Waveguide having a phase-matching region
A waveguide is provided including first and second diffraction gratings and a phase-matching region conterminous with the first and second diffraction gratings and disposed in an optical path between the gratings. For an optical beam propagating along the optical path, the first grating adds a first phase shift to the optical beam reflecting from the first grating, the second grating adds a second phase shift to the optical beam reflecting from the second grating, and the phase-matching region adds a matching phase shift to the optical beam reflecting from the phase-matching region. The matching phase shift is between minimum and maximum values of the first and second phase shifts.
1. A waveguide comprising:
a slab of transparent material having first and second opposed sides;
first and second diffraction gratings supported by the slab at the first side thereof;
a third diffraction grating supported by the slab at the second side thereof and disposed opposite the second diffraction grating; and
a first phase-matching region conterminous with the first and second diffraction gratings and disposed in an optical path extending between the first and third diffraction gratings and including the second diffraction grating, wherein, for an optical beam propagating along the optical path:
the first diffraction grating adds a first phase shift ϕ 1 to the optical beam reflecting therefrom;
the second diffraction grating adds a second phase shift ϕ 2 to the optical beam reflecting therefrom; and
the first phase-matching region adds a first matching phase shift ϕ M1 to the optical beam reflecting therefrom, such that
min(ϕ 1 ,ϕ 2 )≤ϕ M1 ≤max(ϕ 1 ,ϕ 2 ).
2. The waveguide of claim 1 , wherein the first phase-matching region is distinct from the first and second diffraction gratings.
3. The waveguide of claim 2 , wherein the first phase-matching region comprises a dielectric coating.
4. The waveguide of claim 2 , wherein the first phase-matching region comprises a polymer layer.
5. The waveguide of claim 2 , wherein the first phase-matching region comprises a metamaterial.
6. The waveguide of claim 2 , wherein the first phase-matching region comprises a subwavelength grating.
7. The waveguide of claim 2 , wherein |ϕ 1 −ϕ 2 |≤0.6π.
8. The waveguide of claim 2 , wherein the first matching phase shift ϕ M1 monotonically varies from ϕ 1 to ϕ 2 in going from the first diffraction grating to the second diffraction grating.
9. The waveguide of claim 8 , wherein the first phase-matching region comprises a subwavelength grating with monotonically varying grating period in going from the first diffraction grating to the second diffraction grating.
10. The waveguide of claim 1 , wherein the first phase-matching region comprises one of the first and second diffraction gratings, whereby the first and second diffraction gratings are conterminous.
11. The waveguide of claim 1 , wherein the slab comprises the optical path and supports the first phase-matching region at the first side of the slab.
12. The waveguide of claim 1 , wherein the first phase-matching region comprises an area of a reduced thickness of the slab.
13. The waveguide of claim 1 , wherein the slab comprises a dielectric coating supporting the first and second diffraction gratings, wherein the first phase-matching region is void of the dielectric coating.
14. The waveguide of claim 1 , further comprising a second phase-matching region conterminous with the third diffraction grating and disposed in the optical path, wherein, for the optical beam propagating along the optical path:
the third diffraction grating adds a third phase shift ϕ 3 to the optical beam reflecting therefrom; and
the second phase-matching region adds a second matching phase shift ϕ M2 to the optical beam reflecting therefrom, such that
|ϕ 3 −ϕ M2 |<|ϕ 3 −ϕ TIR |,
wherein ϕ TIR is a phase shift added to the optical beam upon total internal reflection (TIR) of the optical beam from inside the slab.
15. An optical module comprising the waveguide of claim 1 and an image projector optically coupled thereto for providing the optical beam, wherein the optical beam comprises a first color channel.
16. The optical module of claim 15 , wherein the image light comprises a plurality of color channels including the first color channel, wherein the condition min(ϕ 1 , ϕ 2 )≤ϕ M ≤max(ϕ 1 , ϕ 2 ) is fulfilled for each one of the plurality of color channels.
17. The optical module of claim 15 , wherein the first phase-matching region is distinct from the first and second diffraction gratings.
18. The waveguide of claim 17 , wherein the first phase-matching region comprises a dielectric coating.
19. The optical module of claim 15 , wherein |ϕ 1 −ϕ 2 |≤0.6π.
20. The optical module of claim 15 , wherein the slab comprises the optical path and supports the first phase-matching region at the first side of the slab.
21. The optical module of claim 15 , wherein the first phase-matching region comprises an area of a reduced thickness of the slab.
22. The optical module of claim 15 , wherein the slab comprises a dielectric coating supporting the first and second diffraction gratings, wherein the first phase-matching region is void of the dielectric coating.
23. The optical module of claim 15 , wherein the waveguide further comprises a second phase-matching region conterminous with the third diffraction grating and disposed in the optical path, wherein, for the optical beam propagating along the optical path:
the third diffraction grating adds a third phase shift ϕ 3 to the optical beam reflecting therefrom; and
the second phase-matching region adds a second matching phase shift ϕ M2 to the optical beam reflecting therefrom, such that
|ϕ 3 −ϕ M2 |<|ϕ 3 −ϕ TIR |,
wherein ϕ TIR is a phase shift added to the optical beam upon total internal reflection (TIR) of the optical beam from inside the slab.
24. A method for improving a modulation transfer function of a waveguide comprising a slab of transparent material having first and second opposed sides and supporting first and second diffraction gratings at the first side and a third diffraction grating at the second side opposite the second diffraction grating, the method comprising:
providing a first phase-matching region between the first and second diffraction gratings, wherein, for an optical beam propagating along an optical path extending between the first and third diffraction gratings and including the second diffraction grating:
the first diffraction grating adds a first phase shift ϕ 1 to the optical beam reflecting therefrom;
the second diffraction grating adds a second phase shift ϕ 2 to the optical beam reflecting therefrom; and
the first phase-matching region adds a first matching phase shift ϕ M1 to the optical beam reflecting therefrom, such that
min(ϕ 1 ,ϕ 2 )≤ϕ M1 ≤max(ϕ 1 ,ϕ 2 ).
25. The method of claim 24 , further comprising:
providing a second phase-matching region conterminous with the third diffraction grating and disposed in the optical path, wherein, for the optical beam propagating along the optical path:
the third diffraction grating adds a third phase shift ϕ 3 to the optical beam reflecting therefrom; and
the second phase-matching region adds a second matching phase shift ϕ M2 to the optical beam reflecting therefrom, such that
|ϕ 3 −ϕ M2 |<|ϕ 3 −ϕ TIR |,
wherein ϕ TIR is a phase shift added to the optical beam upon total internal reflection (TIR) of the optical beam from inside the slab.
26. The method of claim 24 , wherein |ϕ 1 −ϕ 2 |≤0.6π.