Timing Phase
Author: the photonics expert Dr. Rüdiger Paschotta (RP)
Definition: a phase reflecting timing deviations by relating them to the pulse period
Categories: 
Related: timing jitterpulse trainsphase noise
Units: rad
Page views in 12 months: 103
DOI: 10.61835/35e Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn
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What is a Timing Phase?
In the literature, the timing jitter of a mode-locked laser is often specified as the power spectral density not of the timing deviation ($\Delta t$), but rather of the timing phase, which is defined as follows:
(${\varphi _{\textrm{t}}} = 2\pi \;\frac{{\Delta t}}{T} = 2\pi \;{f_{{\textrm{rep}}}}\;\Delta t$)where ($\Delta t$) is the timing error, ($T$) is the pulse period and ($f_\textrm{rep}$) 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 2($\pi$).
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.
Frequently Asked Questions
This FAQ section was generated with AI based on the article content and has been reviewed by the article’s author (RP).
What is the timing phase of a pulse train?
The timing phase describes the timing error ($\Delta t$) of optical pulses relative to the pulse period ($T$). It is defined by the equation (${\varphi _{\textrm{t}}} = 2\pi \;{\Delta t} / T$), where a timing deviation of one full pulse period corresponds to a phase change of ($2\pi$).
How is timing phase noise specified?
Timing phase noise is typically quantified by its power spectral density, which has units of rad²/Hz. This value is often converted to a logarithmic scale and specified in units of dBc/Hz.
What is the difference between timing phase and optical phase?
The timing phase is related to the timing of optical pulses within a pulse train, whereas the optical phase refers to the phase of the underlying optical carrier wave. This distinction is crucial when discussing 'phase noise' in the context of mode-locked lasers.