident beam are orthogonal to the first optical surface.
15. The achromatic lens of claim 14 , wherein:
a first ray is configured to strike the first pattern at a first location that is separated from the central axis by a first distance; and
the first pattern is configured to angularly divert the first ray to strike the second pattern at a second location that is separated from the central axis by the first distance.
16. The achromatic lens of claim 15 , wherein the first and second locations are separated by a first azimuthal angle.
17. The achromatic lens of claim 16 , wherein:
a second ray is configured to strike the first pattern at a third location that is separated from the central axis by a second distance that is different from the first distance; and
the first pattern is configured to angularly divert the second ray to strike the second pattern at a fourth location that is separated from the central axis by the second distance.
18. The achromatic lens of claim 17 , wherein the third and fourth locations are separated by a second azimuthal angle that is different from the first azimuthal angle.
19. The achromatic lens of claim 18 , wherein:
the second distance is less than the first distance; and
the second azimuthal angle is greater than the first azimuthal angle.
20. The achromatic lens of claim 12 , wherein the incident surface and the exiting surfaces are formed as opposing faces of a transparent optical body.