pulseenergy

Pulse energy refers to the energy contained in a single pulse of a time-varying signal, most often discussed in optics and electronics. For a pulse with instantaneous power P(t), the energy is E = ∫ P(t) dt, measured in joules. In practice, pulse energies can range from femtojoules to millijoules depending on the source and application.

The energy depends on the pulse shape. For a simple rectangular pulse with peak power P0 and duration Δt, E = P0 Δt. For a Gaussian optical pulse with full width at half maximum τ, the energy is E = P0 τ sqrt(pi) / (2 sqrt(ln 2)) ≈ 1.06 P0 τ. The exact factor is shape-dependent, so the energy is generally described as E = ∫ P(t) dt.

Pulse energy is related to, but distinct from, average power. If a pulse train has repetition rate f_rep, the average power is P_avg = E × f_rep, and conversely E = P_avg / f_rep.

Applications and considerations. In lasers and nonlinear optics, pulse energy determines the fluence on a target, the onset of nonlinear effects, and material damage thresholds. It is a key parameter in micromachining, ultrafast spectroscopy, and optical communications, where energy per pulse influences signal integrity and nonlinearities.

Measurement. Pulse energy can be measured with calibrated energy meters or calorimeters for single-shot pulses, or inferred from the average power divided by the repetition rate for repetitive pulses. Fast photodiodes and integrating spheres are also used for characterizing energy in practical systems.