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New Theories / Re: Where does quantization of energy of electromagnetic radiation come from?
« on: 02/06/2023 16:40:59 »
Hi.
You can exhibit the propagation of an e-m wave through a simple material with a speed 1/√(μmεm) < c when you reformulate Maxwells equation by replacing the E and B fields with D and H fields where necessary. For a simple dielectric material, the relationship between the electric polarisation, P, of the material and an underlying E field should be linear (so you will have the constitutive relationship D = εm E etc.). Similarly for a simple magnetic material the magnetic susceptibility of the material should also remain constant so that you have a linear constitutive relationship B = μm H between the B and H fields.
Overall then, what you ( @alancalverd ) are saying is that provided you consider "Maxwells equations" to be the version which is often called "Maxwells equations in matter" rather than "Maxwells equations in a vacuum" then everything works fine and you can exhibit a wave that propagates as required with an appropriate speed for the medium. I would agree with that - for simple linear materials.
So that brings us to the "less" bit:
1. Hard Ferromagnetic material can retain a Magnetisation even when the H field is reduced back to 0 after first being a strong non-zero field in some direction. So the relationship between B and H fields inside the material is not the simple linear relationship we would want, instead it can depend on the history of the fields the material has been exposed to.
2. Superconducting materials also have complicated relationships between B and H fields: For example, in Type-I superconductors we can have Magnetic susceptibility χm = -1 throughout some critical range of the H field (giving a relative permeability μr = 1 + χm = 0 ) but then undergoes a discontinuity and we have χm = 0 (and hence μr immediately changing to 1) outside that range.
3. Similarly, not all dielectric materials will be simple linear materials (where the D and E fields would be linearly related). I've not studied it but I have been informed that sometimes the dielectric polarisation of a material isn't even in the same direction as the applied E field (e.g. in some crystalline structures we require a rank-2 tensor, T, to relate the (vector) E field to the (vector) D field: D = T E )
I would not vouch for how (or even "if") an e-m wave can propagate through some of these non-linear materials. For all I know, the propagation of an e-m pulse through some non-linear materials could be extremely unusual:
1. A pulse of e-m radiation sent into the material could travel through the material along path(s) that may not be straight lines.
2. It may not always take the same path but instead may depend on the prior history of E and B fields that were applied to that material. Since the e-m wave is itself changing the E and B fields inside the material when it passes through, the first part of the pulse may exit the material in a different place to where later parts of the pulse exit the material.
Best Wishes.
No. They apply to any medium if you substitute εm and μm for ε0 and μ0.I would more or less agree with that. Let's do the "more" bit first:
You can exhibit the propagation of an e-m wave through a simple material with a speed 1/√(μmεm) < c when you reformulate Maxwells equation by replacing the E and B fields with D and H fields where necessary. For a simple dielectric material, the relationship between the electric polarisation, P, of the material and an underlying E field should be linear (so you will have the constitutive relationship D = εm E etc.). Similarly for a simple magnetic material the magnetic susceptibility of the material should also remain constant so that you have a linear constitutive relationship B = μm H between the B and H fields.
Overall then, what you ( @alancalverd ) are saying is that provided you consider "Maxwells equations" to be the version which is often called "Maxwells equations in matter" rather than "Maxwells equations in a vacuum" then everything works fine and you can exhibit a wave that propagates as required with an appropriate speed for the medium. I would agree with that - for simple linear materials.
So that brings us to the "less" bit:
To make life easy, we measure and publish dimensionless relative permittivities and permeabilities for various materials (including air and metamaterials) so you can just multiply the vacuum value as appropriate.There are some materials for which we just can't - there isn't a simple scalar relating E and D fields OR the B and H fields.
1. Hard Ferromagnetic material can retain a Magnetisation even when the H field is reduced back to 0 after first being a strong non-zero field in some direction. So the relationship between B and H fields inside the material is not the simple linear relationship we would want, instead it can depend on the history of the fields the material has been exposed to.
2. Superconducting materials also have complicated relationships between B and H fields: For example, in Type-I superconductors we can have Magnetic susceptibility χm = -1 throughout some critical range of the H field (giving a relative permeability μr = 1 + χm = 0 ) but then undergoes a discontinuity and we have χm = 0 (and hence μr immediately changing to 1) outside that range.
3. Similarly, not all dielectric materials will be simple linear materials (where the D and E fields would be linearly related). I've not studied it but I have been informed that sometimes the dielectric polarisation of a material isn't even in the same direction as the applied E field (e.g. in some crystalline structures we require a rank-2 tensor, T, to relate the (vector) E field to the (vector) D field: D = T E )
I would not vouch for how (or even "if") an e-m wave can propagate through some of these non-linear materials. For all I know, the propagation of an e-m pulse through some non-linear materials could be extremely unusual:
1. A pulse of e-m radiation sent into the material could travel through the material along path(s) that may not be straight lines.
2. It may not always take the same path but instead may depend on the prior history of E and B fields that were applied to that material. Since the e-m wave is itself changing the E and B fields inside the material when it passes through, the first part of the pulse may exit the material in a different place to where later parts of the pulse exit the material.
Best Wishes.