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.
Of course, the timing phase should never be confused with the optical phase, but that may happen if “phase noise” is mentioned without making clear what kind of phase is meant. Both types of phases occur e.g. in the context of mode-locked lasers.
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