# Quick guide to calculating laser fluence

Monday, September 04, 2023

Monday, September 04, 2023

**What is laser fluence?** It is a measure of energy delivered per unit area.

It tells you how concentrated a laser’s energy is. This is helpful to avoid busting damage thresholds, and to ensure good process quality. Energy density actually refers to the same concept.

A commonly used unit for laser fluence is Joules per square centimeter (J/cm^{2}).

Calculating fluence is quite straightforward. It’s essentially just a simple division.

How the energy is distributed within the laser beam (i.e. the beam’s profile) has a large influence on the peak fluence. Hence, the division will have a slightly different scaling factor, depending on whether the laser has a flat-top profile, a gaussian profile, or something more irregular or exotic.

Gentec-EO's energy density and fluence calculator is publicly available and free to use. Bookmark the page and use it whenever it can save you time.

In popular culture, lasers are little red dots with a sharp outline. There’s all the power in the world inside the red dot, and none at all outside of it. Measuring the diameter of such a laser is as straightforward as measuring the diameter of a circle on a piece of paper.

However, only flat-top lasers actually behave this way, and they represent a minority of lasers on the market.

Most lasers do not abruptly “turn off” at the edge of the beam. They are very bright in the middle, and then *slowly* get dimmer at the edges.

Because laser light tapers off gradually, the boundary between “inside the beam” and “outside the beam” can be a bit fuzzy.

This has led to many beam diameter definitions. The three you will typically come across are FWHM, 1/e2, and D4σ, and they make sense only if the beam is Gaussian. They represent the majority of beam profiles you will come across. Why, you might ask? Mostly because a Gaussian power distribution maintains its shape way more efficiently over a distance than any other profile.

All of that remains theories, and as you may already know, just as a laser beam spreads over distance, there can be a lot of divergence between theory and practice. So, to address that, there is what you call the M^{2} factor. This factor refers to how closely a laser beam resembles a theoretical Gaussian distribution (or bell curve).

Great models can be developed to characterize a beam, but there’s nothing like actually looking at it to assess its profile. Do not mistake what I just said here, even though a typical stormtrooper manages to miss its target indefinitely, if you look directly at your beam, even if you can’t see it, really serious damages can occur in a matter of fractions of seconds.

The best way to know your profile is to use the proper tool. There are plenty of options out there, but the most efficient would be a profiling camera. It would give you the exact intensity distribution in real time of your beam, including if there are any hotspots or defects.

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Let’s start with the simplest of cases: flat-top lasers, where the energy is distributed perfectly evenly all across the beam.

Calculating the fluence is a piece of cake. Just divide the energy by the beam area.

For example, let’s calculate the fluence of a flat-top laser pulse of 10 mJ with a diameter of 4 mm. The surface of such a beam is π * ( 4 mm / 2 )^{2}.

Dividing the pulse energy of 10 mJ by the surface (4 π mm^{2}), we find that the fluence is 10 mJ / 4 π mm^{2} = 0.796 mJ / mm^{2}, or 7.96*10^{-2} J/cm^{2}.

The energy in a Gaussian beam is distributed unevenly, like mentionned before. There is much more power at the center of the beam than at the periphery.

Commonly, we will want the *peak* *fluence*, since it is *peak* fluence we need to watch out for to avoid going over damage thresholds.

The complicated way to get the fluence would be to integrate the energy distribution over the target area.

The simple way is, again, just a simple division. However, notice that this time there is a scaling factor of 2, energy is more concentrated in the center of the beam.

Peak Fluence = E / ( π* w*^{2} / 2 ), where *w* is the 1/e^{2} definition of the Gaussian beam radius.

Let’s calculate the peak fluence of the same laser as before (10 mJ pulses, 4 mm diameter), except this time considering that the profile is Gaussian, rather than flat-top.

Peak Fluence = 10 mJ / (π ( 4 mm / 2 )^{2} / 2) --> 10 mJ/ 2 π mm^{2} = 1.59 mJ/mm^{2}, which is equivalent to 0.159 J/cm^{2}.

Notice that **the peak fluence of the Gaussian beam is twice as high** as the fluence of a laser with the same basic parameters, but a flat-top profile.

You can get some ballpark figures using your laser manufacturer’s specs. However, for your production setup, don't be a stormtrooper, use accurate NIST-traceable energy detectors and the true beam size for consistent quality and maximal yield.