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+//Example 3.3 // no. of modes
+clc;
+clear;
+close;
+format('v',10)
+disp("part (a)")
+n1=1.5;//core refractive index
+n2=1.48;//cladding refrative index
+t=10.11;//thickness of guided layer in micro meter
+h=1.55;//wavelength in µm
+b1=((2*%pi*n1)/(h*10^-6));//phase propagation constant in m^-1
+b2=((2*%pi*n2)/(h*10^-6));//phase propagation constant in m^-1
+m=((2*%pi*t)/h)*(sqrt(n1^2-n2^2));//number of modes
+disp(round(m/2),"number of modes are")
+disp("part (b)")
+n1=1.5;//core refractive index
+n2=1.48;//cladding refrative index
+t1=10.11;//thickness of guided layer in micro meter
+t=t1/2;
+h=1.55;//wavelength in µm
+b1=((2*%pi*n1)/(h*10^-6));//phase propagation constant in m^-1
+b2=((2*%pi*n2)/(h*10^-6));//phase propagation constant in m^-1
+mo=(((2*%pi*t1)/h)*(sqrt(n1^2-n2^2)))/2;//number of modes
+uma0=1.30644;// for m=0 from the curve
+uma1=2.59574;// for m=1 from the curve
+uma2=3.83747;// for m=2 from the curve
+uma3=4.9063;// for m=3 from the curve
+wma0=4.8263;// for m=0 from the curve
+wma1=4.27342;// for m=1 from the curve
+wma2=3.20529;// for m=2 from the curve
+wma3=0.963466;// for m=3 from the curve
+um0=uma0/(t*10^-6);//in m^-1
+um1=uma1/(t*10^-6);//in m^-1
+um2=uma2/(t*10^-6);//in m^-1
+um3=uma3/(t*10^-6);//in m^-1
+wm0=wma0/(t*10^-6);//in m^-1
+wm1=wma1/(t*10^-6);//in m^-1
+wm2=wma2/(t*10^-6);//in m^-1
+wm3=wma3/(t*10^-6);//in m^-1
+bm0=((wm0*t*10^-6)/mo)^2;//for m=0 
+bm1=((wm1*t*10^-6)/mo)^2;//for m=1
+bm2=((wm2*t*10^-6)/mo)^2;//for m=2 
+bm3=((wm3*t*10^-6)/mo)^2;//for m=3
+m0=sqrt((bm0*(b1^2-b2^2))+b2^2);//for m=0 in m^-1
+m1=sqrt((bm1*(b1^2-b2^2))+b2^2);//for m=1 in m^-1
+m2=sqrt((bm2*(b1^2-b2^2))+b2^2);//for m=2 in m^-1
+m3=sqrt((bm3*(b1^2-b2^2))+b2^2);//for m=3 in m^-1
+params = [" " "m" "um[m^-1]" "wm[m^-1]" "bm"  ];
+m = ["0" "1" "2" "3"]';
+um = ["um0" "um1" "um2" "um3"]';
+wm  = string([22.41 11.77 33.41 4.24]');
+bm = string([26 19 22 17]');
+params = ["m" "um[m^-1]" "wm[m^-1]" "bm" "ßm[m^-1]" ];
+city=string([0 1 2 3]');
+towns = string([um0 um1 um2 um3]');
+country = string([wm0 wm1 wm2 wm3]');
+ pop  = string([bm0 bm1 bm2 bm3]');
+ temp = string([m0 m1 m2 m3]');
+ table = [params; [ city towns country pop temp ]]
+ disp(table ,"constants are :")