= Optical frequency comb
{title2=$f_n=n f_r+f_0$}
An <optical frequency comb> has evenly spaced optical <spectral lines>, or teeth. A <mode-locked laser> supplies short <optical pulses> at repetition <frequency> $f_r$, the tooth spacing. The <carrier-envelope offset frequency> $f_0$ positions the whole ruler:
$$
f_n=n f_r+f_0,\qquad n\in\mathbb Z,\qquad 0\leq f_0<f_r.
$$
Only teeth within the emitted <optical spectrum> are present; the extrapolated intercept need not be an emitted tooth.<Passion for Precision by Theodor W. Hänsch>[Passion for Precision, p.157: tooth relation]{ref}
The achievement associated with <John L. Hall> and <Theodor W. Hänsch> is a practical bridge between optical <frequencies> and countable electronic <frequencies>. Instead of constructing a separate chain of <lasers> for each optical measurement, a broad comb supplies many linked reference teeth. Stable <lasers>, short <optical pulses> and strong <nonlinear optics> in <optical fibers> came together around 1999–2000.<Nobel Lecture: Defining and measuring optical frequencies by John L. Hall>[Nobel Lecture: Defining and measuring optical frequencies, pp.1288–1291: chains and comb development]{ref}
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