# Antenna Polarization

## Main Question or Discussion Point

Hi all,

I'm implementing ray tracing ..

If we say that an antenna is linearly vertically polarized, does that mean that the direction of E field emitted from the antenna is vertical with respect to the coordinates of the antenna or vertical with respect to each ray's coordinates?

For example, if a ray is emitted at an elevation angle 45 an azimuth angle 45. If we assume that the E field is vertical with respect to eh antenna coordinates, then it won't be orthogonal to the direction of propagation of that ray right?

## Answers and Replies

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jambaugh
Gold Member
The convention is to define polarization as the direction of the E field. In the example you cite the "vertical" refers to the plane in which it is polarized i.e. the vertical plane containing the line of propagation. The actual polarization vector will be the vector perpendicular to the direction of propagation in this vertical plane.

I'm not sure I totally understand u.

This vertical plane is defined according to which coordinates? the surface fixed coordinates or the ray fixed coordinates?

I don't understand how can the vertical plane contains the line of propagation?

berkeman
Mentor
I'm not sure I totally understand u.

This vertical plane is defined according to which coordinates? the surface fixed coordinates or the ray fixed coordinates?

I don't understand how can the vertical plane contains the line of propagation?
His statement was correct. He said that the direction of polarization is perpendicular to the direction of propagation. So you could have a wave travelling in the x direction, with the E field in the z direction, and the B field in the y direction...

jambaugh
Gold Member
I'm not sure I totally understand u.

This vertical plane is defined according to which coordinates? the surface fixed coordinates or the ray fixed coordinates?

I don't understand how can the vertical plane contains the line of propagation?
Emphasis on plane as in 2 dimensional plane. In your example let $k$ be vertical direction, and say its propagating in the $i+j+\sqrt{2}k$ direction, then the plane spanned by $k$ and $i+j+\sqrt{2}k$ (or equivalently spanned by $i+j$ and $k$) which is the plane perpendicular to the $i-j$ vector. It is the plane of polarization as well as propagation.

The actual polarization vector would be the vector in this plane and orthogonal to the propagation direction, e.g. $-i-j+\sqrt{2}k$.

(latex code looks screwy but I assume that'll be fixed later.)

Section 13-6 in Panofsky and Phillips "Classical Electricity and Magnetism" has a polar plot of radiation from a vertical antenna. The Poynting vector P = E x H at an angle theta from the vertical has the H vector horizontal, with the E vector in the theta direction. Both E and H are perpendicular to the direction of propagation. The E vector has a vertical component, the H vector does not.

Born2bwire
Gold Member
Vertical and horizontal polarization is meaningless until you take into account the orientation of the antenna. Antenna signals are meant to be taken in the far-field. In the far-field, the electromagnetic wave looks, locally, like a plane wave. The orientation of the electric field vector over time at a constant point describes the polarization. Since antennas are meant to be mounted, the polarization is given with respect to the antenna's intended/normal physical orientation. So if the polarization is linear and vertical, and you normally mount the antenna with it's principle axis along $$\hat{z}$$ (z hat), for example a dipole antenna, then the electric field vector will be aligned along $$\hat{z}$$ (z hat) (only in the x-y plane), or, since they generally use spherical coordinates, along $$\hat{\theta}$$ (theta hat) or all points in space.

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I'm sorry I still can't get it. I'm implementing ray tracing so I have rays emitting from all direction of the antenna.

I'm not sure which is correct among the 2 options:

Let Z-axis points to the vertical direction. When a ray emerges from the antenna at direction (theta = 45 and phi = 45)

1) The vertical plane in this case is still the XY-plane??
If so, then the E vector would be at an angle (phi = 135 and theta = 0) to be contained in this vertical plane and still orthogonal to the direction of propagation.
(In this case vertical means the regular vertical direction relative to the antenna itself. All rays would have E in the same vertical plane but at different angle in that plane)

2) The other case is, I would do a transformation of axes so that X-axis would be in the direction of ray propagation and Z-axis would be pointing towards theta = -45. The E field in that case would be Z-axis.
(In this case vertical is relative to each ray. Each ray would have different direction of E. All rays would have E in different planes according to the direction of their propagation)

Which one is correct?

Born2bwire
Gold Member
I'm sorry I still can't get it. I'm implementing ray tracing so I have rays emitting from all direction of the antenna.

I'm not sure which is correct among the 2 options:

Let Z-axis points to the vertical direction. When a ray emerges from the antenna at direction (theta = 45 and phi = 45)

1) The vertical plane in this case is still the XY-plane??
If so, then the E vector would be at an angle (phi = 135 and theta = 0) to be contained in this vertical plane and still orthogonal to the direction of propagation.
(In this case vertical means the regular vertical direction relative to the antenna itself. All rays would have E in the same vertical plane but at different angle in that plane)

2) The other case is, I would do a transformation of axes so that X-axis would be in the direction of ray propagation and Z-axis would be pointing towards theta = -45. The E field in that case would be Z-axis.
(In this case vertical is relative to each ray. Each ray would have different direction of E. All rays would have E in different planes according to the direction of their propagation)

Which one is correct?
Sorry, I should have been explicit, the z hat would only be valid along the x-axis. In general, we talk about polarization in terms of spherical coordinates. If you have a vertically linearly polarized antenna and have it oriented normally, then the electric field vector will be along the theta vector in spherical coordinates. This would have to be transformed to the appropriate coordinate system that you are using.

Thanks a lot for replying .. you really save me every time :)

But why would it be in the theta direction?

Born2bwire
Gold Member
Thanks a lot for replying .. you really save me every time :)

But why would it be in the theta direction?
Think of a wire dipole antenna. The radiation pattern is in the form of a torus of sorts. If you solved the actual far-field radiation you would find that the E-field's vector is always theta hat. This is vertically polarized. You can imagine that the dipole itself creates a set of planes that are are parallel to the dipole. These planes are sheets with one edge along the z-axis and the other edge in the x-y plane. The theta hat polarization means that the electric field vector always lies in one of these vertical planes. It has no horizontal component (a vector that lies in a plane parallel to the x-y plane). The horizontal polarization would be phi hat, because then the vector would always lie in a plane horizontal (perpendicular) to the z-axis (which is parallel to the vertical planes).

Since we are in the far-field, the electric and magnetic polarizations must only have theta and phi vector components. That is because in the far-field, only propagating fields exist and the fields look like a plane wave locally (think of a spherical wave having expanded to a very large radius and taking tiny patch). The r hat direction is always the k vector's direction (direction of propagation) and so the fields must be normal to r hat. This is why it is very convenient to talk of polarizations and fields in terms of spherical coordinates because the characteristics are invariant (where as if you talk about the polarizations and fields in cartesian coordinates the directional vectors will change depending upon the point of observation which is what I forgot about earlier when I said the E field woud be polarized in the z hat direction, this is only true in the x-y plane).

But if it is in the direction of theta hat, we can divide it into 2 components: a vertical (multiplying by cosine theta) and horizontal (multiplying by sine theta). So it won't be vertical right?

If we worked by rays (not planes), a ray would be at angles theta and phi, where would its polarization vector point (assuming vertical polarization and isotropic antenna)?

Born2bwire
Gold Member
The theta direction is always vertical. The vertical component is the component that would lie in a plane parallel to the wire dipole (z hat at origin). This is the theta direction.

In the case for SBR, the ray is the k vector of a local plane wave patch. The ray points in the direction of propagation. The ray will point in the r hat direction (in the local sense) and thus the polarization vectors will be some combination of the theta and phi vectors. There is an amount of book keeping here since the theta and phi would only be in reference to the ray itself, not to any universal coordinate system. So I guess you would have to do some conversions to figure out the resulting polarization of the physical optics currents and the reflected polarizations upon scattering. So, when the ray first leaves the antenna, before any bounces, it is pointing in the r hat direction with the origin at the antenna. Thus, until the first bounce, all the polarization vectors will be theta hat for a vertically polarized antenna. After they bounce these polarizations will change depending on the direction of incidence with respect to the scatterer and maybe the material of the scatterer.

Personally I would recommend consulting an antenna textbook, Balanis wrote one, to make sure I am correct about this. I do not have any of my antenna references with me at my new office so this all off the top of my head. Personally I dislike the antenna engineer's jargon with vertical and horizontal polarizations since it is meaningless outside of antennas.

The theta direction is always vertical. The vertical component is the component that would lie in a plane parallel to the wire dipole (z hat at origin). This is the theta direction.
I thought the theta direction is the vector making an angle theta with Z-axis. But now I got it, theta direction is the direction parallel to the Z-axis at the plane parallel to the wire dipole.

thus the polarization vectors will be some combination of the theta and phi vectors. There is an amount of book keeping here since the theta and phi would only be in reference to the ray itself, not to any universal coordinate system.
Thus, until the first bounce, all the polarization vectors will be theta hat for a vertically polarized antenna.
Does this mean I have to make a transformation of axes according to each ray? The vertical plane would be perpendicular to the ray, the new theta-hat would not be parallel to Z-hat (but perpendicular to the ray direction) and the E would lie in that plane in the direction of theta-hat ? And therefore when I converted the polarization vector back to the universal coordinate system (the one that was used to launch the rays from the antenna) we would have a combination of the phi and theta. Is the correct?

Personally I would recommend consulting an antenna textbook, Balanis wrote one, to make sure I am correct about this. I do not have any of my antenna references with me at my new office so this all off the top of my head. Personally I dislike the antenna engineer's jargon with vertical and horizontal polarizations since it is meaningless outside of antennas.
I have already read that part in Balanis.

Born2bwire
Gold Member
I think it would be helpful if you reviewed spherical coordinates to get a better sense of what I mean by theta and phi vectors/directions.

I have not written a full SBR code and I do not have the original papers handy so I do not know what the actual/recommended implementation is. But, I would assume that the polarization vectors associated with each ray are in reference to a local coordinate system where the direction of the ray is r hat. Otherwise, restricting the polarization vector components to theta and phi would be incorrect. The polarization is only confined to theta and phi directions if the direction of propagation is along the r direction. But of course in a general scattering problem this is not the case.

Keeping a local coordinate system would be convenient though. But yes, if you have a vertically polarized field, in the universal coordinate system the E field may not be restricted to the theta vector. The easiest example would be to place a dipole at x = a where a =\= 0. The displacement of the source off of the origin will make almost all the waves have a phi hat and/or r hat components for the polarization. You may want to use a cartesian coordinate system as your universal coordinate system. The conversion between the two coordinate systems is fairly easy, you can probably find the equations on wikipedia. I keep photocopies of a page out of Griffith's electrodynamic text book that has a wonderful conversion chart between the scalars and vectors of the different coordinate systems.

I think that the polarization w.r.t. the antenna pointed along z can be completely defined by
a) E and H are always perpendicular to the direction of propagation e.g., Poynting vector, and
b) The H vector has no component along z, the length of the antenna; it is always perpendicular to the length of the antenna. Only E can have a component alonf z.
c) For a simple antenna pointed along z, the axis z is the axis of rotation of the radiation intensity pattern; the radiation intensity is not dependent on the angle phi in the plane perpendicular to z.