Refractive index equation help

[misterwicked]

Refractive index is defined as

n = speed of light in a vacuum / speed of light in medium

Since both speed of light in a vacuum and speed of light in medium are real number, refractive index also has to be real. But we know that in general refractive index is complex. So what actually is "n" in the above equation? Is it real part of the complex refractive index, its absolute value or something else?

Thanks.

 

[timthereaper]

From what I understand, it's the real part of the complex number. The imaginary part is just indicative of the amount of absorption loss when light passes through the material.

 

[misterwicked]

Ok, thanks. I have additional question.

The definition for the refractive index n= v/c is usually accompanied by the relation:

n = sqrt(epsilon)

where "epsilon" represents permittivity of the material. Should I suppose that by "permitivity" they mean its real part?

I'm asking this because according to wikipedia (http://en.wikipedia.org/wiki/Refractive_index#Relation_to_dielectric_constant), the following relation:

n + ik = sqrt(epsilon' + i*epsilon'')

which connects complex refractive index and permittivity disagrees with the equation

Re(n) = sqrt(Re(epsilon))

that connects real part of refractive index and real part of permittivity that i supposed above. Any hints to where I am going wrong?

P.S Sorry for the formulae, haven't learnd to write them yet ;)

 

[chrisbaird]

The complex-valued variable n' has components:

n = Real(n'): Describes the refraction, or bending, and slowing of waves in the medium, so that n = c/v
k = Imag(n'): Describes the spatial attenuation of waves in the medium (note that loss, but other things as well can lead to attenuation.)

The correct formula is: n' = sqrt(epsilon) where both n' and epsilon are complex-valued so that

n = Real(sqrt(epsilon))
k = Imag(sqrt(epsilon))

Note that Real(sqrt(epsilon)) is not equal to sqrt(Real(epsilon)) in general. If the material is not lossy so that Imag(epsilon)=0, and you are at a frequency where Real(epsilon) > 0, then the general equation reduces down to: n = sqrt(epsilon). So if epsilon is real and positive, you can use this equation, otherwise you have to use the more general form. Also note that the most general formula has a mu next to the epsilon to account for magnetic effects, so these formulae only really apply to non-magnetic materials where mu=1.

 

[misterwicked]

ok, thanks a lot ;)

 

[singhvi]

The complex-valued variable n' has components:

n = Real(n'): Describes the refraction, or bending, and slowing of waves in the medium, so that n = c/v
k = Imag(n'): Describes the spatial attenuation of waves in the medium (note that loss, but other things as well can lead to attenuation.)

The correct formula is: n' = sqrt(epsilon) where both n' and epsilon are complex-valued so that

n = Real(sqrt(epsilon))
k = Imag(sqrt(epsilon))

Note that Real(sqrt(epsilon)) is not equal to sqrt(Real(epsilon)) in general. If the material is not lossy so that Imag(epsilon)=0, and you are at a frequency where Real(epsilon) > 0, then the general equation reduces down to: n = sqrt(epsilon). So if epsilon is real and positive, you can use this equation, otherwise you have to use the more general form. Also note that the most general formula has a mu next to the epsilon to account for magnetic effects, so these formulae only really apply to non-magnetic materials where mu=1.

could you also tell the formula for reflectivity/transmittivity for a material with complex refractive index, also it would be awesome if you had any references