Plane wave is the simplest form of non-stationary electromagnetic field. It was theoretically predicted circa one and half century ago and was studied together with some related phenomena like reflection and refraction all that time by numerous scholars. And yet, this subject was not studied properly. The main sources of knowledge are Principles of Optics (M. Born and E. Wolf) and Classical Electrodynamics (J.D. Jackson) and as for all the rest authors, I do not think that they would go further. To know what is found in the literature, it suffices to read certain pages of these two books and below, when I say something like "found in the literature", I mean, first of all, these two sources. Description of ordinary reflection and refraction is quite trivial and I do not discuss it.
The first non-trivial phenomenon related to propagation of plane electromagnetic waves is that of total internal reflection. Description of this phenomenon found in the literature is completely unsatisfactory. The authors merely failed to understand it. Complete theory would provide explicit form of amplitudes and phases of incident, reflected and evanescent waves as certain functions of dielectric parameters and the angle of incidence. These expressions should be obtained by matching the fields on the interface with use of boundary conditions. However, the authors could not complete this work properly. All their results have been obtained under a wrong assumption of existence of electromagnetic waves whose wave vector has imaginary part. In fact, no waves of this kind exist. Even after simplifying the task this way, they did not obtain these values and instead of doing this, they turn to experimental data which neither confirm nor contradict their considerations because the authors do not claim anything at all and what they wrote has nothing to do with these data. As their studies have not gave any certain results, they are of no use and the authors would better no to write anything at all.
Theoretical analysis of the phenomenon should give the following results. First, incident, reflected and transmitted evanescent waves have different phases on the interface which should be obtained explicitly. Second, in spite of total reflection, amplitude of the reflected wave, in general, is not equal to that of the incident one. Third, amplitudes and phase shifts depend on possible presence of another dielectric behind the interface which steals some portion of the energy flux. Only understanding the phenomenon would allow the authors complete the analysis properly and obtain these results. However, they failed to do this. Hence, the first non-trivial problem related to plane electromagnetic waves, theoretical physicists of XX century encountered, appeared to be unsolvable for them.
Two more interesting branches of the theory of plane electromagnetic waves would be created by adding an infinitesimally thing conducting layer. One of them would describe interaction of a wave with such a conducting plane, another is more general, in which this plane coincides with an interface between two distinct media. None of them have been considered in the literature. At the same time, theory of plane electromagnetic waves is apparently incomplete without these two branches. During one and half century theoretical physicists have not studied electromagnetic waves propagation in vicinity of conducting plane, at least, openly. But it is better late than never. I have done it. In my work "Maxwell Equations and Total Internal Reflection" viXra:1408.0060, I present complete solution of the problem of total internal reflection and in another work, "Reflection of Plane Electromagnetic Wave from Conducting Plane" viXra:1408.0125, I do all the rest. Among other resullts, I specify conditions under which a plane electromagnetic wave can be totally absorbed and turned into a wave of charge and current densities on the conducting interface. Now the theory of plane electromagnetic wave is complete and I have an opportunity to see, whether anybody needs it. My observations of two decades show that in fact nobody needs any theoretical physics because electricians are able to do anything without understanding any theory.
The first non-trivial phenomenon related to propagation of plane electromagnetic waves is that of total internal reflection. Description of this phenomenon found in the literature is completely unsatisfactory. The authors merely failed to understand it. Complete theory would provide explicit form of amplitudes and phases of incident, reflected and evanescent waves as certain functions of dielectric parameters and the angle of incidence. These expressions should be obtained by matching the fields on the interface with use of boundary conditions. However, the authors could not complete this work properly. All their results have been obtained under a wrong assumption of existence of electromagnetic waves whose wave vector has imaginary part. In fact, no waves of this kind exist. Even after simplifying the task this way, they did not obtain these values and instead of doing this, they turn to experimental data which neither confirm nor contradict their considerations because the authors do not claim anything at all and what they wrote has nothing to do with these data. As their studies have not gave any certain results, they are of no use and the authors would better no to write anything at all.
Theoretical analysis of the phenomenon should give the following results. First, incident, reflected and transmitted evanescent waves have different phases on the interface which should be obtained explicitly. Second, in spite of total reflection, amplitude of the reflected wave, in general, is not equal to that of the incident one. Third, amplitudes and phase shifts depend on possible presence of another dielectric behind the interface which steals some portion of the energy flux. Only understanding the phenomenon would allow the authors complete the analysis properly and obtain these results. However, they failed to do this. Hence, the first non-trivial problem related to plane electromagnetic waves, theoretical physicists of XX century encountered, appeared to be unsolvable for them.
Two more interesting branches of the theory of plane electromagnetic waves would be created by adding an infinitesimally thing conducting layer. One of them would describe interaction of a wave with such a conducting plane, another is more general, in which this plane coincides with an interface between two distinct media. None of them have been considered in the literature. At the same time, theory of plane electromagnetic waves is apparently incomplete without these two branches. During one and half century theoretical physicists have not studied electromagnetic waves propagation in vicinity of conducting plane, at least, openly. But it is better late than never. I have done it. In my work "Maxwell Equations and Total Internal Reflection" viXra:1408.0060, I present complete solution of the problem of total internal reflection and in another work, "Reflection of Plane Electromagnetic Wave from Conducting Plane" viXra:1408.0125, I do all the rest. Among other resullts, I specify conditions under which a plane electromagnetic wave can be totally absorbed and turned into a wave of charge and current densities on the conducting interface. Now the theory of plane electromagnetic wave is complete and I have an opportunity to see, whether anybody needs it. My observations of two decades show that in fact nobody needs any theoretical physics because electricians are able to do anything without understanding any theory.
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