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]
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
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:
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
parametric, process, optics, parametric, process, optical, process, which, light, interacts, with, matter, such, leave, quantum, state, material, unchanged, direct, consequence, this, there, transfer, energy, momentum, angular, momentum, between, optical, fiel. 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 Contents 1 Temporal characteristics 2 Parametric versus non parametric processes 2 1 Linear optics 2 2 Nonlinear optics 3 See also 4 Notes 5 ReferencesTemporal characteristics EditBecause 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 DE 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 DEDt ħ 2 thus the lifetime of a parametric process is roughly Dt ħ 2DE which is appreciably small for any non zero DE 1 Parametric versus non parametric processes EditLinear optics Edit 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 e 0 x E n r i n i 2 E displaystyle mathbf P varepsilon 0 chi mathbf E n r in i 2 mathbf E where e0 is the electric constant x 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 scatteringAlternatively 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 PhosphorescenceNonlinear optics Edit Main article 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 x 3 displaystyle chi 3 effect Optical solitons Cross phase modulation XPM Four wave mixing FWM can also arise from other nonlinearities Cross polarized wave generation XPW a x 3 displaystyle chi 3 effect in which a wave with polarization vector perpendicular to the input is generatedSample 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 photonSee also EditNonlinear opticsNotes Edit a b See Section Parametric versus Nonparametric Processes Nonlinear Optics by Robert W Boyd 3rd ed pp 13 15 References EditBoyd Robert 2008 Nonlinear Optics 3rd ed Academic Press pp 13 15 ISBN 978 0 12 369470 6 Paschotta Rudiger Parametric Nonlinearities Encyclopedia of Laser Physics and Technology Retrieved from https en wikipedia org w index php title Parametric process optics amp oldid 1085751060, wikipedia, wiki, book, books, library,
