Color and multi-spectral image sensor based on 3D engineered material
Methods and devices to build and use multi-functional scattering structures. The disclosed methods and devices account for multiple target functions and can be implemented using fabrication methods based on two-photon polymerization or multi-layer lithography. Exemplary devices functioning as wave splitters are also described. Results confirming the performance and benefits of the disclosed teachings are also described.
1. A method of splitting an electromagnetic wave into a plurality of waves with different wavelengths, the method comprising:
applying the electromagnetic wave to a three-dimensional (3D) scattering structure at a first side thereof, the 3D scattering structure being formed into a set 3D pattern;
scattering off the electromagnetic wave to generate a plurality of electromagnetic waves with different wavelengths, the plurality of electromagnetic waves exiting the 3D scattering structure at output second side thereof; and
forming the 3D pattern using an optimization method employing a Gradient-based algorithm; wherein
a target function of the Gradient-based algorithm is defined based on an electromagnetic intensity of the electromagnetic wave at target locations in a focal plane arranged outside the 3D structure;
a sensitivity of the target function with respect to a refraction index at a point within the 3D structure is calculated based on a sigmoidal projection filter, the filter having a parameter to control a strength of the sigmoidal projection filter,
wherein the sensitivity of the target function is calculated by:
obtaining a uniform refraction index distribution based on an average of a maximum refraction index and a minimum refraction index;
applying the sigmoidal filter to the uniform refraction index distribution, to obtain a filtered refraction index;
adding the minimum refraction index to the filtered refraction index to obtain the refraction index at the point within the 3D structure, and
increasing the strength of the sigmoidal projection filter from one iteration of the Gradient-based algorithm to another.
2. The method of claim 1 , further comprising collecting each wave of the plurality of electromagnetic waves at a corresponding target area outside the 3D scattering structure.
3. The method of claim 2 , wherein each target area corresponds to a sub-pixel of an image sensor.
4. The method of claim 1 , further comprising, before the applying, building the 3D scattering structure by stacking up layers.
5. The method of claim 4 , further comprising forming each layer by:
growing a dielectric layer above a substrate;
transferring a 2D pattern onto the dielectric layer; and
etching away an unprotected material.
6. The method of claim 1 , further comprising, before the applying, building the 3D scattering structure by:
focusing a laser on a liquid polymer, thereby causing the liquid polymer to cross-link and harden at a laser focus; and
moving the laser focus in accordance with an objective function of the Gradient-based algorithm.
7. The method of claim 1 , wherein:
the sensitivity of the target function with respect to a refraction index at a point within the 3D structure is further calculated based on:
a first set of electric fields corresponding to a first simulated electromagnetic waves applied to the first side; and
a second set of electric fields corresponding to a second simulated electromagnetic waves applied to the second side.
8. The method of claim 7 , wherein the second simulated electromagnetic waves are generated via a point source at the focal plane.
9. The method of claim 1 , further comprising enforcing a minimum feature size for the optimizing the 3D pattern with the Gradient-based algorithm.
10. The method of claim 9 , wherein the enforcing the minimum feature size is based on a dilated density.