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Fresnel Reflection and Transmission Coefficients

by whitenight541
Tags: coefficients, fresnel, reflection, transmission
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whitenight541
#1
May2-09, 01:55 AM
P: 49
Hi all,

The relation between the magnitudes of the incident, reflected and transmitted waves are obtained using Fresnel coefficients.

If a field moves from air to a more denser medium, which field should have a greater magnitude (reflected or transmitted)? I thought that it would be the reflected one but I found that the transmission coefficient is greater than the reflected one. So the transmitted wave magnitude is greater than the reflected one ? Am I making any sense? If what I said is true, how come is that possible?

If a field moves from air through a wall of concrete of thickness t, I calculated the transmitted field after the first boundary, but when I tried to calculate the transmitted field at the second boundary, I found out that the transmission coefficient is greater than 1? Is that possible????

Thanks in advance
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Born2bwire
#2
May2-09, 04:35 AM
Sci Advisor
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P: 1,758
A transmission coefficient greater than one is ok, it doesn't necessarily violate the conservation of energy. One thing to keep in mind is that the energy density of a field is dependent upon both the magnitude of the electric and magnetic fields and the permittivity and permeability of the medium. If you pass from air to a dielectric, then the electric field can decrease (the normal electric flux density is continuous across boundaries, so the normal part of the electric field must decrease when entering a region of higher permittivity). When you go from concrete to air, you can expect a slight increase in the electric field for the same reason. If you are dealing with multiple regions, you should look at the Generalized Reflection and Transmission Coefficients. These coefficients take into account all the reflections between interfaces and gives you the complete reflection and transmission coefficients. If you have a single interface, you only have a single reflection and transmission, but if you have multiple interfaces, like with your concrete slab, then you have secondary, tertiary, and so on-ary reflections and transmissions. This comes about from the fact that the field that reflects off of the second interface will strike the first interface and transmit and reflect again. I would assume that Balanis' textbook deals with this but I do not have it front of me at home. Again I know that Chew's Fields and Waves textbook has it.

Also, the Fresnel coefficients do not just give the magnitude of the coefficients, the coefficients can be complex to reflect a phase change that occurs in the transmission and reflection off of the boundaries.


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