Are E and H Fields Perpendicular to the Direction of Propagation?

[!kx!]

Hi all..

I am just stuck upon something very trivial.. We know that E and H fields in an EM wave are perpendicular to each other..
I was also told that they are respectively perpendicular to direction of propagation..
Is it correct? are there any conditions for this to hold..??

 

[Vanadium 50]

Yes, that's also true.

 

[!kx!]

If that's also true, then why do we break up the field components into each of x, y, z components, while doing the usual waveguide analysis?

 

[Vanadium 50]

Because the fields in a waveguide are more complicated than a freely propagating EM wave.

 

[Bob_for_short]

If that's also true, then why do we break up the field components into each of x, y, z components, while doing the usual waveguide analysis?

In a wave guide, apart from pure transversal EMF there are charges and currents so the resulting EMF is different: its equations depend on charges and currents (as sources or boundary conditions). Such a system is different from a plane wave in vacuum.

 

[!kx!]

okay.. So how does this difference come into picture..? (except for the difference in the R.I. of the two medium)??

 

[!kx!]

In a wave guide, apart from pure transversal EMF there are charges and currents so the resulting EMF is different: its equations depend on charges and currents (as sources). Such a system is different from a plane wave in vacuum.

In a topic of field quantization (i am referring to Greiner), the writer has broken the field into transverse normal components.. so should I take it that he is referring to fields in vacuum??

 

[Bob_for_short]

Yes, if you mean photons, i.e., radiated field.

 

[Andy Resnick]

Hi all..

I am just stuck upon something very trivial.. We know that E and H fields in an EM wave are perpendicular to each other..
I was also told that they are respectively perpendicular to direction of propagation..
Is it correct? are there any conditions for this to hold..??

It hasn't been mentioned that this is true for *propagating* waves in free space. TM waves, TE waves, and the near field violate your statements.

 

[!kx!]

@ Andy

could you please explain what is the near field?
and, from above discussion, can it be concluded that TM and TE waves cannot exist in free space, only TEM... ??

 

[Phrak]

How do we define the direction of propagation?...

 

[!kx!]

direction of propagation is the direction in which the wave-disturbance propagates, with time.. after disturbing some point in a medium, the wave will move on with its characteristic speed to disturb some other point..this will correspond to propagation..

 

[Andy Resnick]

@ Andy

could you please explain what is the near field?
and, from above discussion, can it be concluded that TM and TE waves cannot exist in free space, only TEM... ??

TE and TM waves can exist in waveguides. The near field refers to the electromagnetic field within a wavelength (or so) of an object, and it is sometimes referred to as 'the covering field'.

 

[Phrak]

direction of propagation is the direction in which the wave-disturbance propagates, with time.. after disturbing some point in a medium, the wave will move on with its characteristic speed to disturb some other point..this will correspond to propagation..

This works well when you have a well defined beam. We can take the beam, put it through a hole, small comparable to the wavelength, and it will spread throughout space.

A culminated beam can be put through a diffraction grating. The resultant fields, after the grating, have values equal to the superposition of two beams, propagating at a relative angle to each other. Should we call the direction of propagation the average of the two directions, or do we have two directions of propagation?

My point is that a definition sufficient for a beam is insufficient in general. Perhaps there is another way, but the direction of the propagation of energy is one way to define the direction of propagation, and this direction is defined by the direction perpendicular to both the electric and magnetic fields.

 

[!kx!]

The resultant fields, after the grating, have values equal to the superposition of two beams, propagating at a relative angle to each other. Should we call the direction of propagation the average of the two directions, or do we have two directions of propagation?

I didn't quite get you there.. well, if the beams have different direction of propagation, then, what is the purpose of superimposing the fields.. we can put a screen in the way and observe the field pattern; but if the waves are allowed to propagate by themselves, they'll will eventually diverge.. resultant of two differently directed beams does not quite makes some sense to me..
I'll say that the two beams have two different directions of propagation. After all, as far as I know, we take individual beams while doing some analysis..

 

[Born2bwire]

TE and TM waves can exist in waveguides. The near field refers to the electromagnetic field within a wavelength (or so) of an object, and it is sometimes referred to as 'the covering field'.

Except with a waveguide, TE and TM are defined as being in relation to the direction of guided propagation. As far as I know, the waves in a waveguide are still polarized to be normal to the propagation of the wave, but that does not always (or can) be aligned with the guided propagaton direction.

But to further add in general confined waves can be non-TEM waves, though often it is in an artificial sense like with a waveguide. But a true example are surface waves like the Zenneck wave.

 

[!kx!]

As far as I know, the waves in a waveguide are still polarized to be normal to the propagation of the wave, but that does not always (or can) be aligned with the guided propagaton direction.

how are propagation direction and guided propagation direction different??

 

[Phrak]

I didn't quite get you there.. well, if the beams have different direction of propagation, then, what is the purpose of superimposing the fields.. we can put a screen in the way and observe the field pattern; but if the waves are allowed to propagate by themselves, they'll will eventually diverge.. resultant of two differently directed beams does not quite makes some sense to me..

Ideally, the culminated beam sent into the diffraction grating will resolve into two beams, but this isn't generally the case. With a finite aperture (the size of the diffraction grating or culminating beam) this is not the case.

A wave guide is one item that has been discussed in this thread so far. In fact, given a stub antenna as the source, the electric and magnetic fields in a guide are described by an infinite array of point sources arranged in a line. With an infinite number, the beams you refer to never materialize along the length of the guide.

'Direction of propagation' without reference to the electric and magnetic fields is a useful notion in ray optics, but not in general.

 

[!kx!]

well, I quite get an idea..
but, the whole thing is still not very clear to me.. as how electric and magnetic fields are described by an array of point sources..

 

[Born2bwire]

how are propagation direction and guided propagation direction different??

Guided propagation is the direction that the waveguide is designed to send the signal in, like the axis of a coaxial line. The propagation direction is the actual direction that the wave moves along inside the waveguide. Often, the wave propagates in a manner such that it "bounces" around inside the waveguide.

What happens is that in a waveguide problem, you still use the normal Maxwell equations for an isotropic source free environment. So the wave is still truly TEM, however, you solve the equations in terms of the boundary conditions and materials of the waveguide. These restrictions cause the wave to be guided along a desired direction and puts constraints on how the wave can do this. Many times, it prevents you from sending the wave down a waveguide with the wave's propagation direction aligned with the guided direction. Instead, what happens is that the wave propagates at an angle, it bounces on and off of the walls of the waveguide. This results in a standing wave part in the directions normal to the walls (from superposition of the incident and reflected wave) and a propagating part along the direction of guided propagation. Since we only care about the properties of guided propagation with a waveguide, the terms of TE and TM and other characteristics are thrown about rather casually and it can cause confusion in people. Even more confusing is that the standing wave part has no propagation since it is a standing wave (and of course it is confined) but the standing wave can be decomposed into an incident traveling wave and its reflected wave, so that behavior is also hidden. Here's a good website with some slides that demonstrate what I mean, take a look at say page 135 (slide 6): http://www.amanogawa.com/archive/docs/EM12.pdf

This no longer holds when we are talking about, for example, inhomogeneous media or media with sources. If you have a source, then you often get true TE and TM waves with respect to the propagation direction. However, like Andy stated, these are confined to the near-field, as you move away from the source these contributions die out and you are left with only propagating TEM waves. If you have inhomogeneous media, you can get surface waves that are not TEM. The Zenneck surface wave is an example that occurs when you have a dipole antenna on top of a plane of lossy dielectric material.

 

[!kx!]

thnx Born2bwire...
that really helped.. ..it falls together now..

i am still not clear with the picture Phrak is trying to show...!

 

[Phrak]

What happens is that in a waveguide problem, you still use the normal Maxwell equations for an isotropic source free environment. So the wave is still truly TEM, however, you solve the equations in terms of the boundary conditions and materials of the waveguide.

I think we may disagree. If we are talking about a rectangular wave guide in the fundamental mode, it is TEM only along the plane bisecting the guide. In all other regions there is also a longitudinal component of magnetic field. Overall, this classifies the wave as TE₁₀.

!kx!, I don't know what else to add, but you may like to go the Wikipedia article on Poynting vectors.

 

[Born2bwire]

I think we may disagree. If we are talking about a rectangular wave guide in the fundamental mode, it is TEM only along the plane bisecting the guide. In all other regions there is also a longitudinal component of magnetic field. Overall, this classifies the wave as TE₁₀.

!kx!, I don't know what else to add, but you may like to go the Wikipedia article on Poynting vectors.

No, like I explained above, the difference here is that when discussing waveguides, TE, TM, and TEM are not referring to the wave's actual propagation vector but in regards to the vector for guided propagation by the waveguide. These two are different and that is what causes the confusion. While the rectangular waveguide forbids propagating TEM modes in regards to the direction of guided propagation, the actual waves inside the waveguide are still TEM in terms of the wave's own direction of propagation. This is explicitly shown in the lecture slides (slide 6 for example) that I linked above.

This is all trivial because in analyzing the waveguide, we still use the Maxwell's equations for source-free homogeneous isotropic medium which can only allow TEM solutions. The rest is just boundary conditions that reject all but a subset of possible TEM solutions to the wave equations.

 

[Vijuma]

I am working on the paper "Analysing electromagnetic structures with curved boundaries on cartesian FDTD meshes" by Yang Hao and Chris J. Railton. I need to create a simulation on CIRCULAR AND RECTANGULAR WAVEGUIDES. Also need to find the cutoff frequencies of a circular as well as rectangular waveguide according to the paper. Kindly send me some MATLAB codes for circular and rectangular waveguides. Thanks in advance.