This post describes the mechanism that produces large power concentrations in a multi-nanoparticle system where the particles vary widely in particle sizes.
First, let’s set the table. A cascade amplifier is any diode constructed from a series of amplifiers, where each amplifier sends its output to the input of the next amplifier in a daisy chain. Coherent anti-Stokes Raman scattering acts like such a cascade amplifier, except that dipoles tuned to various resonant frequencies drive thermal power to higher power concentration levels zero loss factors. In detail, coherent anti-Stokes Raman scattering, also called Coherent anti-Stokes Raman scattering spectroscopy (CARS), is a form of spectroscopy used primarily in chemistry, physics and related fields. It is sensitive to the same vibrational signatures of dipoles as seen in Raman spectroscopy. Unlike Raman spectroscopy, CARS employs multiple photo harmonics. It produces a signal in which the emitted waves are coherent with one another. As a result, CARS is orders of magnitude stronger than spontaneous Raman emission. CARS is a N-order nonlinear optical process involving multiple coupled dipole sources. These dipoles interact and generate a coherent optical signal at the anti-Stokes frequency. The high order harmonic is resonantly enhanced when the frequency difference between the low order pumps and the dipoles coincides with the frequency of a Raman resonance, which is the basis of the technique's intrinsic vibrational contrast mechanism. Multiple nanoparticles of various sizes interact each with their respective dipole resonant frequencies. The CARS process can be physically explained by using either a classical oscillator model or by using a quantum mechanical model. Classically, the Raman active vibrator is modeled as a (damped) harmonic oscillator with a characteristic frequency. In CARS, these oscillators are not driven by a single optical wave, but by the different resonant frequencies between the dipole pumps and the high order harmonic. This driving mechanism is similar to hearing the low combination beat tone when striking two different high tone piano keys: your ear is sensitive to the difference frequency of the high tones. Similarly, the Raman oscillator is susceptible to the difference frequency of multiple optical waves. When the difference frequency approaches beat resonance, the system of dipole oscillators are driven very efficiently. While intuitive, this classical picture does not take into account the quantum mechanical energy levels of the dipole. Quantum mechanically, the CARS process can be understood as follows. Our dipole is initially in the ground state, the lowest thermal energy state of the system. The pump dipole excites the dipole chain to a virtual vibrational state. A virtual state is not an eigenstate of the dipole and it cannot be occupied but it does allow for transitions between otherwise uncoupled real states. If a dipole is simultaneously present along with the pumps, the virtual state can be used as an instantaneous gateway to address a vibrational eigenstate of the dipole. The joint action of the pumps and the Stokes has effectively established a coupling between the ground state and the vibrationally excited state of the system. The system is now in multiple states at the same time: it resides in a coherent superposition of states. This promotes the system to a virtual state. Again, the molecule cannot stay in the virtual state and will fall back instantaneously to the ground state under the emission of a photon at the anti-Stokes frequency. The pump dipoles are no longer in a superposition, as it resides again in the lowest thermal state, the ground state. In the quantum mechanical model, energy is deposited in the dark mode highest resonant system during the CARS process. The molecule acts like a medium for converting the frequencies of the multiple resonant waves into a CARS signal (a parametric process). There are, however, related coherent Raman processes that occur simultaneously which do deposit energy into the high order resonant cavity at high efficiency. The maximum sustained energy level achieved in this smallest resonant cavity in the cavity chain is determined when losses from the cavity equals input energy levels.
