About unpolarized electromagnetic field, are the electric and magnetic fields still can be distinguished from each other? Are there pictures that show the orientations or angles of electric fields and magnetic fields if the electromagnetic field is unpolarized? I prefer pictures because mere calculations do not show any picture at all. Thank you.
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$\begingroup$ When asking such a question, consider what sort of experiment could answer it. Better yet, do the experiment. Electric field sensors and magnetic field sensors are different things... $\endgroup$– John DotyCommented Apr 24, 2023 at 1:25
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1$\begingroup$ you can't draw an unpolarized field, since it has no direction to point. $\endgroup$– JEBCommented Apr 24, 2023 at 2:02
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1$\begingroup$ What does it mean for the field to be "unpolarized"? $\endgroup$– J. MurrayCommented Apr 24, 2023 at 2:38
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1$\begingroup$ Below in a comment you said that magnetic fields point perpendicular to electric fields. This is NOT necessarily the case, even if it is what we usually mean for light. Polarised light is very easy to define and visualise, but if you want to define unpolarised light, you would have to resort to maths, even if it is relatively simple maths. $\endgroup$– naturallyInconsistentCommented Apr 24, 2023 at 7:55
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$\begingroup$ So, perpendicular is not the right word then because unpolarized EM field have electric and magnetic fields that pointed to random directions. Correct me if there is a mistake. $\endgroup$– SnoopyKidCommented Apr 24, 2023 at 10:34
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1 Answer
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A linear dipole is essentially a receiver of the E-field component that is parallel with it and is almost completely "deaf" to the H-field in any direction. Contrariwise, a circular loop responds to a magnetic field component that is perpendicular to its plane but is "deaf" to an electric field.
An unpolarized plane wave is a random sum of two orthogonal linear polarizations, therefore, if we set up a pair of linear dipoles orthogonal to each other and a pair of magnetic dipoles (circular loops) orthogonal each other, and both pairs are to be combined in one "$3dB$" coupler, resp., then one combination will respond to the randomly polarized E-field while the other the randomly polarized H-field.
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$\begingroup$ So, perpendicular is not the right word then because unpolarized EM field have electric and magnetic fields that pointed to random directions. Correct me if there is a mistake. $\endgroup$ Commented Apr 24, 2023 at 10:34
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$\begingroup$ Fix a coordinate system. Let the direction of propagation of a plane wave be $\hat z$ Then at any given instant there is an E field in the plane perpendicular to it: $\mathbf E = E_x\hat x + E_y\hat y$ The values of $E_x$ and $E_y$ are random variates, so there is no definite direction in which $\mathbf E$ points. If you have two linear dipoles one along $\hat x$, the other $\hat y$, then the former detects $E_x$, the latter $E_y$. They could be independently measured with a square-law detector/filter and then added to form and estimate of signal power by $\langle E_x^2+E_y^2\rangle$. $\endgroup$ Commented Apr 24, 2023 at 10:44
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$\begingroup$ Let's see if I get it. But because the electric fields are distributed randomly, next to the particular magnetic field will be another electric field and so on. Therefore, the electric fields and magnetic fields are distributed randomly? $\endgroup$ Commented Apr 24, 2023 at 10:53
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$\begingroup$ Now you can do the same with a pair of loops, one measuring $H_x$ and the other $H_y$, then a square-law detector/filter will get you the estimate of $\langle H_x^2+H_y^2\rangle$, this gives another estimate of the wave power independent of the electric field measurement. A similar idea, so-called "energy receiving antenna", in the ancient history of cell phones many years ago was promoted by Bell Labs to improve on the reception of depolarized waves; they used two orthogonal loops in whose common diameter was placed one linear dipole; they assumed fixed $E_{vert}$. $\endgroup$ Commented Apr 24, 2023 at 10:54
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$\begingroup$ I cannot grasp these complicated maths, do you have image examples that distinguished the electric field from magnetic field in unpolarized Electromagnetic field? Sorry. $\endgroup$ Commented Apr 24, 2023 at 10:56