Careful. The Poynting theorem says that the power leaving a given volume is proportional to the surface integral of E cross B over a closed surface enclosing the volume. However, it's incorrect in general to say that E cross B is the local direction of energy flow, though it works in many cases (e.g. monochromatic waves in sufficiently large geometries).
For instance, you can charge up a high voltage capacitor and leave it next to a rare-earth magnet--there's no energy flow at all, but the Poynting vector can be pretty large.
Cheers
Phil Hobbs
--
Dr Philip C D Hobbs
Principal
ElectroOptical Innovations
55 Orchard Rd
Briarcliff Manor NY 10510
845-480-2058
hobbs at electrooptical dot net
http://electrooptical.net
Yup, exactly the same problem. At the speed of light distances go to zero. All very strange. We sell this muon lifetime apparatus that touches on the time dilation issue. The muon life time is about 2 micro seconds. All the muons come from high energy cosmic ray collisions in the upper atmosphere. They have speeds near c. Now if their own clocks didn=92t run a lot slower than ours only a tiny fraction of them would make it down to the ground. (2us X c =3D 600 m) But we see lots!
Hi Tim, I don't know much about antennas, (antenni?) I do believe that you can use the reciprocity theorem to say that they are the same at transmitting and receiving, so that whether transmitting or receiving it=92s both a near field situation.
What things look like in the intermediate region is probably complicated. (I=92ve got vague memories of a problem in grad school where we separated out the near field terms that decreased as 1/r^3 or faster and the far field term that went as 1/r^2 or 1/r.?? sorry too long ago.
As far as transmitting a =91far field=92 pattern, I wonder if a microwave horn does a good job of that?
Yes, I remember reading about this a long time ago -- can't remember where. It was one of the confirmations performed about relativity. I remember some of the details of the experiment, too, in order to actually test the idea.
It would seem like a good candidate if anything. Goes from a confined wave somewhat tighter than c (remember, phase velocity > c in waveguide, of course group velocity < c so it's okay), to something expanded, closer to free space dimensions, then the horn ends and it's like... what? oh well carry on...
Reminds me of a quote from my professor. Spoken with a Serbian accent. "You kind of fool the wave, open it up gradually so it doesn't reflect until it's too late, and by then it's already gone... kind of like how I got my wife!"
Tim
--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms
You can have a linear polarized wave without a circular polarized wave, but can't have a circular polarized wave without it being composed of linear polarized waves, so the linear polarized wave is the fundamental type of wave.
I received this email from an antenna expert showing this geometrically:
examples A and B generate circularly polarized waves using two linear polarized waves, and example C can be thought of as emitting a very high number of linear polarized waves each offset by a small angle depending on the helical antenna diameter and turn pitch. So you can take a circular polarized wave and see how it is made of linear polarized waves, but can you take a linear polarized wave and see how it is made of circular polarized waves? Espeically since linear polarized waves are much more common in nature I think they are the fundamental type of wave, and all other types are superpositions of linear waves.
Ahem. For earth to satellite and satellite to earth communications; adjacent transponder channels have opposite circular polarizations, this increases effective bandwith as the sidebands of the two adjacent channels can be significantly overlapped without interference. The two polarizations can be sorted out at the antenna with a little help from the receiver.
Or you can perform the exact same procedure using the endfire helical, or phase shift / space shift orthogonals, and generate linear polarization back again. So by applying your argument again (almost sounds....circular ;) ), you've just proven that circular is also the fundamental type of wave. ;-)
Tim
--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms
Actually, it turns out that vertical and horizontal (linear) polarizations are duals, mathematically and physically, of CW and CCW circular polarizations. See also 1/4 wave plate in optics.
I'm not sure if you can go from circular to linear polarization with helical antenna's? The geometry is a bit hard to visualize.
One thing that makes linear polarization more fundamental than circular polarization is that it gives a simpler explanation that circular polarization can provide. Apparently there are no strong natural sources of circular polarized light, or in other words, 99.9%+ of all known light appears to be linearly polarized. So if you want to believe that circularly polarized light is the fundamental type of light, then how is the circular polarized light converted to linear polarized light
Thanks for the link, the explanation at wikipedia:
formatting link
The crystal's geometry has a different refractive index for vertical polarized light as compared to horizontal polarized light, which can create circularly/elliptically polarized light as the linearly polarized light is phase shifted a different amount depending on if it is vertically or horizontally polarized.
If the light sent through the crystal is composed of either vertical or horizontal polarized light, then there will be no change in the polarization.
Thanks for the link, the explanation at wikipedia:
formatting link
The crystal's geometry has a different refractive index for vertical polarized light as compared to horizontal polarized light, which can create circularly/elliptically polarized light as the linearly polarized light is phase shifted a different amount depending on if it is vertically or horizontally polarized.
If the light sent through the crystal is composed of either vertical or horizontal polarized light, then there will be no change in the polarization.
It seems to me 99% of light is not polarized at all -- black body radiators don't care, for instance. I don't know that any other primary physical phenomena cares (radiation, emission, absorption, etc.). Interactions with matter can do interesting things; reflections are well known to increase polarization (hence polarized sunglasses). Reflection is a surface thing, so it gives a reference plane to the polarization. Surfaces in space tend to be random, so I imagine the amount of polarization is small and averages to zero. I'm not very familiar with astronomical sources of polarization. I just read that magnetic fields are known to produce circular polarization. You'll see far more surfaces (dust, objects, etc.) and volumes (dust clouds, nebulas) than intense magnetic fields (compact objects such as planets and stars), especially in terms of what the light goes through (e.g. translucent dust clouds).
This explains the greater incidence of linear polarization, but makes no statement as to its fundamental nature. If you'd like to make a practical argument, then there is a lot of linear polarization out there, and it's somewhat easier to make a linearly polarized antenna.
As I mentioned previously, QM gives a useful reason for circular to be fundamental-- it carries angular momentum, on the order of hbar per photon. A sufficiently weak, linearly polarized beam will have circular polarization, if you look at each photon. The circularity averages to zero, since each photon is a coin flip. But there *is* a coin, and it's either 1 or -1, never zero or sideways. If the photons were fundamentally linearly polarized, they would carry no angular momentum on any scale, individual or average.
If they were linearly polarized, would there be any way to tell? Is there a quanta of tangential momentum which could be delivered which averages to angular momentum, for an apparently circular polarized beam? I don't see any way this would work, so it looks like circular is the winner.
Tim
--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms
I'm not quite sure what you are saying, But take one CW wave and add it to a CCW circularly polarized wave (of the same amplitude and frequency) and you get a linear polarized wave. (I'm waving my hands around in circles, if you can't see.)
Saying one is more fundamental, is like saying that Cartesian coordinates are more fundamental than polar coordinates. They are both equivalent at some point and you pick which is more useful...
As Tim says most light we see is unpolarized... randomly polarized.
There are lots of atomic processes that give circularly polarized light. (Almost always there is some magnetic field involved.)
Any one know of examples of (natural) circularly polarized light without a B field?
I would also think that randomly polarized light can be understood most simply as being composed of multiple linearly polarized light emissions. In other words, the fundamental light emission would be linearly polarized as transverse waves. Sorry I see no point in debating about photons, if you believe in light travelling rectilinearly and instantaneously then we should agree to disagree! :)
There is a physical explanation and theory of light as transverse waves that is independent of any coordinate system. See this page for an explanation of how two circularly polarized waves interfere and create a single linearly polarized wave:
formatting link
From that page: " Consider the animation of circularly polarized light above. If we superimpose this wave with a circularly polarized wave of the opposite "handedness" where the blue component is 1/4 wavelength behind (instead of ahead), the two blue components will completely cancel because they are 180 degrees (half a wavelength) out of phase. Thus, we would be left with just a linearly polarized wave."
The model of circularly polarized light (from that page) is of horizontal and vertical phase shifted linearly polarized light, so when they interfere a CW and CCW circularly polarized wave, they are really just cancelling one axis of the linearly polarized light and constructively interfering on the orthogonal axis. The description is always based on interactions between linearly polarized light everywhere I read, and it is not a coordinate system is is physical wave interference.
You can go the other way and say that for example a horizontal linearly polarized wave is composed of CW and CCW circularly polarized waves, but that is a more complex way to imagine the fundamental nature of light I think, but still valid.
I understand if you pick whichever view is most useful at the time, I am interested about the emissions and absorptions of light from matter, ie. electron orbital state changes, to see if it is a random axis linearly polarized wave per orbital jump or not.
I never understood why high energy electromagnetic waves acted more like particles, but I see there is a simple explanation for it now. Antenna gain is proportional to frequency, so for an emission from an atom, the higher the frequency of the emission (ie. gamma ray from the nucleus) the higher the gain will be, with the atom acting as a directional reflector. The antenna gain plot for a gamma ray will have a highly directional, very narrow cone angle.
ElectronDepot website is not affiliated with any of the manufacturers or service providers discussed here.
All logos and trade names are the property of their respective owners.