## How many photons are in a laser pulse?

Have you ever wondered how many photons you generate each time you fire a pulse of laser energy? I have!

Fortunately, I can work it out because I’m a physicist. It’s the kind of thing us physicists do!! It keeps us off the streets at night……

So, to calculate this number we need to know the energy of each individual photon. This is quite easy to do using a formula from quantum physics:

E = h f

where ‘E’ is the photon energy, ‘h’ is Planck’s constant and ‘f’ is the frequency of the light. Max Planck was a very clever physicist who helped to develop quantum physics back in the early 1900s. Using the above simple formula we can calculate the energy of a photon of any wavelength (remember, wavelength = the speed of light / frequency).

So, below I show the energy of photons of a number of wavelengths typically used in dermatology lasers:

 Wavelength (nm) Photon energy (joules) 532 – Nd:YAG, 2nd harmonic 3.734 x 10^-19 585 – pulsed dye laser 3.396 x 10^-19 694 – ruby laser 2.862 x 10^-19 755 – alex laser 2.631 x 10^-19 1064 – Nd:YAG 1.867 x 10^-19

Notice that the individual photon energy falls as they become ‘redder’!

Now, we simply divide the number of photons (above) into the pulse energy used in a treatment. Let’s say that the pulse energy is 1 joule; so the number of  photons for each wavelength is:

 Wavelength (nm) Number of photons 532 2.6781 x 10^18 585 2.9449 x 10^18 694 3.4936 x 10^18 755 3.8007 x 10^18 1064 5.3562 x 10^18

That’s a LOT of photons!!!

To put that into some sort of perspective, let’s compare these numbers against something more tangible.

How many grains of sand are there on the planet Earth? Well, according tothere are approximately 5.6 x 10^21 grains!!!

That’s   5,600,000,000,000,000,000,000!

So, by this reckoning, when you fire off 1000 pulses of 1064nm laser energy at 1J per pulse, you will have generated approximately the same number of photons as the total number of grains of sand on the entire planet!

If your laser runs at 10 Hz (10 shots per second) then you only need 100 seconds, or less than two minutes, of shots to equal all that sand.

Makes you think…..

Mike.

mike.murphy@dermalase.co.uk