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# Peak Power

Author: the photonics expert

Definition: maximum optical power of a pulse

More general term: optical power

Units: W

Formula symbol: <$P_\textrm{p}$>

The peak power of a light pulse is the maximum occurring optical power. Due to the short pulse durations which are possible with optical pulses, peak powers can become very high even for moderate pulse energies. For example, a pulse energy of 1 mJ in a 10-fs pulse, as can be generated with a mode-locked laser and a regenerative amplifier of moderate size, already leads to a peak power of the order of 100 GW, which is approximately the combined power of a hundred large nuclear power stations. Focusing such a pulse to a spot with e.g. 4 μm radius leads to enormous peak intensities of the order of 4 × 1021 W/m2 = 4 × 1017 W/cm2. Peak powers in the terawatt range can be generated with devices of still moderate size (fitting into a 20-m2 room). Large facilities based on multi-stage chirped-pulse amplifiers can even generate pulses with petawatt peak powers.

For handling the large numbers associated with high peak powers, the following prefixes are often used:

• 1 kW (kilowatt) = 103 W
• 1 MW (megawatt) = 106 W
• 1 GW (gigawatt) = 109 W
• 1 TW (terawatt) = 1012 W
• 1 PW (petawatt) = 1015 W

## Measurement of Peak Power

For relatively long pulses, the peak power can be measured directly e.g. with a photodiode which monitors the optical power versus time. For pulse durations below a few tens of picoseconds, this method is no longer viable. The peak power is then often calculated from the (full width at half-maximum, FWHM) pulse duration <$\tau_\textrm{p}$> (measured e.g. with an optical autocorrelator) and the pulse energy <$E_\textrm{p}$>. The conversion depends on the temporal shape of the pulse. For example, for soliton pulses (with a sech2 shape) the peak power is

$${P_{\rm{p}}} \approx 0.88\frac{{{E_{\rm{p}}}}}{{{\tau _{\rm{p}}}}}$$

For Gaussian-shaped pulses, the constant factor is ≈ 0.94 instead of 0.88. If pulses are subject to strong nonlinear pulse distortions or similar effects, a significant part of their pulse energy may be contained in their temporal wings, and the relation between peak power and pulse energy may be substantially modified.

Some authors even totally ignore such factors and present the simple ratio of pulse energy and pulse duration as the peak power.

## Ambiguities

Strictly, the peak power as defined above (the maximum occurring optical power) is ambiguous; it depends on the temporal resolution (or bandwidth) of the power measurement. For example, Q-switched lasers often exhibit mode beating, i.e., an oscillation of power related to the beating of electric-field oscillations in different resonator modes. A photodetector may be too slow to resolve these power oscillations, and one may intentionally ignore such fast oscillations for the definition of peak power.

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## Questions and Comments from Users

2021-05-26

How can one calculate the profile-dependent factor for an arbitrary pulse shape?