## Parametric and nonparametric process Firstly we define what is parametric process. Parametric processes are those processes does not involve real state excitation or absorption, follow phase (and energy) matching condition. The population can be removed from the ground state only for those brief intervals of time ($\cong \frac{\hbar}{\delta E}$ from uncertainty principle) when it resides in a virtual level. >[!Note]- >The term "population" here (and in physics) denotes the distribution of particles with respect to energy states. In contrast, nonparametric processes are those involve transfers from a real level to another real level. Namely there are real absorption process. This leads to two big differences between them: - Parametric process can always be described by a real susceptibility, while for nonparametric process complex $\chi$ is required. - Photon energy is always conserved for parametric process, while for nonparametric this is not always true (energy could be transferred to phonon, electrons or other particle). The nonlinear effects described in [[Understanding parametric nonlinear optical processes]] are all parametric processes. Nonparametric processes are those involve absorptions, like two-photon absorption, stimulated Raman scattering (Stokes/anti-Stokes scattering), energy of photons converted to photons or that of electrons (electron-photon interaction like Compton scattering). >[!Notice] >Therefore, nonparametric processes do not have to have phonon involved, besides the electron-photon interaction, two-photon absorption then spontaneous emission could also be an nonparametric effect since real state is involved. But energy of photons is still conserved. Some of the interesting nonparametric processes, although not directly related to our topics (2nd and 3rd order processes) in nonlinear optics, are worth a look out of curiosity. They are discussed in chapter 7 in the book. - Saturable absorption Some systems have the property that the absorption coefficient decrease with the intensity, which follows, $\alpha = \frac{\alpha_0}{1 + I / I_s}$ One result of this is optical bi-stability. - Two-photon absorption The system takes two photons and excited to a real state, the absorption cross-section is $\sigma=\sigma^{(2)}I$ So it is linearly dependent on the intensity. For conventional linear absorption, the absorption cross-section is a constant. The atomic transition rate $R$ is, $R=\frac{\sigma I}{\hbar \omega}$ Therefore, for two-photon absorption, $R=\frac{\sigma^{(2)}I^{2}}{\hbar \omega}$ The atomic transition rate scales as the square of the intensity. ![[Drawing 2024-09-05 23.04.08.excalidraw.svg]] - Stimulated Raman scattering This is how Raman microscopy relies on. In the transition, a phonon is involved. For Stokes shift, the phonon is annihilated and a photon at the Stokes-shifted frequency is created. This makes the molecule/atom excited at energy $\hbar \omega_{\rm v}$. ![[Drawing 2024-09-05 23.10.15.excalidraw.svg]]