US 11,815,671 B2
Flat optics for image differentiation
Jason G. Valentine, Nashville, TN (US); You Zhou, Nashville, TN (US); and Hanyu Zheng, Nashville, TN (US)
Assigned to Vanderbilt University, Nashville, TN (US)
Filed by Vanderbilt University, Nashville, TN (US)
Filed on Sep. 4, 2020, as Appl. No. 17/012,189.
Claims priority of provisional application 62/895,804, filed on Sep. 4, 2019.
Prior Publication US 2021/0063717 A1, Mar. 4, 2021
Int. Cl. G02B 21/12 (2006.01); G02B 1/00 (2006.01); H04N 23/56 (2023.01); H04N 23/54 (2023.01); G02B 3/00 (2006.01)
CPC G02B 21/12 (2013.01) [G02B 1/002 (2013.01); G02B 1/005 (2013.01); H04N 23/56 (2023.01); G02B 3/0056 (2013.01); H04N 23/54 (2023.01)] 18 Claims
OG exemplary drawing
 
1. A flat photonic differentiator, comprising:
a substrate;
a photonic crystal comprising a two-dimensional array of resonators positioned on the substrate, wherein each of the resonators has a first refractive index, a width, a height, and is centered in a unit cell of the substrate with a length; and
a cladding layer with a second refractive index positioned on the substrate, wherein the resonators are embedded within the cladding layer, wherein the width, the height, the length, the first refractive index, and the second refractive index are configured to realize an optical transfer function in transmitted light through the photonic differentiator to produce a spatially differentiated image, wherein the width, height, length, first refractive index, and second refractive index are related by

OG Complex Work Unit Math
where D is the width, a is the length, h is the height, λ0 is a free space wavelength of a working wavelength of the differentiator, navg is an average of the first refractive index and the second refractive index, and i, j, and k are dimensional constants for the width, length, and height, respectively.