Directionality of a Laser Beam

[Septim]

Hello everyone,

I am an undergraduate student studying lasers. I have hard time to comprehend why does the beam diffract upon leaving the laser, does it have something to do with the wavefront being limited in size? Can you explain why does the following formula exists and how is it derived?
$\Delta\Omega\approx\frac{\lambda^2}{A}≈(\Deltaθ)^2$

 

[sophiecentaur]

To convince yourself about this, you can take a model in the form of a line of co-phased sources, representing the exit aperture of the laser in 1D (many wavelengths wide, of course). Then calculate field at infinity in various directions by adding all the contributions, vectorially, using the path differences. (À la Young's slits calculation). It's a good exercise to do on a spreadsheet. This will give you an interference pattern with a max in the 'forward' direction and spreading out on either side. This is the first step to showing what will happen with an infinite number of points in a line. A laser with a circular output aperture will have a different pattern in detail but you have a qualitative idea. You can go into 2D and introduce any refinements you want but it's easier at that stage to believe what the books tell you.

 

[Septim]

Thanks, I think the reasoning that goes with slits can also be applied to the aperture of the laser.

 

[sophiecentaur]

Many people seem to think there's something 'special' about lasers. Coming from an RF background, I see them as being just like an open waveguide. The sums for that were established quite some while ago. ;-)

 

[sardar]

Hello undergraduate student,

The directionality of a laser beam is determined by a property called the beam divergence, which is the measure of how much the beam spreads out as it propagates. This divergence is related to the size of the laser beam and the wavelength of the light being emitted. As the beam leaves the laser, it begins to diverge due to diffraction, which is the bending of light as it passes through an aperture or around an obstacle.

The formula you mentioned, \Delta\Omega\approx\frac{\lambda^2}{A}≈(\Deltaθ)^2, is known as the Rayleigh criterion and it describes the relationship between the beam divergence (\Delta\Omega), the wavelength of the light (\lambda), and the size of the laser beam (A). It is derived from the diffraction theory and is used to calculate the minimum spot size that a laser beam can achieve at a certain distance from the source. As the beam diverges, the spot size will increase, and this formula helps us understand and predict this behavior.

In summary, the directionality of a laser beam is affected by the size of the beam and the wavelength of the light, leading to diffraction and the spreading of the beam over distance. The Rayleigh criterion is a useful tool for understanding and predicting this behavior. I hope this helps clarify the concept for you. Keep studying and good luck with your studies in lasers!