Methods and apparatus for power-equalized optical frequency comb generation
An optical device for generating a frequency comb includes an optical source and a first waveguide comprising a nonlinear optical medium operable to mix at least two input optical waves to generate a plurality of first optical waves. The optical device also includes a second waveguide concatenated to the first waveguide and characterized by a first dispersion characteristics and operable to compress the waveforms of the plurality of first optical waves and to reduce a frequency chirp introduced by the first waveguide. The optical device additionally includes a third waveguide concatenated to the second waveguide. The third waveguide comprises a nonlinear optical medium and is operable to mix the plurality of first optical waves to generate a plurality of second optical waves and to increase a total number of second optical waves with respect to a total number of first optical waves.
1. An optical device for generating a frequency comb comprising:
an optical source including at least two input optical waves characterized by a first input frequency and a second input frequency, respectively, wherein the first input frequency and the second input frequency are separated by a frequency spacing;
a first waveguide comprising a nonlinear optical medium characterized by a nonlinear optical response and operable to mix the at least two input optical waves to generate a plurality of first optical waves characterized by respective first frequencies separated from each other by the frequency spacing and characterized by a frequency chirp;
a second waveguide concatenated to the first waveguide, wherein the second waveguide is characterized by a first dispersion characteristics such that the second waveguide is operable to compress the waveforms of the plurality of first optical waves and to reduce the frequency chirp introduced by the first waveguide; and
a third waveguide concatenated to the second waveguide, wherein the third waveguide comprises a nonlinear optical medium and is operable to mix the plurality of first optical waves to generate a plurality of second optical waves characterized by respective second frequencies separated from each other by the frequency spacing, and wherein the third waveguide is characterized by a second dispersion characteristics such that the third waveguide is operable to increase a total number of second optical waves with respect to a total number of first optical waves.
2. The optical device of claim 1 wherein the first waveguide is characterized by a third order susceptibility that is greater than about 2 (W·km) −1 .
3. The optical device of claim 1 wherein the second waveguide is characterized by a positive chromatic dispersion parameter D such that the second waveguide is operable to reduces a self-phase modulation introduced by the first waveguide.
4. The optical device of claim 1 wherein the third waveguide is characterized by a dispersion slope that is not greater than about 0.05 ps/km-nm 2 within a spectral bandwidth of the plurality of second optical waves.
5. The optical device of claim 1 wherein the third waveguide is characterized by a dispersion parameter having a peak value that is non-positive within the spectral span of the frequency comb.
6. The optical device of claim 1 wherein the third waveguide is characterized by a unit-length chromatic dispersion parameter that is not greater than about +1 ps/km-nm within a spectral span of the frequency comb.
7. The optical device of claim 1 wherein each of the first waveguide and the third waveguide is characterized by a unit-length dispersion that is not greater than about 2 ps/km-nm within a spectral bandwidth of the plurality of first optical waves and a spectral bandwidth of the plurality of second optical waves, respectively.
8. The optical device of claim 1 wherein each of the first waveguide and the third waveguide comprises optical media with third-order nonlinear susceptibility greater than 3×10 −23 m 2 /V 2 .
9. The optical device of claim 1 further comprising:
a fourth waveguide concatenated to the third waveguide, wherein the fourth waveguide is characterized by a third dispersion characteristics such that the fourth waveguide is operable to reduce the frequency chirp in the plurality of second optical waves introduced by the third waveguide; and
a fifth waveguide concatenated to the fourth waveguide, wherein the fifth waveguide comprises a nonlinear optical medium and is operable to mix the plurality of second optical waves to generate a plurality of third optical waves characterized by respective third frequencies separated from each other by the frequency spacing, and wherein the fifth waveguide is characterized a fourth dispersion characteristics that increases a total number of third optical waves in comparison with the total number of second optical waves.
10. A method of generating a frequency comb comprising:
providing at least two input optical waves characterized by respective input frequencies separated from each other by a frequency spacing;
mixing, via a first waveguide, the at least two input optical waves to provide a plurality of first optical waves characterized by respective first frequencies separated from each other by the frequency spacing, wherein the first waveguide comprises a nonlinear optical medium having a nonlinear response that introduces a frequency chirp in the plurality of first optical waves;
compressing, via a second waveguide concatenated to the first waveguide, the plurality of first optical waves to provide a plurality of first compressed optical waves, wherein the second waveguide is characterized by a first dispersion characteristics such that the second waveguide reduces the frequency chirp introduced by the first waveguide; and
mixing, via a third waveguide concatenated to the second waveguide, the plurality of first compressed optical waves to provide a plurality of second optical waves characterized by respective second frequencies separated from each other by the frequency spacing, wherein the third waveguide is characterized by a second dispersion characteristics that increases a total number of second optical waves in comparison to a total number of first optical waves.
11. The method of claim 10 further comprising:
compressing, via a fourth waveguide concatenated to the third waveguide, the plurality of second optical waves to provide a plurality of second compressed optical waves, wherein the fourth waveguide is characterized by a third dispersion characteristics such that the fourth waveguide reduces the frequency chirp introduced by the third waveguide; and
mixing, via a fifth waveguide concatenated to the fourth waveguide, the plurality of second compressed optical waves to provide a plurality of third optical waves characterized by respective third frequencies separated from each other by the frequency spacing, wherein the fifth waveguide is characterized by a fourth dispersion characteristics that maximizes a total number of third optical waves.
12. The method of claim 11 further comprising repeating compressing and mixing one or more times.
13. The method of claim 10 further comprising applying a post-fabrication treatment to form the third waveguide and achieve the second dispersion characteristics.
14. The method of claim 13 wherein the post-fabrication treatment comprises applying a longitudinal tension to the third waveguide.
15. The method of claim 13 wherein the post-fabrication treatment comprises irradiating the third waveguide with ultraviolet radiation.
16. The method of claim 15 wherein irradiating the third waveguide with ultraviolet radiation changes a refractive index of the third waveguide.
17. The method of claim 13 wherein the post-fabrication treatment comprises a chemical process that changes a refractive index of the third waveguide.
18. The method of claim 10 further comprising applying a post-fabrication treatment to the second waveguide to achieve the first dispersion characteristics.