Optical Frequency Comb
Optical frequency comb: tooth frequencies ν_n = n f_rep + f_ceo, the carrier-envelope phase slip per pulse, teeth in the spectrum, and the electric field of consecutive pulses.
Tooth nearest the centre
193.414520000 THz
n = 773658; ν_n = n f_rep + f_ceo, f_ceo = 20.0000 MHz
CE phase slip per pulse
0.5027 rad
Δφ_CE = 2π f_ceo/f_rep = 0.1600π; f_rep/f_ceo = 12.5000
Teeth in the spectral FWHM
8.825e4
transform-limited Gaussian, Δν = 0.4413/τ = 22.06 THz
Optical cycles in the FWHM
3.87
period 5.170 fs, pulse spacing 4.000 ns
A mode-locked pulse train is a comb of teeth ν_n = n f_rep + f_ceo. When the carrier slips by Δφ_CE against the envelope from one pulse to the next, the whole comb shifts by f_ceo = (Δφ_CE/2π) f_rep from the harmonics of f_rep. An f-to-2f interferometer measures it as 2ν_n − ν_2n; locking f_ceo, or setting it to zero, stabilizes the carrier-envelope phase. Offsets outside [0, f_rep) are wrapped into it. The spectral width assumes a transform-limited Gaussian pulse.
Comb teeth around n = 773658
- Comb teeth n f_rep + f_ceo
- Grid n f_rep (f_ceo = 0)
Electric field of three consecutive pulses
- Pulse 1 (φ = φ₀ + 0Δφ)
- Pulse 2 (φ = φ₀ + 1Δφ)
- Pulse 3 (φ = φ₀ + 2Δφ)
Model and references
Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers
Comb equation ν_n = n f_rep + f_ceo with Δφ_CE = 2π f_ceo/f_rep, f_ceo taken in [0, f_rep). The tooth count assumes a transform-limited Gaussian pulse. Linewidths and comb stabilization loops are not modelled.
- Telle H. R. et al. (1999). Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation. Appl. Phys. B 69, 327–332. doi:10.1007/s003400050813
- Jones D. J. et al. (2000). Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis. Science 288, 635–639. doi:10.1126/science.288.5466.635
- Udem Th., Holzwarth R., Hänsch T. W. (2002). Optical frequency metrology. Nature 416, 233–237. doi:10.1038/416233a