Second harmonic generation in resonant optical structures

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.