Talk:Electromagnetic wave equation

message: I've noticed that the equations given in the article (including the ones in the introduction) are for waves in vacuum, but that is not clear. The article even states "The electromagnetic wave equation (...) describes the propagation (...) through a medium or in a vacuum." right before the equations. Is there a reason for this? Other articles (for example Maxwell's Equations) present first the general formulation and then the vacuum case. Shouldn't this be corrected? Arnoques (talk) 19:08, 21 November 2008 (UTC)
replies: text: I agree. I came to this page to find the general solution and was surprised to not find it. Blablabliam (talk) 17:40, 21 January 2022 (UTC)
replies: text: You missed that  v_{ph}  depends on the media parameters.  The equation is general. Constant314 (talk) 18:12, 21 January 2022 (UTC)
thread_title: Equations for waves in a medium

message: Shouldn't we have a centralized debate over nomenclature somewhere? I haven't found it. (Disclaimer: I was raised on Purcell and Griffiths.) Melchoir 22:28, 11 November 2005 (UTC)
thread_title:  Discussion of nomenclature

message: Rdrosson,
it has been a pleasure writing with you. Complexica 22:57, 6 November 2005 (UTC)
replies: text: Keep up the good work.  You have a lot of good ideas, and you have made some excellent contributions to improving this article. -- Rdrosson 23:47, 6 November 2005 (UTC)
thread_title: Writing this article

message: You get more general wave equation whenever you consider Maxwell's equations for source-free and charge-free linear media at a frequency ω:
: \nabla \times \frac{1}{\mu} \nabla \times \mathbf{E} = \frac{\omega^2}{c^2} \varepsilon \mathbf{E}
with the constraint \nabla\cdot\varepsilon\mathbf{E}=0.  Or, in terms of the magnetic field:
:\nabla \times \frac{1}{\varepsilon} \nabla \times \mathbf{H} = \frac{\omega^2}{c^2} \mu \mathbf{H}
with the constraint \nabla\cdot\mu\mathbf{H}=0.
For lossless materials, these have propagating solutions with a well-defined group velocity whenever you have at least one direction with translational symmetry, including discrete translational symmetry (periodicity, as in a photonic crystal).  The solutions in such cases are given by Bloch waves.
(Note that it is easier to write in general as a function of frequency ω than as a function of time, to handle the case of dispersive materials.  As a function of time, you need to convolve the susceptibility with the correpsonding field, which gets messy.)
It would be nice if the article weren't quite so narrow.  Right now, I feel like there is so much focus on special cases and on reiterating stuff that appears in Maxwell's equations that you can't quite see the forest for the trees.
—Steven G. Johnson 20:42, 16 December 2005 (UTC)
thread_title:  Way too specific 

message: This article failed WP:WIAGA 2b (lck of inline sitations. Tarret 22:12, 20 September 2006 (UTC)
thread_title: GA Failed

message: If you look at [Maxwell - First to propose that light is an electromagnetic wave], it would be helpfull, to introduce by defining ρ=0 in the objected area. 
A little bit confusing if after having read about Maxwells div(D)=ρ, you see suddenly div(E)=0
LRJ 138.246.7.104 20:31, 15 March 2007 (UTC)
thread_title:  div E = 0 ? 

message: I think that the Inconsistencies section could use some more work.  One thing that is not made clear is whether or not the changing electric field actually creates a change in the line integral of the magnetic field (it does, but this is not made clear.)  Second, perhaps the relationship between \nabla\cdot j and j\,\! could be expanded.  Finally, I don't see the relationship between conservation of charge and the displacement current.  Perhaps substituting \nabla\cdot j = -\frac{\partial \rho}{\partial t} back into the equations above would make this clearer.
Iain marcuson 20:03, 21 October 2007 (UTC)
thread_title:  Inconsistencies between . . . 

message: I have explained (I hope) what seems to be wrong with the diagram :Image:Spectre.svg at Talk:Terahertz radiation#Spectrum graph, where a related, derived, diagram was also removed. 84user (talk) 23:09, 27 May 2009 (UTC)
replies: text: So should we put in the better diagram?  The issues with the old diagram seem minor.  Its purpose is to show a quick glance of the EM spectrum.  Not to be a strict reference. Daniel.Cardenas (talk) 01:14, 28 May 2009 (UTC)
thread_title:  Diagram misleading 

message: In the text accompanying each equation, the symbols used in that equation should be defined so that someone not familiar with what they denote/mean will be able to know what those symbols denote/mean.  The first two equations on this page fail to define three the symbols used therein.  — Preceding unsigned comment added by 147.177.39.192 (talk) 13:24, 14 September 2011 (UTC)
replies: text: I only see one symbol that might require being defined -- The time partial differential \frac{\partial}{\partial t}. What other symbols are you talking about? Dauto (talk) 17:35, 14 September 2011 (UTC)
thread_title:  define symbols used in the equations? 

message: This article seems to intend to examine general electromagnetic waves, yet only discusses propagating waves in vacuum which are observed infinitely far away from radiation sources. This misses out on other important classes of waves that obey the same equation but occur nearer to sources or nearby material interfaces/surfaces. These other solutions cannot be described conveniently by superpositions of real plane waves, due to their divergent nature.
First of all, we can consider plane waves where the wavevector is complex. For example, an evanescently decaying wave near a surface, as in total internal reflection, is described by the in-plane wavevector being real-valued and exceeding \omega/c, however, the out of plane wavevector is imaginary so that \vec k^2 = \omega^2/c^2 (note in contrast that |\vec k| \neq \omega/c, for evanescent waves !).
In addition, there are solutions that obey the homogeneous Maxwell equations, corresponding to the fields in vacuum around some source. For example the field around a radiating dipole follows the wave equation everywhere, except at the position of the dipole itself. The solution includes near fields that are not conveniently described by superpositions of plane waves.
Another related limitation is that the entire article is focussed on a simple form of wave equation which only occurs in vacuum or in isotropic media, but which is not applicable to some other basic kinds of linear media. For instance the equations shown cannot describe propagation of light through a birefringent material like calcite.
--Nanite (talk) 17:37, 1 October 2015 (UTC)
thread_title:  Many more wave solutions: evanescent waves and near fields, birefringence, ... 

message: The general solution given in this section is not quite correct, as I see it. The expressions for  and  are formulated in terms of exactly the same , implying that  and  fields are the same (which they can't be already due to dimensions). Isn't it that one could salvage this by multiplying the expression for  by the speed of light and taking the cross product of one of the two with the normalized  vector? The further expressions below do not have this problem, as they are formulated in terms of independent  and . But I strongly think that this is also not the best way, as these two obviously are related, namely in the same way as above, the absolute values differ by a factor  and one is perpendicular to the other. This is implied in the statement "the magnetic field ... is related to the electric field by the relation", but I strongly think this should be made explicit. Seattle Jörg (talk) 09:45, 24 March 2022 (UTC)
replies: text: I agree with your concern.  I know what it means, but it could be misleading.  Also, the solution is a plane wave.  There are other solutions that are not plane waves. For example, there are also cylindrical wave and spherical wave solutions.  Constant314 (talk) 16:03, 24 March 2022 (UTC)
replies: text: No, it is not necessarily a plane wave, it is just a travelling wave with any functional form along its propagation direction. For very mild assumptions, you can write this travelling wave as a (possibly infinite) sum of plane waves, that is, essentially a Fourier transform. For any of those summands the thing with multiplication by c and cross product holds, you can pull those through the summation, so it holds also for the general travelling wave. Specifically, it holds also for circularly polarized waves (which are the sum of two plane waves with 90° phase shift). Seattle Jörg (talk) 15:20, 4 April 2022 (UTC)
replies: text: The solution shown is a plane wave because the solution is everywhere the same on any plain perpendicular to the wave vector.  That is not the case with cylindrical solutions, which are also  homogeneous solutions.  I believe that it is true that you can decompose a cylindrical wave, at a point, into a sum of plane waves, I also believe that that sum will not converge to the cylindrical wave everywhere.  You can certainly improve what is written, just please do not imply that all the homogeneous solutions have form g(k·x - ωt), unless you have a reliable source that says that. Constant314 (talk) 15:49, 4 April 2022 (UTC)
replies: text: Don't cylindrical waves require a source at the axis, and therefore are not homogeneous?  And re plane wave, do some sources take that to mean sinusoidal, or not? Dicklyon (talk) 16:30, 4 April 2022 (UTC)
replies: text: Cylindrical solutions to boundry value problems require axial symmetry.  A practical example is a round fiber optic, a coaxial cable, and a round wave guide. In an unbounded vacuum, cylindrical waves are just as good as plane waves for being homogeneous.Constant314 (talk) 17:14, 4 April 2022 (UTC)
replies: text: Then spherical waves are homogeneous solutions, too? Singularities at axis or center are OK? Dicklyon (talk) 17:58, 4 April 2022 (UTC)
replies: text: I believe that spherical waves are also homogeneous solutions.  Homogeneous solutions are the source free solutions.  So, point source, line source, or plane source doesn't matter.  As far as I know, there are no physical source distributions that can produce a plane wave, cylindrical wave, or a spherical wave.  They are all equal in that way. Constant314 (talk) 18:11, 4 April 2022 (UTC)
replies: text: Sorry, perhaps this discussion got a bit off track because my initial comment was not formulated perfectly accurately: the first lines of the section we are talking about say that the general solution can be written as a linear superposition of waves of the form... And this is true. It is even true if you restrict g to be a sine function, because any (or nearly any) function can be Fourier-transformed. So the point I am making is that the g of E and B field are not the same, but related in a known way which we should make explicit. So no, not all homogeneous solutions are travelling waves, but all can be written as superpositions of travelling waves. Does anybody doubt that? Seattle Jörg (talk) 10:53, 5 April 2022 (UTC)
thread_title:  Solutions to the homogeneous electromagnetic wave equation 

message: :The B-class criteria #1 states;  The "More citations needed" tag at the top of the page is untypical of a B-class article. Considering the enormous amount of unsourced content, which includes many equations, the article fails the criteria so I am reassessing to C-class.
:The "See also" section and three subsections have thirty-one links which appear to be rather long. When this is added to the "Further reading" section, with four subsections and fifteen links, they could both be examined for trimming. Especially when "Undergraduate-level textbooks" and Graduate-level textbooks" are included since Wikipedia is not a textbook or repository.  --  Otr500 (talk) 13:22, 1 March 2023 (UTC)
thread_title: Article issues and classification