# Wave Guides: Understanding Reality

• quasar987
In summary, the conversation discusses the representation of waveguides using perfect conductors, and questions whether it accurately reflects reality. The possibility of using different models, such as free electron or quantum treatments, is also mentioned. The concept of boundary conditions and their impact on the behavior of fields is explored, with the conclusion that the parallel component of the electric field is small outside the conductor and leads to energy loss and attenuation of the wave. The question of why the parallel component is small is raised, and it is noted that inside the conductor, it is much smaller than the parallel component outside.
quasar987
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There's something I don't understand about wave guides.

We assume a perfect conductor guide, so that the atenuation is total and instantaneous and $\vec{E}=0$ inside the guide. But the parallel component of E is continuous at the boundary, so just outside the conductor, $\vec{E}_{\parallel}=0$.

But I'm thiking, this can't be a good representation of reality! Because no conductor is truly a perfect conductor. The attenuation is never total or instantaneous. In truth, $\vec{E}_{\parallel}$ just inside the conductor must have the same value as $\vec{E}_{\parallel}$ just outside of it and such a non zero value is perfectly consistent with theory.

The question you are asking really isn't particular to waveguides... what about the fields at a metal surface? There are all kinds of fun way to think about modeling a surface interface.

First -- Do you want to model the bulk via a free electron/jellium manner (the usual way to think of metals)? Do you want to model it like a "fluid" with some olmic damping or other things thrown in (magnetohydrodynamics)? Do you want to represent it as an array of electrons and atoms tied together, and therefore the electrons interact with the fields but are also in some harmonic-like potential well (better for insulators)?

Then -- How do the fields interact with the atoms? Do you want to model that classically, use a simple quantum treatment, use a many body theory like "hartree-fock", use something more complex like "density functional theory"?

Then -- Do you want the bulk to be a simple step interface to vaccum, or a smooth continuous profile? Those are reasonable, but probably still not quite accurate. (as that deals mostly with the perpendicular component of the fields.. and surely roughness affects the parallel components right??)

Eventually it usually comes down to picking a model, picking a profile, integrating the current density or charge density over that surface region(which are sources in Mawell's equations) and then looking at little guassian boxes or the like, as they cross this interface. What are your boundary conditions then?

Fun stuff, right? I think so!

My problem is that even though perfect conductors do not exits, supposing that a given conducting guide has 0 resistivity doesn't produce a result that is even near reality. Because in the perfect conductor case, the boundary conditions are drastically different: E field is 0 inside for the perfect conductor while is drops continuously for the real one, and this does not impose the condition that E be 0 just outside the conductor.

The case for good, but not perfect, conducting walls is treated in most grad EM textbooks. E_parallel just outside the conductor is very small and falls quickly to zero inside the conductor. The small parallel component leads to
some energy loss at the conductor which results in attenuation of the wave.

If the parallel component is small just outside the conductor like you say, then the perfect conductor approximation is good.

But why should it be small? Why couldn't it be just any size?!? I'd still be continuous!

Inside the conductor, E_par << B_par for a good conductor.
Since E_par is continuous, it must be << just outside.

## 1. What is a wave guide?

A wave guide is a physical structure that is designed to guide electromagnetic waves, such as light or radio waves, through a specific path. It typically consists of a hollow metal tube or a dielectric material with specific dimensions and shapes.

## 2. How does a wave guide work?

A wave guide works by confining and directing electromagnetic waves through its structure. This is achieved by creating a boundary between the wave guide and the surrounding medium, often through a combination of reflection and refraction.

## 3. What are the applications of wave guides?

Wave guides have various applications in fields such as telecommunications, radar, and medical imaging. They are used to transmit and receive signals, as well as to control the direction and polarization of electromagnetic waves.

## 4. Are there different types of wave guides?

Yes, there are different types of wave guides, including rectangular, circular, and coaxial wave guides. Each type has its own unique properties and is used for specific applications.

## 5. How do wave guides relate to our understanding of reality?

Wave guides play a crucial role in our understanding of reality as they help us manipulate and control electromagnetic waves, which are fundamental to our understanding of the physical world. They also allow us to study and observe various phenomena, providing insights into the nature of reality.

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