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Assume an electromangetic wave with the wavelength of 1 mm and a straight wavefront of 1 cm wide. So, in vacuum, does the wavefront spread out to the sides and get wider?

P.S. It would be nice if you could explain with what methods we could produce such a precise wave shape, especially on the edges/endpoints of the wavefront as the diffraction tends to prevent it.

Xfce4
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    Well, you can’t keep it 1mm in diameter - it will spread. – Jon Custer Sep 21 '21 at 13:39
  • Electromagnetic waves follow the wave equation of which $\cos [k(x - ct)]$ is a solution. So you can make waves that don't spread out if the initial conditions are right. – Connor Behan Sep 21 '21 at 13:56
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    Consider the Fourier components of the wavefront perpendicular to the direction of propagation. A plane wave has an infinite frequency range. A 1mm spot does not. So the 1mm spot spreads as it propagates. Also look at Gaussian optics theory. – Jon Custer Sep 21 '21 at 13:57
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    @ConnorBehan - that works for plane waves, not the OP’s situation. – Jon Custer Sep 21 '21 at 13:59
  • @JonCuster You mean the wavefront (not the wavelength) will get longer/larger, right? If this is related with Huygen's principles on the edges, then it looks like the spread would be just too fast and also would imply that we could detect the light from the sides (the wave amplitude would be very small tough). Am I wrong? – Xfce4 Sep 21 '21 at 14:11
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    Not surprisingly, Huygens principal and the Fourier components are directly linked. Why does the spread have to be ‘too fast’ - is the spread of a Gaussian beam too fast? Same math applies. – Jon Custer Sep 21 '21 at 14:20
  • I expect it to be fast because it 'seemed' to me that the speed of diameter increase around a single point source (Huygen's principle) is the speed of light, in the case of electromagnetic waves. – Xfce4 Sep 21 '21 at 14:23

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Due to quantum (and possibly other) effects, primarily the uncertainty principle, there will always be some spread, as explained here. It is not possible, even in principle, to produce a light beam with zero divergence, unless it is infinitely large (in which case is a plane wave). In general, the greater the initial diameter of the beam, the smaller the divergence.

The picture in the article does not accurately depict such a plane wave because the plane wavefronts are actually infinitely large, unlike what the picture seems to suggest.

Vincent Thacker
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