Every emitting species (atom, molecule, colour centre etc.) has a natural transition linewidth. This can be broadened in a solid/liquid/gaseous environment by a number of factors. Homogeneous broadening affects each emitting species identically, inhomogeneous broadening effects each one differently. In the latter case, the result is a broad Gaussian linewidth, made up of a number of spectrally shifted lineshapes, each of which has been homogenously groadened from the Lorentzioan lineshape of the idealised forced dipole oscillator.

Does it mean that inhomogeneous broadening can take place in gaseous medium only?

No - molecules in a liquid are in constant motion, and so their local solvent cage is constantly changing. At any moment in time, each molecule has a different environment causing a significant inhomogeneous broadening. The time for the environment to change such that the (homogenrous)  lineshape of any one species traverses the breadth of the inhomogeneous lineshape is the "Spectral cross relaxation time".  In an amorphous solid, this inhomogeneity is effectively frozen in time.

The homogenous (collisional) lineshape broadening  is dependent on  pressure in gases.

The inhomogeneous broadening arises from temperature in gases.

The homogenous broadening in solids depends on temperature.

The inhomogeneous broadening in solids arises from dislocations and voids.

The natural broadening is a consequence of uncertainty principles. 

The homogeneous and inhomogeneous broadening may occur in solids ( crstals), liquids (dyes), gases and semiconductors (LED and laser diods).

It means that solid state lasers such as semiconductor lasers are inherently homogeneously broadened and to make them inhomogeneously broadened we have to modify their internal structure to include dislocations and voids.

At any instant in time, different atoms are in a different state of collision, and so strictly speaking, collisional broadening is inhomogeneous, but the time between collisions is very short, and very quickly they all on average experience the same perturbation. This also appplies for Doppler broadening.

You should note that Pressure and temperature are related!!!!!

And that not all solid state is crystalline, in which terms like "dislocations and voids" apply

Is there any relation between homogeneous broadening and spatial hole burning phenomenon in semiconductor lasers?

SPECTRAL hole burning is used to encode information in an inhomogeneous lineshape, in which an individual homogeneous lineshape can temporarily (saturable absorption) or permanently (photochemistry) be burnt in a much broader inhomogeneous lineshape.

Most important application for lineshape  broadening  is in small signal gain and saturation intensity of broadened gain media:

Stimulated Cross-section (nu)= [A21 lambda2/ 8pi n2] g (nu)

and , Small-signal gain (nu)=inverted population× Stimulated  cross- section (nu)

and, Saturation intensity (nu)= h nu / Stimulated cross section.T2

Therefore, the gain and saturation properties are related to the homogeneous or inhomogeneous broadened width. The latter depends on temperature or pressure.

In experiments, Temperature and pressure are separately controlled. Please kindly visit our papers available in RG on the gain and saturation properties of various broadened gain media: Nitrogen ion laser (collisional broadening), XeF excimer  laser (collisional broadening), CVL (Doppler broadening), Rd6G dye laser ( dominant  homogeneous broadening) and Yb: Silica fiber laser ( dominant homogeneous broadening).

Note: Dominant broadening is found by ratio of Hom. Linewidth/ In hom. Linewidth :

Ratio>>1 Hom. Broadening  is dominant.

Ratio

What is the difference between the homogeneous and inhomogeneous broadening lineshape?

Homogeneous, in a perfect gas, should be Lorentzian, whereas inhomogeneous should be Gaussian.

The broadened  line affect on gain and saturation property of gain media:

Small Signal Gain = Populated Inversion * Stimulated Emission Cross-Section

Stimulated Emission Cross Section= g(nu) A.lambda2/8pi n2

g(nu)= Line-shape that is inversely proportional to broadened Line-width according to Lorentzian (homogeneous) or Gaussian (Inhomogeneous) distributions.

Please visit our papers pertaining  gain and saturation of various lasers in RG.

In general the homogeneous broadening arises from the transition of carriers from level to another energy level, and when there is transitions between sub-levels of the destination level the inhomogeneous broadening appears. Inhomogeneous broadening causes the spectral hole burning phenomena.

Homogeneous broadening results in the natural linewidth, and is the same for all atoms/molecules in a system. Inhomogeneous is due to collisional broadening, morphological defects in a solid, sample inhomogeneity etc.

Why laser dots have inhomogeneous broadening?

Homogeneous broadening means the line broadening is the same for all oscillating systems (e.g. natural/lifetime or collisional broadening). It exhibits a Lorentzian line shape. In a homogeneously broadened gain medium the laser modes supported by said medium will compete for gain. Inhomogeneous broadening means there are slightly different resonant frequencies across the medium (e.g. energetic disorder in the material, doping). The lineshape is a Gaussian. Here the material absorption and emission will interact differently with different excitation wavelengths. An inhomogeneously broadened medium allows for simultaneous lasing of multiple longitudinal modes and also for the effect of spectral hole burning.

https://www.rp-photonics.com/inhomogeneous_broadening.html

https://en.wikipedia.org/wiki/Homogeneous_broadening

Article Lasing in Si₃N₄-organic hybrid (SiNOH) waveguides

https://en.wikipedia.org/wiki/Homogeneous_broadening

Here is a snippet from Dr. A.M. Kelley's book Condensed-Phase Molecular spectroscopy and photophysics:

"Homogeneous broadening affects every individual molecule in the ensemble in the same way. If you could take a spectrum of just one molecule (which can be done in some situations) the transition would still have the same width.

Inhomogeneous broadening results from different molecules having slightly different resonant frequencies because they are in slightly different local environments within the liquid or solid. The observed broadening of the spectrum arises from a superposition of a large number of slightly different spectra. If you could take a spectrum of just one molecule, it would be narrower than the spectrum of the ensemble average".

If nee more details on this goto chapter-7 page 132, there is a detailed explanation on why these effects occur and how you can have one in particular.

I hope this helps

Regards

Ajay Khanna