1. And their applications
Frequency combs
And their applications

2. Program What is a frequency comb? What do we need them for?
The Kerr-effect
Modelocking
Dispersion management
What do we need them for?
Precision measurements
Nonlinear optics
What applications place which demands?
How can we meet these demands?

3. A simple laser
Note that this assumption is wrong!

4. Multimode operation

5. Multimode operation

6. Single mode operation

7. A modelocked laser We want to lase on as many modes as possible
Instead of etalons, we place an aperture
Mode profile is cut, making the cavity leaky
How does this help?

8. The Kerr effect
In the AC Kerr effect, the refractive index depends on intensity
Where does this nonlinearity come from?
In the Lorentz model: oscillation charges are harmonic
Of course, the potential electrons feel is not actually harmonic

9. The Kerr effect Typically: In short, we can write
In a Kerr medium, because of symmetry, so
So indeed
Typically:

10. The Kerr effect
Optical thickness:
The flat plate becomes a lens

11. A modelocked laser Kerr lens modelocking
The cavity works again if the intensity is high enough
CW this would be impossible
With short pulses, the peak intensity is high enough
Kerr lens modelocking

12. Limits spectral width = 1/(pulse duration)
repetition rate = modespacing (see exercises)
group velocity depends on wavelength
red and blue parts of the pulse will dephase
how can we compensate?

13. Solution prisms hard to align bulky hard to find the right glass!
chirped mirror
engineer the dispersion
hard to make, easy to use

14. Applications: a frequency ruler
Direct beat frequency < a few GHz
Beating both with modelocked laser
Figure out and with wavemeter
and are always

15. Atomic hydrogen 1s2s 2s to 1s decay is dipole forbidden
Excite with 2-photon transition inside a cavity
Applying an electric field that slightly mixes 2s and 2p
The hydrogen atom emits a Lyman-α photon if it was excited
The smaller the electric field, the smaller the signal, but how higher the accuracy

16. Atomic hydrogen 1s2s

17. Frequency measurement
We can measure a frequency difference with a high accuracy
However, as we cannot measure absolute frequencies
How can we figure out the offset and where does it come from?
Dispersion: group velocity and phase velocity are different

18. High harmonic generation
Adapted from: Nature Physics 2, (2006)

19. F-2F Absolute optical frequency measurement
and carrier envelope phase stabilization