Parametric process (optics)
Encyclopedia
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 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.
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, thus the lifetime of a parametric process is roughly Δt~ħ/ΔE, which is appreciably small for any non-zero ΔE.
, 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 effect 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:
Sample non-parametric nonlinear processes:
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
, momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
, or angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...
between the optical field
Optical field
The optical field is a term used in physics and vector calculus to designate the electric field shown as E in the electromagnetic wave equation which can be derived from Maxwell's Equations...
and the physical system
Physical system
In physics, the word system has a technical meaning, namely, it is the portion of the physical universe chosen for analysis. Everything outside the system is known as the environment, which in analysis is ignored except for its effects on the system. The cut between system and the world is a free...
. In contrast a non-parametric process is a process in which any part of the quantum state of the system changes.
Temporal characteristics
Since a parametric process prohibits a 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 photonPhoton
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
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
Virtual state (physics)
The term virtual state is commonly used to refer to two different types of states in physical systems. It may refer to a very short-lived, unobservable quantum state or a real, but unstable, state...
. By the Heisenberg Uncertainty Principle we know that ΔEΔt~ħ, thus the lifetime of a parametric process is roughly Δt~ħ/ΔE, which is appreciably small for any non-zero ΔE.
Linear optics
In a linear optical system the dielectric polarization, P, responds linearly to the presence of an electric fieldElectric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
, E, and thus we can write
where ε0 is the electric constant
Electric constant
The physical constant ε0, commonly called the vacuum permittivity, permittivity of free space or electric constant is an ideal, physical constant, which is the value of the absolute dielectric permittivity of classical vacuum...
, χ is the (complex
Complex number
A complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...
) electric susceptibility
Electric susceptibility
In electromagnetism, the electric susceptibility \chi_e is a dimensionless proportionality constant that indicates the degree of polarization of a dielectric material in response to an applied electric field...
, and nr(ni) is the real(imaginary) component of the refractive index
Refractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....
of the medium. The effects of a parametric process will effect 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
Dielectric
A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material, as in a conductor, but only slightly shift from their average equilibrium positions causing dielectric...
with the following effects:
- RefractionRefractionRefraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...
- DiffractionDiffractionDiffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
- Elastic scatteringScatteringScattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...
- Rayleigh scatteringRayleigh scatteringRayleigh scattering, named after the British physicist Lord Rayleigh, is the elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the light. The particles may be individual atoms or molecules. It can occur when light travels through...
- Mie scatteringMie theoryThe Mie solution to Maxwell's equations describes the scattering of electromagnetic radiation by a sphere...
- Rayleigh scattering
Alternatively, non-parametric processes often involve loss (or gain) and give rise to:
- AbsorptionAbsorption (electromagnetic radiation)In physics, absorption of electromagnetic radiation is the way by which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed to other forms of energy for example, to heat. The absorption of light during wave propagation is...
- Inelastic scatteringScatteringScattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...
- Raman scatteringRaman scatteringRaman scattering or the Raman effect is the inelastic scattering of a photon. It was discovered by Sir Chandrasekhara Venkata Raman and Kariamanickam Srinivasa Krishnan in liquids, and by Grigory Landsberg and Leonid Mandelstam in crystals....
- Brillouin scatteringBrillouin scatteringBrillouin scattering, named after Léon Brillouin, occurs when light in a medium interacts with time dependent optical density variations and changes its energy and path. The density variations may be due to acoustic modes, such as phonons, magnetic modes, such as magnons, or temperature gradients...
- Raman scattering
- Various optical emission processes
- PhotoluminescencePhotoluminescencePhotoluminescence is a process in which a substance absorbs photons and then re-radiates photons. Quantum mechanically, this can be described as an excitation to a higher energy state and then a return to a lower energy state accompanied by the emission of a photon...
- FluorescenceFluorescenceFluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation of a different wavelength. It is a form of luminescence. In most cases, emitted light has a longer wavelength, and therefore lower energy, than the absorbed radiation...
- LuminescenceLuminescenceLuminescence is emission of light by a substance not resulting from heat; it is thus a form of cold body radiation. It can be caused by chemical reactions, electrical energy, subatomic motions, or stress on a crystal. This distinguishes luminescence from incandescence, which is light emitted by a...
- PhosphorescencePhosphorescencePhosphorescence is a specific type of photoluminescence related to fluorescence. Unlike fluorescence, a phosphorescent material does not immediately re-emit the radiation it absorbs. The slower time scales of the re-emission are associated with "forbidden" energy state transitions in quantum...
- Photoluminescence
Nonlinear opticsNonlinear opticsNonlinear optics is the branch of optics that describes the behavior of light in nonlinear media, that is, media in which the dielectric polarization P responds nonlinearly to the electric field E of the light...
In a nonlinear mediaNonlinear optics
Nonlinear optics is the branch of optics that describes the behavior of light in nonlinear media, that is, media in which the dielectric polarization P responds nonlinearly to the electric field E of the light...
, the dielectric polarization P responds nonlinearly to the electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
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
Polarization
Polarization is a property of certain types of waves that describes the orientation of their oscillations. Electromagnetic waves, such as light, and gravitational waves exhibit polarization; acoustic waves in a gas or liquid do not have polarization because the direction of vibration and...
dependent.
Sample parametric nonlinear processes:
- Second harmonic generationSecond harmonic generationAn optical frequency multiplier is a nonlinear optical device, in which photons interacting with a nonlinear material are effectively "combined" to form new photons with greater energy, and thus higher frequency...
(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 generationHigh Harmonic Generation- Perturbative Harmonic Generation :Perturbative Harmonic Generation is a process whereby laser light of frequency ω and photon energy ħω can be used to generate new frequencies of light. The newly generated frequencies are integer multiples nħω of the original light's frequency...
(HHG), generation of light with frequencies much greater than the original (typically 100 to 1000 times greater) - Sum frequency generationSum frequency generationSum-frequency generation is a non-linear optical process. This phenomenon is based on the annihilation of two input photons at angular frequencies \omega_1 and \omega_2 while, simultaneously, one photon at frequency \omega_3 is generated...
(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 conversionSpontaneous parametric down conversionSpontaneous parametric down-conversion is an important process in quantum optics, used especially as a source of entangled photon pairs, and of single photons.-Basic process:...
(SPDC), the amplification of the vacuum fluctuations in the low gain regime - Optical Kerr effectKerr effectThe Kerr effect, also called the quadratic electro-optic effect , is a change in the refractive index of a material in response to an applied electric field. The Kerr effect is distinct from the Pockels effect in that the induced index change is directly proportional to the square of the electric...
, intensity dependent refractive index - Four-wave mixingFour-wave mixingFour-wave mixing is an intermodulation phenomenon in optical systems, whereby interactions between 3 wavelengths produce a 4th wavelength in the signal. It is similar to the third-order intercept point in electrical systems...
(FWM) - Self-focusingSelf-focusingSelf-focusing is a non-linear optical process induced by the change in refractive index of materials exposed to intense electromagnetic radiation. A medium whose refractive index increases with the electric field intensity acts as a focusing lens for an electromagnetic wave characterised by an...
- Kerr-lens modelockingKerr-lens modelockingKerr-lens modelocking is a method of modelocking lasers via a nonlinear optical process known as the optical Kerr effect. This method allows the generation of pulses of light with a duration as short as a few femtoseconds....
(KLM) - Self-phase modulationSelf-phase modulationSelf-phase modulation is a nonlinear optical effect of light-matter interaction.An ultrashort pulse of light, when travelling in a medium, will induce a varying refractive index of the medium due to the optical Kerr effect...
(SPM), a
effect - Optical solitonSoliton (optics)In optics, the term soliton is used to refer to any optical field that does not change during propagation because of a delicate balance between nonlinear and linear effects in the medium. There are two main kinds of solitons:...
s - Cross-phase modulationCross-phase modulationCross-phase modulation is a nonlinear optical effect where one wavelength of light can affect the phase of another wavelength of light through the optical Kerr effect.- Applications of XPM :...
(XPM) - Four-wave mixingFour-wave mixingFour-wave mixing is an intermodulation phenomenon in optical systems, whereby interactions between 3 wavelengths produce a 4th wavelength in the signal. It is similar to the third-order intercept point in electrical systems...
(FWM), can also arise from other nonlinearities - Cross-polarized wave generationCross-polarized wave generationCross polarized wave generation is a nonlinear optical process that can be classified in the group of frequency degenerate [four wave mixing] processes. It can take place only in media with anisotropy of third order nonlinearity...
(XPW), a
effect in which a wave with polarization vector perpendicular to the input is generated
Sample non-parametric nonlinear processes:
- Stimulated Raman scattering
- Raman amplificationRaman amplificationRaman amplification is based on the Stimulated Raman Scattering phenomenon, when a lower frequency 'signal' photon induces the inelastic scattering of a higher-frequency 'pump' photon in an optical medium in the nonlinear regime. As a result of this, another 'signal' photon is produced, with the...
- Two-photon absorptionTwo-photon absorptionTwo-photon absorption is the simultaneous absorption of two photons of identical or different frequencies in order to excite a molecule from one state to a higher energy electronic state. The energy difference between the involved lower and upper states of the molecule is equal to the sum of the...
, simultaneous absorption of two photons, transferring the energyEnergyIn physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
to a single electron - Multiphoton absorption
- Multiple photoionisation, near-simultaneous removal of many bound electrons by one photon