Bent waveguide simulator: Example

Objective

Define a 3 layer bent waveguide with substrate refractive index n_s=1.0, cladding refractive index n_c=1.0, and core refractive index n_f=1.5, radius of the bent waveguide is R=5 μm and the core width d=0.5 μm.
Find the TE mode(s) supported by this waveguide and plot the fields.

1. Make sure that all the required program files are available. See Circurs for more information.
2. Use the example file "bwg_example.cpp".
3. Compile the code "bwg_example.cpp" using the script "mo". This will produce an executable "bwg_example".
4. Run the executable "bwg_example".

Code usage

1. Required header file
2. Defining bent waveguide
3. Finding modes and accessing propagation constants
4. Accessing field values and plotting modes

• Required header file: Include following header file to a define bent waveguide.

  #include "bmsinc.h"

• Defining bent waveguide

  double R=5.0; // Radius of bent waveguide int layer = 1; // no. of internal layer double d = 0.5; // width of bend waveguide core double lambda=1.1; // vacuum wavelength Dvector Bhx(layer+1); // locations of dielectric layer interfaces Dvector Bn(layer+2); // refractive indices for dielectric layers // dielectric layer interfaces are defined with respect to radius R Bhx(0) = -d; // inner layer position= R-d Bhx(1) = 0.0; // outer layer position= R Bn(0) = 1.0; // = n_s (cladding refractive index) Bn(1) = 1.5; // = n_f (core refractive index) Bn(2) = 1.0; // = n_c (cover refractive index) // Define bent waveguide BSlabWaveguide bwg(layer, Bhx, lambda, Bn, R);

• Finding modes and accessing propagation constants

  // Required parameters for mode solver BSLAMS_Parameters bpar; // Define container to hold modes of bent waveguide BSlabModeArray bma; // finding modes of BWG // Roots of dispersion equation are searched in complex plane // in region [b0, b1]x[a0, a1]. double b0 = 5.2; // lower limit for beta double b1 = 6.5; // upper limit for beta double a0 = -6e-3; // lower limit for alpha double a1 = -1e-3; // upper limit for alpha int Nb = 10; // [b0, b1] is divided in Nb points. int Na = 6; // [a0, a1] is divided in Na points. // finding modes of bent waveguide in [b0, b1]x[a0, a1] int Nbm=bend_mode_analysis(bwg, TE, b0, b1, Nb, a0, a1,Na, bpar, bma); // to power normalise modes double tmp_totpower; for (int j= 0; j < Nbm; j++) { // compute total modal power using analytic method // at an angular position theta=0.0 tmp_totpower =bma(j).totpower(0.0); bma(j).normalize(tmp_totpower); // to normalize modal power } // Display propagation constants cout <<"\nPropagation constants of mode(s):\n"; for (int j= 0; j < Nbm; j++) { cout <<"Mode " << j <<"\t gamma=(" << bma(j).gamma.re <<", " << bma(j).gamma.im <<")" <<"\t beta=" << bma(j).beta <<"\t alpha=" << bma(j).alpha <<"\n"; }

• Accessing field values and plotting modes

  // Field values of TE0 mode double r, p, x, z; r=5.385164807; // radial distance p=0.380506377; // angular position = pi/2 x=5.0; z=2.0; Complex f; f=bma(0).field_cart(EY, x, z); cout <<"Complex valued y component of electric field at" <<" (x, z)= (" << x <<", " << z <<") : (" << f.re <<", " << f.im <<") \n"; f=bma(0).field(EY, r, p); cout <<"Complex valued y component of electric field at" <<" (r, p)= (" << r <<", " << p <<") : (" << f.re <<", " << f.im <<") \n"; cout <<"Real part of y component of electric field at" << " r=" << r <<": " << bma(0).field(EY, REP, r) <<"\n"; // Interval on which field is plotted Interval Bdisplay(bwg.R - 4.0, bwg.R+ 5.0); for (int j= 0; j < Nbm; j++) { //plot of real, imaginary and absolute value and phase of field bma(j).mfile(EY, 1.0, Bdisplay, 600, '0', '0'+j, 'r'); //real+im //plot of absolute value bma(j).mfile(EY, MOD, 1.0, Bdisplay, 1000, '0', '0'+j, 'L'); } Cvector amp(1); amp(0)=CC1; // Amplitude of Fundamental mode double x0, x1, z0, z1; // defining window int Nx, Nz; // defining discrtization points x0= 0.0; x1= 7.0; Nx=200; z0= -7.0; z1=7.0; Nz=400; // plot of absolute value of EY over [x0, x1]x[z0, z1] window bma.plot(amp, EY, MOD, x0, x1, Nx, z0, z1, Nz, '0', '0'); // plot of real value of EY over [x0, x1]x[z0, z1] window bma.plot(amp, EY, REP, x0, x1, Nx, z0, z1, Nz, '0', '0'); // animation of propagation of real value of EY over // [x0, x1]x[z0, z1] window bma.movie(amp, x0, x1, Nx, z0, z1, Nz, 40, '0', '0');