# Laser Pulse Calculator

Created by Davide Borchia
Last updated: Jul 01, 2022

LASERs can turn on and off at incredibly high speed (though not necessarily so), creating a train of LASER pulses: our LASER pulse calculator takes as input a few characteristic quantities and returns most fundamental features of the pulses.

Here you will learn:

• What is a laser pulse train, and what are the main quantities associated with it;
• How to calculate the laser pulse duty cycle;
• How to calculate a laser pulse energy;
• How to calculate the peak power of a pulsed laser for three different pulse shapes;
• How to calculate the intensity of a pulsed laser;

And much more!

## What is a laser pulse?

A laser pulse is a short, relatively energetic burst of light that propagates with the properties of a Gaussian beam in a specific direction. The pulse is defined by an abrupt increase in power, followed by a similar, ideally symmetric, decrease.

Few characteristic quantities define a laser pulse:

• The pulse duration $T$, that is the full width at half-maximum (FWHM) of the pulse (in the time dimension);
• The repetition rate $f$, that is the frequency of the pulses (how many pulses in a second/unit time);
• The average power $P_{\text{avg}}$ of each pulse; and
• The spot diameter $S$, that is the diameter of the pulsed beam.

The LASER pulse's shape also has relevance in the calculations. The shape of the pulse quantifies the fashion in which the power of the beam rises and decreases. The most common shapes are:

• Rectangular pulse;
• Gaussian pulse; and
• Sech2 pulse (based on the hyperbolic secant function: check our hyperbolic functions calculator to know more).

## How to calculate the laser pulse characteristic quantities?

The first quantity we calculate is the duty cycle of the LASER pulse train. To do so, we need to multiply the duration of each pulse by the repetition rate, obtaining the amount of time the laser is on:

$D = T\cdot f\cdot 100\%$

The multiplication by $100%$ allows you to express the laser duty cycle as the percentage of the time unit the laseris on.

The distance from peak to peak, that is, the separation between pulses, depends on the repetition rate since it is the periodicity of the pulse. We calculate it with:

$\Delta T = \frac{1}{f}$

The pulse depends on the average power of the pulse:

$E_{\text{pulse}} = \frac{P_{\text{avg}}}{f}$

We use this quantity to calculate the peak power of the pulse. At this step, the shape of the pulse becomes relevant, hence we have three possible expressions:

\begin{align*} &\text{(rectangular)}\\ P_{\text{peak, rect}}& = \frac{E_{\text{pulse}}}{f}\\ &\text{(Gaussian)}\\ P_{\text{peak, gaus}} &=2\sqrt{\frac{\log{(2)}}{\pi}} \frac{E_{\text{pulse}}}{f}\\ &\text{(sech}^2\text{)}\\ P_{\text{peak, sech}^2} &= \cosh{}^{-1}(\sqrt{2})\frac{E_{\text{pulse}}}{f} \end{align*}

Now that you know how to calculate the peak power of a pulsed laser, we can also learn how to calculate the intensity of a laser pulse.

🔎 The of lasers vary wildly, from a few milliwatt to powerful Megawatt lasers used in astronomy, defence and high energy physics!

To calculate the intensities of a laser pulse, we need to consider the beam spot size: the smaller the spot, the higher the intensity since the power of the pulse is concentrated in a smaller area.

🙋 You can use our tool in reverse, for example giving in input the energy of the pulse to calculate the average power of the pulsed laser.

The equations for the peak intensity and average intensity of a laser pulse are:

\begin{align*} I_{\text{avg}} &= \frac{P_{\text{avg}}}{A}\\ \\ I_{\text{peak}} & = \frac{P_{\text{peak}}}{A} \end{align*}

Where $A$ is the area of the circular beam spot size:

$A = \frac{S}{2}^2\cdot\pi$

Don't mistake the laser intensity for the laser brightness. For the latter, visit our laser brightness calculator!

Davide Borchia
Laser specification
Average power (P avg)
mW
Pulse shape
Gaussian
Pulse duration (T)
ns
Repetition rate (f)
MHz
Beam spot size diameter (S)
mm
Laser properties
Peak power (P peak)
mW
Pulse to pulse distance (ΔT)
ns
Duty cycle (D)
Pulse energy (E pulse)
nJ
Average intensity (I avg)
mW
/mm²
Peak intensity (I peak)
W
/mm²
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