Learning Forum

[m202373352]

老师您好，目前我正在参照官网案例“CWDM_splitter_1310_4ch_2D_TE_topology”进行光子器件的逆向设计工作，目前遇到了一个问题，还请老师解答一下：

官网案例给的是2D仿真，我所进行的是3D仿真。再进行base_simulation建模时，我是完全参考案例中的设置进行的，即在设置fom监视器时，会在相应位置处设置一个mesh，mesh的跨度刚好为2个dx。但是我在运行仿真时，会出现警告：“WARNING: The monitor "fom_1" is not aligned with the grid. Its distance to the nearest mesh point is [2.00000159e-07]. This can introduce small phase errors which sometimes result in inaccurate gradients.”。我也已经检查了所设置监视器的位置和mesh的位置，发现没有问题，监视器的位置刚好处于mesh的中心。

不清楚究竟是什么原因造成的，还请老师予以解答。下面是我所写的脚本。祝您身体健康，工作顺利！

switchtolayout;

selectall;

delete;

 

## SIM PARAMS

L_block=6e-6;

H_block=6e-6;

num_of_outport=4;

num_of_input=num_of_outport;

with_of_input=2.0e-6;

length_input=5e-6;

length_output=5e-6;

h_si=220e-9;

inputmode=[1,2,3,4];

 

opt_size_x=L_block;

opt_size_y=H_block;

opt_size_z=h_si;

 

size_x=opt_size_x+1e-6;

size_y=opt_size_y+1e-6;

size_z=2e-6;

 

with_of_output=0.5e-6;

gap_of_outport=H_block/num_of_outport;

 

wg_index = 3.48;

bg_index = 1.44;

 

dx = 20e-9;

 

addfdtd; ##

set("dimension",2); # 1 = 2D, 2 = 3D

set("x",0);

set("x span",size_x);

set("y",0);

set("y span",size_y);

set("z",0);

set("z span",size_z);

set("mesh accuracy",3);

set("simulation time",4000e-15);

set("index",bg_index);

set("auto shutoff min",1e-7);

 

 

addrect; ##

set("name","input");

set("x max", -L_block/2);

set("x min", -L_block/2-length_input);

set("y min", -H_block/2);

set("y max",-H_block/2+with_of_input);

set("z", 0);

set("z span", h_si);

set("index",wg_index);

 

for (index=linspace(-(num_of_outport-1)/2,(num_of_outport-1)/2,num_of_outport)){

addrect; ##

set("index",wg_index);

#set("material","Si (Silicon) - Palik");

set("z", 0);

set("z span", h_si);

set("x min", L_block/2);

set("x max", L_block/2+length_output);

set("y", index*gap_of_outport);

set("y span",with_of_output);

}

 

addmode;##

set("name","source");

set("direction","Forward");

set("injection axis", "x-axis");

set("x", -size_x/2+0.2e-6);

set("z",0);

set("z span",2e-6);

set("y", -H_block/2+with_of_input/2);

set("y span",5e-6);

set("wavelength start",1.55e-6); ##

set("wavelength stop",1.55e-6);

updatesourcemode(1);

 

 

addpower;#

set("name","opt_fields");

set('monitor type','3D'); # 1 = point, 2 = linear x, 3 = linear y, 4 = linear z, 5 = 2D x-normal, 6 = 2D y-normal, 7 = 2D z-normal, 8 = 3D

set("z",0);

set("z span",opt_size_z);

set("x", 0);

set("x span",opt_size_x);

set("y", 0);

set("y span",opt_size_y);

 

 

index=linspace(-(num_of_outport-1)/2,(num_of_outport-1)/2,num_of_outport);

for (xnum=1:num_of_outport){

addpower;

set("name","fom_"+num2str(xnum));

set("monitor type",5); # 1 = point, 2 = linear x, 3 = linear y, 4 = linear z, 5 = 2D x-normal, 6 = 2D y-normal, 7 = 2D z-normal, 8 = 3D

set("x", size_x/2-0.2e-6);

set("z",0);

set("z span",2e-6);

set("y", index(xnum)*gap_of_outport);

set("y span",1.5e-6);

if(1){

addmodeexpansion;##

set("name","mode_expansion"+num2str(xnum));

set("monitor type",1); # 1 = 2D x-normal, 2 = 2D y-normal

set("x", size_x/2-0.2e-6);

set("z",0);

set("z span",2e-6);

set("y", index(xnum)*gap_of_outport);

set("y span",1.5e-6);

select("mode_expansion"+num2str(xnum));

setexpansion("input", "fom_"+num2str(xnum));

set("mode selection","user select"); # use the 'user select' option

seteigensolver("use max index",1); # specify a custom value for 'n'

updatemodes(1);

}

 

addmesh; ##

set("name","fom_"+num2str(xnum)+"_mesh");

set("set maximum mesh step",1);

set("override x mesh",1);

set("dx",dx);

set("override y mesh",0);

set("override z mesh",0);

set("x",size_x/2-0.2e-6);

set("x span",2*dx);

set("y",index(xnum)*gap_of_outport);

set("y span",1.5e-6);

set("z",0);

set("z span",size_z);

 

}

 

 

## For visualization later

addindex;

set('name','global_index');

set('x min',-size_x/2);

set('x max',size_x/2);

set('y min',-size_y/2);

set('y max',size_y/2);

set('z min',-size_z/2);

set('z max',size_z/2);

set('enabled',false);

 

## Optional: Naive design which can be used as initial guess

index=linspace(-(num_of_outport-1)/2,(num_of_outport-1)/2,num_of_outport);

addstructuregroup;

set("name","initial_guess");

for( i=1:num_of_outport ) {

addwaveguide;

set("name","bend"+num2str(i));

set("base width",500e-9);

set("base height",220e-9);

set("base angle",90);

poles = [-opt_size_x/2,-H_block/2+with_of_input-i*with_of_input/4+with_of_input/8;

0,-H_block/2+with_of_input-i*with_of_input/4+with_of_input/8;

0,index(num_of_outport-(i-1))*gap_of_outport;

opt_size_x/2,index(num_of_outport-(i-1))*gap_of_outport];

set("poles",poles);

set("index",wg_index);

addtogroup("initial_guess");

}

 

 

 

 

[Kirill]

This topic has been moved to the Photonics – Chinese forum. Thank you!

[m202373352]

此外，我在建模的时候发现了一个不太正常的现象，不知道该如何解释：

在用脚本进行建模时，我发现如果采用“x min”"x max""ymin""ymax""zmin""zmax"来确定几何的位置，发现几何的中心位置并不是最大值和最小值的中点；但是如果换成用"x"和"x span"(y和z也是如此)，发现就没有这个问题。但是本质上二者不应该是等价的吗，为什么建模出来的结果确实有差别的？这种差别会不会影响仿真的结果呢？还要麻烦老师一并解答，非常感谢！

具体的测试代码即截图如下：

采用最大值和最小值，即" min"和" max"来确定几何位置：

size_x=7e-6;

size_y=7e-6;

L=6e-6;

H=2e-6;

h_si=220e-9;

 

addfdtd;

set('dimension','2D');

set('index',1.44);

set('mesh accuracy',3);

set('x min',-size_x/2);

set('x max',size_x/2);

set('y min',-size_y/2);

set('y max',size_y/2);

set('auto shutoff min',1e-6);

set('simulation time',5000e-15);                                                                                

addrect;

set('index',1.44);

set('x min',-L/2);

set('x max',L/2);

set('y min',-H/2);

set('y max',H/2);

set('z min',-h_si/2);

set('z max',h_si/2);

采用中心位置和span来确定几何位置：

size_x=7e-6;

size_y=7e-6;

L=6e-6;

H=2e-6;

h_si=220e-9;

addfdtd;

set('dimension','2D');

set('index',1.44);

set('mesh accuracy',3);

set('x',0);

set('x span',size_x);

set('y',0);

set('y span',size_y);

set('auto shutoff min',1e-6);

set('simulation time',5000e-15);

addrect;

set('index',1.44);

set('x',0);

set('x span',L);

set('y',0);

set('y span',H);

set('z',0);

set('z span',h_si);

[GuanYo Dong]

你好,

這兩問題,確實有可能是數值誤差引起的。您可以理解數位運算的時候小數點的長度有限,所以難免最後一個位數需要取捨,因此越多的運算就會累積越多這種誤差。

那您的第二個問題比較好說明,
當中心點是由max跟min決定,那我們的max跟min 一個正一個負,一點點偏差就容易看到0附近的誤差,
當由中心點跟span來計算min與max,因為min與max的值不在0,那個誤差可能存在但是占比GUI中我們看不出來,其實也不一定不存在。

這種誤差建議相同的運算我們算一次之後給一個名稱帶入，避免重複算,對於大量運算也會比較快
比如我們知道 power monitor 跟 index monitor  Z的中心位置就是a+b/2, 那我們用A=a+b/2,之後定義Z中心就用A去代替

請您先試試看這種方式來修改第一題的腳本。

莎益博 董冠佑

[m202373352]

好的，感谢您的回复