= Pulse train
A \b[pulse train] is a sequence of <pulses>. An ideal periodic <pulse train> repeats the same waveform at a fixed period $T$, with <pulse repetition frequency> $f_{\rm rep}=1/T$. A finite burst, varying pulse heights or <pulse timing jitter> can break exact periodicity without removing the useful description as a <pulse train>. The repetition interval describes spacing; it is distinct from one pulse's duration.
If $p(t)$ is one localized waveform, an ideal infinite <pulse train> is
$$
x(t)=\sum_{n\in\mathbb Z}p(t-nT).
$$
Equivalently, it is the <convolution> of $p$ with a <Dirac comb>. Its <Fourier series> coefficients are samples of the single pulse's <Fourier transform>:
$$
c_k=\frac1T\int_{-\infty}^{\infty}p(t)e^{-2\pi i kt/T}\,dt.
$$
Thus the repetition period sets harmonic spacing $1/T$, while the pulse shape sets the coefficient envelope. This statement concerns the repeated waveform itself; an optical electric field additionally has carrier phase information that a measured optical-power trace does not contain.
For optical power pulses with negligible continuous background, the <average power of a laser pulse train> obeys $\overline P=E_pf_{\rm rep}$ when every complete pulse has <laser pulse energy> $E_p$. For a nonoverlapping <rectangular pulse> of duration $\tau$, $E_p=P_{\rm pk}\tau$ and the <duty cycle> is $D=\tau/T$, so $\overline P=DP_{\rm pk}$. For other shapes, a width such as the <full width at half maximum> needs a <pulse energy shape factor> before it determines <peak power>.<Average and Peak Power - A Tutorial by Newport>[Photonics Technical Note1, one-page rectangular-pulse diagram and average-power/duty-cycle equations]{ref}
An original rectangular example has $T=100\,\mathrm{ns}$, $\tau=2\,\mathrm{ns}$ and $E_p=10\,\mathrm{nJ}$. The <pulse repetition frequency> is $10\,\mathrm{MHz}$, the <duty cycle> is $0.02$, the <peak power> is $5\,\mathrm W$ and the <average power> is $0.10\,\mathrm W$. A slow power meter can report that average while failing to resolve either the $2\,\mathrm{ns}$ width or individual <pulse-to-pulse energy fluctuation>.
A fast <photodetector> and <oscilloscope> instead display successive electrical responses. Their bandwidth and impulse response limit the optical timing information available. Counting the spacing tests the <pulse repetition frequency>; integrating calibrated individual responses tests <laser pulse energy>. <Pulse energy measurement with a photodiode> explains the charge-integration step. Separating those measurements avoids inferring the pulse width from an average-power reading alone.
Back to article page
