Waves are weird things, but diffraction makes somewhat sense to me when viewed through the Huygens-Fresnel principle. Except I don’t see how the laser can remain in a narrow beam if that’s how waves behave. Is there a high school level explanation works for both why waves diffract and why laser beams stay narrow?
the laser part…
the waves coming out of a laser DO diffract/spread. They just START (in theory) perfectly both in phase and going exactly the same direction.
Diffraction “spreading” is inversely proportional to the width of the aperture.
So take a 2 mm wide laser beam.
At say 100 meters that beam will have spread to a width of XYZ (not doing the calc right now), where XYZ is bigger than 2 mm.
At 200 meters it will be roughly twice XYZ wide.
A wider beam to start with will spread/diffract less in the same distance, due to diffraction being inversely proportional to the beam width.
An infinitely wide beam would never spread even over an infinite distance 
A laser beam doesn’t stay narrow, it just diffracts at a much lower rate (angle) than, say, a flashlight.
From here: Diffraction - Wikipedia
Also check out the hot link here: Gaussian beam - Wikipedia
naita, the reason lasers stay narrow for so long is that they are very wide relative to the wavelength of light. If you’re only a small angle off from looking straight down the beam, all those spots across the face of the beam tend to cancel out when you add them up.
Using the Huygens-Fresnel principle you can see how a wave propagates through space. There are at least three types of wavefronts that will propasgate as copies of themselves, although they might change size – a plane wave, a spherical wave, and a single-mode laser wavefront, the simplest of which is a TEM[sub]00[/sub] wavefront, which has a Gaussian intensity profile, brightest in the center and tailing off in a bell-shaped curve. (There are other wavefronts that will propagate as well, but this one has the smallest size).
As you properly put it, the H-F principle holds that each point on a wavefront acts as a new source. There’s also a directional sensitivity to the beam emanating from each point. If you essentially add up the contributions from each point on the wavefront, you get the resulting wavefront farther down the track. A plane wave (a sheet of light, essentially, extending to infinity) will propagate forward as a sheet. A spherical shell of light will propagate outwards, orming a similar, albeit larger, sheet. You can sorta see that these work by the essential symmetry of the situation. It’s not at all obvious that a gaussian laser wavefront will propagate to form a larger gaussian wavefront, but it does. If you want the gory details, see Goodman’s Introduction to Fourier Optics, or Amnon Yariv’s Quantum Electronics, or Siegman’s Lasers, or any of a number of texts. Unfortunately, they’re not high-school level. To add up the contributions from the wavefront requires calculus, and, even in the approximations normally used (like in Goodman), there’s a lot of it.
The essence is that the beam has a smallest point, called the waist. Going in either direction from this, the beam expands, but slowly at first, by an amount determined by the waist size, the beam wavelength, and the refractive index of the medium it’s passing through. There’s a characteristic length, the Rayleigh Range, over which the size is relatively constant. Outside that, the beam expands about at a constant solid angle, the far-field angle. (In reality, the points of constant relative intensity actually define a hyperboloid of revolution).
I don’t have the time and energy (I could have, but I have different priorities) to resuscitate my calculus skills sufficiently to make sense of the equations, but would I get the same diffraction starting with a cross-section of a beam with a diameter of x, as from an aperture of diameter x blocking a wider beam?
I think that’s what other posts have said, but I’m afraid I’m misunderstanding and not accounting for some nasty maths.
Roughly speaking yes, assuming you are talking about a laser beam or blocking a larger laser beam to make one of a size equivalent to the smaller beam.
The only real difference is the intensity distribution across the aperture, which affects the diffraction “downstream” to some extent, but that more of a detail than a major driver.
If you want another interesting aspect of diffraction look up Poison’s spot (Poisson’s spelling?) I actually used one once.