Inhomogeneous Broadening
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Homogeneous broadening is a type of
emission spectrum The emission spectrum of a chemical element or chemical compound is the Spectrum (physical sciences), spectrum of frequencies of electromagnetic radiation emitted due to electrons making a atomic electron transition, transition from a high energ ...
broadening in which all atoms radiating from a specific level under consideration radiate with equal opportunity. If an optical emitter (e.g. an atom) shows homogeneous broadening, its
spectral linewidth A spectral line is a weaker or stronger region in an otherwise uniform and continuous spectrum. It may result from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used ...
is its natural linewidth, with a Lorentzian profile.


Broadening in laser systems

Broadening in laser physics is a physical phenomenon that affects the spectroscopic line shape of the laser emission profile. The laser emission is due to the (excitation and subsequent) relaxation of a quantum system (atom,
molecule A molecule is a group of two or more atoms that are held together by Force, attractive forces known as chemical bonds; depending on context, the term may or may not include ions that satisfy this criterion. In quantum physics, organic chemi ...
, ion, etc.) between an
excited state In quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Add ...
(higher in energy) and a lower one. These states can be thought of as the eigenstates of the energy operator. The difference in energy between these states is proportional to the frequency/wavelength of the photon emitted. Since this energy difference has a fluctuation, then the frequency/wavelength of the "macroscopic emission" (the beam) will have a certain width (i.e. it will be "broadened" with respect to the "ideal" perfectly monochromatic emission). Depending on the nature of the fluctuation, there can be two types of broadening. If the fluctuation in the frequency/wavelength is due to a phenomenon that is the same for each quantum emitter, there is homogeneous broadening, while if each quantum emitter has a different type of fluctuation, the broadening is ''inhomogeneous''. Examples of situations where the fluctuation is the same for each system (homogeneous broadening) are natural or lifetime broadening, and collisional or
pressure broadening A spectral line is a weaker or stronger region in an otherwise uniform and continuous spectrum. It may result from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used ...
. In these cases each system is affected "on average" in the same way (e.g. by the collisions due to the pressure). The most frequent situation in solid state systems where the fluctuation is different for each system (inhomogeneous broadening) is when because of the presence of
dopant A dopant (also called a doping agent) is a small amount of a substance added to a material to alter its physical properties, such as electrical or optics, optical properties. The amount of dopant is typically very low compared to the material b ...
s, the local
electric field An electric field (sometimes called E-field) is a field (physics), physical field that surrounds electrically charged particles such as electrons. In classical electromagnetism, the electric field of a single charge (or group of charges) descri ...
is different for each emitter, and so the
Stark effect The Stark effect is the shifting and splitting of spectral lines of atoms and molecules due to the presence of an external electric field. It is the electric-field analogue of the Zeeman effect, where a spectral line is split into several compon ...
changes the energy levels in an inhomogeneous way. The homogeneous broadened emission line will have a Lorentzian profile (i.e. will be best fitted by a Lorentzian function), while the inhomogeneously broadened emission will have a
Gaussian profile In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = \frac e^\ ...
. One or more phenomena may be present at the same time, but if one has a wider fluctuation, it will be the one responsible for the character of the broadening. These effects are not limited to laser systems, or even to optical spectroscopy. They are relevant in magnetic resonance as well, where the frequency range is in the radiofrequency region for
NMR Nuclear magnetic resonance (NMR) is a physical phenomenon in which atomic nucleus, nuclei in a strong constant magnetic field are disturbed by a weak oscillating magnetic field (in the near and far field, near field) and respond by producing ...
, and one can also refer to these effects in EPR where the lineshape is observed at fixed (
microwave Microwave is a form of electromagnetic radiation with wavelengths shorter than other radio waves but longer than infrared waves. Its wavelength ranges from about one meter to one millimeter, corresponding to frequency, frequencies between 300&n ...
) frequency and in a
magnetic field A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...
range.


Semiconductors

In
semiconductors A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping levels ...
, if all oscillations have the same eigenfrequency \omega_0 and the broadening in the imaginary part of the
dielectric function In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter (epsilon), is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more ...
\varepsilon_2(\omega) results only from a finite damping \gamma, the system is said to be homogeneously broadened, and \varepsilon_2(\omega) has a Lorentzian profile. If the system contains many oscillators with slightly different frequencies about \omega_0 however, then the system is inhomogeneously broadened.


See also

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Homogeneity (physics) In physics, a homogeneous material or system has the same properties at every point; it is uniform without irregularities. (accessed November 16, 2009). Tanton, James. "homogeneous." Encyclopedia of Mathematics. New York: Facts On File, Inc., 2 ...
*
Voigt profile The Voigt profile (named after Woldemar Voigt) is a probability distribution given by a convolution of a Cauchy-Lorentz distribution and a Gaussian distribution. It is often used in analyzing data from spectroscopy or diffraction. Definition Wi ...
*
Spectral line shape Spectral line shape or spectral line profile describes the form of an electromagnetic spectrum in the vicinity of a spectral line – a region of stronger or weaker intensity in the spectrum. Ideal line shapes include Lorentz distribution, Lorent ...


References

{{DEFAULTSORT:Homogeneous Broadening Laser science Atomic, molecular, and optical physics