Recent content by Cryo

I guess it depends on how pedantic you want to be. You will have no propagting modes in a waveguide that is too 'narrow'. But non-propagating solutions can exist. Parallel-plate capacitor deep in quasistatic regime is an example that comes to mind.

I have written about the first derivative of the determinant here https://www.physicsforums.com/threads/i-cant-verify-a-relationship-between-cofactor-and-determinant.970419/post-6165630 given a matrix ##A## that depends on some variable ##x##: ##A_{ij}=A_{ij}\left(x\right)##, the derivative...

https://www.fibercore.com/expertise/fiberpaedia/graded-index-mm-fiber "In the fiber manufacturing process, this graded refractive index profile is usually achieved by doping the silica core with a graded level of germanium. " Basically you add some atoms to the main glass material, which...

Are you familiar with decibels? If ##T=0.03## in normal form (unitless), then in dB it would be ##10\times \log_{10} \left(T\right)\approx -15.2dB##. Note also that in some cases, especially in engineering it is common to plot power in decibels. I am not sure what your setup is, but if pressure...

How about defining your terms? All of them? Also if you want to talk about curved space-time, please specify which derivatives you are talking about. Simple partial derivatives, covariant derivatives, if covariant, are you using Levi-Civita connection. etc

A. Neumaier, I would be very glad to learn from you. Can you please clarify a couple of things? In the reference I gave above, (Barnett, Jeffers, Gatti, Loudon, "Quantum optics of lossy beam splitters", Phys. Rev. A 57, 2134 (1998) ) they treat a lossy beam splitter. The loss in the beam...

In the simplest case you have electromagnetic field, quantized, before the filter and after the filter. So you may have a creation operator for the photon before the filter ##\hat{a}_{in,h}^\dagger##, ##\hat{a}_{in,v}^\dagger## and the boundary condition (matrix) that represents the filter which...

Oh, you want photons. Well in this case have a look in Loudons "The Quantum Theory of Light". Basically you quantize the electromagnetic field, and get the electric and magnetic field operators. After that a lot of the treatment of filters is like in classical electrodynamics. It's the detection...

I think all of the stuff relating to polarizers is covered by Maxwell's Equations. As already mentioned by hutchphd there are many different kinds, but if you are comfortable with Maxwell's Equations then all of it is simple. Pick a filter you like, e.g...

Have a look

As for references. Have a look in S. Weinberg's Lectures on Quantum Mechanics, Ch 10.4 (NB! Not the field theory book). I think Sakurai's Modern Quantum Mechanics also had a bit on this

Why not begin by finding the vector potential? You have a solenoid, with complex winding current, but its main purpose is to create the magnetic field in a localized region in the XY-plane, and directed out of the page (along Z). You can describe this aptly with a point-like magnetization...

Regarding the expansion. Electric, magnetic and toroidal multipoles provide complete basis, so any non-static charge-current configuration can be written in terms of these multipoles, but only if you avoid taking the zero size approximation. If you do take the zero-size approximation, as is...

Many questions... Have you had a look at Electromagnetic toroidal excitations in matter and free space N. Papasimakis, V. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev Nat. Mater. 15, 263 (2016) (https://rdcu.be/6I2l) and Optical anapoles V. Savinov, N. Papasimakis, D.P. Tsai & N.I...