# Are a laser's wavelength, spot size, energy per pulse, and pulse duration independent parameters? Or can some be derived from others?

An Nd:YAG laser that has the following properties:

$$\lambda=1024$$ nm (wavelength)

$$d = 5.8$$ µm (spot size)

$$\tau=30$$ ps (pulse duration)

$$E_L=50$$ µJ (energy per pulse).

Given any two of the above parameters, can the other two be derived? Or are all 4 independent? I am asking because in this paper it appears like only a laser's energy per pulse and pulse duration are considered when computing the bubble wall velocity (it's wavelength and spot size are ignored).

Equations 5-20 appears to ignore the spot size $$d=5.8$$ µm and wavelength $$\lambda=1024$$ nm (I only see $$E_L$$ and $$\tau$$ used in the equations 5-20.). Is there a reason to ignore a laser's wavelength and spot size if you already know energy per pulse and pulse duration?

Yes, if all your other design parameters are free, then these parameters are all in principle independent.

In any particular laser system, there might be engineering trade-offs that relate one to another.

For example, if a particular peak power is required, then pulse duration and energy per pulse must be balanced to achieve the required peak power.

Or, if the output aperture of the laser and the range to the target are fixed, then optical wavelength and minimum achievable spot size are related.

• But what happens if I implement a simulation using these 4 parameters independently. Is it possible to change the wavelength to something like 200nm, but the energy still remains as 50 micro joules? Don't you think something is wrong with that? Shouldn't the laser energy automatically change if I attempt to vary the wavelength (and vice versa) ? Jul 8, 2020 at 21:38
• @user1068636, no. It would have to be a completely different laser design to have such a different wavelength. The possible output power would depend entirely on the details of that design and there's no a priori reason to expect it to be lower, higher, or the same as your 1024 nm laser. Jul 8, 2020 at 21:49
• Are you suggesting these four parameters are actually not independent? Jul 8, 2020 at 21:51
• I'm saying any relations between them depend strongly on other parameters that you've left unspecified. There's no way, if all you know about a laser is three of the parameters, to predict the fourth one. Jul 8, 2020 at 21:52
• I would greatly appreciate it if you could point me to a reference calculation that uses at least these four parameters. Something like the example I showed you, where if the wavelength changes it affects the laser energy. Jul 8, 2020 at 21:54