How many photons are produced in a laser pulse?
Thursday, September 07, 2023
Ever wondered how many photons make up one laser pulse?
Of course, this could sound arbitrary since pulse width, energy per pulse and wavelength would all affect the result. Therefore, it depends on many things, notably the laser itself. So, we’ll give you some ballpark numbers, and will also show you how you can compute these values for your own laser setup.
The math behind the numbers
If I showed you a basket full of apples, could you guess the number of apples it contains? What about if I told you the weight of one apple and the weight of the basket, then could you calculate how many apples are in the basket?
Finding how many photons are in one pulse is the same thing! By dividing the total energy of a pulse by the energy of one photon within the pulse, we find the number of photons.
The real question then is how to find the pulse’s energy and the photon’s energy.
Finding the individual photon energy is really simple since the only piece of information you actually need is the wavelength of the laser. Special thanks to our buddy Max Planck here for its famous relation E=hν, in which we can plug ν = c/λ.
(Where h is Planck’s constant, c is the speed of light, ν is the photon frequency, and λ is the photon wavelength.)
Now that we have the photon energy, it’s time to find the total energy of the pulse. Most manufacturers would simply give this information to you, but let’s get more rigorous here and satisfy our thirst for knowledge, shall we?
To determine it yourself, you are going to need an energy meter. No matter the pulse, at Gentec-EO, we probably have a suitable detector for it, and if we do not, our custom projects team is here to catch the ball and make one for your exotic pulse. You can ask about that to our friends from the NIF of LLNL who are working on the creation of small suns to generate sustainable energy.
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What about extra-short pulses?
The principle remains the same, but if we wanted a laser pulse to contain as few photons as possible, we would aim for two things. First of all, low pulse energy. Second, as much energy as possible in each photon. This would imply shortest wavelength possible. Following Planck’s equation, you would understand that the energy of a photon is inversely proportional to its wavelength.
Returning to the apple and basket analogy, to have the least amount of apple in a given basket, you would aim to get the smallest basket possible and the biggest apples. Ultimately, obtaining a single apple in a very small basket. When pulsed lasers are involved though, if you expect to reach 1 photon per pulse, you’ll probably end up as far from the target as a shot from a stormtrooper is.
Gentec-EO’s PE3B photodiode detectors, one of our most sensitive energy meters, can give accurate measurements in the femtojoules range. The noise level of it is as low as 8 femtojoules when working at 634 nm.
If we translate that amount of energy per pulse and combine it with let’s say an excimer laser at 193 nm. How many photons will it contains? Well, you will still be looking at a little less than 8000 photons. What would this look like at 634 nm with our PE3B you might ask? It will reach 25,000 photons, and keep in mind that it’s only the noise level! If that sounds like a lot, read on – You’ll fall off your chair.
High-power pulses
In 2021, HiLASE Centre broke the world record for the highest average power from a high-energy laser. Using a Gentec-EO detector, the team determined that each pulse packed 145 Joules of energy! Knowing that the wavelength of this laser is 1030 nm, let’s find out how many photons are in one pulse.
First, we find the energy of one 1030 nm photon using E = hc/λ:
E = (6.63 * 10-34 Js) x (3 * 108 m/s) / (1030 * 10-9m) = 1.93 * 10-19 J
Dividing the total energy of one pulse (145 Joules) by that value, we find that one pulse of the HiLASE laser contains as many as 7.5 * 1020 photons. That’s 750 000 000 000 000 000 000 photons, or seven hundred and fifty quintillion!
If you can’t quite wrap your head around such a big number, here’s a fun fact. There are about 350 quintillion gallons of water in all of Earth’s oceans. In other words, there are only half as many gallons of water in the ocean as there are photons in one of HiLASE’s record-breaking pulses!
