Refractive Index calculation of sample

[Shaumik]

Hi

 

Got stuck in a calculation. Any suggestions will be highly appreciated

 

I am trying to calculate the RI and other optical constants for an acrylic slab (thickness = 1.65 mm) - TAKING MULTIPLE REFLECTIONS within the slab into consideration. I took the reference wave and the sample wave. Calculated the phase change to be 34 degrees.

 

I deduced some equations of T, phi ®, phi (t) and beta and alpha. But there are too many unknown parameters to solve the equation to get the value.

 

WHAT SHOULD I CONSIDER TO CALCULATE THE REFRACTIVE INDEX CONSIDERING MULTIPLE REFLECTIONS WITHIN THE SAMPLE.

[Enthalpy]

I need more explanations - other readers maybe as well.

Are you making a measurement and inferring the index?

As an exercize, or to characterize precisely one sample? Acrylic's index is already well documented.

How does light pass through your sample, what do you observe? What do you call "phase change"?

Edited September 18, 2012 by Enthalpy

[Shaumik]

hi. Thanks for your response. I have just build a continuous wave Terahertz setup and started doing experiments. I am passing the THz wave in free space as the reference waveform and then through the acrylic as the sample spectrum. Since there is change in refractive index (in free space and acrylic), I am seeing a phase change. I calculated the phase by merging the waveforms and interpolation.

 

Like we can find out the phase, if we know the refractive index and extinction coefficient, attenuation and propagation const, i am trying to solve from the back side, calculating the phase and find the refractive index and the other optical constants. Since, it's will be like a film with a finite thickness, i believe, we will see a fabry perot etalon case here.

 

I am doing it as an exercise, for the following purposes:

 

i) to be clear about the characteristics.

ii) i know the acrylic refractive index. I am doing the back calculations, to see how the refractive index changes in the THz ranges.

iii) to give a signature to other unknown materials in the THz range, I am just starting off this one as a practice.

 

Thanks

 

 

I need more explanations - other readers maybe as well.

Are you making a measurement and inferring the index?

As an exercize, or to characterize precisely one sample? Acrylic's index is already well documented.

How does light pass through your sample, what do you observe? What do you call "phase change"?

[Klaynos]

I've done something similar using thz-tds, how familiar are you with Fresnel equations? The three layer Fresnel reflection equation is probably what you're interested in. You will probably need different angles to get a decent uncertainty but that'll probably depend on your bandwidth and sample thickness.

[Enthalpy]

Several math paths are possible. I suppose propagation is perpendicular to the surfaces.

 

Microwave people would use S parameters (or scattering parameters): S11, S12, S21, S22

http://en.wikipedia....ring_parameters

 

If you don't want to invest in them, you can just compute in one step the multiple reflections that way:

if R is the amplitude of the pair of reflections (complex number, for field, not for power) then 1+R+R²+R³+R⁴... is 1/(1-R).

 

Or equivalently, you write that some fields are continous at both interfaces, and solve the set of linear equations between the complex amplitudes, including the reflected fields.

 

----------

 

 

I'm interested in CW THz generators for having suggested some there (sorry for the horrible mess):

http://www.physforum...opic=15617&st=0

could you describe your generator, possibly through a link? Thanks!

[Shaumik]

Thank you Klaynos for your suggestions, i am familiar with Fresnel equations. I actually considered the case where we have multiple reflections like a Fabry Perot Etalon. I will consider your suggestions, will get back asap.

 

I've done something similar using thz-tds, how familiar are you with Fresnel equations? The three layer Fresnel reflection equation is probably what you're interested in. You will probably need different angles to get a decent uncertainty but that'll probably depend on your bandwidth and sample thickness.

 

Thanks lot for your suggestions. I used Fabry Perot Etalon case. I will go through all whatever you have told carefully.

 

I will get back.

 

 

 

 

Several math paths are possible. I suppose propagation is perpendicular to the surfaces.

 

Microwave people would use S parameters (or scattering parameters): S11, S12, S21, S22

http://en.wikipedia....ring_parameters

 

If you don't want to invest in them, you can just compute in one step the multiple reflections that way:

if R is the amplitude of the pair of reflections (complex number, for field, not for power) then 1+R+R²+R³+R⁴... is 1/(1-R).

 

Or equivalently, you write that some fields are continous at both interfaces, and solve the set of linear equations between the complex amplitudes, including the reflected fields.

 

----------

 

 

I'm interested in CW THz generators for having suggested some there (sorry for the horrible mess):

http://www.physforum...opic=15617&st=0

could you describe your generator, possibly through a link? Thanks!