Raman scattering Hamiltonian

Free carrier contributions to Raman scattering are represented by the free carrier term in the perturbation Hamiltonian for the propagation of light in matter. The resulting relation between Raman cross section and response function x(<7. (<7. -00 for... 

Figure 6.1-2 The time-dependent picture of resonance Raman scattering panel A interaction of the incident photon with the electronic transition moment sends the initial vibrational state / > to the excited electronic surface, where it is propagated by the excited-state vibrational Hamiltonian panel B the Raman overlap < /li(i) as a...

Hamiltonian, which takes part in the first step of the perturbation theory. On this way we will need to discuss along with the creation of an odd number of e-h pairs, also the Raman scattering processes with the creation of an even number of e-h pairs and simultaneously of one real photon. The pure electron-photon interaction mechanism requires the introduction of the virtual and final states of two types one of them is the pure e-h states, when their number is n= 1,3,5,. Another type is the combined electron-hole-photon states, when an even number of e-h pairs =2,4,6,... is accompanied by the creation of one virtual or real photon. 

The theory of Raman scattering is virtually identical to that for two-photon absorption the principal difference is that E -D for the incident wave need not be identical to Ei D for the scattered wave. Thus ( 7 2) is not necessarily zero and terms involving can appear in the effective Hamiltonian that drives the transition. Richman et al. (1963) observed the Raman spectrum of LaClj and... 

In the quantum-mechanical derivation of the Raman scattering cross-section, one considers the two-photon process in which a photon changes its frequency (o, wavevector k, and polarization e via scattering from the values (0, k, e ) to the values (ft>s, s,Cs), while the scattering material experiences a transition from i) to /). The interaction Hamiltonian between light and matter is given by... 

We have reviewed the EOM-PMA method for the calculation of two-pulse-induced (spontaneous emission, pump-probe, photon echo) and three-pulse-induced (transient grating, photon echo, coherent anti-Stokes-Raman scattering, four-wave-mixing) optical signals. In the EOM-PMA, the interactions of the system with the relevant laser pulses are incorporated into the system Hamiltonian and the driven system dynamics is simulated numerically exactly. 

From Equations (5.52) and (5.53) we can see that, in general, the interaction Hamiltonian Hr for Raman scattering consists of a triple product in the a s and s. In particular, Stokes scattering is associated with the action of a term a/djat on the initial total wave function of the system />s= /> > 0>v, which yields a final state where the vibration state (initially a vacuum state) is increased by one unit, while a photon is removed from the incident laser and a Stokes photon is created ... 

The textbook case of the harmonic oscillator in one dimension with mass m presented in this section is meant to feature neutron scattering experiments, compared to infrared and Raman spectroscopy. The Hamiltonian... 

We next turn to the spontaneous Raman and fluorescence lineshapes. In an SRF experiment, we have a single incident classical field (a ) and a single scattered mode (a>2). We shall use the Hamiltonian [Eq. (2)] with the only difference that the sum in Eq. (4) runs over j = 1,2, with El being the classical incident field and 2 being the scattered field, which will be treated quantum mechanically. In an SRF experiment, we monitor the scattered field with both time and frequency resolution. The operator representing the rate of emission of co2 photons is... 

The solution to the Hamiltonian of a vibration system is a Fourier series with multiple terms of frequencies being fold of that of the primary mode [30]. For example, the frequency of the secondary 2D mode should be twofold that of the primary D mode of diamond. Instead of the multi-phonon resonant scattering, Raman frequencies are the characteristics of the solution. Generally, one can measure the Raman frequency of a particular x mode as co = co o + Aco, where cOxO is the reference point from which the Raman shift Aco proceeds. The cOxo may vary with the frequency of the incident radiation and substrate conditions, but not the nature and the trends induced by the applied stimuli. By expanding the interatomic potential in a Taylor series at its equilibrium and considering the effective atomic z, one can derive the vibration frequency shift of a harmonic system,... 

---