Pulsed Laser Emission: Power and Energy Calculations

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Determining whether emission from a pulsed laser is compatible with a device or application can require referencing parameters that are not supplied by the laser's manufacturer. When this is the case, the necessary parameters can typically be calculated from the available information. Calculating peak pulse power, average power, pulse energy, and related parameters can be necessary to achieve desired outcomes including:

• Protecting biological samples from harm.
• Measuring the pulsed laser emission without damaging photodetectors and other sensors.
• Exciting fluorescence and non-linear effects in materials.

Pulsed laser radiation parameters are illustrated in Figure 1 and described in the table. For quick reference, a list of equations are provided below. The document available for download provides this information, as well as an introduction to pulsed laser emission, an overview of relationships among the different parameters, and guidance for applying the calculations. 

Equations:
Period and repetition rate are reciprocal:			and
Pulse energy calculated from average power:
Average power calculated from pulse energy:
Peak pulse power estimated from pulse energy:
Peak power and average power calculated from each other:
		and
Peak power calculated from average power and duty cycle*:
		*Duty cycle () is the fraction of time during which there is laser pulse emission.

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Figure 1: Parameters used to describe pulsed laser emission are indicated in the plot (above) and described in the table (below). Pulse energy (E) is the shaded area under the pulse curve. Pulse energy is, equivalently, the area of the diagonally hashed region. 

Parameter	Symbol	Units	Description
Pulse Energy	E	Joules [J]		A measure of one pulse's total emission, which is the only light emitted by the laser over the entire period. The pulse energy equals the shaded area, which is equivalent to the area covered by diagonal hash marks.
Period	Δt	Seconds [s]		The amount of time between the start of one pulse and the start of the next.
Average Power	Pavg	Watts [W]		The height on the optical power axis, if the energy emitted by the pulse were uniformly spread over the entire period.
Instantaneous Power	P	Watts [W]		The optical power at a single, specific point in time.
Peak Power	Ppeak	Watts [W]		The maximum instantaneous optical power output by the laser.
Pulse Width		Seconds [s]		A measure of the time between the beginning and end of the pulse, typically based on the full width half maximum (FWHM) of the pulse shape. Also called pulse duration.
Repetition Rate	frep	Hertz [Hz]		The frequency with which pulses are emitted. Equal to the reciprocal of the period.