Frequency comb

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An ultrashort pulse of light in the time domain. In this figure, the amplitude and intensity are Gaussian functions. Note how the author chooses to set the maximum of the function into the maximum of the envelope.

A Dirac comb is an infinite series of Dirac delta functions spaced at intervals of T.

A frequency comb allows a direct link from RF standards to the optical light sources in the near infrared regime. The optical frequency comb technique is used in laser-based spectroscopy, which uses interference effects to generate a series of femtosecond-length pulses. Lasers which use the frequency comb technique allow for readings from light of all visible wavelengths.

The optical frequency synthesizer technology is based on a femtosecond laser frequency comb. I does only work with few cycle pulses. It requires the stabilization of two important parameters: Repetition rate ωr and offset frequency ω0. From the exact knowledge of these two radio frequencies one can derive the optical frequency of any mode ωn=n ωr + ω0.

This technique has also been extended to the extreme ultraviolet range, which may allow for more precise clocks and X-ray frequencies.

Theodor W. Hänsch and John L. Hall share the Nobel Prize in Physics 2005 for contributions to the development of laser-based precision spectroscopy, including the optical frequency comb technique.

Applications for the frequency comb technique include frequency chain generation, optical atomic clocks, high precision spectroscopy, and GPS technology.

1 Mathematics
2 Measurement
3 Steering
4 Closing the control loop
5 Applications
6 See also
7 External links

[edit] Mathematics

The "offset frequency ω0" is the change of "Carrier Envelope Offset" with time (slipage per cavity cycle). This other name says a lot:

Then apply fourier transformation (especially the Convolution theorem) and check with the nice images found on google!

[edit] Measurement

Carrier Envelope Offset is mostly measured by the 'frequency - 2*frequency' - technique. For this the spectral bandwidth has to span one octave. Ti:Sapphire lasers have a gain bandwidth: 720..1050. The intra-cavity Kerr effect in broadens the pulse to the range of dispersion compensation of the chirped mirrors: 620..1100 (see external link). External of the cavity the pulse is focused into a nonlinear crystal to generate second harmonic radiation. Due to cascading the fundamental and the second harmonic are further broadened leading to spectral overlap. This region of the spectrum is filtered out and focused onto a 10 µm diameter PIN-Photo diode. This small photo-diode has a very low capacitance, therefore even the weak signal and low number of carriers generated produce a measurable voltage signal which is amplified (and buffered) by a Junction Field-Effect Transistor, sampled and converted by a syncronly pacing Digital-to-analog converter.

[edit] Steering

Large offset corrections are done mechanically by changing the dispersion of the cavity. At least 3 degrees of freedom are needed to steer: Carrier Envelope Offset, repetition rate, and Group Velocity Dispersion. Small corrections are done by dimming (regulating) the pump laser by means of an Acousto-optic modulator. This changes intensity in the laser cavity and therefore the phase shift due to the Kerr effect. It is claimed that in the range of pump power in which the laser is running stable the full range of 2 π phase shift is possible. A direct and really fast phase modulation by means of a pockels cell is usually made superfluous by a good mechanical and optical design of the laser.

[edit] Closing the control loop

The carrier is allowed to advance 180° in phase every repetition. These systems can only fix the offset to anything near 45° (for example: 45°, 225°, 45° or 135°, 315°, 135°, 315°). Systems, which allow any offset could use 120°, but often use 90°. The values of a complete cycle is stored in a FIFO. A weighted sum is used to modulate the syncron acousto-optic modulator and added to the desired value for the servos for the geometry. The weights are chosen to make the loop stable and moreover low noise.