A parametric process is an optical process in which light interacts with matter in such a way as to leave the quantum state of the material unchanged. As a direct consequence of this there can be no net transfer of energy, momentum, or angular momentum between the optical field and the physical system. In contrast a non-parametric process is a process in which any part of the quantum state of the system changes.
Since a parametric process prohibits a net change in the energy state of the system, parametric processes are considered to be 'instantaneous' processes. This can be seen as follows: if an atom absorbs a photon with energy E, the atom's energy will increase by ΔE = E. Since we are assuming this is a parametric process, the quantum state cannot change and thus this energy state must be a virtual state. By the Heisenberg Uncertainty Principle we know that ΔEΔt~ħ/2, thus the lifetime of a parametric process is roughly Δt~ħ/2ΔE, which is appreciably small for any non-zero ΔE.
In a linear optical system the dielectric polarization, P, responds linearly to the presence of an electric field, E, and thus we can write
P
=
ε
0
χ
E
=
(
n
r
+
i
n
i
)
2
E
,
where ε0 is the electric constant, χ is the (complex) electric susceptibility, and nr(ni) is the real(imaginary) component of the refractive index of the medium. The effects of a parametric process will affect only nr, whereas a nonzero value of ni can only be caused by a non-parametric process.
Thus in linear optics a parametric process will act as a lossless dielectric with the following effects:
Refraction
Diffraction
Elastic scattering
Rayleigh scattering
Mie scattering
Alternatively, non-parametric processes often involve loss (or gain) and give rise to:
Absorption
Inelastic scattering
Raman scattering
Brillouin scattering
Various optical emission processes
Photoluminescence
Fluorescence
Luminescence
Phosphorescence
In a nonlinear media, the dielectric polarization P responds nonlinearly to the electric field E of the light. As a parametric process is in general coherent, many parametric nonlinear processes will depend on phase matching and will usually be polarization dependent.
Sample parametric nonlinear processes:
Second harmonic generation (SHG), or frequency doubling, generation of light with a doubled frequency (half the wavelength)
Third harmonic generation (THG), generation of light with a tripled frequency (one-third the wavelength) (usually done in two steps: SHG followed by SFG of original and frequency-doubled waves)
High harmonic generation (HHG), generation of light with frequencies much greater than the original (typically 100 to 1000 times greater)
Sum frequency generation (SFG), generation of light with a frequency that is the sum of two other frequencies (SHG is a special case of this)
Difference frequency generation (DFG), generation of light with a frequency that is the difference between two other frequencies
Optical parametric amplification (OPA), amplification of a signal input in the presence of a higher-frequency pump wave, at the same time generating an idler wave (can be considered as DFG)
Optical parametric oscillation (OPO), generation of a signal and idler wave using a parametric amplifier in a resonator (with no signal input)
Optical parametric generation (OPG), like parametric oscillation but without a resonator, using a very high gain instead
Spontaneous parametric down conversion (SPDC), the amplification of the vacuum fluctuations in the low gain regime
Optical Kerr effect, intensity dependent refractive index
Four-wave mixing (FWM)
Self-focusing
Kerr-lens modelocking (KLM)
Self-phase modulation (SPM), a
χ
(
3
)
effect
Optical solitons
Cross-phase modulation (XPM)
Four-wave mixing (FWM), can also arise from other nonlinearities
Cross-polarized wave generation (XPW), a
χ
(
3
)
effect in which a wave with polarization vector perpendicular to the input is generated
Sample non-parametric nonlinear processes:
Stimulated Raman scattering
Raman amplification
Two-photon absorption, simultaneous absorption of two photons, transferring the energy to a single electron
Multiphoton absorption
Multiple photoionisation, near-simultaneous removal of many bound electrons by one photon
