Homogeneous broadening

Homogeneous broadening

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Homogeneous broadening is a type of emission spectrum
Emission spectrum
The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted by the element's atoms or the compound's molecules when they are returned to a lower energy state....

 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
Spectral linewidth
The spectral linewidth characterizes the width of a spectral line, such as in the electromagnetic emission spectrum of an atom, or the frequency spectrum of an acoustic or electronic system...

 is its natural linewidth, with a lorentzian profile.

Broadening in laser systems

Broadening in laser physics is a physical phenomenon that affects the lineshape 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 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 an indeterminacy, 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 indeterminacy, there can be two types of broadening. If the indeterminacy 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. 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 trace impurity element that is inserted into a substance in order to alter the electrical properties or the optical properties of the substance. In the case of crystalline substances, the atoms of the dopant very commonly take the place of elements that...

s, the local electric field is different for each emitter, and so the Stark effect
Stark effect
The Stark effect is the shifting and splitting of spectral lines of atoms and molecules due to presence of an external static electric field. The amount of splitting and or shifting is called the Stark splitting or Stark shift. In general one distinguishes first- and second-order Stark effects...

 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). One or more phenomenon 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
Magnetic resonance
Magnetic resonance can mean:*Nuclear magnetic resonance*Electron spin resonance*Magnetic resonance imaging *Functional magnetic resonance imaging *Muon spin spectroscopy...

 as well, where the frequency range is in the radiofrequency region for NMR
NMR may refer to:Applications of Nuclear Magnetic Resonance:* Nuclear magnetic resonance* NMR spectroscopy* Solid-state nuclear magnetic resonance* Protein nuclear magnetic resonance spectroscopy* Proton NMR* Carbon-13 NMR...

, and one can also refer to these effects in EPR
Electron paramagnetic resonance
Electron paramagnetic resonance or electron spin resonance spectroscopyis a technique for studying chemical species that have one or more unpaired electrons, such as organic and inorganic free radicals or inorganic complexes possessing a transition metal ion...

 where the lineshape is observed at fixed (microwave
Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...

) frequency and in a magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...