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Ponderomotive Energy
In strong-field laser physics, ponderomotive energy is the cycle-averaged quiver energy of a free electron in an electromagnetic field. Equation The ponderomotive energy is given by :U_p = , where e is the electron charge, E is the linearly polarised electric field amplitude, \omega_0 is the laser carrier frequency and m is the electron mass. In terms of the laser intensity I, using I=c\epsilon_0 E^2/2, it reads less simply: :U_p \cdot , where \epsilon_0 is the vacuum permittivity. For typical orders of magnitudes involved in laser physics, this becomes: : U_p (\mathrm) = 9.33 \cdot I(10^ \mathrm^2) \cdot \lambda(\mathrm)^2 , where the laser wavelength is \lambda= 2\pi c/\omega_0, and c is the speed of light. The units are electronvolts (eV), watts (W), centimeters (cm) and micrometers (μm). Atomic units In atomic units, e=m=1, \epsilon_0=1/4\pi, \alpha c=1 where \alpha \approx 1/137. If one uses the atomic unit of electric field,CODATA Valueatomic unit of electric f ...
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Laser Physics
Laser science or laser physics is a branch of optics that describes the theory and practice of lasers. Laser science is principally concerned with quantum electronics, laser construction, optical cavity design, the physics of producing a population inversion in laser media, and the temporal evolution of the light field in the laser. It is also concerned with the physics of laser beam propagation, particularly the physics of Gaussian beams, with laser applications, and with associated fields such as nonlinear optics and quantum optics. History Laser science predates the invention of the laser itself. Albert Einstein created the foundations for the laser and maser in 1917, via a paper in which he re-derived Max Planck’s law of radiation using a formalism based on probability coefficients ( Einstein coefficients) for the absorption, spontaneous emission, and stimulated emission of electromagnetic radiation. The existence of stimulated emission was confirmed in 1928 by Rudol ...
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Electromagnetic Field
An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical counterpart to the quantized electromagnetic field tensor in quantum electrodynamics (a quantum field theory). The electromagnetic field propagates at the speed of light (in fact, this field can be identified ''as'' light) and interacts with charges and currents. Its quantum counterpart is one of the four fundamental forces of nature (the others are gravitation, weak interaction and strong interaction.) The field can be viewed as the combination of an electric field and a magnetic field. The electric field is produced by stationary charges, and the magnetic field by moving charges (currents); these two are often described as the sources of the field. The way in which charges and currents interact with the electromagnetic field is ...
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Electron Charge
The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundamental physical constant. In the SI system of units, the value of the elementary charge is exactly defined as e =  coulombs, or 160.2176634 zeptocoulombs (zC). Since the 2019 redefinition of SI base units, the seven SI base units are defined by seven fundamental physical constants, of which the elementary charge is one. In the centimetre–gram–second system of units (CGS), the corresponding quantity is . Robert A. Millikan and Harvey Fletcher's oil drop experiment first directly measured the magnitude of the elementary charge in 1909, differing from the modern accepted value by just 0.6%. Under assumptions of the then-disputed atomic theory, the elementary charge had also been indirectly inferred to ~3% accuracy from bl ...
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Polarization (waves)
Polarization ( also polarisation) is a property applying to transverse waves that specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. A simple example of a polarized transverse wave is vibrations traveling along a taut string ''(see image)''; for example, in a musical instrument like a guitar string. Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to the string. In contrast, in longitudinal waves, such as sound waves in a liquid or gas, the displacement of the particles in the oscillation is always in the direction of propagation, so these waves do not exhibit polarization. Transverse waves that exhibit polarization include electromagnetic waves such as light and radio waves, gravitational waves, and transverse sound waves ( shear waves) in solids. An electromagneti ...
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Carrier Frequency
In telecommunications, a carrier wave, carrier signal, or just carrier, is a waveform (usually sinusoidal) that is modulated (modified) with an information-bearing signal for the purpose of conveying information. This carrier wave usually has a much higher frequency than the input signal does. The purpose of the carrier is usually either to transmit the information through space as an electromagnetic wave (as in radio communication), or to allow several carriers at different frequencies to share a common physical transmission medium by frequency division multiplexing (as in a cable television system). The term originated in radio communication, where the carrier wave creates the waves which carry the information (modulation) through the air from the transmitter to the receiver. The term is also used for an unmodulated emission in the absence of any modulating signal. In music production, carrier signals can be controlled by a modulating signal to change the sound property o ...
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Electron Mass
The electron mass (symbol: ''m''e) is the mass of a stationary electron, also known as the invariant mass of the electron. It is one of the fundamental constants of physics. It has a value of about or about , which has an energy-equivalent of about or about Terminology The term "rest mass" is sometimes used because in special relativity the mass of an object can be said to increase in a frame of reference that is moving relative to that object (or if the object is moving in a given frame of reference). Most practical measurements are carried out on moving electrons. If the electron is moving at a relativistic velocity, any measurement must use the correct expression for mass. Such correction becomes substantial for electrons accelerated by voltages of over . For example, the relativistic expression for the total energy, ''E'', of an electron moving at speed v is :E = \gamma m_\text c^2 , where the Lorentz factor is \gamma = 1/\sqrt . In this expression ''m''e is the "rest ...
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Intensity (physics)
In physics, the intensity or flux of radiant energy is the power transferred per unit area, where the area is measured on the plane perpendicular to the direction of propagation of the energy. In the SI system, it has units watts per square metre (W/m2), or kg⋅ s−3 in base units. Intensity is used most frequently with waves such as acoustic waves (sound) or electromagnetic waves such as light or radio waves, in which case the ''average'' power transfer over one period of the wave is used. ''Intensity'' can be applied to other circumstances where energy is transferred. For example, one could calculate the intensity of the kinetic energy carried by drops of water from a garden sprinkler. The word "intensity" as used here is not synonymous with " strength", "amplitude", " magnitude", or " level", as it sometimes is in colloquial speech. Intensity can be found by taking the energy density (energy per unit volume) at a point in space and multiplying it by the velocity at ...
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Atomic Units
The Hartree atomic units are a system of natural units of measurement which is especially convenient for atomic physics and computational chemistry calculations. They are named after the physicist Douglas Hartree. By definition, the following four fundamental physical constants may each be expressed as the numeric value 1 multiplied by a coherent unit of this system: * Reduced Planck constant: \hbar, also known as the atomic unit of action * Elementary charge: e, also known as the atomic unit of charge * Bohr radius: a_0, also known as the atomic unit of length * Electron mass: m_\text, also known as the atomic unit of mass Atomic units are often abbreviated "a.u." or "au", not to be confused with the same abbreviation used also for astronomical units, arbitrary units, and absorbance units in other contexts. Defining constants Each unit in this system can be expressed as a product of powers of four physical constants without a multiplying constant. This makes it a coh ...
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Ponderomotive Force
In physics, a ponderomotive force is a nonlinear force that a charged particle experiences in an inhomogeneous oscillating electromagnetic field. It causes the particle to move towards the area of the weaker field strength, rather than oscillating around an initial point as happens in a homogeneous field. This occurs because the particle sees a greater magnitude of force during the half of the oscillation period while it is in the area with the stronger field. The net force during its period in the weaker area in the second half of the oscillation does not offset the net force of the first half, and so over a complete cycle this makes the particle move towards the area of lesser force. The ponderomotive force Fp is expressed by :\mathbf_= -\frac \nabla (E^2) which has units of newtons (in SI units) and where ''e'' is the electrical charge of the particle, ''m'' is its mass, ''ω'' is the angular frequency of oscillation of the field, and ''E'' is the amplitude of the electric ...
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Electric Constant
Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric constant, or the distributed capacitance of the vacuum. It is an ideal (baseline) physical constant. Its CODATA value is: : (farads per meter), with a relative uncertainty of It is a measure of how dense of an electric field is "permitted" to form in response to electric charges, and relates the units for electric charge to mechanical quantities such as length and force. For example, the force between two separated electric charges with spherical symmetry (in the vacuum of classical electromagnetism) is given by Coulomb's law: :F_\text = \frac \frac Here, ''q''1 and ''q''2 are the charges, ''r'' is the distance between their centres, and the value of the constant fraction 1/4 \pi \varepsilon_0 (known as the Coulomb constant, ''k''e) is ap ...
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Harmonic Generation
Harmonic generation (HG, also called multiple harmonic generation) is a nonlinear optical process in which n photons with the same frequency interact with a nonlinear material, are "combined", and generate a new photon with n times the energy of the initial photons (equivalently, n times the frequency and the wavelength divided by n). General process In a medium having a substantial nonlinear susceptibility, harmonic generation is possible. Note that for even orders (n = 2,4,\dots), the medium must have no center of symmetry (non-centrosymmetrical). Because the process requires that many photons are present at the same time and at the same place, the generation process has a low probability to occur, and this probability decreases with the order n. To generate efficiently, the symmetry of the medium must allow the signal to be amplified (through phase matching, for instance), and the light source must be intense and well-controlled spatially (with a collimated laser) and temporal ...
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