Hello,

I'm currently working with a group of physicists who fabricate so-called
"metamaterials". Don't worry, I don't want to bother you with details, but
the bottom-line is that those materials possess a negative index of
refraction (ior). Since this is very unusual and the consequences are not
obvious at once, we would like to make some examples what would happen if
you sticked e.g. your feet not into water but into this material (you could
see your feet in front of you...).

My question now is: Is it possible to change POV-ray's source code in order
to implement negative ior's? Or is it too difficult?

Unfortunately I'm not that familiar with the code, it would take ages for me
to find it...

Thx in advance...

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Sorry,

I found this in the beginner's newsgroup (hadn't looked there before):
"I thought it allowed IOR to be less than 1.0, but if not, you can
certainly invert your shape and fill the rest of the universe with a
higher IOR value. Only the difference in the IOR values at the interface
are significant for determining the angle of refraction."

Physically, this is not the same. A positive ior is positive and doesn't
exhibit very strange features even if it is <1.0.

"wolfman" <wol### [at] physikuni-karlsruhede> wrote:
> Hello,
>
> I'm currently working with a group of physicists who fabricate so-called
> "metamaterials". Don't worry, I don't want to bother you with details, but
> the bottom-line is that those materials possess a negative index of
> refraction (ior). Since this is very unusual and the consequences are not
> obvious at once, we would like to make some examples what would happen if
> you sticked e.g. your feet not into water but into this material (you could
> see your feet in front of you...).
>
> My question now is: Is it possible to change POV-ray's source code in order
> to implement negative ior's? Or is it too difficult?
>
> Unfortunately I'm not that familiar with the code, it would take ages for me
> to find it...
>
> Thx in advance...

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wolfman wrote:
> Sorry,
> 
> I found this in the beginner's newsgroup (hadn't looked there before):

Come on - if you have read Mike's reply you probably have read mine as 
well so i don't need to repeat it...

Note that according to the most common definitions of the index of 
refraction a negative one is not possible (this has nothing to do with 
physics but mere mathematics).  So if you want to know if POV-Ray 
correctly handles what you call negative ior you first have to decide 
what a negative ior actually is.

And just for the record: for refraction (which is not the only place 
where ior is used) POV-Ray uses Heckbert's method, see 'Derivation of 
Refraction Formulas' on:

http://www.cs.cmu.edu/~ph/


Christoph

-- 
POV-Ray tutorials, include files, Landscape of the week:
http://www.tu-bs.de/~y0013390/ (Last updated 24 Jul. 2005)
MegaPOV with mechanics simulation: http://megapov.inetart.net/

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Christoph Hormann <chr### [at] gmxde> wrote:

> Note that according to the most common definitions of the index of
> refraction a negative one is not possible (this has nothing to do with
> physics but mere mathematics).  So if you want to know if POV-Ray
> correctly handles what you call negative ior you first have to decide
> what a negative ior actually is.

The sign of the index of refraction is arbitrary, going strictly by the
mathematics. The physical principle that fixes the sign is conservation of
energy. To conserve energy across a material boundary, normal materials
have to have a positive IOR and these metamaterials have to have a negative
IOR.

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Tom York wrote:
> Christoph Hormann <chr### [at] gmxde> wrote:
> 
> 
>>Note that according to the most common definitions of the index of
>>refraction a negative one is not possible (this has nothing to do with
>>physics but mere mathematics).  So if you want to know if POV-Ray
>>correctly handles what you call negative ior you first have to decide
>>what a negative ior actually is.
> 
> 
> The sign of the index of refraction is arbitrary, going strictly by the
> mathematics. The physical principle that fixes the sign is conservation of
> energy. To conserve energy across a material boundary, normal materials
> have to have a positive IOR and these metamaterials have to have a negative
> IOR.
> 
> 
[Semiologic mode on: (I need more explanation)]

The refraction is the propagation of the EM wave inside the material.
The positive IOR (IOR>0) might be used to keep the information that the
EM wave is moving from zone A made of material to zone B made of air (or
whatever). Same for the opposite, moving from B to A.
That's refraction. So far so good.
Now, if I try to imagine your negatif IOR (really, IOR < 0 ? not just
IOR < 1 ?) as an interface which when encountered by the EM wave send
the EM wave back in the zone it is coming from, it is not what I would
call refraction (usually it's called reflection).
There is of course the classical "total reflection angle" due to
refraction, but that's only a side effect.

Please note also that even an IOR < 1 would be quite puzzling: it would
means that light would travel faster than in the void when inside this
material (faster than c). it would be an interesting universe.
(especially if the information can be made to travel with the
corresponding EM wave)... Nahhh, just dreaming.

There is also a possible usage for the sign of the IOR, which could be
an oversimplification of the phase change/polarisation of a signal.
Assuming a clockwise rotation of E toward M, going thru one "negatif
ior" material could end up with an opposite rotation (anticlockwise).

Now, maybe your "metamaterial" is just a mirror with subsurface
scattering/refraction ? A kind of variable angle of reflection ?

[end of questionning]

- --
Eifersucht ist die Leidenschaft, die mit Eifer sucht, was Leiden schafft.
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Le Forgeron <jgr### [at] freefr> wrote:
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>
>
> The refraction is the propagation of the EM wave inside the material.
> The positive IOR (IOR>0) might be used to keep the information that the
> EM wave is moving from zone A made of material to zone B made of air (or
> whatever). Same for the opposite, moving from B to A.
> That's refraction. So far so good.
> Now, if I try to imagine your negatif IOR (really, IOR < 0 ? not just
> IOR < 1 ?) as an interface which when encountered by the EM wave send
> the EM wave back in the zone it is coming from, it is not what I would
> call refraction (usually it's called reflection).
> There is of course the classical "total reflection angle" due to
> refraction, but that's only a side effect.
>
> Please note also that even an IOR < 1 would be quite puzzling: it would
> means that light would travel faster than in the void when inside this
> material (faster than c). it would be an interesting universe.
> (especially if the information can be made to travel with the
> corresponding EM wave)... Nahhh, just dreaming.
> There is also a possible usage for the sign of the IOR, which could be
> an oversimplification of the phase change/polarisation of a signal.
> Assuming a clockwise rotation of E toward M, going thru one "negatif
> ior" material could end up with an opposite rotation (anticlockwise).
>
> Now, maybe your "metamaterial" is just a mirror with subsurface
> scattering/refraction ? A kind of variable angle of reflection ?
>
> [end of questionning]

The refractive index n is defined as n^2=permittivity*permeability, so n=+/-
sqrt(permittivity*permeability) (in reality, it's even more complicated).
Hence the negative sign in some cases.
Let's consider an interface between two "normal" materials. An incident beam
coming from material 1 which has a smaller n than material 2 is refracted
towards the surface normal in material 2 according to Snell's law
sin(theta1)/sin(theta2)=n2/n1. The refracted beam propagates "on the other
side"  of the surface normal than the incident beam.
Now, if you replace material 2 by a "metamaterial" with n2<0, the refracted
beam propagates "on the same side" of the surface normal as the incident
beam. That's what would be weird to look at!
Another strange thing in a metamaterial is that the group velocity of a wave
is antiparallel to its propagation direction, the wave vector k is
antiparallel to the Poynting vector S. S determines the overall energy flow
as well as the propagation direction, so that's consistent with the
conservation of energy, thanks Tom York!

If you don't believe me, google "metamaterials", there is lot's of stuff.

So, back to my problem, has anybody any idea of where the IOR is implemented
in POV-ray? Or what can I do to be able to have a negative sign for the
IOR?

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wolfman wrote:
> 
> The refractive index n is defined as n^2=permittivity*permeability, so n=+/-
> sqrt(permittivity*permeability) (in reality, it's even more complicated).

Just to make it clear: n^2=permittivity*permeability is not a 
definition, it's just a furmula n is supposed to comply with (and there 
is no unique solution for n).  n = sqrt(permittivity*permeability) would 
be a definition but it would not allow negative n (sqrt(x) is positive 
or imaginary for any non-complex x).

> If you don't believe me, google "metamaterials", there is lot's of stuff.

No one said this - you just did not say what negative ior means to you 
previously.

> So, back to my problem, has anybody any idea of where the IOR is implemented
> in POV-ray? 

Using

grep -r -I -E "[[:space:][:punct:]]ior[[:space:][:punct:]]" *

on the POV-Ray code finds pretty much every use of IOR.

> Or what can I do to be able to have a negative sign for the
> IOR?

Again: why do you assume you can't use a negative IOR.

Christoph

-- 
POV-Ray tutorials, include files, Landscape of the week:
http://www.tu-bs.de/~y0013390/ (Last updated 24 Jul. 2005)
MegaPOV with mechanics simulation: http://megapov.inetart.net/

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Thank you.

wolfman wrote:
> Now, if you replace material 2 by a "metamaterial" with n2<0, the refracted
> beam propagates "on the same side" of the surface normal as the incident
> beam. That's what would be weird to look at!

With a little more google, I start to see... the ray go thru the
surface, but instead of crossing the normal, it reflect on it.

> 
> If you don't believe me, google "metamaterials", there is lot's of stuff.

Best so far: http://www.answers.com/topic/metamaterial

> 
> So, back to my problem, has anybody any idea of where the IOR is implemented
> in POV-ray? Or what can I do to be able to have a negative sign for the
> IOR?

Yep! you want to play with the computation of refracted rays.
That should be a small patch... I leave you tweaking the parser to
accept the negative ior (but notice that ABS(IOR) should still =>1, even
with metamaterial, no revolution of physics)

Then a few explanation for povray: a ray keep its current ior value, and
it get updated by the ratio of the leaving/entering thru an interface.
So far, so good, you only have to be able to handle the computation of
the direction of the refracted ray.

You want to change BacktraceRefract in lighting.cpp,
in particular the test of line 3056 (reference of 3.6.1)  (testing that
change is nearly irrelevant, may be that test is ok)
and mainly the relevant ELSE block

Looking at it, it seems (but YOU check!) that a change in Refract_Guts
(same file) could be enough. (you need to trap the ior<0, because it use
the square root a loot..., that's only a small function to update...)

Good luck.

I wonder if such strange things could make it so late in 3.7 ?





- --
Eifersucht ist die Leidenschaft, die mit Eifer sucht, was Leiden schafft.
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Le Forgeron wrote:
> Best so far: http://www.answers.com/topic/metamaterial

The doppler shift is reversed!?   <boggle!>

-- 
   Darren New / San Diego, CA, USA (PST)
    "Yes, someone maintains a big web site
     about that. I think her name is Wiki."

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Christoph Hormann <chr### [at] gmxde> wrote:
> Just to make it clear: n^2=permittivity*permeability is not a
> definition, it's just a furmula n is supposed to comply with (and there
> is no unique solution for n).  n = sqrt(permittivity*permeability) would
> be a definition but it would not allow negative n (sqrt(x) is positive
> or imaginary for any non-complex x).

n*n = x, but also (-n)*(-n) = x. The positive n is the principal value of
the root, not the only valid value.

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