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In my previous questions I ask about ionizing air molecules such as nitrogen which requires 15.58 eV or oxygen which requires 12.07 eV. If you do the equation wavelength = 1240 eV nm / (photon energy) required for ionization to occur. In this case if I wanted to ionize nitrogen I would need a laser with a wavelength of ~80 nm.

This is the single-photon process, but based on what I have heard I see that if you do a two-photon process you can increase your wavelength to more readily available laser and still output the same photon energy.

If what I'm saying is true then how do I make this happen? What wavelength at what pulse rate would I need to output 15.58 eV? I just don't understand how you make it a two photon process that is all. I know even a two photon process is probably going to be low, but maybe I can apply the same feedback I receive into a eight-photon process and so on and so forth. Any help would be much appreciated!

Emilio Pisanty
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Reese Houseknecht
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The repetition rate of the pulses is completely irrelevant to the probability of getting multiphoton processes: once a given pulse is over, then its ionization events are done with, and it doesn't matter how soon the next pulse comes, it will be an independent event.

The probability of multiphoton processes (at a given wavelength) is governed by the intensity of the light: that is, the total energy flux at a given point, which you get by dividing the pulse energy (that's the average beam power divided by the repetition rate) over the pulse duration and the area of the focal spot, at least as an order-of-magnitude estimate. Note, moreover, that for an $n$-photon process, the rate of ionization scales as the $n^\rm{th}$ power of the intensity, which means that a small decrease in the intensity will take a much higher dent in the rate: if you make 95% of the intensity you wanted, for a 6-photon process, the rate will go down by 30%.

Moreover, for the avalanche-driven aspects of laser-induced optical breakdown, the dependence on intensity can be a good deal sharper. If you don't have the intensity to drive the positive feedback loop, it just won't happen.

If you just want to produce laser-induced optical breakdown of air to see pretty sparks, then RP photonics puts the threshold for breakdown in the neighbourhood of $≈ 2 × 10^{13} \:\mathrm{ W/cm^2}$ for pulse durations of the order of one picosecond.

Emilio Pisanty
  • 137,480