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The coherence time, usually designated τ, is calculated by dividing the coherence length by the phase velocity of light in a medium; approximately given by = where λ is the central wavelength of the source, Δν and Δλ is the spectral width of the source in units of frequency and wavelength respectively, and c is the speed of light in vacuum.
There are two closely related measures. The pulse repetition interval measures the time between the leading edges of two pulses but is normally expressed as the pulse repetition frequency (PRF), the number of pulses in a given time, typically a second. The duty cycle expresses the pulse width as a fraction or percentage of one complete cycle.
A mode-locked laser is capable of emitting extremely short pulses on the order of tens of picoseconds down to less than 10 femtoseconds.These pulses will repeat at the round trip time, that is, the time that it takes light to complete one round trip between the mirrors comprising the resonator.
CEP in the frequency domain: The frequency spectrum of the above pulse train is a frequency comb which shows an offset if it is continued until a frequency of zero. This offset is the carrier-envelope frequency f C E O {\displaystyle f_{\mathrm {CEO} }} , and f r e p = 1 / T r e p {\displaystyle f_{\mathrm {rep} }=1/T_{\mathrm {rep} }} is the ...
These two lower-frequency beams are called the "signal" and "idler", respectively. This light emission is based on the nonlinear optical principle. The photon of an incident laser pulse (pump) is, by a nonlinear optical crystal, divided into two lower-energy photons. The wavelengths of the signal and the idler are determined by the phase ...
FROG is simply a spectrally resolved autocorrelation, which allows the use of a phase-retrieval algorithm to retrieve the precise pulse intensity and phase vs. time. It can measure both very simple and very complex ultrashort laser pulses, and it has measured the most complex pulse ever measured without the use of a reference pulse.
Such a laser is said to be "mode-locked" or "phase-locked". These pulses occur separated in time by τ = 2L/c, where τ is the time taken for the light to make exactly one round trip of the laser cavity. This time corresponds to a frequency exactly equal to the mode spacing of the laser, Δν = 1/τ.
Beyond the obvious consideration of a sufficiently short pulse width, the dependence of the frequency bandwidth must be accounted for. The equation Change in wavelength distribution as pulse widths broaden. ΔνΔt ≥ K [3] demonstrates that, for any beam shape (K), the beam bandwidth (Δν) is inversely proportional to its pulse width.