Metal clad waveguide:

Contents

Surface wave guide
Surface plasmon resonamce
SPR configuration
Surface plasmon wave
SPWs Application
Differenr structures of plasmon waveguides
Metal core dielectric cladding waveguide
Metal clad waveguide

In metal clad waveguide the core is a dielectric material and the clad is metal. So the core has positive dielectric constant and clad has negative dielectric constant as shown in figure.

Here also for symmetric structure ξ1= ξ3 and for asymmetric ξ1 is not equal to ξ3.

 

The derivation of characteristics equation of an asymmetric metal clad dielectric wave guide:

 

The variation of the propagation constant with frequency other than TM0 modes:   

The normalized frequency v is given by

       v=ak (n1^2-n2^2) ^1/2……………. (1)

And the transverse propagation constant is

      u =ur –jui =aq………………… (2)

The normalized propagation constant is given by

     b= 1- (u^2/v^2)………… (3)

      Assuming,              b=br-ibi

Equating the real part we get

                br =1- (ur^2/v^2)

br is real part of the normalized propagation constant

Using the above equations we get

                sin (2v (1-br)) = (-1) ^ N (1-br)…………………….. (4) 

 

The MATLAB program for the above equation (4) is shown here:

 

for N=0:1:3

x=0.99;

for v= (N+0.5)*22/14:0.01:10

for n=0:1:20

func = sin (2*v*x)-(-1) ^ N*x;

diff=2*v*cos (2*v*x)-(-1) ^N;

x=x-(func/diff);

end

br= (1-x*x);

plot (v, br);

hold on;

end

end

xlabel (‘--àv’);

ylabel (‘--àbr’);

 

                

 

Variation of propagation constant with normalized frequency

 

Here we have found out only the characteristics curve of propagation constant of asymmetric metal clad wave guide by using MATLAB.

 

Asymmetric metal clad dielectric wave guide:

The variation of the attenuation constant with frequency  other than TM0 modes:

 

For the calculation of the attenuation for modes in the asymmetric waveguide structure. The attenuation stems from the three sources------

1.       Absorption in the core region,

2.       Transmission into medium 2 on reflection at the 1-2 interface,

3.        Transmission into medium 3 on reflection at the 1-3 interface.

The losses (2) & (3) occur because total internal reflection is strictly only possible at an interface between lossless dielectric. The presence of loss implies a complex wave transmission coefficient. It follows that the attenuation coefficient of a ray taking the path of the form shown in figure. In one round trip of the zig-zag path, the relative  power loss occurs.

 

 

 

 

After several calculation we get finally a mode dependent part (p) which can be written in normalized variables & a material dependent part (x)

 

       α/k= v/x

 

      p= ur * ur * ur/( v*v*v)  (2 ur- tan2ur)

 

The MATLAB program for the above equation is shown here:

for N=0:1:3
x=0.99;
for v= (N+0.5)*22/14:0.01:10;
for n=0:1:20
func = x^3*((2*x)-tan(2*x))/v^3;
diff= ((3*x^2*(2*x+tan(2*x)))+(x^3*(2-2*(sec(2*x)*sec(2*x)))))/v^3;
x=x-(func/diff);
end
ur=x;
plot (v, ur);
hold on;
end
end

xlabel(‘--àv’);

ylabel(‘--àur’);

 

 

 

        Variation of attenuation constant with normalized frequency

 

  

The special case of TM0 mode:

           

            For the above two calculations we have not considered the TM0 mode for each case. From different calculations we found that TM0 mode has its field distribution largely confined to this interface. As well as in TM0 the wave continues to propagate, hence there is no cut-off frequency- for these two reasons TM0 is not used in this case.

 

 

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