Second harmonic generation in resonant optical structures

1. An optical apparatus for generating an output wave that has a converted frequency of twice or one-half the frequency of a pump wave, comprising:

a microresonator comprising a nonlinear optical medium having a thickness δ and having at least a first resonant mode and a second resonant mode; and

an optical coupler for injecting the pump wave into the microresonator from a pump source, thereby to excite one of said first and second modes;

wherein:

the first mode has substantially radial polarization and the second mode has substantially vertical polarization;

the first and second modes have the same radial order which is an integer at least 1;

the pump wave and each of said first and second modes has a respective frequency and a respective in-material wavelength for propagation within the nonlinear optical medium;

the second-mode frequency is substantially twice the first-mode frequency; and

the thickness δ is less than one-half the in-material wavelength of the pump wave for propagation within the nonlinear optical medium.

2. The optical apparatus of claim 1 , further comprising a tuning circuit coupled to the microresonator and configured to tune the microresonator over an operating range, wherein the second-mode frequency is twice the first-mode frequency at least at one tuning state within the operating range.

3. The optical apparatus of claim 2 , further comprising a sensing element optically coupled to an output path from the microresonator and configured to provide an output signal indicative of an optical power level.

4. The optical apparatus of claim 3 , wherein the tuning circuit is configured to tune the frequencies of the first and second modes in response to the output signal from the sensing element.

5. The optical apparatus of claim 4 , wherein the tuning circuit comprises an electric heater in thermal contact with the microresonator for thermo-optical tuning and a voltage bias electrode in electrical communication with the microresonator for electro-optical tuning.

6. The optical apparatus of claim 1 , wherein the thickness δ is less than 200 nm.

7. The optical apparatus of claim 1 , further comprising at least one selective optical element positioned in an output path from the microresonator and configured to separate light having the frequency of the first mode from light having the frequency of the second mode.

8. The optical apparatus of claim 7 , wherein the at least one selective optical element comprises a polarization-selective optical element configured to separate TE-polarized light from TM-polarized light.

9. The optical apparatus of claim 7 , wherein the at least one selective optical element comprises a wavelength-selective optical element configured to separate light at the first mode frequency from light at the second mode frequency.

10. The optical apparatus of claim 1 , wherein the nonlinear optical medium consists essentially of lithium niobate.

11. The optical apparatus of claim 1 , wherein the microresonator is a microring, microdisk, or spherical resonator.

12. The optical apparatus of claim 1 , wherein the microresonator is a microdisk resonator.

13. The optical apparatus of claim 1 , wherein the microresonator is periodically poled.

14. The optical apparatus of claim 1 , wherein light from the pump source excites the first mode, thereby to generate second-harmonic light in the second mode.

15. The optical apparatus of claim 1 , wherein light from the pump source excites the second mode, thereby to generate down-converted light in the first mode.

16. The optical apparatus of claim 1 , wherein the thickness δ is less than 1/3.5 times the in-material wavelength of the pump wave for propagation within the nonlinear optical medium.

17. A method of optical conversion from a pump wave to an output wave that has a converted frequency of twice or one-half the frequency of a pump wave, comprising:

injecting the pump wave into a microresonator that comprises a nonlinear optical medium having a thickness δ, wherein the injecting is performed so as to excite a first resonant mode of the microresonator at a first-mode resonant frequency; and

tuning the microresonator so as to create a tuning state in which a second resonant mode of the resonator has a frequency that is twice or one-half the frequency of the first resonant mode;

wherein:

one of said first and second modes has substantially radial polarization and the other has substantially vertical polarization;

the first and second modes both have the same radial order which is an integer at least 1;

the pump wave and each of said first and second modes has a respective in-material wavelength for propagation within the nonlinear optical medium; and

the thickness δ is less than one-half the in-material wavelength of the pump wave for propagation within the nonlinear optical medium.

18. The method of claim 17 , further comprising energizing periodic poling electrodes positioned on the microresonator.

19. The method of claim 17 , further comprising:

sensing at least one optical power level on an output path from the microresonator, thereby to provide a feedback signal; and

tuning the microresonator in response to the feedback signal.

20. The method of claim 19 , wherein the tuning comprises jointly operating an electro-optical tuning circuit and a thermo-optical tuning circuit.

21. The method of claim 17 , wherein light from the pump source excites a first resonant mode of the microresonator having one-half the frequency of the second resonant mode of the resonator, thereby to generate second-harmonic light in the second mode.

22. The method of claim 17 , wherein light from the pump source excites a first resonant mode of the microresonator having twice the frequency of the second resonant mode of the resonator, thereby to generate down-converted light in the second mode.