In the literature, the timing jitter of a mode-locked laser is often specified as the power spectral density not of the timing deviation Δt, but rather of the timing phase, which is defined as follows:
where Δt is the timing error, T is the pulse period and frep the pulse repetition rate.
This definition is inspired by considering the emitted pulse train as a (usually highly anharmonic) oscillation of the optical power, which in the noiseless case can be seen as consisting of a sinusoidal signal and integer harmonics thereof, i.e. as a Fourier series. One pulse period corresponds to a change in the timing phase by 2π.
The power spectral density corresponding to the timing phase has units of rad2 Hz−1. It is also common to specify 10 times its logarithm to base 10 in units of dBc/Hz.
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