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 of frequencies of electromagnetic radiation emitted due to an electron making a atomic electron transition, transition from a high energy state to a lower energy st ...
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 dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to iden ...
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 Spectral line shape describes the form of a feature, observed in spectroscopy, corresponding to an energy change in an atom, molecule or ion. This shape is also referred to as the spectral line profile. Ideal line shapes include Lorentzian, Gaussia ...
of the laser emission profile. The laser emission is due to the (excitation and subsequent) relaxation of a quantum system (atom, molecule, ion, etc.) between an excited state (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 dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission (electromagnetic radiation), emission or absorption (electromagnetic radiation), absorption of light in a narrow frequency range, ...
. 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 dopants, the local electric field 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 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^ The parameter \mu i ...
. 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, and one can also refer to these effects in EPR where the lineshape is observed at fixed ( microwave) frequency and in a
magnetic field A magnetic field is a vector 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 to its own velocity and to ...
range.


Semiconductors

In a
semiconductors A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glas ...
, if all oscillations have the same eigenfrequency \omega_0 and the broadening in the imaginary part of the dielectric function \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

*
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 ...
* Spectral line shape


References

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