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Simply integrate the optical power (according to your pulse shape) over time, which must result in the pulse energy. That leads to a condition for that factor.

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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.

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2.2.2.1 Parabolic Trough (PT). The Sun's rays are directed toward the heat receivers located at the central line of parabolic mirrors. The receiver surfaces are ...

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Who Invented the Lens Used at the Pigeon Point Lighthouse?Augustine Jean Fresnel (pronounced fray-nell) Fresnel (born May 10, 1788, died July 14, 1827), a French physicist, was commissioned by France in 1822 to develop a better lighting system for the French lighthouses. Rather than try to develop a brighter light source, Fresnel set about designing a better, more efficient method of using the light which 1820's technology could produce. 19th Century lighthouses used silvered-metal parabolic reflectors, placed behind a lamp, to direct the light seaward. This system was not very efficient, and worked poorly as an aid to navigation. Remember that light produced by a lamp, or any source, radiates out in all directions. Fresnel's task was to find the most efficient method to direct all, or nearly all, of the lamp's light rays out to sea. To improve upon the parabolic reflector, Fresnel looked to glass lenses for a method of directing more of the light from a lamp seaward. Molding a single lens to do the job was impractical. A lens suitable for a lighthouse would be far too large to be cast as a single lens. Instead Fresnel designed a system of smaller lens and prisms, arranged in a stair-step configuration. He used this system to bend, fold, and focus the light out to sea. The result was a lens that was able to use about 80 percent of the light available from the lamp! In the case of the lens used at Pigeon Point, about 70,000 candlepower was produced by the original lamp. This type of lens, called a Fresnel  lens, was a technological breakthrough! The new lens was far more efficient in its use of the small amount of light produced by a ?page_id=22000">lard oil lamp. In addition, a Fresnel lens could be disassembled and shipped in sections and configured into virtually limitless numbers of light characteristics, that is, patterns of flashes of light divided by periods of darkness.

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.

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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

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

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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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Who Invented the Lens Used at the Pigeon Point Lighthouse?Augustine Jean Fresnel (pronounced fray-nell) Fresnel (born May 10, 1788, died July 14, 1827), a French physicist, was commissioned by France in 1822 to develop a better lighting system for the French lighthouses. Rather than try to develop a brighter light source, Fresnel set about designing a better, more efficient method of using the light which 1820's technology could produce. 19th Century lighthouses used silvered-metal parabolic reflectors, placed behind a lamp, to direct the light seaward. This system was not very efficient, and worked poorly as an aid to navigation. Remember that light produced by a lamp, or any source, radiates out in all directions. Fresnel's task was to find the most efficient method to direct all, or nearly all, of the lamp's light rays out to sea. To improve upon the parabolic reflector, Fresnel looked to glass lenses for a method of directing more of the light from a lamp seaward. Molding a single lens to do the job was impractical. A lens suitable for a lighthouse would be far too large to be cast as a single lens. Instead Fresnel designed a system of smaller lens and prisms, arranged in a stair-step configuration. He used this system to bend, fold, and focus the light out to sea. The result was a lens that was able to use about 80 percent of the light available from the lamp! In the case of the lens used at Pigeon Point, about 70,000 candlepower was produced by the original lamp. This type of lens, called a Fresnel  lens, was a technological breakthrough! The new lens was far more efficient in its use of the small amount of light produced by a ?page_id=22000">lard oil lamp. In addition, a Fresnel lens could be disassembled and shipped in sections and configured into virtually limitless numbers of light characteristics, that is, patterns of flashes of light divided by periods of darkness.