while i was calculating group velocity for desired wavelength (1550 nm) using w-k diagram,i came across an interesting problem.
in w-k diagram there are more than one phase constant corresponding to single frequency.
so by calculating slope of w-k diagram we got more than one group velocity for a single frequency.
sir is it practically possible????
if yes then which group velocity i should consider for first order dispersion analysis.
here i am attaching w-k diagram find using optifdtd tool.
Hi,
This is certainly possible. If you have multiple propagating modes in your structure you can have multiple frequencies. If the propagation velocity is also depending on the excitation frequency the waves are called dispersive.
Since I am not quite sure what your application is I will just refer to my applications, where you encounter a similar behaviour.
In the case of thinwalled structures (plate-like; shell-like), which I am more familiar with, guided waves are propagating. In homogeneous materials these waves are called Lamb waves. Here you also encounter, depending on the excitation frequency, infinitely many propagating modes but at least always two. A symmetric mode and a antisymmetric mode. You see, for this special class of waves there are also at least two different group velocities belonging to the two different propagating modes. In your application it should be similar.
Hope this helps.
Best
Hi,
I've wondering if it could be the aliasing phenomenon? As in the Discret fourier transform, when you sampling a continuous field with a sample rate "a", your result is 2pi/a periodic. Usually we focus on wavenumber in the range [-pi/a,pi/a]. but in fact you have an infinite value of wavenumber which are 2pi/a periodic. Since in your figure is almost symmetric around k=7.5, so i'am wondering if your pi/a=7.5? At your point A (k=3) your point C (k=12). For point A it the same wave for k=-3,because they are the same wave just propagating in 2 opposite directions. Since it is 2pi/a periodic, we have -3+2pi/a=-3+15=12. So it is normal that same frequency for point A and point C, they are the same wave propagating in 2 opposite directions.
Hope this helps.
Best
Thank you Sascha sir
i am working on slow light wave guides with line defect.and want to calculate group velocity of wave at (1550nm).but as in w-k diagram two propagation constant are there for single frequency.so there will be two group velocities for same frequency.
which one i should consider for analysis.
Since I am not familiar with light waves I cannot answer that question. You could do you are analysis twic with both values and see what happens.
Sorry that I am not able to help you with this question any further.
Good luck with your project!
Dear Amit,
I'm usually working with waveguides at the microwaves frequencies, but the phenomena is the same.
In a wave guide you have several modes allowed, TE and TM, in each of these modes you can find a group velocity in a the diagram, This is you are watching in the picture.
You can take the dimensions of the optical fiber and can compute the cutoff frequency for each mode and you can reproduce theorethically the diagram, in order to check and understand the physicall situation. These diagram w-k is simetric.
In your picture the group velocity is the same at the points B anc C just the sign of the group velocity is diferent.
this is characteristic for media with internal structure (for example, the layered media);
so, the problem can be seen in the more abstract sense.
Thank you Fano sir
How light is slow down in photonic crystal wave guides.
and why it deepens on period of air holes we are using.
hi amit
i'm working on photonic crystal waveguide and want to calculate group velocity, group index ,...
may it possible help me?
what software do you working with?
do you have kind of training file or film, pdf...?
i'm gratefull helping me.
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