Multi-layer coating structure to minimize phase shifts, method of manufacture, waveguide and head mount display
An apparatus includes a waveguide and one or more partially reflective surfaces embedded inside the waveguide, wherein each of the one or more partially reflective surfaces includes a multi-layer coating structure, wherein a first portion of the multi-layer coating structure induces an overall phase shift of light propagating through the first portion of the multi-layer coating structure and wherein a second portion of the multi-layer coating structure is selected to decrease the overall phase shift.
1. An apparatus comprising:
a waveguide; and
a plurality of partially reflective co-parallel surfaces embedded inside the waveguide at an angle relative to side-wall surfaces of the waveguide and configured to couple light out of the waveguide towards a predetermined eye motion box,
wherein each of the partially reflective co-parallel surfaces comprises a multi-layer coating structure,
wherein a first portion of the multi-layer coating structure induces an overall phase shift of light propagating through the first portion of the multi-layer coating structure, and
wherein a second portion of the multi-layer coating structure is selected to decrease the overall phase shift.
2. The apparatus according to claim 1 ,
wherein the first portion of the multi-layer coating structure is selected to meet one or more optical characteristics other than coating induced phase shift.
3. The apparatus according to claim 2 ,
wherein the one or more optical characteristics comprises one or more of reflection and transmission, chromaticity and polarization.
4. The apparatus according to claim 1 ,
wherein one or more of a refractive index of a material of the second portion of the multi-layer coating structure and a thickness of the second portion of the multi-layer coating structure are selected to reduce the overall phase shift of the light propagating through the first portion of the multi-layer coating structure.
5. The apparatus according to claim 4 ,
wherein the one or more of the refractive index of the material of the second portion of the multi-layer coating structure and the thickness of the second portion of the multi-layer coating structure are selected based on the overall phase shift of the light propagating through the first portion of the multi-layer coating structure and a central wavelength of a relevant spectrum of the light propagating through the first portion of the multi-layer coating structure.
6. The apparatus according to claim 5 ,
wherein the one or more of the refractive index of the material of the second portion of the multi-layer coating structure and the thickness of the second portion of the multi-layer coating structure are selected such that:
d
~
λ
0
φ
0
2
π
0
n
2
(
λ
0
)
cos
(
θ
2
)
-
n
1
(
λ
0
)
cos
(
θ
1
)
+
n
1
(
λ
0
)
sin
(
θ
1
)
[
tan
(
θ
1
)
-
tan
(
θ
2
)
]
,
where:
n 1 is a refractive index of the material of the first portion of the multi-layer coating structure,
n2 is the refractive index of the material of the second portion of the multi-layer coating structure,
φ 0 is the overall phase shift induced by the first portion of the multi-layer coating structure, which needs to be decreased,
λ 0 is the central wavelength or dominant wavelength in the relevant spectrum,
θ 1 is an incident angle of the central field when impinging the each of the one or more partially reflective surfaces, and
θ
2
=
sin
-
1
[
n
2
(
λ
0
)
sin
(
θ
1
)
n
1
(
λ
0
)
]
.
7. The apparatus according to claim 1 ,
wherein the first portion of the multi-layer coating structure is arranged in an ambient material of the waveguide, and
wherein the second portion of the multi-layer coating structure is arranged on top of the first portion of the multi-layer coating structure.
8. The apparatus according to claim 1 ,
wherein a phase difference between rays that propagate through the multi-layer coating structure and rays that propagate in a medium and do not propagate through the multi-layer coating structure is limited to a predetermined threshold value, or the phase difference between ascending and descending rays propagating through the multilayer coating structure is limited to a predetermined threshold value.
9. A method of manufacturing a waveguide, the method comprising:
providing a plurality of partially reflective co-parallel surfaces embedded inside the waveguide at an angle relative to side-wall surfaces of the waveguide and configured to couple light out of the waveguide towards a predetermined eye motion box,
wherein each of the partially reflective co-parallel surfaces is provided by forming a multi-layer coating structure,
wherein a first portion of the multi-layer coating structure is provided to induce an overall phase shift of light propagating through the first portion of the multi-layer coating structure, and
wherein a second portion of the multi-layer coating structure is selected to decrease the overall phase shift.
10. The method according to claim 9 ,
wherein the first portion of the multi-layer coating structure is selected to meet one or more optical characteristics other than coating induced phase shift.
11. The method according to claim 10 ,
wherein the one or more optical characteristics comprises one or more of reflection and transmission, chromaticity and polarization.
12. The method according to claim 9 ,
wherein one or more of a refractive index of a material of the second portion of the multi-layer coating structure and a thickness of the second portion of the multi-layer coating structure are selected based on the overall phase shift of the light propagating through the first portion of the multi-layer coating structure.
13. The method according to claim 12 ,
wherein the one or more of the refractive index of the material of the second portion of the multi-layer coating structure and the thickness of the second portion of the multi-layer coating structure are selected based on the overall phase shift of the light propagating through the first portion of the multi-layer coating structure and a central wavelength or dominant wavelength of a relevant spectrum of the light propagating through the first portion of the multi-layer coating structure.
14. The method according claim 13 ,
wherein the one or more of the refractive index of the material of the second portion of the multi-layer coating structure and the thickness of the second portion of the multi-layer coating structure are selected such that:
d
~
λ
0
φ
0
2
π
n
2
(
λ
0
)
cos
(
θ
2
)
-
n
1
(
λ
0
)
cos
(
θ
1
)
+
n
1
(
λ
0
)
sin
(
θ
1
)
[
tan
(
θ
1
)
-
tan
(
θ
2
)
]
,
where:
n 1 is a refractive index of the material of the first portion of the multi-layer coating structure,
n2 is the refractive index of the material of the second portion of the multi-layer coating structure,
φ 0 is the overall phase shift induced by the first portion of the multi-layer coating structure, which needs to be decreased,
λ 0 is the central wavelength in the relevant spectrum,
θ 1 is an incident angle of the central field when impinging the each of the one or more partially reflective surfaces, and
θ
2
=
sin
-
1
[
n
2
(
λ
0
)
sin
(
θ
1
)
n
1
(
λ
0
)
]
.
15. The method according to claim 9 ,
wherein forming the multi-layer coating structure of the each of the one or more partially reflective surfaces comprises:
arranging the first portion of the multi-layer coating structure in an ambient material of the waveguide; and
arranging the second portion of the multi-layer coating structure on top of the first portion of the multi-layer coating structure.
16. A non-transitory computer-readable storage medium storing instructions for designing a plurality of partially reflective co-parallel surfaces embedded inside a waveguide at an angle relative to side-wall surfaces of the waveguide and configured to couple light out of the waveguide towards a predetermined eye motion box, the instructions causing one or more processors to at least perform:
designing a multi-layer coating structure for each of the partially reflective co-parallel surfaces,
wherein a first portion of the multi-layer coating structure is provided to induce an overall phase shift of light propagating through the first portion of the multi-layer coating structure, and
wherein a second portion of the multi-layer coating structure is selected to decrease the overall phase shift.
17. The non-transitory computer-readable storage medium according to claim 16 ,
wherein designing the multi-layer coating structure comprises selecting the first portion of the multi-layer coating structure to meet one or more optical characteristics other than coating induced phase shift.
18. The non-transitory computer-readable storage medium according to claim 17 ,
wherein the one or more optical characteristics comprises one or more of reflection and transmission, chromaticity and polarization.
19. The non-transitory computer-readable storage medium according to claim 16 ,
wherein designing the multi-layer coating structure comprises selecting one or more of a refractive index of a material of the second portion of the multi-layer coating structure and a thickness of the second portion of the multi-layer coating structure based on the overall phase shift of the light propagating through the first portion of the multi-layer coating structure.
20. The non-transitory computer-readable storage medium according to claim 19 ,
wherein designing the multi-layer coating structure comprises selecting the one or more of the refractive index of the material of the second portion of the multi-layer coating structure and the thickness of the second portion of the multi-layer coating structure based on the overall phase shift of the light propagating through the first portion of the multi-layer coating structure and a central wavelength of a relevant spectrum of the light propagating through the first portion of the multi-layer coating structure.
21. The non-transitory computer-readable storage medium according to claim 16 ,
wherein designing the multi-layer coating structure comprises calculating the overall phase shift of light propagating through the first portion of the multi-layer coating structure.
22. An apparatus comprising:
a waveguide; and
a plurality of partially reflective co-parallel surfaces embedded inside the waveguide at an angle relative to side-wall surfaces of the waveguide and configured to couple light out of the waveguide towards a predetermined eye motion box,
wherein each of the partially reflective co-parallel surfaces comprises a multi-layer coating structure, and
wherein one or more layers of the multi-layer coating structure are selected to limit an overall phase shift of light propagating through one or more other layers of the multi-layer coating structure to below a predetermined threshold.
23. The apparatus according to claim 22 ,
wherein the one or more other layers of the multi-layer coating structure are selected to meet one or more optical characteristics other than coating induced phase shift.
24. The apparatus according to claim 23 ,
wherein the one or more optical characteristics comprises one or more of reflection and transmission, chromaticity and polarization.
25. The apparatus according to claim 22 ,
wherein one or more of a refractive index of a material of the one or more layers of the multi-layer coating structure and a thickness of the one or more layers of the multi-layer coating structure are selected based on the overall phase shift of the light propagating through the one or more other layers of the multi-layer coating structure in a relevant spectrum of the light propagating through the one or more layers of the multi-layer coating structure.
26. The apparatus according to claim 25 ,
wherein the one or more of the refractive index of the material of the one or more layers of the multi-layer coating structure and the thickness of the one or more layers of the multi-layer coating structure are selected based on the overall phase shift of the light propagating through the one or more other layers of the multi-layer coating structure and a central or dominant wavelength of a relevant spectrum or a weighted average of a relevant spectrum of the light propagating through the one or more other layers of the multi-layer coating structure.
27. The apparatus according to claim 26 ,
wherein the one or more of the refractive index of the material of the one or more layers of the multi-layer coating structure and the thickness of the one or more layers of the multi-layer coating structure are selected such that:
d
~
λ
0
φ
0
2
π
n
2
(
λ
0
)
cos
(
θ
2
)
-
n
1
(
λ
0
)
cos
(
θ
1
)
+
n
1
(
λ
0
)
sin
(
θ
1
)
[
tan
(
θ
1
)
-
tan
(
θ
2
)
]
,
where:
n 1 is a refractive index of the material of the one or more other layers of the multi-layer coating structure,
n2 is the refractive index of the material of the one or more layers of the multi-layer coating structure,
φ 0 is the overall phase shift induced by the one or more other layers of the multi-layer coating structure, which needs to be limited,
λ 0 is the central or dominant wavelength in the relevant spectrum,
θ 1 is an incident angle of the central field when impinging the each of the one or more partially reflective surfaces, and
θ
2
=
sin
-
1
[
n
2
(
λ
0
)
sin
(
θ
1
)
n
1
(
λ
0
)
]
.
28. The apparatus according to claim 22 ,
wherein the one or more layers of the multi-layer coating structure are arranged as a first portion of the multi-layer coating structure,
wherein the one or more other layers of the multi-layer coating structure are arranged as a second portion of the multi-layer coating structure,
wherein the second portion of the multi-layer coating structure is arranged in an ambient material of the waveguide, and
wherein the first portion of the multi-layer coating structure is arranged on top of the second portion of the multi-layer coating structure.
29. A non-transitory computer-readable storage medium storing instructions for designing a plurality of partially reflective co-parallel surfaces embedded inside a waveguide at an angle relative to side-wall surfaces of the waveguide and configured to couple light out of the waveguide towards a predetermined eye motion box, the instructions causing one or more processors to at least perform:
designing a multi-layer coating structure for each of the partially reflective co-parallel surfaces,
wherein each of the one or more partially reflective surfaces comprises a multi-layer coating structure, and
wherein one or more layers of the multi-layer coating structure are selected to limit an overall phase shift of light propagating through one or more other layers of the multi-layer coating structure to below a predetermined threshold.
30. The non-transitory computer-readable storage medium according to claim 29 ,
wherein designing the multi-layer coating structure comprises selecting the one or more other layers of the multi-layer coating structure to meet one or more optical characteristics other than coating induced phase shift.
31. The non-transitory computer-readable storage medium according to claim 30 ,
wherein the one or more optical characteristics comprises one or more of reflection and transmission, chromaticity and polarization.
32. The non-transitory computer-readable storage medium according to claim 29 ,
wherein designing the multi-layer coating structure comprises selecting one or more of a refractive index of a material of the one or more layers of the multi-layer coating structure and a thickness of the one or more layers of the multi-layer coating structure based on the overall phase shift of the light propagating through the one or more other layers of the multi-layer coating structure in a relevant spectrum of the light propagating through the one or more layers of the multi-layer coating structure.
33. The non-transitory computer-readable storage medium according to claim 32 ,
wherein designing the multi-layer coating structure comprises selecting the one or more of the refractive index of the material of the one or more layers of the multi-layer coating structure and the thickness of the one or more layers of the multi-layer coating structure based on the overall phase shift of the light propagating through the one or more other layers of the multi-layer coating structure and a central or dominant wavelength of a relevant spectrum or a weighted average of a relevant spectrum of the light propagating through the one or more other layers of the multi-layer coating structure.
34. The non-transitory computer-readable storage medium according to claim 33 ,
wherein designing the multi-layer coating structure comprises selecting the one or more of the refractive index of the material of the one or more layers of the multi-layer coating structure and the thickness of the one or more layers of the multi-layer coating structure such that:
d
~
λ
0
φ
0
2
π
n
2
(
λ
0
)
cos
(
θ
2
)
-
n
1
(
λ
0
)
cos
(
θ
1
)
+
n
1
(
λ
0
)
sin
(
θ
1
)
[
tan
(
θ
1
)
-
tan
(
θ
2
)
]
,
where:
n 1 is a refractive index of the material of the one or more other layers of the multi-layer coating structure,
n2 is the refractive index of the material of the one or more layers of the multi-layer coating structure,
φ 0 is the overall phase shift induced by the one or more other layers of the multi-layer coating structure, which needs to be limited,
λ 0 is the central or dominant wavelength in the relevant spectrum,
θ 1 is an incident angle of the central field when impinging the each of the one or more partially reflective surfaces, and
θ
2
=
sin
-
1
[
n
2
(
λ
0
)
sin
(
θ
1
)
n
1
(
λ
0
)
]
.
35. The non-transitory computer-readable storage medium according to claim 29 ,
wherein designing the multi-layer coating structure comprises:
arranging the one or more layers of the multi-layer coating structure as a first portion of the multi-layer coating structure;
arranging the one or more other layers of the multi-layer coating structure as a second portion of the multi-layer coating structure;
arranging the second portion of the multi-layer coating structure in an ambient material of the waveguide; and
arranging the first portion of the multi-layer coating structure on top of the second portion of the multi-layer coating structure.