Layer having a non-linear taper and method of fabrication
A method for forming a non-linear thickness-profile in a first layer of a first material is disclosed. The method comprises forming an accelerator layer of a second material on the first layer and forming a mask layer disposed on the accelerator layer, wherein the mask layer enables the accelerator layer to expose the first layer to a first etchant in a first region, where the exposure time for each point along a first axis varies non-linearly as a function of distance from a first point on the first axis. Since the time for which the first layer is exposed to the first etch in the first region is non-linear, the thickness of the first layer in the first region changes non-linearly along the first axis.
1. A planar-lightwave circuit (PLC) including a first surface waveguide, the first surface waveguide comprising:
a first cladding layer comprising a first material characterized by a first refractive index;
a second cladding layer comprising a second material characterized by a second refractive index; and
a first layer comprising a third material characterized by a third refractive index that is greater than each of the first and second refractive indices, the first layer being between the first and second cladding layers, and the first layer having a first region, second region, and third region that is between the first region and second region, wherein the third region abuts the first region at a first point along a first axis, and wherein the third region abuts the second region at a second point along the first axis;
wherein the first layer has a first thickness in the first region, a second thickness in the second region, and a third thickness in the third region that changes between the first thickness at the first point and the second thickness at the second point according to a substantially sinusoidal function of position, z, along the first axis; and
wherein the first surface waveguide has a first mode-field profile in the first region, a second mode-field profile in the second region, and a third mode-field profile, MFD(h(z)), that changes between the first mode-field profile and second mode-field profile between the first point and the second point, MFD(h(z)) being characterized by a substantially sinusoidal function of position, z, along the first axis.
2. The PLC of claim 1 wherein the third thickness changes in substantially sinusoidal fashion along the first axis between the first point and the second point.
3. The PLC of claim 1 wherein the first surface waveguide has a first width in the first region, a second width in the second region, and a third width in the third region that changes monotonically along the first axis from the first point to the second point.
4. The PLC of claim 1 wherein the third thickness along the first axis between the first point and second point is characterized by one half period of a sinusoidal function.
5. The PLC of claim 1 wherein the first layer is characterized by a taper-angle at each point along the first axis between the first point and second point, and wherein the taper angle increases at a constant rate along the first axis from the first point to the second point.
6. The PLC of claim 3 wherein the third width changes non-linearly along the first axis from the first point to the second point.
7. A planar-lightwave circuit (PLC) that includes a first surface waveguide, the first surface waveguide comprising a core, wherein first surface waveguide comprises:
a first region in which the core has a first thickness, wherein, in the first region, the first surface waveguide is characterized by a first refractive-index contrast that is based on the first thickness;
a second region in which the core has a second thickness, wherein, in the second region, the first surface waveguide is characterized by a second refractive-index contrast that is based on the second thickness; and
a third region that is between the first region and the second region and abuts the first region at a first point along a first axis and abuts the second region at a second point along the first axis, wherein the surface waveguide has a third refractive-index contrast that is based on a third thickness of the core, wherein the third refractive-index contrast changes between the first refractive-index contrast and the second refractive-index contrast according to a substantially sinusoidal function of position between the first point and the second point.
8. The PLC of claim 7 wherein the first surface waveguide includes a core layer comprising a first material, the core layer having the first thickness in the first region, the second thickness in the second region, and a third thickness in the third region that changes continuously and non-linearly between the first thickness at the first point and the second thickness at the second point according to a sinusoidal function of position, z, along the first axis.
9. The PLC of claim 8 wherein the third thickness is characterized by one half period of a sinusoidal function.
10. The PLC of claim 8 wherein the first layer is characterized by a taper-angle at each point along a first axis between the first point and second point, and wherein the taper angle changes according to a substantially sinusoidal function of position along the first axis from the first point to the second point.
11. A planar-lightwave circuit (PLC) including a first surface waveguide, the first surface waveguide comprising:
a first cladding layer comprising a first material characterized by a first refractive index;
a second cladding layer comprising a second material characterized by a second refractive index; and
a first layer comprising a third material characterized by a third refractive index that is greater than each of the first and second refractive indices, the first layer being between the first and second cladding layers, and the first layer having a first region, second region, and third region that is between the first region and second region, wherein the third region abuts the first region at a first point along a first axis, and wherein the third region abuts the second region at a second point along the first axis;
wherein the first layer has a first thickness in the first region, a second thickness in the second region, and a third thickness in the third region that changes between the first thickness and the second thickness along the first axis between the first point and the second point according to a substantially sinusoidal function of position along the first axis.
12. The PLC of claim 11 wherein the first surface waveguide has a first mode-field profile in the first region, a second mode-field profile in the second region, and a third mode-field profile, MFD(h(z)), that changes continuously and non-linearly between the first mode-field profile and second mode-field profile between the first point and the second point, MFD(h(z)) being characterized by a substantially sinusoidal function of position, z, along the first axis.
13. The PLC of claim 12 wherein the third thickness is characterized by one half period of a sinusoidal function.
14. The PLC of claim 11 wherein the first layer is characterized by a taper-angle at each point along a first axis between the first point and second point, and wherein the taper angle increases at a constant rate along the first axis from the first point to the second point.
15. The PLC of claim 11 wherein the first surface waveguide has a third refractive-index contrast that changes between the first refractive-index contrast and the second refractive-index contrast according to a substantially sinusoidal function of position between the first point and the second point.