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 Incoming links: Defining and Measuring Optical Frequencies: The Optical Clock Opportunity – and More by John L. Hall

Carrier-envelope offset frequency 2026-10-18

The carrier-envelope offset frequency expresses the carrier's pulse-to-pulse phase slip relative to its envelope. Fixing the repetition frequency leaves this slip undetermined.^[ref] With the positive-exponential convention derived above,

f_{0} = f_{r} Δ ϕ / (2 π)

f_{r}

. Changing

f_{0}

translates every tooth equally; differentiating

f_{n} = n f_{r} + f_{0}

at fixed

n

gives

δ f_{n} = n δ f_{r} + δ f_{0} .

Thus at

n = 2 \times 1 0^{6}

, a chosen

1 Hz

change in spacing moves that tooth by

2 MHz

if

f_{0}

stays fixed. The large multiplier is why a stable-looking pulse train is insufficient for accurate optical metrology.

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