1维严格耦合波方法matlab代码

Binary grating

We want to analyze a binary metallic grating, e.g. from paper: Li,

Haggans, "Convergence of the coupled-wave method for metallic

lamellar diffraction gratings," J. Opt. Soc. Am. A 10, 1184-1189 (1993).

It consist of a lamellar grating with a groove depth of 1 μm. The

dielectric has an optical index of 0.22-i*6.71. The incident wavelength

λ, the period Λ, and the height of the grating is 1 μm. The angle of

incidence is equal to 30º. The incident polarization is TM.

Firstly, we have to set the following parameters in the file

grating=0; % 0=binary grating

Lambda=1;

thickness_total=1;

n1=1;

n3=0.22-6.71*1i;

ng=1;

nr=n3;

duty_cycle=.5;

shift=.5;

measurement=0; % 0=shows all diffraction efficiencies

only evanescent orders

sum_eff =

0.945793600567703 0.011854620163793 0.957648220731496

There are only two reflected diffraction orders, all transmitted orders are evanescent. Sum of reflected

orders is equal to 0.94579, whereas sum of transmitted order is 0.01185. This grating is lossy, so the

total sum 0.9576482 is lesser than 1. Secondly, we want to investigate, if the convergence of the zero-

order diffraction efficiency is satisfied. We have to set:

measurement=1; % 1=dependence of the diff. efficiency on the number of orders

diffraction_efficiencies_c=1; % reflected orders

studying_order=0;

We get a figure as shown here:

You can see, that number_of_orders=41 is sufficient, but in order to obtain accurate results we can

increase this parameter to 101 orders. Next, if we want to see field the component abs(Hy), we have to

change properties as follows:

measurement=0;

plot_field_region_1=1; %1-yes, incident region

plot_field_region_2=1; %1-yes, grating region

plot_field_region_3=1; %1-yes, substrate region

field_component_operation=1; % 1-abs, 2-angle, 3-real, 4-imag

planar_field_component=2; % TM → H_y

y

z

x

y

z

Finally, this grating is made of gold, if we will change wavelength, we will use dispersion model/data.

RCWA-1D program is able to easily incorporate dispersion model/data. Set use_dispersion=1, open

file setup_dispersion.m, and write/uncomment

n3=rix_spline(lambda,'gold_palik.txt'); % application of a spline function to

Palik's gold data

nr=n3;

Sinusoidal grating

Now, we want to study a spectral dependence of the sinusoidal grating (Λ=2 μm, d=1 μm, n

use_dispersion=2; % 1-yes, 2-no, see file setup_dispersion.m setup_dispersion.m

theta0=30; % incident angle [degree]

polarization=0; % 0-conical diffraction, 1-TM polarization, 2-TE polarization

phi0=30; % conical angle [degree], 0=planar diffraction

psi0=30; % polarization angle [degree], 0-TM polarization, 90-TE polarization

grating=3; % switch grating

Lambda=1; % grating period [um] (exception grating=10)

thickness_total=1; % total thickness [um] (exception grating=10)

% refractive indicies

%---------------------------------------------------

number_of_layers=20;

Field profile abs(Hy)

Field profile with grating boundaries

(thin white line)

measurement=0;

We get this result:

reflected orders

order efficiency

-2.000000000000000 0.004421523239889

-1.000000000000000 0.004224700994904

0 0.000676667880030

0 0.143246725076277

1.000000000000000 0.513569971871019

2.000000000000000 0.012344314183415

sum_eff =

0.014884884292066 0.985115115706159 0.999999999998225

Before calculating a spectral dependence of the sinusoidal grating, we have to check the convergence

of the diffraction efficiencies on the number of aproximate layers → measurement 7. For example, we

are interested in only the zero transmitted order.

measurement=7; % measurement 1 --- check studying_order

maximum_layer=80;

step=5;

We get a figure as shown

here.

You can see in the figure above that we should increase the number of layers, i.e. to 50 layers. To study

spectral dependence (0.7—1.3 μm) set measurement to 2. To save all results of all diffraction orders set

save_m to 1 and choose a proper name of this file.

switch grating

case 3 % sinusoidal grating

number_of_layers=50;

case 2 %

minimum_wavelength=0.7; %um

maximum_wavelength=1.3; %um

step=0.01;

Following figure will apear:

This is only the graph of the zero transmitted order. The file (conical_sinusoidal_grating.mat)

containing all results is saved in directory /measurements (actual data are stored in the file

conical_sinusoidal_grating.dat). These data are avaiable through file

load_measurements_results.m. If you want to see/save the spectral dependence of the first transmitted

order change respective variables.

load_measurements_results.m

load conical_sinusoidal_grating.mat;