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. ;-)