All Questions
Tagged with refraction dielectric
28
questions
2
votes
0
answers
27
views
Definition of the displacement field in classical field Lagrangian
In a BSM related paper (in appendix B), the authors use an effective Lagrangian $\mathcal{L}_{EFT}$, and define the following fields:
$$ \mathbf{D} = \frac{\partial\mathcal{L}_{EFT}}{\partial\mathbf{E}...
- 143
0
votes
1
answer
123
views
Wave propagation in inhomogeneous media
There is a problem I'm trying to solve for some time now and is about the standard (?) approximation that it is made when one tries to solve the Helmholtz equation in inhomogeneous media, that is
\...
- 11
3
votes
2
answers
134
views
Why is $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$?
I'm sorry if this is a duplicate but I didn't find my answer. I'm currently studying maxwell's equations and I know that by comparing the wave equation for either the magnetic or the electric field
\...
- 33
0
votes
1
answer
84
views
Why does the relative permittivity of Sapphire not match the square of its refractive index?
According to the Wikipedia, the refractive index of sapphire is around $n = 1.8$ while its relative permittivity $\varepsilon_{\mathrm r}$ is between $9$ and $11$ (depending on the direction). Given ...
- 329
1
vote
1
answer
112
views
Where can I find tables of the refractive index (real and complex part) or dielectric function as a function of frequency for different materials?
I need this information to do simulations for my master's thesis but I don't know if there is a bibliography or a repository on the internet with this information. They are simple materials, water, ...
1
vote
1
answer
29
views
Planck radiation law of a dielectric layer
Suppose we have a rectangular slab of thickness $h$, width $a$ and length $b$. The upper surface of the slab is put at constant temperature $T$ while all the rest is at initial temperature $T_0$. ...
- 593
1
vote
1
answer
173
views
The difference between the equation of Permittivity and Permeability in a medium
I notice that the equations of Permittivity and Permeability in a linear medium are exactly opposite of each other. One is $$\mathbf{D} \equiv \varepsilon \mathbf{E}$$ while the other one is $$\mathbf{...
- 11
4
votes
2
answers
708
views
Intuitive meaning of the permittivity and the permeability in Electromagnetism
I wonder what the correct way to intuitively understand the concepts of electrical permittivity and magnetic permeability would be.
The electric permittivity $\varepsilon$ of a medium is defined as a ...
- 974
2
votes
1
answer
204
views
Reflectivity coefficients at dielectric interface
In the book Principles of Lasers by Orazio Svelto, at chapter 4.3 "Wave Reflection and Transmission at a Dielectric Interface", the author tells that
If the wave is initially in the medium ...
- 1,904
3
votes
0
answers
73
views
Time lag between observed electrical field and polarity of light?
I was listening to the Feynman lectures on physics Vol. 3, Ch.2 the other day, and he was talking about the relationship between light polarity and the electric field of light as it is transmitting ...
- 361
0
votes
1
answer
279
views
Highest refractive index dielectric
What is the material or metamaterial that is a very good dielectric and has a very high refractive index at least in frequencies below $500\ MHz$?
- 119
0
votes
1
answer
1k
views
Dielectric constant change in the atmosphere?
I'm curious about the refractive index changing in the atmosphere. As I understand it (and I may very well be wrong/naive) when a ray of light enters from one medium into another, the electric field ...
- 90
1
vote
1
answer
201
views
Why can't $ε_r<1$ (at low frequencies)?
I've heard it said that the vacuum permittivity is the lowest possible permittivity for any substance, that no substance can have $ε_r<1$. Is this true? If so, why is this different from ...
- 389
2
votes
2
answers
1k
views
Maxwell's equations, nonlinear media, and dynamic response
Maxwell's equations in the vacuum with electric permittivity $\epsilon_0$ and magnetic permeability $\mu_0$ are given as:
$$\nabla \cdot \vec E = \frac{\rho}{ \epsilon_0}$$
$$\nabla \cdot \vec B = 0$...
- 24.8k
19
votes
1
answer
2k
views
How can the refractive index be below 1 in a dielectric?
Upon checking the optical properties of different dielectrics, I found the interesting case of $Al_2O_3$. It seems to be reported with a refractive index below 1 in the infrared range of $10 - 12~\mu ...
- 4,788
1
vote
2
answers
451
views
Contradiction on the behavior of refractive index
The refractive index is given by:
$$ n = \sqrt{\mu_r \epsilon_r} $$
This equation is symmetric about wavelength and is same for all wavelength of light i.e. since $\mu_r$ and $\epsilon_r$ are ...
- 39
4
votes
2
answers
5k
views
Can relative permittivity be less than 1?
Relative permittivity shows that force of interaction in some media is 3 times less than in vacuum ($\varepsilon = 3$) for example. When looking tables of permittivity I never saw a value less than 1.
...
- 255
0
votes
0
answers
90
views
Photon explanation of dielectric effects?
When an electromagnetic wave passes through a medium, the electric component of the wave will induce a dipole. I believe this can happen in a number of different ways, including rotating of a polar ...
1
vote
1
answer
3k
views
Converting a complex index of refraction to a complex dielectric constant
I have a material's $n,k$ file, containing the complex index of refraction for every wavelength: $n(\omega)+ i\ k(\omega)$.
Now I would like to convert it to the dielectric constants: $\epsilon_{\...
- 111
1
vote
0
answers
141
views
Dielectric constants from refractive index and absorption spectra
I would like to calculate the dispersion relation (dielectric constants $\varepsilon'$ and $\varepsilon''$) from two spectra: refractive index $n$ and absorption (in %). I tried to use the relation $$\...
- 4,788
1
vote
0
answers
560
views
Reflection and transmission coefficients
Suppose we have a plane wave with s-polarization travelling through a medium with refractive index $n_1$ in direction $\vec{k}$ perpendicular to a surface of a dieletric with refractive index $n_2$; ...
0
votes
1
answer
2k
views
Variation of refractive index with concentration of salt in water
I know that the refractive index of water increases with increased concentration of salt.
But I also read that
$$n = \sqrt{\varepsilon_r\mu_r}$$
And that the relative dielectric constant decreases ...
0
votes
1
answer
1k
views
Deriving the real and imaginary parts of the complex refractive index in a dielectric medium
I have been trying to demonstrate that for a refractive index $n=n_R+in_I$ we have $$n_I=-\frac{Ne^2\gamma\omega}{2m\epsilon_0[(\omega_0^2-\omega^2)^2+\gamma^2\omega^2]},$$ $$n_R=1+\frac{Ne^2(\omega_0^...
- 4,607
3
votes
1
answer
136
views
When exactly do we substitute $\epsilon_0 \rightarrow \epsilon$ and $\mu_o \rightarrow \mu $?
If everything is embedded into vacuum, why aren't Maxwells Equations always with $\mu_o$ and $\epsilon_o$?
When exactly do we have to make the substitution $\epsilon_0 \rightarrow \epsilon$ and $\...
- 1,619
1
vote
1
answer
800
views
Why phase velocity of light is slower in a dielectric than vacuum?
Why does light speed suffer a reduction when it passes through a homogeneous dielectric medium? I know my math says so, i.e.- a highly polarizable ($\chi$) medium is associated with high $\epsilon$ (=$...
- 31
6
votes
2
answers
3k
views
Refractive index of dielectric in different frames of reference
The setup
A transparent isotropic dielectric medium moving in the negative $x'$ direction at speed $v$ in frame $S'$ is stationary in frame $S$, where it has refractive index $n$. In other words, ...
- 6,425
8
votes
4
answers
29k
views
Real and imaginary parts of dielectric constant vs refractive index?
So for a complex dielectric constant $\epsilon = \epsilon_a + i\epsilon_b$, the wave vector and index of refraction are related to it through $k = \frac{\omega}{c}n$ and $n = \sqrt{\frac{\mu \epsilon}{...
- 2,913
2
votes
2
answers
3k
views
Why define relative permittivity and relative permeability?
I am reading something about electomagnetic field and the first introduce the free space permittivity and permeability for the electric field and magnetic field. And later when discussing the field in ...
- 2,383