Snell's law with a complex refractive index

In summary, the textbook says that NsinA=N'sinB still holds, but the sinB, for example, may be a complex number. To get B, one must use a for I am N. Thank you.
  • #1
zhanghe
44
2
hello everyone

Consider extinction coefficient k, n becomes N=n-ik.
the textbook says NsinA=N'sinB still holds itself.

But the sinB,for exmple, may be a complex number, i want to know
how to get B?
how to understand this situation, which is the refractive angle?
the B's real part?
 
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  • #2
The electric field in a plane wave E~exp[i(kx-wt)], where k=w N/c.
If N=n-ia, then E~exp[i(nw/c)x-wt)exp[-ax].
This means n is still used by Snell.
k is usually the wave number, so I used a for I am N.
 
  • #3
thank you
and you mean that the refrective angle only depends on Re N--n
and has nothing to do with I am N--a(using your signal), right?
 
  • #4
pam said:
The electric field in a plane wave E~exp[i(kx-wt)], where k=w N/c.
If N=n-ia, then E~exp[i(nw/c)x-wt)exp[-ax].
This means n is still used by Snell.
k is usually the wave number, so I used a for I am N.

Why you write exp{i[(nw/c)x-wt]}*exp(-ax) and not exp{i[(nw/c)x-wt]}*exp(axw/c) ?
 
Last edited:
  • #5
Sorry. That was a misprint. It should be axw/c.

"and you mean that the refrective angle only depends on Re N--n"
I'm afraid I oversimplified. The boundary conditions have to be applied at the interface, and the derivation done from scratch. It gets quite complicated.
 
  • #6
these days ,i thought further that maybe it's only a kind of appearance to describe the polirized light phase shift at the interface of different media.
but i wonder which is the refractive angle if k ,ie absorption exist.
for example. air/silicon,whose N is 1 and 4.4-0.8i, respectively.
to Snell, 1*sin(AOI)=(4.4-0.8i)*sin(AOR),
AOR will be a complex number, how to get the real AOR in experiments?
 

1. What is Snell's law with a complex refractive index?

Snell's law with a complex refractive index is an extension of Snell's law, which relates the angle of incidence and refraction for light passing through different mediums. However, in this case, the refractive index is a complex number, which takes into account the absorption of light by the medium.

2. How is Snell's law with a complex refractive index different from Snell's law?

Snell's law only takes into account the real part of the refractive index, which represents the speed of light in the medium. However, Snell's law with a complex refractive index also considers the imaginary part, which represents the absorption of light by the medium.

3. What is the significance of using a complex refractive index in Snell's law?

The use of a complex refractive index in Snell's law allows for more accurate predictions of the behavior of light in different mediums, as it takes into account the absorption of light by the medium. This is especially important in materials with high levels of absorption, such as semiconductors.

4. How is a complex refractive index measured?

A complex refractive index can be measured using techniques such as ellipsometry or spectroscopic ellipsometry, which measure the phase difference and amplitude of polarized light as it passes through a medium. These measurements can then be used to calculate the complex refractive index.

5. What are some practical applications of Snell's law with a complex refractive index?

Snell's law with a complex refractive index is commonly used in the design and optimization of optical devices, such as lenses, mirrors, and filters. It is also used in the study of materials with high levels of light absorption, such as in the development of solar cells and photonic devices.

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