Interacting phenomenon between light and matter
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.
[1]
Temporal characteristics
Because a parametric process prohibits a net change in the energy state of the system, parametric processes are "instantaneous". For example, if an atom absorbs a
photon with energy E, the atom's energy increases by ΔE = E, but as a parametric process, the quantum state cannot change and thus the elevated energy state must be a temporary
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.
[1]
Parametric versus non-parametric processes
Linear optics
In a linear optical system the dielectric
polarization, P, responds linearly to the presence of an
electric field, E, and thus we can write
![{\displaystyle {\mathbf {P} }=\varepsilon _{0}\chi {\mathbf {E} }=(n_{r}+in_{i})^{2}{\mathbf {E} },}](https://wikimedia.org/api/rest_v1/media/math/render/svg/40781f7b09f3732185a6943597547444ce86f916)
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:
Alternatively, non-parametric processes often involve loss (or gain) and give rise to:
Nonlinear optics
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
-
Self-focusing
-
Kerr-lens modelocking (KLM)
-
Self-phase modulation (SPM), a
effect
-
Optical solitons
-
Cross-phase modulation (XPM)
-
Four-wave mixing (FWM), can also arise from other nonlinearities
-
Cross-polarized wave generation (XPW), a
effect in which a wave with polarization vector perpendicular to the input is generated
Sample non-parametric nonlinear processes:
See also
Notes
References