Effective refractive index when two transparent medium are joined in s

[jayeshtrivedi]

Dear All,

If two layers of thickness d1 and d2 stacked on each other and having their absolute refractive index n1 and n2 .

Can we find effective refractive index of the combination with this data?

Thanks in advance.

Jayesh.

 

[Simon Bridge]

This is something you should be able to figure out for yourself.
Define "effective refractive index".
Apply the definition.

i.e. http://physics.stackexchange.com/questions/69231/effective-refractive-index

 

[Claude Bile]

Yes, but the calculation is not straightforward, because it depends on the mode profile - which is generally found by solving wave-equations.

Once you know the mode profile, the calculation becomes relatively straightforward, essentially it is just an average of the two indices, weighted by the mode fraction in each layer.

Claude.

 

[my2cts]

It is quite easy to program the solution for any number of layers using transfer matrices.
See wikipedia or any promising search result:
http://sjbyrnes.com/fresnel-solver-sourcecode.pdf

 

[sardar]

Dear Jayesh,

Thank you for your question. The effective refractive index of a combination of two transparent mediums can be calculated using a formula known as the Bruggeman effective medium theory. This theory takes into account the individual refractive indices and thicknesses of the two layers to determine the overall refractive index of the combination. The formula is as follows:

n_eff = (n1^3 + n2^3 + 2*n1^2*n2*d2/d1)/(n1^2 + n2^2 + 2*n1*n2*d2/d1)

Where n_eff is the effective refractive index, n1 and n2 are the refractive indices of the two layers, and d1 and d2 are the thicknesses of the layers.

I hope this information helps. If you have any further questions, please don't hesitate to ask.

Best regards,