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Waveguide Dispersion Curve

Posted 2013/01/11 11:00 GMT-5 RF & Microwave Engineering, Acoustics & Vibrations, Structural Mechanics 2 Replies

Emran Khander
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The MATLAB coding for solving second order differential equation(D(λ)=- (λ /c)*(d^2n/d λ^2)) of wave guide dispersion is heavily needed. I have values of effective index n, c is constant and variable lambda is varied from 1.34-1.70 um . I have already completed the MATLAB coding of material dispersion, confinement loss. But i am failing to do coding of wave guide dispersion. I can use diff command if n is not given . But here both n and lambda is known. Thats why i face problem as there is no equation of effective index,n. So please anyone help me.It is urgently needed.......
2 Replies Last Post 2013/05/02 9:42 GMT-4
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Hello Emran Khander

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Hassanain Al-Taiy
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Posted: 1 decade ago 2013/05/02 6:05 GMT-4
Dear Emeran

i hope that you are well, i want to simulate the dispersion curve in comsol by changing the acoustic freq., so please if you have idea for which Eq. i must you to draw the curve between the K and Freq. ?



Best regards
Dear Emeran i hope that you are well, i want to simulate the dispersion curve in comsol by changing the acoustic freq., so please if you have idea for which Eq. i must you to draw the curve between the K and Freq. ? Best regards
Felipe Beltran-Mejia
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Posted: 1 decade ago 2013/05/02 9:42 GMT-4
Hi Emran,

I believe matlab does not have an easy way to derivate as (for example) Mathematica does.

The reason is that numerical derivation is not a trivial subject.

As a first approach you can use the polyfit function in matlab and then derivating the output order-m polynomial is a trivial task. But beware! this is only accurate if your interpolated data behaves as a polynomial of order m.

Recently, I had to implement the Richardson's method to find the group dispersion (second derivate) for very low values in a very noisy function. I found this method very accurate and easy to implement. Check Numerical Recipes (www.nr.com) and look for the dfridr function that explains the mentioned algorithm.

cheers,
--
Felipe BM
Hi Emran, I believe matlab does not have an easy way to derivate as (for example) Mathematica does. The reason is that numerical derivation is not a trivial subject. As a first approach you can use the polyfit function in matlab and then derivating the output order-m polynomial is a trivial task. But beware! this is only accurate if your interpolated data behaves as a polynomial of order m. Recently, I had to implement the Richardson's method to find the group dispersion (second derivate) for very low values in a very noisy function. I found this method very accurate and easy to implement. Check Numerical Recipes (www.nr.com) and look for the dfridr function that explains the mentioned algorithm. cheers, -- Felipe BM

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