Question

I am trying to estimate the clamped intensity of a 90 fs femtosecond laser when it passes through a flow of nitrogen that is exiting a nozzle. Prior to the nozzle, the incoming nitrogen flow is heated by an electric arc that significantly raises its temperature, resulting in the flow at the nozzle exit being a plasma at thermal non-equilibrium with a population of about 99.9 % N2 and 0.1 % atomic N.

Since the clamped intensity in literature is usually calculated by performing a balance of self-focusing and defocusing due to the 'plasma' from the high peak intensity of the laser, it would involve accounting for the non-linear intensity-based refractive index of the medium.
n = n2I
While there is literature that goes over the density-dependent non-linear index (n2) for diatomic nitrogen, there isn't any readily available data that I could use to include the effect of the monoatomic nitrogen within my volume of interest.
Since my background is in Aerospace, I was curious if anyone had any suggestions of an approach I could follow to get it or some literature that I could look into. I was also wondering if I am overthinking the problem and if an assumption of a negligible contribution to non-linear refractive index change due to the extremely small atomic nitrogen concentration would be valid.

Answer 1

Estimating the clamped intensity of a femtosecond laser in plasma requires considering the non-linear refractive indexes of N₂ and N. Lack of data on monoatomic nitrogen might warrant computational estimation or empirical determination, or you could assume negligible contribution from the 0.1% of N if the system is insensitive to it.

Step-by-step explanation:

Estimating the clamped intensity of a femtosecond laser in a plasma generated by an electric arc in nitrogen requires an understanding of the non-linear optical properties of the gases involved. Given the high percentage of diatomic nitrogen (N₂) present in the plasma, it stands to reason that available literature on the non-linear refractive index of diatomic nitrogen would be the main basis for your calculations. However, even a small percentage of atomic nitrogen (N) can have non-negligible effects on the laser's behavior due to non-linear optical effects if its non-linear refractive index is significantly different from diatomic nitrogen.

When no direct literature exists on monoatomic nitrogen's non-linear refractive index contribution, one approach could be to use computational methods such as quantum chemical calculations to estimate the missing data. Alternatively, you might consider conducting a controlled experiment to empirically determine n₂ for atomic nitrogen. But if your calculation's sensitivity to this parameter is low, it might be reasonable, as a first approximation, to assume that the contribution of the 0.1% atomic nitrogen to the overall change in the non-linear refractive index is negligible.

Inspection of relevant literature or prior research might provide data on similar systems or guidelines on how to make reasonable assumptions in these cases. For instance, research on inertial confinement fusion or laser interaction with plasma could offer useful parallels. Nonetheless, careful consideration in minimizing the introduced error from such an assumption should be taken, especially if the system is highly sensitive to small changes in optical properties.