Waveguide Modes, tan((pi*d/​lambda)-(m​*pi/2))=sq​rt((sin^2t​etac/sin^2​teta)-1)

3 次查看（过去 30 天）
zeynep kahraman
zeynep kahraman 2018-5-22
回答： John BG 2018-5-23
tan((pi*d/lambda)-(m*pi/2))=sqrt((sin^2tetac/sin^2teta)-1)
  3 个评论
显示 1更早的评论
Walter Roberson
Walter Roberson 2018-5-22
My guess is
syms c d lambda m teta real
eqn = tan((pi*d./lambda)-(m*pi/2)) == sqrt(sin(teta*c).^2./sin(teta).^2-1);
solve(eqn, teta)
John BG
John BG 2018-5-22
Hi Zeynep
this is John BG <mailto:jgb2012@sky.com jgb2012@sky.com>
what type of wave-guide are you analyzing?
what is the frequency range?
is that c light speed in air? or is the wave-guide filled with dielectric?

请先登录，再进行评论。

请先登录，再回答此问题。

回答（2 个）

zeynep kahraman
zeynep kahraman 2018-5-23
Hi JOHN; thetac=acos(n2/n1) (critical angle) lambda=lambdazero/n1 M=sin(thetac)/(t/(2*d)) number of modes and d,lambdazero,n1,n2 = input
John BG
John BG 2018-5-23
Hi Zeynep Kahraman
this is John BG <mailto:jgb2012@sky.com jgb2012@sky.com>
1.
The equation itself can be approach in different ways, Symbolic or numeric.
I tend to go for numeric 1st, kind of habit.
d=.1
lambda0=1e-9
n1=1
n2=4
theta=[0:.01:2*pi];
f2= tan((pi*d*n1/lambda0)-(sin(acos(n2/n1))./(theta/(2*d)) *pi/2)-((sin(acos(n2/n1)))^2./(sin(theta)).^2-1).^.5)
subplot(2,2,1)
plot(theta,real(f2));title('real');grid on
subplot(2,2,3)
plot(theta,imag(f2));title('imag');grid on
subplot(2,2,2)
plot(theta,abs(f2));title('||');grid on
subplot(2,2,4)
plot(theta,angle(f2));title('phase');grid on
.
2.
That is the mathematical equation, I had to guess all the inputs, so if you supply the input parameters I will plot again with with d n1 n2 that you choose.
3.
Regarding the type of waveguide:
The equation resembles a dielectric interface for optical wave-guide.
Literature reference [RAMO]
Fields and Waves in Communications Electronics, 2nd ed
by Simon Ramo, John Whinnery, Theodore Duzer. Ed: JWiley&Sons
chapter 14
pg743
pg744
3.
Would you please give some details about the geometry of the interface the equation models? is it possible for you to attach a diagram to the question?
Zeynep Kahraman
If you find the above ok for you to proceed in your work then it means you find this answer useful. Then would you please be so kind to consider marking my answer as Accepted Answer?
To any other reader, if you find this answer useful please consider clicking on the thumbs-up vote link
Zeynep if you need further development, perhaps you would like to consider supplying values for d n1 n2 and lambda0.
thanks in advance for time and attention
John BG
<mailto:jgb2012@sky.com jgb2012@sky.com>

类别

在 Help Center 和 File Exchange 中查找有关 Vector Volume Data 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by