Laser Broadening: Impact on Wavelengths

[chrisphd]

In Quantum mechanics lectures we are learning that several factors influence the wavelength produced from a laser. These factors include doppler broadening of moving atoms in the laser, the uncertainty of the transition energy levels themselves due to the uncertainty principle, etc. Previously we learned that in a laser cavity of length L, due to boundary conditions, only certain wavelengths are possible, ie, wavelength*n/2 = L, where n is an integer.

Question:
Shouldn't the boundary condition limit the output of a laser to a single frequency rather than a small range of frequencies from w to w+dw?

 

[f95toli]

No, because there is no such thing as a cavity with an exact length.
Fabry-Pérot etalons (which are essentially "cavities") can be used to stabilize lasers, but they are still be limited by variations in the length due to e.g. thermal variations.
Building good etalons is almost a field of its own in science (I know a couple of people who spend ALL their time doing it) and you should be able to find plenty of papers that describes how it is done.

 

[Entropia]

I would like to clarify that while the boundary condition does play a role in limiting the possible wavelengths produced by a laser, it is not the only factor that influences the output. In fact, as mentioned in the content, there are several other factors such as doppler broadening and the uncertainty principle that also impact the resulting wavelengths.

The boundary condition, as described, only allows for specific wavelengths that satisfy the equation wavelength*n/2 = L, where n is an integer. However, this does not mean that only a single frequency can be produced. In reality, there is a range of wavelengths that can satisfy this equation, resulting in a small range of frequencies from w to w+dw.

Moreover, the uncertainty principle also plays a crucial role in determining the range of frequencies that can be produced by a laser. According to this principle, there is always a level of uncertainty in the energy levels of atoms, which can result in a broadening of the wavelength range.

Therefore, it is important to consider all these factors when discussing the impact of laser broadening on wavelengths. While the boundary condition does limit the output to a certain range, it is not the sole factor responsible for the resulting wavelengths.