I have been trying to understand the second and third-order nonlinear processes (specifically SHG and two-photon absorption). I am still unable to understand how the order of these nonlinear processes is determined. I was unable to find adequate information about this in the Nonlinear optics by Robert Boyd. Please help me understand this, or suggest me a source to study more about it.
These articles might be useful,
http://www.physics.ttk.pte.hu/files/TAMOP/FJ_Nonlinear_Optics/4_secondorder_interactions.html
http://www.physics.ttk.pte.hu/files/TAMOP/FJ_Nonlinear_Optics/5_thirdorder_interactions.html
Please go through Fundamentals of Nonlinear Optics
By Peter E. Powers.
Can you specify what you mean with "order" of the processes?
If you mean the "order" in terms of the "second-order" or "third-order" nonlinear process, than this simply refers to the number of the series expansion term of the susceptibility. Here, the "first-order" term refers to the well known "linear" susceptibilty, which for example is decribing effects refraction and other linear processes, while the higher harmonics refer to the respective nonlinear processes. Check any textbook on nonlinear optics. It should feature somewhere the expansion of the induced Polarisation in terms of something like
P = epsilon_0 (chi(1) E + chi(2) E^2 + chi(3) E^3) + ...)
Regards,
Michael
The order of an optical process is determined by the number of waves that take part in that process. A process involving (n+1) waves will be an n-th order process. An by the waves involved, both the incoming and outgoing waves have to be considered. For eg, in linear absorption, one wave is absorbed and one wave is emitted later, i.e, it's a process involving 2 waves; so it's a 1st order process. SHG involves 2 incoming waves and gives out 1 wave of double the frequency; it involves 3 waves and therefore is a 2nd order process. Now, the mechanism of 2-photon absorption is that 2 photons are absorbed, and while emitting, it emits 2 waves, a signal wave of high eney and an idler wave of low energy, making it a 4 wave process, and therefore it is a 3rd order process. Similarly, you can determine the order of an optical process from the number of waves involved in the process.
Thank you Prof. Michael Rüsing , now I understand, I will go through this point.
Ziyad Thekkayil I just checked your answer. Would you please explain more about TPA when you say it is a 4-wave process?
Shiva Mahmoudi In two-photon absorption, the system absorbs 2 photons, and while relaxation, 2 waves are emitted - a signal wave and an idler wave, resulting in a total of 4 waves.
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