What is the relationship between a laser's gain curve and its natural linewidth?

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Discussion Overview

The discussion centers on the relationship between a laser's gain curve and its natural linewidth, exploring definitions, characteristics, and implications of both concepts in the context of laser physics.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on the definition of the gain curve and its relationship to the natural linewidth, questioning if they are the same concept.
  • Another participant explains that the gain curve represents the gain at various frequencies per round trip in the laser cavity and notes that it is not the same as the natural linewidth.
  • A participant inquires whether the natural linewidth corresponds to the width of the mode currently lasing or if it refers to the linewidth associated with a single photon emitted from an atom.
  • It is stated that the natural linewidth arises from natural broadening due to the uncertainty of the energy gap width, which is influenced by the finite lifetime of atoms in the upper state, and is typically around 8 MHz.
  • Additional forms of broadening, such as Doppler broadening, are mentioned, along with the influence of laser cavity finesse on the emitted mode linewidth.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the relationship between the gain curve and natural linewidth, with differing interpretations and clarifications being offered.

Contextual Notes

The discussion highlights the complexity of the concepts involved, including the dependence of natural linewidth on upper state lifetime and the influence of various broadening mechanisms, which remain unresolved in terms of their interplay with the gain curve.

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Can someone please explain what exactly the gain curve of a laser is? Is it exactly the same thing as the natural linewidth of the laser [a graph of intensity vs frequency] or am I off track?

I found this graphhttp://www.phys.ksu.edu/perg/vqm/laserweb/Ch-5/C5s1p5.htm that tries to explain the gain curve but it has the y-axis labelled as GL, the loop gain. What exactly is this? Is it a measure of intensity/laser power?
 
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A gain curve depicts how much gain a particular frequency will have per round trip in the laser cavity. Actual gain will depend on mirror reflectivities. Loop gain is a good way to depict the gain in a particular active medium without having to rely on parameters of the laser cavity.

The gain curve gives a general idea of how many longitudinal modes will appear and their relative intensities. For example, if the longitudinal mode separation was 1 THz and the gain curve had a width of 5 THz above threshold, you can expect about 5 longitudinal modes to appear, with the relative intensities of each tapering off as one moves from the centre of the gain curve.

The Gain curve is not the same as the natural linewidth of a laser.

Claude.
 
Ok, so would you say that the natural linewidth is the width of the mode that the laser is currently lasing at?

Or is the natural linewidth [as the term 'natural' suggests] the linewidth associated with a single photon as emited from an atom?
 
The natural linewidth is the linewidth due to natural broadening. Natural Broadening is due to the uncertainty of the width of the energy gap, which arises because of the finite lifetime of atoms in the upper state.

Typically the natural linewidth is about 8 MHz. The natural linewidth is dependent on the upper state lifetime.

There are other forms of broadening, such as Doppler broadening.

The linewidth of the emitted mode also depends on the finesse of the laser cavity.

Claude.