Achromatic optical device based on birefringent materials having positive and negative birefringence dispersions

1. An optical device, comprising:

a first layer including a first birefringent material having a negative birefringence dispersion property; and

a second layer including a second birefringent material having a positive birefringence dispersion property,

wherein the negative birefringence dispersion property indicates that a first birefringence of the first birefringent material increases as a wavelength of a light increases, and the positive birefringence dispersion property indicates that a second birefringence of the second birefringent material decreases as the wavelength of the light increases, and

wherein the first birefringence and the second birefringence have the same sign.

2. The optical device of claim 1 , wherein a sum of a first product between a first thickness and the first birefringence of the first layer and a second product between a second thickness and the second birefringence of the second layer, is substantially proportional to the wavelength of the light within a predetermined wavelength range.

3. The optical device of claim 1 , wherein at least one of the first layer or the second layer includes a liquid crystal polymer film.

4. The optical device of claim 3 , wherein the first birefringent material includes polymerized reactive mesogens (“RMs”) having the negative birefringence dispersion property, and the second birefringent material includes polymerized RMs having the positive birefringence dispersion property.

5. The optical device of claim 4 , wherein:

a structured pattern of the first layer includes the polymerized RMs having the negative birefringence dispersion property aligned in a first in-plane alignment pattern, and

a structured pattern of the second layer includes the polymerized RMs having the positive birefringence dispersion property aligned in a second in-plane alignment pattern.

6. The optical device of claim 1 , further comprising a substrate coupled to the first layer.

7. The optical device of claim 6 , further comprising an alignment structure disposed between the substrate and the first layer, and configured to define a structured pattern for at least one of the first layer or the second layer.

8. The optical device of claim 1 , wherein the optical device includes a passive or an active optical device.

9. An optical device, comprising:

a substrate; and

a birefringent medium layer coupled to the substrate and including a combination of a first birefringent material having a negative birefringence dispersion property and a second birefringent material having a positive birefringence dispersion property,

wherein the negative birefringence dispersion property indicates that a first birefringence of the first birefringent material increases as a wavelength of a light increases, and the positive birefringence dispersion property indicates that a second birefringence of the second birefringent material decreases as the wavelength of the light increases, and

wherein the first birefringence and the second birefringence have the same sign.

10. The optical device of claim 9 , wherein concentrations of the first birefringent material and the second birefringent material are configured to provide a total phase retardation of the birefringent medium layer that is substantially constant with respect to a predetermined wavelength range.

11. The optical device of claim 9 , wherein the birefringent medium layer includes a liquid crystal polymer film.

12. The optical device of claim 9 , wherein the first birefringent material includes polymerized reactive mesogens (“RMs”) having the negative birefringence dispersion property, and the second birefringent material includes polymerized RMs having the positive birefringence dispersion property.

13. The optical device of claim 12 , wherein a structured pattern of the birefringent medium layer includes the polymerized RMs having the negative birefringence dispersion property and the polymerized RMs having the positive birefringence dispersion property mixed and aligned in a predetermined in-plane alignment pattern.

14. The optical device of claim 9 , further comprising an alignment structure disposed between the substrate and the birefringent medium layer, and configured to at least partially define a structured pattern of the birefringent medium layer.

15. An optical film, comprising:

a birefringent medium layer including a mixture of a first liquid crystal material having a negative birefringence dispersion property and a second liquid crystal material having a positive birefringence dispersion property,

wherein the negative birefringence dispersion property indicates that a first birefringence of the first liquid crystal material increases as a wavelength of a light increases, and the positive birefringence dispersion property indicates that a second birefringence of the second liquid crystal material decreases as the wavelength of the light increases, and

wherein the first birefringence and the second birefringence have the same sign.

16. The optical film of claim 15 , wherein the birefringent medium layer includes a liquid crystal polymer film.

17. The optical film of claim 15 , wherein the first liquid crystal material includes polymerized reactive mesogens (“RMs”) having the negative birefringence dispersion property, and the second liquid crystal material includes polymerized RMs having the positive birefringence dispersion property.

18. The optical film of claim 17 , wherein a structured pattern of the birefringent medium layer includes the polymerized RMs having the negative birefringence dispersion property and the polymerized RMs having the positive birefringence dispersion property mixed and aligned in a predetermined in-plane alignment pattern.

19. The optical device of claim 1 , wherein the first birefringence and the second birefringence are positive birefringences.

20. The optical device of claim 9 , wherein the first birefringence and the second birefringence are positive birefringences.