Electro-optic devices having engineered electrodes

1. An optical device, comprising:

a waveguide including at least a portion of at least one optical material having an electro-optic effect, the at least one optical material including at least one of lithium niobate and lithium tantalate; and

an electrode including a channel region and a plurality of extensions protruding from the channel region, the plurality of extensions being closer to a portion of the waveguide than the channel region is, the electrode carrying an electrical signal;

wherein a microwave mode of the electrical signal carried in the channel region intersects the at least one optical material.

2. The optical device of claim 1 , wherein the plurality of extensions have a pitch along the channel region, the pitch being less than a microwave wavelength in the electrode divided by π.

3. The optical device of claim 2 , wherein the waveguide is configured to carry an optical signal, wherein the electrode is configured to carry the electrical signal, and wherein the at least one optical material has a microwave dielectric constant of at least 1.5 multiplied by an optical dielectric constant for the optical signal.

4. The optical device of claim 1 wherein the waveguide carries an optical signal, the electrode carries the electrical signal, and wherein the plurality of extensions are configured to reduce a velocity mismatch between the optical signal and the electrical signal.

5. The optical device of claim 1 , wherein the plurality of extensions have at least one distance from the waveguide such that total optical loss is less than 8 dB.

6. The optical device of claim 1 , wherein the waveguide and the electrode reside on a substrate, and wherein the plurality of extensions have a location, the location being selected from a first location and a second location, the first location being between the substrate and the channel region and the second location being such that the channel region is between the substrate and the plurality of extensions.

7. The optical device of claim 1 , wherein the waveguide and the electrode reside on a substrate structure, the substrate structure being selected from a first substrate having a low substrate microwave dielectric constant less than eleven, the first substrate in combination with an underlayer between the substrate and the waveguide, and a second substrate having a high microwave dielectric constant greater than eleven in combination with the underlayer, the underlayer having a low underlayer microwave dielectric constant of less than eleven.

8. The optical device of claim 1 , wherein the waveguide and the electrode reside on a substrate having a void therein, the void being aligned with the portion of the waveguide and the plurality of extensions.

9. The optical device of claim 1 , wherein the plurality of extensions have a length that is less than a microwave wavelength in the electrode divided by π, the length being a distance at least one of the plurality of extensions protrudes from the channel region toward the waveguide.

10. The optical device of claim 1 , wherein the waveguide includes a ridge portion a thin film portion.

11. The optical device of claim 1 , wherein each of the plurality of extensions includes a connecting portion coupled to the channel region and a retrograde portion, the connecting portion being between the retrograde portion and the channel region.

12. The optical device of claim 1 , wherein the electrode has a frequency dependent electrode loss for a frequency window in a frequency range from DC to not more than five hundred GHz, the frequency dependent electrode loss being less than 0.8 dB per square root of an electrical signal frequency per centimeter, the electrical signal frequency being measured in GHz, the frequency window being at least 10 GHz.

13. The optical device of claim 1 , wherein the electrode has an absorption electrode loss for a frequency window in an electrode signal frequency from DC to not more than five hundred GHz, the absorption electrode loss being less than 0.005 dB per GHz per centimeter, the frequency window being at least 10 GHz.

14. The optical device of claim 1 , wherein the electrode includes an electrode bending section, wherein the waveguide includes a waveguide bending section, and wherein the electrode bending section and the waveguide bending section are configured to provide a path difference between an optical signal for the waveguide and the electrical signal for the electrode.

15. The optical device of claim 1 , further comprising:

an additional electrode including an additional channel region and an additional plurality of extensions, the additional plurality of extensions residing closer to the portion of the waveguide than the additional channel region is.

16. A subassembly, comprising:

an optical modulator, the optical modulator including a waveguide and an electrode, the waveguide including at least a portion of at least one optical material having an electro-optic effect, the electrode including a channel region and plurality of extensions, the plurality of extensions residing between the channel region and the waveguide, the plurality of extensions being closer to a portion of the waveguide than the channel region is, the electrode carrying an electrical signal, wherein a microwave mode of the electrical signal carried in the channel region intersects the at least one optical material, the at least one optical material including at least one of lithium niobate and lithium tantalate; and

a driver coupled to the optical modulator and configured to electrically drive the electrode.

17. A method, comprising:

providing a waveguide including at least a portion of at least one optical material having an electro-optic effect, the at least one optical material including at least one of lithium niobate and lithium tantalate; and

providing an electrode including:

providing a channel region; and

providing a plurality of extensions protruding from the channel region, the plurality of extensions being closer to a portion of the waveguide than the channel region is, the electrode carrying an electrical signal;

wherein a microwave mode of the electrical signal carried in the channel region intersects the at least one optical material.

18. The method of claim 17 , wherein the providing the plurality of extensions further includes:

fabricating the plurality of extensions at a pitch along the channel region, the pitch being less than a microwave wavelength in the electrode divided by pi.

19. The method of claim 17 wherein the waveguide carries an optical signal, the electrode carries the electrical signal, and wherein the providing the plurality of extensions further includes:

configuring the plurality of extensions to reduce a velocity mismatch between the optical signal and the electrical signal.

20. The method of claim 17 , wherein the electrode has a frequency dependent electrode loss for a frequency window in a frequency range from DC to not more than five hundred GHz, the frequency dependent electrode loss being less than 0.8 dB per square root of an electrode signal frequency per centimeter, the electrode signal frequency being measured in GHz, the frequency window being at least 10 GHz.

21. The optical device of claim 1 , wherein the channel region is substantially coplanar with at least a portion of the waveguide.

22. The optical device of claim 1 , wherein the substrate structure is selected from a first substrate structure and a second substrate structure, the first substrate structure including an underlayer and a first substrate, the underlayer having the substrate microwave dielectric constant and a thickness of at least three micrometers, the second substrate structure including a second substrate selected from sapphire, quartz, and fused silica.