Above Threshold ionization by multi photon (http://www.cat.gov.in/lasernews/ln971/ati.html)

Ionization and Odd harmonic Generation:

In the multiphoton ionization of an atom with ionization potential IP by radiation of photon energy hn₀, the energy of the free electron on ionization is given by_, = s hn₀ - IP. At normal intensities of light, the value of s (the number of photons absorbed) is such that (s-1) hn₀ IP s hn₀ and e hn₀. Further, the probability of absorption of s+1 photons is much less than that of s photons. However, in a number of experiments in low density gas targets at laser intensity of I ~ 10¹²-10¹⁴ W/cm², it was observed that the free electron energy is much in excess of the above limit. In fact, the energy spectrum of the electrons (Fig.2) showed many distinct peaks at energies

Fig.2 : ATI Electron energy spectrum

given by e = (s+n) h n₀ - IP , where n = 1,2,3..... In some cases, the value of n is observed to be as large as 10. It is now established that the maximum value of n is related to the ponderomotive energyas n_maxh n₀ = 3 - 3.5 times U_p. This clearly means that electrons prefer to absorb more photons than necessary to become free on ionization. This process of ionization is called Above Threshold Ionization (ATI)^2,5.

It is found that along with ATI electrons, the plasma (created by ionization of a gas) also emits odd harmonics of n₀ such that hn = N hn₀ where N = 1, 3, 5,.... (Fig. 3). This process is called Odd Harmonic Generation. Here too, similar to ATI, the maximum value of N is related to the ponderomotive energy as N_max hn₀ = IP+ (3-3.5)

Fig.3 : Odd Harmonic spectrum from plasma

times U_p. It is therefore not surprising that the two processes of above threshold ionization and harmonic generation are related. Occurrence of these processes can be primarily understood by considering the atomic potential well and its cyclic distortion due to the strong field of the radiation. (comparable to the atomic field). Fig.4 shows a simplified picture of the potential well and the linear potential due to radiation field.

Fig.4: Potential well distortion by laser field.

When the potential is lowered on one side due to the peak of the field, the bound electron tries to escape from the atom as it has more energy than that necessary to escape in that direction. However, before it can escape, the field direction gets reversed and the potential is raised on that side and lowered on the opposite side. So the electron is pushed back into the atom and it tries to escape from the opposite side. However, once again, before it can escape, field changes its direction. As a result, the electron keeps oscillating in the vicinity of the atom and keeps gaining energy from the field in the process as depicted in Fig.5.

Now two processes are possible. As the energy of the electron increases, its probability of tunneling through the raised potential becomes

Fig.5: Graphical explanation of ATI and OHG.

significant. It is clear from Fig.5 that such an electron will have energy much above the zero energy (threshold) and hence this process is called above threshold ionization.

Alternatively, the energetic electron can lose its energy by emission of a photon. An energetic electron may be visualized as being in a virtual state reached by absorption of a certain number (N) of photons (from the radiation field) by the ground state atom. Therefore, the electron can come down to the ground state by emission of a single photon of energy Nhn. However, since, DL = 1 for dipole transition, only odd values of N (for which the parity of virtual and ground state would be different) are allowed. Consequently, the spectrum of emitted radiation would consist of only odd harmonics (Fig.3).