Tutorial

• Installation:

  $ pip install grcwa
  

  Or,

  $ git clone git://github.com/weiliangjinca/grcwa
  $ pip install .
  

• Example 1: transmission and reflection of a square lattice of a hole: see ex1.py in the example folder.

• Example 2: Transmission and reflection of two patterned layers: (see ex2.py in the example folder), as illustrated in the figure below (only a unit cell is plotted)

  

  • Periodicity in the lateral direction is L_x = L_y = 0.2, and frequency is 1.0.

  • The incident light has an angel pi/10.

    import grcwa
    import numpy as np
    grcwa.set_backend('autograd') # if autograd needed
    
     # lattice constants
     L1 = [0.2,0]
     L2 = [0,0.2]
     # Truncation order (actual number might be smaller)
     nG = 101
     # frequency
     freq = 1.
     # angle
     theta = np.pi/10
     phi = 0.
    
     # setup RCWA
     obj = grcwa.obj(nG,L1,L2,freq,theta,phi,verbose=1)
    

  • Geometry: the thicknesses of the four layers are 0.1,0.2,0.3, and 0.4. For patterned layers, we consider total grid points N_x * N_y = 100*100 within the unit cell.

  • Dielectric constant: 2.0 for the 0-th layer; 4.0 (1.0) for the 1st layer in the orange (void) region; 6.0 (1.0) for the 2nd layer in the bule (void) region; and 3.0 for the last layer.

    Np = 2 # number of patterned layers
    Nx = 100
    Ny = 100
    
    thick0 = 0.1
    pthick = [0.2,0.3]
    thickN = 0.4
    
    ep0 = 2.
    epN = 3.
    
    obj.Add_LayerUniform(thick0,ep0)
    for i in range(Np):
        obj.Add_LayerGrid(pthick[i],Nx,Ny)
    obj.Add_LayerUniform(thickN,epN)
    
    obj.Init_Setup()
    

  • Patterned layer: the 1-th layer a circular hole of radius 0.5 L_x, and the 2-nd layer has a square hole of 0.5 L_x

    radius = 0.5
    a = 0.5
    
    ep1 = 4.
    ep2 = 6.
    epbkg = 1.
    
    # coordinate
    x0 = np.linspace(0,1.,Nx)
    y0 = np.linspace(0,1.,Ny)
    x, y = np.meshgrid(x0,y0,indexing='ij')
    
    # layer 1
    epgrid1 = np.ones((Nx,Ny))*ep1
    ind = (x-.5)**2+(y-.5)**2<radius**2
    epgrid1[ind]=epbkg
    
    # layer 2
    epgrid2 = np.ones((Nx,Ny))*ep2
    ind = np.logical_and(np.abs(x-.5)<a/2 and np.abs(y-.5)<a/2))
    epgrid2[ind]=epbkg
    
    # combine epsilon of all layers
    epgrid = np.concatenate((epgrid1.flatten(),epgrid2.flatten()))
    obj.GridLayer_geteps(epgrid)
    

  • Incident light is s-polarized

    planewave={'p_amp':0,'s_amp':1,'p_phase':0,'s_phase':0}
    obj.MakeExcitationPlanewave(planewave['p_amp'],planewave['p_phase'],planewave['s_amp'],planewave['s_phase'],order = 0)
    
    # solve for R and T
    R,T= obj.RT_Solve(normalize=1)
    

• Example 3: topology optimization of reflection of a single patterned layer, see ex3.py in the example folder.