Optical device with athermal slots for temperature dependence curvature reduction
In one aspect of the invention, roughly stated, Applicants have discovered that a compensation material within slot elongated in a direction parallel to a segment of waveguide in an arrayed waveguide grating apparatus can compensate for both first and second order change in refractive index of the base waveguide material over temperature. Unlike the transverse slots of conventional linear athermalization techniques, the elongated slot generally parallel to the base material defines a composite waveguide section having a second order effective index of refraction temperature dependency which can be utilized to accurately minimize the temperature dependence of the overall optical path length to both the first and second order. The techniques described herein are also generalizeable to neutralization of the optical path length temperature dependence to any order.
1. An arrayed waveguide apparatus comprising a plurality of waveguides from an input free-space region to an output free-space region, each waveguide in the plurality comprising:
a core material;
a cladding material; and
a compensation material within a slot elongated in a direction parallel to the core material, the slot being parallel to a segment of the core material, the compensation material having an effective index of refraction temperature dependency which differs from that of the core and cladding materials.
2. The apparatus of claim 1 , wherein:
each waveguide in the plurality has a respective optical path length between an input boundary of the input free-space region and an output boundary of the output free-space region which differs from that of an adjacent waveguide in the plurality by a respective effective optical path length difference; and
at least the first and second order derivatives with respect to temperature for each of the optical path length differences are substantially equal to zero throughout a temperature range of −5 degrees Celsius to +70 degrees Celsius.
3. The apparatus of claim 2 , wherein:
at least the first and second order derivatives with respect to temperature for each of the optical path length differences are substantially equal to zero throughout a temperature range of −30 degrees Celsius to +70 degrees Celsius.
4. The apparatus of claim 1 , wherein for each waveguide in the plurality:
the core material has a physical path length between an input boundary of the input free-space region and an output boundary of the output free-space region which differs from that of the core material of an adjacent waveguide in the plurality by a first path length difference; and
the compensation material has an operative path length in the direction parallel to the core material and which differs from that of the compensation material of an adjacent waveguide in the plurality by a second path length difference.
5. The apparatus of claim 4 , wherein each waveguide in the plurality includes:
a first slot on a first side of the segment of the core material and containing the compensation material; and
a second slot on a second side of the segment of the core material and containing the compensation material.
6. The apparatus of claim 4 , wherein a ratio of the first path length difference to the second path length difference is substantially the same for each waveguide in the plurality.
7. The apparatus of claim 1 , wherein the slot for each waveguide in the plurality is discontiguous from the slots of each of the other waveguides.
8. The apparatus of claim 1 , wherein each waveguide in the plurality further includes a second compensation material in a second slot elongated in a direction parallel to a second segment of the core material, the second compensation material having an effective index of refraction temperature dependency which differs from that of the core, cladding and compensation materials.
9. The apparatus of claim 1 , further comprising a second compensation material within at least one of the input free-space region and the output free-space region, the second compensation material having an effective index of refraction temperature dependency which differs from that of the core and cladding materials.
10. The apparatus of claim 9 , wherein the compensation material and the second compensation material are the same.
11. A method for manufacturing an arrayed waveguide apparatus comprising forming a plurality of waveguides from an input free-space region to an output free-space region, forming each waveguide in the plurality comprising:
forming a core material;
forming a cladding material; and
forming a compensation material within a slot elongated in a direction parallel to the core material, the slot being parallel to a segment of the core material, the compensation material having an effective index of refraction temperature dependency which differs from that of the core and cladding materials.
12. The method of claim 11 , wherein:
each waveguide in the plurality has a respective optical path length between an input boundary of the input free-space region and an output boundary of the output free-space region which differs from that of an adjacent waveguide in the plurality by a respective effective optical path length difference; and
at least the first and second order derivatives with respect to temperature for each of the optical path length differences are substantially equal to zero throughout a temperature range of −5 degrees Celsius to +70 degrees Celsius.
13. The method of claim 12 , wherein:
at least the first and second order derivatives with respect to temperature for each of the optical path length differences are substantially equal to zero throughout a temperature range of −30 degrees Celsius to +70 degrees Celsius.
14. The method of claim 11 , wherein for each waveguide in the plurality:
the core material has a physical path length between an input boundary of the input free-space region and an output boundary of the output free-space region which differs from that of the core material of an adjacent waveguide in the plurality by a first path length difference; and
the compensation material has an operative path length in the direction parallel to the core material and which differs from that of the compensation material of an adjacent waveguide in the plurality by a second path length difference.
15. The method of claim 14 , wherein forming each waveguide in the plurality includes:
forming a first slot on a first side of the segment of the core material and containing the compensation material; and
forming a second slot on a second side of the segment of the core material and containing the compensation material.
16. The method of claim 14 , wherein a ratio of the first path length difference to the second path length difference is substantially the same for each waveguide in the plurality.
17. The method of claim 11 , wherein the slot for each waveguide in the plurality is discontiguous from the slots of each of the other waveguides.
18. The method of claim 11 , wherein forming each waveguide in the plurality further includes forming a second compensation material in a second slot elongated in a direction parallel to a second segment of the core material, the second compensation material having an effective index of refraction temperature dependency which differs from that of the core, cladding and compensation materials.
19. The method of claim 11 , further comprising forming a second compensation material within at least one of the input free-space region and the output free-space region, the second compensation material having an effective index of refraction temperature dependency which differs from that of the core and cladding materials.
20. The method of claim 19 , wherein the compensation material and the second compensation material are the same.
21. An arrayed waveguide apparatus comprising a plurality of waveguides from an input free-space region to an output free-space region,
each waveguide in the plurality comprising:
core and cladding materials which confine optical energy in at least one dimension orthogonal to a direction of propagation of the optical energy; and
a composite waveguide section which maintains confinement of the optical energy in the at least the one dimension;
wherein each waveguide in the plurality has a respective optical path length between an input boundary of the input free-space region and an output boundary of the output free-space region which differs from that of an adjacent waveguide in the plurality by a respective effective optical path length difference; and
at least the first and second order derivatives with respect to temperature for each of the optical path length differences are substantially equal to zero throughout a temperature range of −5 degrees Celsius to +70 degrees Celsius.
22. The apparatus of claim 21 , wherein:
at least the first and second order derivatives with respect to temperature for each of the optical path length differences, are substantially equal to zero throughout a temperature range of −30 degrees Celsius to +70 degrees Celsius.
23. The apparatus of claim 21 , wherein the composite waveguide section comprises a compensation material proximate the core material, the compensation material having an effective index of refraction temperature dependency which differs from that of the core and cladding materials.
24. The apparatus of claim 23 , wherein the compensation material for each waveguide in the plurality is discontiguous from the slots of each of the other waveguides.
25. The apparatus of claim 23 , wherein each waveguide in the plurality further includes a second composite waveguide section, the second composite waveguide section comprising a second compensation material proximate the core material, the second compensation material having an effective index of refraction temperature dependency which differs from that of the core, cladding and compensation materials.
26. The apparatus of claim 25 , wherein for each waveguide in the plurality:
the core material has a physical path length between the input boundary of the input free-space region and the output boundary of the output free-space region which differs from that of the core material of an adjacent waveguide in the plurality by a first path length difference; and
the compensation material has an operative path length in a direction parallel to the core material and which differs from that of the compensation material of an adjacent waveguide in the plurality by a second path length difference.
27. The apparatus of claim 26 , wherein a ratio of the first path length difference to the second path length difference is substantially the same for each waveguide in the plurality.
28. The apparatus of claim 23 , further comprising a second compensation material within at least one of the input free-space region and the output free-space region, the second compensation material having an effective index of refraction temperature dependency which differs from that of the core and cladding materials.
29. The apparatus of claim 28 , wherein the compensation material and the second compensation material are the same.
30. The apparatus of claim 21 , wherein each waveguide in the plurality includes:
a first slot on a first side of the core material within the composite waveguide section and containing a compensation material, the compensation material having an effective index of refraction temperature dependency which differs from that of the core and cladding materials; and
a second slot on a second side of the core material within the composite waveguide section and containing the compensation material.