`rcore = 0.8; rclad = 4.;
rootNum = 10; om = 0.0; orbitNum = 1;

glass = 1.45; air = 1.; \[Lambda] = 1.55;
k0 = (2 \[Pi])/\[Lambda]; b = k0*glass;

reg = ImplicitRegion[x^2 + y^2 <= rclad^2, {x, y}]; f =
Function[{vertices, area}, Block[{x, y}, {x, y} = Mean[vertices];
If[x^2 + y^2 <= rcore^2, area > 0.001, area > 0.01]]];
mesh = ToElementMesh[reg, MeshRefinementFunction -> f];

\[Epsilon][x_, y_] := If[x^2 + y^2 <= rcore^2, glass^2, air^2]

helm = \!\(
\*SubsuperscriptBox[\(\[Del]\), \({x, y}\), \(2\)]\(u[x,