Hello,
I'd like to understand what complex refractive indices can be found in nature. Specifically I am trying to get an order of magnitude estimation on the imaginary part of the refractive index. In what type of active lasing medium would this be the largest ? and how large would it actually get ? 10^-4 ? 0.01 ? 0.1 ?
It sounds like a simple question, but I had a surprisingly hard time getting a simple answer from the literature.
Can anyone help ?
Hanan
Dear Hanan
You can find an excellent refractive index data base in
http://refractiveindex.info/
Dear Carlos,
The site you mentioned in indeed an excellent reference for the refractive index, but as far as I understand doesn't contain any refractive index info for active gain medium (i.e. negative absorption coefficients). Am I wrong ?
Hanan
Dear Hanan!
About Your first line of interest what complex refractive index (RI)in nature can be found I recommend remarkable database fron M.N.Polyansky "Refractive index database" in http://refractiveIndex.INFO. About your second question with laser medium I shall say the following. Answer depends on the type of lasing media. Laser media with luminescence centers (as a rule with low concentration of the centers) real part of refractive index n>> -k and +k - imagine part of RI. If You know the gain or absorption on given wavelengh in cm^-1, You can calculate the image part k (another name-extinction, see good optic manual). Above mentioned unequality results from low concentration of luminescent centers in compare matrix. In the case of gas and semiconductor laser above mentioned unequality directs may be to equality because highes concentration of lasing centers, gain of similar lasers was calculated and measured multiply, however I don`t know real experimental works devoted precisely this plane of study.
Bring my best wishes be suscesfull!
Dear Hanan,
Few comments:
1. I am sure you know that but just in case - absorption is also characterized by complex IR, not just amplification (gain). Absorption and Amplification just have opposite signs or imaginary part of RI.
2. In almost any media, that can be used as a gain media for lasers, absorption (in unpumped state and/or away from energies at which the population inversion is achieved) is much higher than amplification, and so is absolute value of imaginary part of RI.
3. For the gain (amplification), it is important to distinguish the modal gain (optical gain experienced by a lasing mode inside the laser cavity) from material gain (directly related to the imaginary part of the refractive index of the gain medium). The modal gain is equal to the product of material gain and the optical confinement factor (the fraction of the transverse optical mode overlapping the active layer and therefore experiencing optical gain). This overlap factor can be close to unity in bulk and gas lasers, but can be just few % in some semiconductor lasers. Obviously the lower the overlap, the higher the material gain must be to support lasing action.
4. Few numbers. Typically optical gain is defined as 4*pi*(Confinement Factor)*(Complex Index of gain material)/wavelength.
For a typical semiconductor laser with quantum wells serving as gain medium, the numbers are approximately:
Optical Gain ~ 100 (1/cm)
Confinement factor ~0.05
wavelength ~ 1e-4 cm
So the material gain is approximately ~100/4/pi/0.05*0.0001=0.16
Again optical loss can be 10 times that (and of opposite sign).
Hope this helps.
Gleb
Dear Gleb,
Thanks for answering in such detail, it's exactly what i needed. You helped immensly !
Thanks for kind words, but i think I got a decimal point wrong. My numbers should correspond to the complex part of refractive index of 0.016, not 0.16.
Gleb
Hmmm ... yes, that makes more sense.
I was mostly refering to your explanation on the confinement factor, it's the link I was missing.
In any case, regarding loss- I wanted to add that the imaginary part of the refractive index can get to be exceedingly large in metals, even larger than the real part (so it's two orders of magnitude higher). It's not what I was asking, but just in case anyone else ever reads this and wants to know ...
Hanan
Dear Hanan,
As you noted, the values of the real and imaginary parts of the refractive index depend on: i) what material(s) you consider and ii) the frequency range of interest.
Some have suggested consulting tabulated data. This is indeed a good option if you lack any optical data of your own. On the other hand, depending on the problem you are trying to solve, some sources report significantly different results. (E.g. the handbook by E.D. Palik (1985) and the paper in Phys. Rev. B by Johnson and Christy (1972)). In other words, tabulated data are convenient, but there is a catch. However, for an order of magnitude estimate they should suffice.
Please note that the real and imaginary parts of a refractive index are not independent of each other, but they are related to each other through the Kramers-Kronig relations. So if you have information about only one of them, you can calculate the other one (as a function of frequency). Such a calculation assumes that the medium obeys causality.
Regards, Wijnand
Very interesting discussion!
In all mentioned refractive index databases you can find the imaginary part of the refractive index exceeding 3. Apparently, such values follow from ellypsometric measurements and demonstrate rather their limits. On my opinion, the realistic values in visible and UV range should be much lower.
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